Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile

NASA Astrophysics Data System (ADS)

Cui, Jie; Li, Zhiying; Krems, Roman V.

2015-10-01

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A-H to make predictions of the dynamical properties for another molecule related to A-H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A-X. We assume that the effect of the -H →-X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can be used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C6H5CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C6H6 collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C6H5CN with He.

Parameter identification of thermophilic anaerobic degradation of valerate.

PubMed

Flotats, Xavier; Ahring, Birgitte K; Angelidaki, Irini

2003-01-01

The considered mathematical model of the decomposition of valerate presents three unknown kinetic parameters, two unknown stoichiometric coefficients, and three unknown initial concentrations for biomass. Applying a structural identifiability study, we concluded that it is necessary to perform simultaneous batch experiments with different initial conditions for estimating these parameters. Four simultaneous batch experiments were conducted at 55 degrees C, characterized by four different initial acetate concentrations. Product inhibition of valerate degradation by acetate was considered. Practical identification was done optimizing the sum of the multiple determination coefficients for all measured state variables and for all experiments simultaneously. The estimated values of kinetic parameters and stoichiometric coefficients were characterized by the parameter correlation matrix, the confidence interval, and the student's t-test at 5% significance level with positive results except for the saturation constant, for which more experiments for improving its identifiability should be conducted. In this article, we discuss kinetic parameter estimation methods.

An almost-parameter-free harmony search algorithm for groundwater pollution source identification.

PubMed

Jiang, Simin; Zhang, Yali; Wang, Pei; Zheng, Maohui

2013-01-01

The spatiotemporal characterization of unknown sources of groundwater pollution is frequently encountered in environmental problems. This study adopts a simulation-optimization approach that combines a contaminant transport simulation model with a heuristic harmony search algorithm to identify unknown pollution sources. In the proposed methodology, an almost-parameter-free harmony search algorithm is developed. The performance of this methodology is evaluated on an illustrative groundwater pollution source identification problem, and the identified results indicate that the proposed almost-parameter-free harmony search algorithm-based optimization model can give satisfactory estimations, even when the irregular geometry, erroneous monitoring data, and prior information shortage of potential locations are considered.

Market-Based Coordination of Thermostatically Controlled Loads—Part I: A Mechanism Design Formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Sen; Zhang, Wei; Lian, Jianming

This paper focuses on the coordination of a population of Thermostatically Controlled Loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the bidding and market clearing strategy to motivate self-interested users to realize efficient energy allocation subject to a peak power constraint. Using the mechanism design approach, we propose a market-based coordination framework, which can effectively incorporate heterogeneous load dynamics, systematically deal with user preferences, account for the unknown load model parameters, and enable the real-world implementation with limited communication resources. This paper is divided into two parts. Part I presents a mathematical formulation of themore » problem and develops a coordination framework using the mechanism design approach. Part II presents a learning scheme to account for the unknown load model parameters, and evaluates the proposed framework through realistic simulations.« less

Target Capturing Control for Space Robots with Unknown Mass Properties: A Self-Tuning Method Based on Gyros and Cameras.

PubMed

Li, Zhenyu; Wang, Bin; Liu, Hong

2016-08-30

Satellite capturing with free-floating space robots is still a challenging task due to the non-fixed base and unknown mass property issues. In this paper gyro and eye-in-hand camera data are adopted as an alternative choice for solving this problem. For this improved system, a new modeling approach that reduces the complexity of system control and identification is proposed. With the newly developed model, the space robot is equivalent to a ground-fixed manipulator system. Accordingly, a self-tuning control scheme is applied to handle such a control problem including unknown parameters. To determine the controller parameters, an estimator is designed based on the least-squares technique for identifying the unknown mass properties in real time. The proposed method is tested with a credible 3-dimensional ground verification experimental system, and the experimental results confirm the effectiveness of the proposed control scheme.

Target Capturing Control for Space Robots with Unknown Mass Properties: A Self-Tuning Method Based on Gyros and Cameras

PubMed Central

Li, Zhenyu; Wang, Bin; Liu, Hong

2016-01-01

Satellite capturing with free-floating space robots is still a challenging task due to the non-fixed base and unknown mass property issues. In this paper gyro and eye-in-hand camera data are adopted as an alternative choice for solving this problem. For this improved system, a new modeling approach that reduces the complexity of system control and identification is proposed. With the newly developed model, the space robot is equivalent to a ground-fixed manipulator system. Accordingly, a self-tuning control scheme is applied to handle such a control problem including unknown parameters. To determine the controller parameters, an estimator is designed based on the least-squares technique for identifying the unknown mass properties in real time. The proposed method is tested with a credible 3-dimensional ground verification experimental system, and the experimental results confirm the effectiveness of the proposed control scheme. PMID:27589748

Gaussian process model for extrapolation of scattering observables for complex molecules: From benzene to benzonitrile

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Jie; Krems, Roman V.; Li, Zhiying

2015-10-21

We consider a problem of extrapolating the collision properties of a large polyatomic molecule A–H to make predictions of the dynamical properties for another molecule related to A–H by the substitution of the H atom with a small molecular group X, without explicitly computing the potential energy surface for A–X. We assume that the effect of the −H →−X substitution is embodied in a multidimensional function with unknown parameters characterizing the change of the potential energy surface. We propose to apply the Gaussian Process model to determine the dependence of the dynamical observables on the unknown parameters. This can bemore » used to produce an interval of the observable values which corresponds to physical variations of the potential parameters. We show that the Gaussian Process model combined with classical trajectory calculations can be used to obtain the dependence of the cross sections for collisions of C{sub 6}H{sub 5}CN with He on the unknown parameters describing the interaction of the He atom with the CN fragment of the molecule. The unknown parameters are then varied within physically reasonable ranges to produce a prediction uncertainty of the cross sections. The results are normalized to the cross sections for He — C{sub 6}H{sub 6} collisions obtained from quantum scattering calculations in order to provide a prediction interval of the thermally averaged cross sections for collisions of C{sub 6}H{sub 5}CN with He.« less

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression.

PubMed

Ding, A Adam; Wu, Hulin

2014-10-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method.

Estimation of Ordinary Differential Equation Parameters Using Constrained Local Polynomial Regression

PubMed Central

Ding, A. Adam; Wu, Hulin

2015-01-01

We propose a new method to use a constrained local polynomial regression to estimate the unknown parameters in ordinary differential equation models with a goal of improving the smoothing-based two-stage pseudo-least squares estimate. The equation constraints are derived from the differential equation model and are incorporated into the local polynomial regression in order to estimate the unknown parameters in the differential equation model. We also derive the asymptotic bias and variance of the proposed estimator. Our simulation studies show that our new estimator is clearly better than the pseudo-least squares estimator in estimation accuracy with a small price of computational cost. An application example on immune cell kinetics and trafficking for influenza infection further illustrates the benefits of the proposed new method. PMID:26401093

Modern control concepts in hydrology. [parameter identification in adaptive stochastic control approach

NASA Technical Reports Server (NTRS)

Duong, N.; Winn, C. B.; Johnson, G. R.

1975-01-01

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Parameter and state estimation in a Neisseria meningitidis model: A study case of Niger

NASA Astrophysics Data System (ADS)

Bowong, S.; Mountaga, L.; Bah, A.; Tewa, J. J.; Kurths, J.

2016-12-01

Neisseria meningitidis (Nm) is a major cause of bacterial meningitidis outbreaks in Africa and the Middle East. The availability of yearly reported meningitis cases in the African meningitis belt offers the opportunity to analyze the transmission dynamics and the impact of control strategies. In this paper, we propose a method for the estimation of state variables that are not accessible to measurements and an unknown parameter in a Nm model. We suppose that the yearly number of Nm induced mortality and the total population are known inputs, which can be obtained from data, and the yearly number of new Nm cases is the model output. We also suppose that the Nm transmission rate is an unknown parameter. We first show how the recruitment rate into the population can be estimated using real data of the total population and Nm induced mortality. Then, we use an auxiliary system called observer whose solutions converge exponentially to those of the original model. This observer does not use the unknown infection transmission rate but only uses the known inputs and the model output. This allows us to estimate unmeasured state variables such as the number of carriers that play an important role in the transmission of the infection and the total number of infected individuals within a human community. Finally, we also provide a simple method to estimate the unknown Nm transmission rate. In order to validate the estimation results, numerical simulations are conducted using real data of Niger.

Method and apparatus for sensor fusion

NASA Technical Reports Server (NTRS)

Krishen, Kumar (Inventor); Shaw, Scott (Inventor); Defigueiredo, Rui J. P. (Inventor)

1991-01-01

Method and apparatus for fusion of data from optical and radar sensors by error minimization procedure is presented. The method was applied to the problem of shape reconstruction of an unknown surface at a distance. The method involves deriving an incomplete surface model from an optical sensor. The unknown characteristics of the surface are represented by some parameter. The correct value of the parameter is computed by iteratively generating theoretical predictions of the radar cross sections (RCS) of the surface, comparing the predicted and the observed values for the RCS, and improving the surface model from results of the comparison. Theoretical RCS may be computed from the surface model in several ways. One RCS prediction technique is the method of moments. The method of moments can be applied to an unknown surface only if some shape information is available from an independent source. The optical image provides the independent information.

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative–quantitative modeling

PubMed Central

Streif, Stefan; Savchenko, Anton; Rumschinski, Philipp; Borchers, Steffen; Findeisen, Rolf

2012-01-01

Summary: Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if–then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLabTM-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. Availability: ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/ Contact: stefan.streif@ovgu.de PMID:22451270

ADMIT: a toolbox for guaranteed model invalidation, estimation and qualitative-quantitative modeling.

PubMed

Streif, Stefan; Savchenko, Anton; Rumschinski, Philipp; Borchers, Steffen; Findeisen, Rolf

2012-05-01

Often competing hypotheses for biochemical networks exist in the form of different mathematical models with unknown parameters. Considering available experimental data, it is then desired to reject model hypotheses that are inconsistent with the data, or to estimate the unknown parameters. However, these tasks are complicated because experimental data are typically sparse, uncertain, and are frequently only available in form of qualitative if-then observations. ADMIT (Analysis, Design and Model Invalidation Toolbox) is a MatLab(TM)-based tool for guaranteed model invalidation, state and parameter estimation. The toolbox allows the integration of quantitative measurement data, a priori knowledge of parameters and states, and qualitative information on the dynamic or steady-state behavior. A constraint satisfaction problem is automatically generated and algorithms are implemented for solving the desired estimation, invalidation or analysis tasks. The implemented methods built on convex relaxation and optimization and therefore provide guaranteed estimation results and certificates for invalidity. ADMIT, tutorials and illustrative examples are available free of charge for non-commercial use at http://ifatwww.et.uni-magdeburg.de/syst/ADMIT/

Optimal hemodynamic response model for functional near-infrared spectroscopy

PubMed Central

Kamran, Muhammad A.; Jeong, Myung Yung; Mannan, Malik M. N.

2015-01-01

Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650–950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > tcritical and p-value < 0.05). PMID:26136668

Optimal hemodynamic response model for functional near-infrared spectroscopy.

PubMed

Kamran, Muhammad A; Jeong, Myung Yung; Mannan, Malik M N

2015-01-01

Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650-950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > t critical and p-value < 0.05).

Concurrent hyperthermia estimation schemes based on extended Kalman filtering and reduced-order modelling.

PubMed

Potocki, J K; Tharp, H S

1993-01-01

The success of treating cancerous tissue with heat depends on the temperature elevation, the amount of tissue elevated to that temperature, and the length of time that the tissue temperature is elevated. In clinical situations the temperature of most of the treated tissue volume is unknown, because only a small number of temperature sensors can be inserted into the tissue. A state space model based on a finite difference approximation of the bioheat transfer equation (BHTE) is developed for identification purposes. A full-order extended Kalman filter (EKF) is designed to estimate both the unknown blood perfusion parameters and the temperature at unmeasured locations. Two reduced-order estimators are designed as computationally less intensive alternatives to the full-order EKF. Simulation results show that the success of the estimation scheme depends strongly on the number and location of the temperature sensors. Superior results occur when a temperature sensor exists in each unknown blood perfusion zone, and the number of sensors is at least as large as the number of unknown perfusion zones. Unacceptable results occur when there are more unknown perfusion parameters than temperature sensors, or when the sensors are placed in locations that do not sample the unknown perfusion information.

Parameter discovery in stochastic biological models using simulated annealing and statistical model checking.

PubMed

Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J

2014-01-01

Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.

Design of a DNA chip for detection of unknown genetically modified organisms (GMOs).

PubMed

Nesvold, Håvard; Kristoffersen, Anja Bråthen; Holst-Jensen, Arne; Berdal, Knut G

2005-05-01

Unknown genetically modified organisms (GMOs) have not undergone a risk evaluation, and hence might pose a danger to health and environment. There are, today, no methods for detecting unknown GMOs. In this paper we propose a novel method intended as a first step in an approach for detecting unknown genetically modified (GM) material in a single plant. A model is designed where biological and combinatorial reduction rules are applied to a set of DNA chip probes containing all possible sequences of uniform length n, creating probes capable of detecting unknown GMOs. The model is theoretically tested for Arabidopsis thaliana Columbia, and the probabilities for detecting inserts and receiving false positives are assessed for various parameters for this organism. From a theoretical standpoint, the model looks very promising but should be tested further in the laboratory. The model and algorithms will be available upon request to the corresponding author.

Extensions of Rasch's Multiplicative Poisson Model.

ERIC Educational Resources Information Center

Jansen, Margo G. H.; van Duijn, Marijtje A. J.

1992-01-01

A model developed by G. Rasch that assumes scores on some attainment tests can be realizations of a Poisson process is explained and expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. How additional between-subject and within-subject factors can be incorporated is discussed. (SLD)

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Stochastic Inversion of 2D Magnetotelluric Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong

2010-07-01

The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, itmore » provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

Comparing Different Approaches of Bias Correction for Ability Estimation in IRT Models. Research Report. ETS RR-08-13

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; Zhang, Jinming

2008-01-01

The method of maximum-likelihood is typically applied to item response theory (IRT) models when the ability parameter is estimated while conditioning on the true item parameters. In practice, the item parameters are unknown and need to be estimated first from a calibration sample. Lewis (1985) and Zhang and Lu (2007) proposed the expected response…

Modern control concepts in hydrology

NASA Technical Reports Server (NTRS)

Duong, N.; Johnson, G. R.; Winn, C. B.

1974-01-01

Two approaches to an identification problem in hydrology are presented based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time invariant or time dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and conform with results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second, by using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Genomic data assimilation for estimating hybrid functional Petri net from time-course gene expression data.

PubMed

Nagasaki, Masao; Yamaguchi, Rui; Yoshida, Ryo; Imoto, Seiya; Doi, Atsushi; Tamada, Yoshinori; Matsuno, Hiroshi; Miyano, Satoru; Higuchi, Tomoyuki

2006-01-01

We propose an automatic construction method of the hybrid functional Petri net as a simulation model of biological pathways. The problems we consider are how we choose the values of parameters and how we set the network structure. Usually, we tune these unknown factors empirically so that the simulation results are consistent with biological knowledge. Obviously, this approach has the limitation in the size of network of interest. To extend the capability of the simulation model, we propose the use of data assimilation approach that was originally established in the field of geophysical simulation science. We provide genomic data assimilation framework that establishes a link between our simulation model and observed data like microarray gene expression data by using a nonlinear state space model. A key idea of our genomic data assimilation is that the unknown parameters in simulation model are converted as the parameter of the state space model and the estimates are obtained as the maximum a posteriori estimators. In the parameter estimation process, the simulation model is used to generate the system model in the state space model. Such a formulation enables us to handle both the model construction and the parameter tuning within a framework of the Bayesian statistical inferences. In particular, the Bayesian approach provides us a way of controlling overfitting during the parameter estimations that is essential for constructing a reliable biological pathway. We demonstrate the effectiveness of our approach using synthetic data. As a result, parameter estimation using genomic data assimilation works very well and the network structure is suitably selected.

Calibration of two complex ecosystem models with different likelihood functions

NASA Astrophysics Data System (ADS)

Hidy, Dóra; Haszpra, László; Pintér, Krisztina; Nagy, Zoltán; Barcza, Zoltán

2014-05-01

The biosphere is a sensitive carbon reservoir. Terrestrial ecosystems were approximately carbon neutral during the past centuries, but they became net carbon sinks due to climate change induced environmental change and associated CO2 fertilization effect of the atmosphere. Model studies and measurements indicate that the biospheric carbon sink can saturate in the future due to ongoing climate change which can act as a positive feedback. Robustness of carbon cycle models is a key issue when trying to choose the appropriate model for decision support. The input parameters of the process-based models are decisive regarding the model output. At the same time there are several input parameters for which accurate values are hard to obtain directly from experiments or no local measurements are available. Due to the uncertainty associated with the unknown model parameters significant bias can be experienced if the model is used to simulate the carbon and nitrogen cycle components of different ecosystems. In order to improve model performance the unknown model parameters has to be estimated. We developed a multi-objective, two-step calibration method based on Bayesian approach in order to estimate the unknown parameters of PaSim and Biome-BGC models. Biome-BGC and PaSim are a widely used biogeochemical models that simulate the storage and flux of water, carbon, and nitrogen between the ecosystem and the atmosphere, and within the components of the terrestrial ecosystems (in this research the developed version of Biome-BGC is used which is referred as BBGC MuSo). Both models were calibrated regardless the simulated processes and type of model parameters. The calibration procedure is based on the comparison of measured data with simulated results via calculating a likelihood function (degree of goodness-of-fit between simulated and measured data). In our research different likelihood function formulations were used in order to examine the effect of the different model goodness metric on calibration. The different likelihoods are different functions of RMSE (root mean squared error) weighted by measurement uncertainty: exponential / linear / quadratic / linear normalized by correlation. As a first calibration step sensitivity analysis was performed in order to select the influential parameters which have strong effect on the output data. In the second calibration step only the sensitive parameters were calibrated (optimal values and confidence intervals were calculated). In case of PaSim more parameters were found responsible for the 95% of the output data variance than is case of BBGC MuSo. Analysis of the results of the optimized models revealed that the exponential likelihood estimation proved to be the most robust (best model simulation with optimized parameter, highest confidence interval increase). The cross-validation of the model simulations can help in constraining the highly uncertain greenhouse gas budget of grasslands.

EFFICIENT MODEL-FITTING AND MODEL-COMPARISON FOR HIGH-DIMENSIONAL BAYESIAN GEOSTATISTICAL MODELS. (R826887)

EPA Science Inventory

Geostatistical models are appropriate for spatially distributed data measured at irregularly spaced locations. We propose an efficient Markov chain Monte Carlo (MCMC) algorithm for fitting Bayesian geostatistical models with substantial numbers of unknown parameters to sizable...

Identifying mechanical property parameters of planetary soil using in-situ data obtained from exploration rovers

NASA Astrophysics Data System (ADS)

Ding, Liang; Gao, Haibo; Liu, Zhen; Deng, Zongquan; Liu, Guangjun

2015-12-01

Identifying the mechanical property parameters of planetary soil based on terramechanics models using in-situ data obtained from autonomous planetary exploration rovers is both an important scientific goal and essential for control strategy optimization and high-fidelity simulations of rovers. However, identifying all the terrain parameters is a challenging task because of the nonlinear and coupling nature of the involved functions. Three parameter identification methods are presented in this paper to serve different purposes based on an improved terramechanics model that takes into account the effects of slip, wheel lugs, etc. Parameter sensitivity and coupling of the equations are analyzed, and the parameters are grouped according to their sensitivity to the normal force, resistance moment and drawbar pull. An iterative identification method using the original integral model is developed first. In order to realize real-time identification, the model is then simplified by linearizing the normal and shearing stresses to derive decoupled closed-form analytical equations. Each equation contains one or two groups of soil parameters, making step-by-step identification of all the unknowns feasible. Experiments were performed using six different types of single-wheels as well as a four-wheeled rover moving on planetary soil simulant. All the unknown model parameters were identified using the measured data and compared with the values obtained by conventional experiments. It is verified that the proposed iterative identification method provides improved accuracy, making it suitable for scientific studies of soil properties, whereas the step-by-step identification methods based on simplified models require less calculation time, making them more suitable for real-time applications. The models have less than 10% margin of error comparing with the measured results when predicting the interaction forces and moments using the corresponding identified parameters.

A Sparse Bayesian Learning Algorithm for White Matter Parameter Estimation from Compressed Multi-shell Diffusion MRI.

PubMed

Pisharady, Pramod Kumar; Sotiropoulos, Stamatios N; Sapiro, Guillermo; Lenglet, Christophe

2017-09-01

We propose a sparse Bayesian learning algorithm for improved estimation of white matter fiber parameters from compressed (under-sampled q-space) multi-shell diffusion MRI data. The multi-shell data is represented in a dictionary form using a non-monoexponential decay model of diffusion, based on continuous gamma distribution of diffusivities. The fiber volume fractions with predefined orientations, which are the unknown parameters, form the dictionary weights. These unknown parameters are estimated with a linear un-mixing framework, using a sparse Bayesian learning algorithm. A localized learning of hyperparameters at each voxel and for each possible fiber orientations improves the parameter estimation. Our experiments using synthetic data from the ISBI 2012 HARDI reconstruction challenge and in-vivo data from the Human Connectome Project demonstrate the improvements.

A black box optimization approach to parameter estimation in a model for long/short term variations dynamics of commodity prices

NASA Astrophysics Data System (ADS)

De Santis, Alberto; Dellepiane, Umberto; Lucidi, Stefano

2012-11-01

In this paper we investigate the estimation problem for a model of the commodity prices. This model is a stochastic state space dynamical model and the problem unknowns are the state variables and the system parameters. Data are represented by the commodity spot prices, very seldom time series of Futures contracts are available for free. Both the system joint likelihood function (state variables and parameters) and the system marginal likelihood (the state variables are eliminated) function are addressed.

Computational methods for estimation of parameters in hyperbolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.; Murphy, K. A.

1983-01-01

Approximation techniques for estimating spatially varying coefficients and unknown boundary parameters in second order hyperbolic systems are discussed. Methods for state approximation (cubic splines, tau-Legendre) and approximation of function space parameters (interpolatory splines) are outlined and numerical findings for use of the resulting schemes in model "one dimensional seismic inversion' problems are summarized.

The Routine Fitting of Kinetic Data to Models

PubMed Central

Berman, Mones; Shahn, Ezra; Weiss, Marjory F.

1962-01-01

A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible. PMID:13867975

Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models.

PubMed

Garcia, Tanya P; Ma, Yanyuan

2017-10-01

We develop consistent and efficient estimation of parameters in general regression models with mismeasured covariates. We assume the model error and covariate distributions are unspecified, and the measurement error distribution is a general parametric distribution with unknown variance-covariance. We construct root- n consistent, asymptotically normal and locally efficient estimators using the semiparametric efficient score. We do not estimate any unknown distribution or model error heteroskedasticity. Instead, we form the estimator under possibly incorrect working distribution models for the model error, error-prone covariate, or both. Empirical results demonstrate robustness to different incorrect working models in homoscedastic and heteroskedastic models with error-prone covariates.

Investigation on Insar Time Series Deformation Model Considering Rheological Parameters for Soft Clay Subgrade Monitoring

NASA Astrophysics Data System (ADS)

Xing, X.; Yuan, Z.; Chen, L. F.; Yu, X. Y.; Xiao, L.

2018-04-01

The stability control is one of the major technical difficulties in the field of highway subgrade construction engineering. Building deformation model is a crucial step for InSAR time series deformation monitoring. Most of the InSAR deformation models for deformation monitoring are pure empirical mathematical models, without considering the physical mechanism of the monitored object. In this study, we take rheology into consideration, inducing rheological parameters into traditional InSAR deformation models. To assess the feasibility and accuracy for our new model, both simulation and real deformation data over Lungui highway (a typical highway built on soft clay subgrade in Guangdong province, China) are investigated with TerraSAR-X satellite imagery. In order to solve the unknows of the non-linear rheological model, three algorithms: Gauss-Newton (GN), Levenberg-Marquarat (LM), and Genetic Algorithm (GA), are utilized and compared to estimate the unknown parameters. Considering both the calculation efficiency and accuracy, GA is chosen as the final choice for the new model in our case study. Preliminary real data experiment is conducted with use of 17 TerraSAR-X Stripmap images (with a 3-m resolution). With the new deformation model and GA aforementioned, the unknown rheological parameters over all the high coherence points are obtained and the LOS deformation (the low-pass component) sequences are generated.

Distributed Optimization Design of Continuous-Time Multiagent Systems With Unknown-Frequency Disturbances.

PubMed

Wang, Xinghu; Hong, Yiguang; Yi, Peng; Ji, Haibo; Kang, Yu

2017-05-24

In this paper, a distributed optimization problem is studied for continuous-time multiagent systems with unknown-frequency disturbances. A distributed gradient-based control is proposed for the agents to achieve the optimal consensus with estimating unknown frequencies and rejecting the bounded disturbance in the semi-global sense. Based on convex optimization analysis and adaptive internal model approach, the exact optimization solution can be obtained for the multiagent system disturbed by exogenous disturbances with uncertain parameters.

ON IDENTIFIABILITY OF NONLINEAR ODE MODELS AND APPLICATIONS IN VIRAL DYNAMICS

PubMed Central

MIAO, HONGYU; XIA, XIAOHUA; PERELSON, ALAN S.; WU, HULIN

2011-01-01

Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice. PMID:21785515

Teaching-learning-based Optimization Algorithm for Parameter Identification in the Design of IIR Filters

NASA Astrophysics Data System (ADS)

Singh, R.; Verma, H. K.

2013-12-01

This paper presents a teaching-learning-based optimization (TLBO) algorithm to solve parameter identification problems in the designing of digital infinite impulse response (IIR) filter. TLBO based filter modelling is applied to calculate the parameters of unknown plant in simulations. Unlike other heuristic search algorithms, TLBO algorithm is an algorithm-specific parameter-less algorithm. In this paper big bang-big crunch (BB-BC) optimization and PSO algorithms are also applied to filter design for comparison. Unknown filter parameters are considered as a vector to be optimized by these algorithms. MATLAB programming is used for implementation of proposed algorithms. Experimental results show that the TLBO is more accurate to estimate the filter parameters than the BB-BC optimization algorithm and has faster convergence rate when compared to PSO algorithm. TLBO is used where accuracy is more essential than the convergence speed.

Summary of the DREAM8 Parameter Estimation Challenge: Toward Parameter Identification for Whole-Cell Models.

PubMed

Karr, Jonathan R; Williams, Alex H; Zucker, Jeremy D; Raue, Andreas; Steiert, Bernhard; Timmer, Jens; Kreutz, Clemens; Wilkinson, Simon; Allgood, Brandon A; Bot, Brian M; Hoff, Bruce R; Kellen, Michael R; Covert, Markus W; Stolovitzky, Gustavo A; Meyer, Pablo

2015-05-01

Whole-cell models that explicitly represent all cellular components at the molecular level have the potential to predict phenotype from genotype. However, even for simple bacteria, whole-cell models will contain thousands of parameters, many of which are poorly characterized or unknown. New algorithms are needed to estimate these parameters and enable researchers to build increasingly comprehensive models. We organized the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 8 Whole-Cell Parameter Estimation Challenge to develop new parameter estimation algorithms for whole-cell models. We asked participants to identify a subset of parameters of a whole-cell model given the model's structure and in silico "experimental" data. Here we describe the challenge, the best performing methods, and new insights into the identifiability of whole-cell models. We also describe several valuable lessons we learned toward improving future challenges. Going forward, we believe that collaborative efforts supported by inexpensive cloud computing have the potential to solve whole-cell model parameter estimation.

Adaptive Parameter Estimation of Person Recognition Model in a Stochastic Human Tracking Process

NASA Astrophysics Data System (ADS)

Nakanishi, W.; Fuse, T.; Ishikawa, T.

2015-05-01

This paper aims at an estimation of parameters of person recognition models using a sequential Bayesian filtering method. In many human tracking method, any parameters of models used for recognize the same person in successive frames are usually set in advance of human tracking process. In real situation these parameters may change according to situation of observation and difficulty level of human position prediction. Thus in this paper we formulate an adaptive parameter estimation using general state space model. Firstly we explain the way to formulate human tracking in general state space model with their components. Then referring to previous researches, we use Bhattacharyya coefficient to formulate observation model of general state space model, which is corresponding to person recognition model. The observation model in this paper is a function of Bhattacharyya coefficient with one unknown parameter. At last we sequentially estimate this parameter in real dataset with some settings. Results showed that sequential parameter estimation was succeeded and were consistent with observation situations such as occlusions.

Model Reduction via Principe Component Analysis and Markov Chain Monte Carlo (MCMC) Methods

NASA Astrophysics Data System (ADS)

Gong, R.; Chen, J.; Hoversten, M. G.; Luo, J.

2011-12-01

Geophysical and hydrogeological inverse problems often include a large number of unknown parameters, ranging from hundreds to millions, depending on parameterization and problems undertaking. This makes inverse estimation and uncertainty quantification very challenging, especially for those problems in two- or three-dimensional spatial domains. Model reduction technique has the potential of mitigating the curse of dimensionality by reducing total numbers of unknowns while describing the complex subsurface systems adequately. In this study, we explore the use of principal component analysis (PCA) and Markov chain Monte Carlo (MCMC) sampling methods for model reduction through the use of synthetic datasets. We compare the performances of three different but closely related model reduction approaches: (1) PCA methods with geometric sampling (referred to as 'Method 1'), (2) PCA methods with MCMC sampling (referred to as 'Method 2'), and (3) PCA methods with MCMC sampling and inclusion of random effects (referred to as 'Method 3'). We consider a simple convolution model with five unknown parameters as our goal is to understand and visualize the advantages and disadvantages of each method by comparing their inversion results with the corresponding analytical solutions. We generated synthetic data with noise added and invert them under two different situations: (1) the noised data and the covariance matrix for PCA analysis are consistent (referred to as the unbiased case), and (2) the noise data and the covariance matrix are inconsistent (referred to as biased case). In the unbiased case, comparison between the analytical solutions and the inversion results show that all three methods provide good estimates of the true values and Method 1 is computationally more efficient. In terms of uncertainty quantification, Method 1 performs poorly because of relatively small number of samples obtained, Method 2 performs best, and Method 3 overestimates uncertainty due to inclusion of random effects. However, in the biased case, only Method 3 correctly estimates all the unknown parameters, and both Methods 1 and 2 provide wrong values for the biased parameters. The synthetic case study demonstrates that if the covariance matrix for PCA analysis is inconsistent with true models, the PCA methods with geometric or MCMC sampling will provide incorrect estimates.

A review of the meteorological parameters which affect aerial application

NASA Technical Reports Server (NTRS)

Christensen, L. S.; Frost, W.

1979-01-01

The ambient wind field and temperature gradient were found to be the most important parameters. Investigation results indicated that the majority of meteorological parameters affecting dispersion were interdependent and the exact mechanism by which these factors influence the particle dispersion was largely unknown. The types and approximately ranges of instrumented capabilities for a systematic study of the significant meteorological parameters influencing aerial applications were defined. Current mathematical dispersion models were also briefly reviewed. Unfortunately, a rigorous dispersion model which could be applied to aerial application was not available.

Rhelogical constraints on ridge formation on Icy Satellites

NASA Astrophysics Data System (ADS)

Rudolph, M. L.; Manga, M.

2010-12-01

The processes responsible for forming ridges on Europa remain poorly understood. We use a continuum damage mechanics approach to model ridge formation. The main objectives of this contribution are to constrain (1) choice of rheological parameters and (2) maximum ridge size and rate of formation. The key rheological parameters to constrain appear in the evolution equation for a damage variable (D): ˙ {D} = B <<σ >>r}(1-D){-k-α D (p)/(μ ) and in the equation relating damage accumulation to volumetric changes, Jρ 0 = δ (1-D). Similar damage evolution laws have been applied to terrestrial glaciers and to the analysis of rock mechanics experiments. However, it is reasonable to expect that, like viscosity, the rheological constants B, α , and δ depend strongly on temperature, composition, and ice grain size. In order to determine whether the damage model is appropriate for Europa’s ridges, we must find values of the unknown damage parameters that reproduce ridge topography. We perform a suite of numerical experiments to identify the region of parameter space conducive to ridge production and show the sensitivity to changes in each unknown parameter.

Summary of the DREAM8 Parameter Estimation Challenge: Toward Parameter Identification for Whole-Cell Models

PubMed Central

Karr, Jonathan R.; Williams, Alex H.; Zucker, Jeremy D.; Raue, Andreas; Steiert, Bernhard; Timmer, Jens; Kreutz, Clemens; Wilkinson, Simon; Allgood, Brandon A.; Bot, Brian M.; Hoff, Bruce R.; Kellen, Michael R.; Covert, Markus W.; Stolovitzky, Gustavo A.; Meyer, Pablo

2015-01-01

Whole-cell models that explicitly represent all cellular components at the molecular level have the potential to predict phenotype from genotype. However, even for simple bacteria, whole-cell models will contain thousands of parameters, many of which are poorly characterized or unknown. New algorithms are needed to estimate these parameters and enable researchers to build increasingly comprehensive models. We organized the Dialogue for Reverse Engineering Assessments and Methods (DREAM) 8 Whole-Cell Parameter Estimation Challenge to develop new parameter estimation algorithms for whole-cell models. We asked participants to identify a subset of parameters of a whole-cell model given the model’s structure and in silico “experimental” data. Here we describe the challenge, the best performing methods, and new insights into the identifiability of whole-cell models. We also describe several valuable lessons we learned toward improving future challenges. Going forward, we believe that collaborative efforts supported by inexpensive cloud computing have the potential to solve whole-cell model parameter estimation. PMID:26020786

A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions

NASA Astrophysics Data System (ADS)

Ma, Lin

2017-11-01

This paper develops a method for precisely determining the tension of an inclined cable with unknown boundary conditions. First, the nonlinear motion equation of an inclined cable is derived, and a numerical model of the motion of the cable is proposed using the finite difference method. The proposed numerical model includes the sag-extensibility, flexural stiffness, inclination angle and rotational stiffness at two ends of the cable. Second, the influence of the dynamic parameters of the cable on its frequencies is discussed in detail, and a method for precisely determining the tension of an inclined cable is proposed based on the derivatives of the eigenvalues of the matrices. Finally, a multiparameter identification method is developed that can simultaneously identify multiple parameters, including the rotational stiffness at two ends. This scheme is applicable to inclined cables with varying sag, varying flexural stiffness and unknown boundary conditions. Numerical examples indicate that the method provides good precision. Because the parameters of cables other than tension (e.g., the flexural stiffness and rotational stiffness at the ends) are not accurately known in practical engineering, the multiparameter identification method could further improve the accuracy of cable tension measurements.

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm.

PubMed

Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam

2014-07-01

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Multisite EPR oximetry from multiple quadrature harmonics.

PubMed

Ahmad, R; Som, S; Johnson, D H; Zweier, J L; Kuppusamy, P; Potter, L C

2012-01-01

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported. Copyright © 2011 Elsevier Inc. All rights reserved.

Parametric system identification of catamaran for improving controller design

NASA Astrophysics Data System (ADS)

Timpitak, Surasak; Prempraneerach, Pradya; Pengwang, Eakkachai

2018-01-01

This paper presents an estimation of simplified dynamic model for only surge- and yaw- motions of catamaran by using system identification (SI) techniques to determine associated unknown parameters. These methods will enhance the performance of designing processes for the motion control system of Unmanned Surface Vehicle (USV). The simulation results demonstrate an effective way to solve for damping forces and to determine added masses by applying least-square and AutoRegressive Exogenous (ARX) methods. Both methods are then evaluated according to estimated parametric errors from the vehicle’s dynamic model. The ARX method, which yields better estimated accuracy, can then be applied to identify unknown parameters as well as to help improving a controller design of a real unmanned catamaran.

3D tomographic reconstruction using geometrical models

NASA Astrophysics Data System (ADS)

Battle, Xavier L.; Cunningham, Gregory S.; Hanson, Kenneth M.

1997-04-01

We address the issue of reconstructing an object of constant interior density in the context of 3D tomography where there is prior knowledge about the unknown shape. We explore the direct estimation of the parameters of a chosen geometrical model from a set of radiographic measurements, rather than performing operations (segmentation for example) on a reconstructed volume. The inverse problem is posed in the Bayesian framework. A triangulated surface describes the unknown shape and the reconstruction is computed with a maximum a posteriori (MAP) estimate. The adjoint differentiation technique computes the derivatives needed for the optimization of the model parameters. We demonstrate the usefulness of the approach and emphasize the techniques of designing forward and adjoint codes. We use the system response of the University of Arizona Fast SPECT imager to illustrate this method by reconstructing the shape of a heart phantom.

Multi-objective optimization in quantum parameter estimation

NASA Astrophysics Data System (ADS)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

Bootstrap Standard Errors for Maximum Likelihood Ability Estimates When Item Parameters Are Unknown

ERIC Educational Resources Information Center

Patton, Jeffrey M.; Cheng, Ying; Yuan, Ke-Hai; Diao, Qi

2014-01-01

When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…

Temporal gravity field modeling based on least square collocation with short-arc approach

NASA Astrophysics Data System (ADS)

ran, jiangjun; Zhong, Min; Xu, Houze; Liu, Chengshu; Tangdamrongsub, Natthachet

2014-05-01

After the launch of the Gravity Recovery And Climate Experiment (GRACE) in 2002, several research centers have attempted to produce the finest gravity model based on different approaches. In this study, we present an alternative approach to derive the Earth's gravity field, and two main objectives are discussed. Firstly, we seek the optimal method to estimate the accelerometer parameters, and secondly, we intend to recover the monthly gravity model based on least square collocation method. The method has been paid less attention compared to the least square adjustment method because of the massive computational resource's requirement. The positions of twin satellites are treated as pseudo-observations and unknown parameters at the same time. The variance covariance matrices of the pseudo-observations and the unknown parameters are valuable information to improve the accuracy of the estimated gravity solutions. Our analyses showed that introducing a drift parameter as an additional accelerometer parameter, compared to using only a bias parameter, leads to a significant improvement of our estimated monthly gravity field. The gravity errors outside the continents are significantly reduced based on the selected set of the accelerometer parameters. We introduced the improved gravity model namely the second version of Institute of Geodesy and Geophysics, Chinese Academy of Sciences (IGG-CAS 02). The accuracy of IGG-CAS 02 model is comparable to the gravity solutions computed from the Geoforschungszentrum (GFZ), the Center for Space Research (CSR) and the NASA Jet Propulsion Laboratory (JPL). In term of the equivalent water height, the correlation coefficients over the study regions (the Yangtze River valley, the Sahara desert, and the Amazon) among four gravity models are greater than 0.80.

Dynamic parameter identification of robot arms with servo-controlled electrical motors

NASA Astrophysics Data System (ADS)

Jiang, Zhao-Hui; Senda, Hiroshi

2005-12-01

This paper addresses the issue of dynamic parameter identification of the robot manipulator with servo-controlled electrical motors. An assumption is made that all kinematical parameters, such as link lengths, are known, and only dynamic parameters containing mass, moment of inertia, and their functions need to be identified. First, we derive dynamics of the robot arm with a linear form of the unknown dynamic parameters by taking dynamic characteristics of the motor and servo unit into consideration. Then, we implement the parameter identification approach to identify the unknown parameters with respect to individual link separately. A pseudo-inverse matrix is used for formulation of the parameter identification. The optimal solution is guaranteed in a sense of least-squares of the mean errors. A Direct Drive (DD) SCARA type industrial robot arm AdeptOne is used as an application example of the parameter identification. Simulations and experiments for both open loop and close loop controls are carried out. Comparison of the results confirms the correctness and usefulness of the parameter identification and the derived dynamic model.

Pattern-Based Inverse Modeling for Characterization of Subsurface Flow Models with Complex Geologic Heterogeneity

NASA Astrophysics Data System (ADS)

Golmohammadi, A.; Jafarpour, B.; M Khaninezhad, M. R.

2017-12-01

Calibration of heterogeneous subsurface flow models leads to ill-posed nonlinear inverse problems, where too many unknown parameters are estimated from limited response measurements. When the underlying parameters form complex (non-Gaussian) structured spatial connectivity patterns, classical variogram-based geostatistical techniques cannot describe the underlying connectivity patterns. Modern pattern-based geostatistical methods that incorporate higher-order spatial statistics are more suitable for describing such complex spatial patterns. Moreover, when the underlying unknown parameters are discrete (geologic facies distribution), conventional model calibration techniques that are designed for continuous parameters cannot be applied directly. In this paper, we introduce a novel pattern-based model calibration method to reconstruct discrete and spatially complex facies distributions from dynamic flow response data. To reproduce complex connectivity patterns during model calibration, we impose a feasibility constraint to ensure that the solution follows the expected higher-order spatial statistics. For model calibration, we adopt a regularized least-squares formulation, involving data mismatch, pattern connectivity, and feasibility constraint terms. Using an alternating directions optimization algorithm, the regularized objective function is divided into a continuous model calibration problem, followed by mapping the solution onto the feasible set. The feasibility constraint to honor the expected spatial statistics is implemented using a supervised machine learning algorithm. The two steps of the model calibration formulation are repeated until the convergence criterion is met. Several numerical examples are used to evaluate the performance of the developed method.

Identification of vehicle suspension parameters by design optimization

NASA Astrophysics Data System (ADS)

Tey, J. Y.; Ramli, R.; Kheng, C. W.; Chong, S. Y.; Abidin, M. A. Z.

2014-05-01

The design of a vehicle suspension system through simulation requires accurate representation of the design parameters. These parameters are usually difficult to measure or sometimes unavailable. This article proposes an efficient approach to identify the unknown parameters through optimization based on experimental results, where the covariance matrix adaptation-evolutionary strategy (CMA-es) is utilized to improve the simulation and experimental results against the kinematic and compliance tests. This speeds up the design and development cycle by recovering all the unknown data with respect to a set of kinematic measurements through a single optimization process. A case study employing a McPherson strut suspension system is modelled in a multi-body dynamic system. Three kinematic and compliance tests are examined, namely, vertical parallel wheel travel, opposite wheel travel and single wheel travel. The problem is formulated as a multi-objective optimization problem with 40 objectives and 49 design parameters. A hierarchical clustering method based on global sensitivity analysis is used to reduce the number of objectives to 30 by grouping correlated objectives together. Then, a dynamic summation of rank value is used as pseudo-objective functions to reformulate the multi-objective optimization to a single-objective optimization problem. The optimized results show a significant improvement in the correlation between the simulated model and the experimental model. Once accurate representation of the vehicle suspension model is achieved, further analysis, such as ride and handling performances, can be implemented for further optimization.

An easy-to-use tool for the evaluation of leachate production at landfill sites.

PubMed

Grugnaletti, Matteo; Pantini, Sara; Verginelli, Iason; Lombardi, Francesco

2016-09-01

A simulation program for the evaluation of leachate generation at landfill sites is herein presented. The developed tool is based on a water balance model that accounts for all the key processes influencing leachate generation through analytical and empirical equations. After a short description of the tool, different simulations on four Italian landfill sites are shown. The obtained results revealed that when literature values were assumed for the unknown input parameters, the model provided a rough estimation of the leachate production measured in the field. In this case, indeed, the deviations between observed and predicted data appeared, in some cases, significant. Conversely, by performing a preliminary calibration for some of the unknown input parameters (e.g. initial moisture content of wastes, compression index), in nearly all cases the model performances significantly improved. These results although showed the potential capability of a water balance model to estimate the leachate production at landfill sites also highlighted the intrinsic limitation of a deterministic approach to accurately forecast the leachate production over time. Indeed, parameters such as the initial water content of incoming waste and the compression index, that have a great influence on the leachate production, may exhibit temporal variation due to seasonal changing of weather conditions (e.g. rainfall, air humidity) as well as to seasonal variability in the amount and type of specific waste fractions produced (e.g. yard waste, food, plastics) that make their prediction quite complicated. In this sense, we believe that a tool such as the one proposed in this work that requires a limited number of unknown parameters, can be easier handled to quantify the uncertainties. Copyright © 2016 Elsevier Ltd. All rights reserved.

Application of multiple modelling to hyperthermia estimation: reducing the effects of model mismatch.

PubMed

Potocki, J K; Tharp, H S

1993-01-01

Multiple model estimation is a viable technique for dealing with the spatial perfusion model mismatch associated with hyperthermia dosimetry. Using multiple models, spatial discrimination can be obtained without increasing the number of unknown perfusion zones. Two multiple model estimators based on the extended Kalman filter (EKF) are designed and compared with two EKFs based on single models having greater perfusion zone segmentation. Results given here indicate that multiple modelling is advantageous when the number of thermal sensors is insufficient for convergence of single model estimators having greater perfusion zone segmentation. In situations where sufficient measured outputs exist for greater unknown perfusion parameter estimation, the multiple model estimators and the single model estimators yield equivalent results.

Estimating the frequency interval of a regularly spaced multicomponent harmonic line signal in colored noise

NASA Astrophysics Data System (ADS)

Frazer, Gordon J.; Anderson, Stuart J.

1997-10-01

The radar returns from some classes of time-varying point targets can be represented by the discrete-time signal plus noise model: xt equals st plus [vt plus (eta) t] equals (summation)i equals o P minus 1 Aiej2(pi f(i)/f(s)t) plus vt plus (eta) t, t (epsilon) 0, . . ., N minus 1, fi equals kfI plus fo where the received signal xt corresponds to the radar return from the target of interest from one azimuth-range cell. The signal has an unknown number of components, P, unknown complex amplitudes Ai and frequencies fi. The frequency parameters fo and fI are unknown, although constrained such that fo less than fI/2 and parameter k (epsilon) {minus u, . . ., minus 2, minus 1, 0, 1, 2, . . ., v} is constrained such that the component frequencies fi are bound by (minus fs/2, fs/2). The noise term vt, is typically colored, and represents clutter, interference and various noise sources. It is unknown, except that (summation)tvt2 less than infinity; in general, vt is not well modelled as an auto-regressive process of known order. The additional noise term (eta) t represents time-invariant point targets in the same azimuth-range cell. An important characteristic of the target is the unknown parameter, fI, representing the frequency interval between harmonic lines. It is desired to determine an estimate of fI from N samples of xt. We propose an algorithm to estimate fI based on Thomson's harmonic line F-Test, which is part of the multi-window spectrum estimation method and demonstrate the proposed estimator applied to target echo time series collected using an experimental HF skywave radar.

Model misspecification detection by means of multiple generator errors, using the observed potential map.

PubMed

Zhang, Z; Jewett, D L

1994-01-01

Due to model misspecification, currently-used Dipole Source Localization (DSL) methods may contain Multiple-Generator Errors (MulGenErrs) when fitting simultaneously-active dipoles. The size of the MulGenErr is a function of both the model used, and the dipole parameters, including the dipoles' waveforms (time-varying magnitudes). For a given fitting model, by examining the variation of the MulGenErrs (or the fit parameters) under different waveforms for the same generating-dipoles, the accuracy of the fitting model for this set of dipoles can be determined. This method of testing model misspecification can be applied to evoked potential maps even when the parameters of the generating-dipoles are unknown. The dipole parameters fitted in a model should only be accepted if the model can be shown to be sufficiently accurate.

A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term.

PubMed

Tsai, Jason S-H; Hsu, Wen-Teng; Lin, Long-Guei; Guo, Shu-Mei; Tann, Joseph W

2014-01-01

A modified nonlinear autoregressive moving average with exogenous inputs (NARMAX) model-based state-space self-tuner with fault tolerance is proposed in this paper for the unknown nonlinear stochastic hybrid system with a direct transmission matrix from input to output. Through the off-line observer/Kalman filter identification method, one has a good initial guess of modified NARMAX model to reduce the on-line system identification process time. Then, based on the modified NARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown continuous-time nonlinear system, with an input-output direct transmission term, which also has measurement and system noises and inaccessible system states. Besides, an effective state space self-turner with fault tolerance scheme is presented for the unknown multivariable stochastic system. A quantitative criterion is suggested by comparing the innovation process error estimated by the Kalman filter estimation algorithm, so that a weighting matrix resetting technique by adjusting and resetting the covariance matrices of parameter estimate obtained by the Kalman filter estimation algorithm is utilized to achieve the parameter estimation for faulty system recovery. Consequently, the proposed method can effectively cope with partially abrupt and/or gradual system faults and input failures by the fault detection. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Multiparameter Estimation in Networked Quantum Sensors

NASA Astrophysics Data System (ADS)

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-01

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Optimization of Biomathematical Model Predictions for Cognitive Performance Impairment in Individuals: Accounting for Unknown Traits and Uncertain States in Homeostatic and Circadian Processes

PubMed Central

Van Dongen, Hans P. A.; Mott, Christopher G.; Huang, Jen-Kuang; Mollicone, Daniel J.; McKenzie, Frederic D.; Dinges, David F.

2007-01-01

Current biomathematical models of fatigue and performance do not accurately predict cognitive performance for individuals with a priori unknown degrees of trait vulnerability to sleep loss, do not predict performance reliably when initial conditions are uncertain, and do not yield statistically valid estimates of prediction accuracy. These limitations diminish their usefulness for predicting the performance of individuals in operational environments. To overcome these 3 limitations, a novel modeling approach was developed, based on the expansion of a statistical technique called Bayesian forecasting. The expanded Bayesian forecasting procedure was implemented in the two-process model of sleep regulation, which has been used to predict performance on the basis of the combination of a sleep homeostatic process and a circadian process. Employing the two-process model with the Bayesian forecasting procedure to predict performance for individual subjects in the face of unknown traits and uncertain states entailed subject-specific optimization of 3 trait parameters (homeostatic build-up rate, circadian amplitude, and basal performance level) and 2 initial state parameters (initial homeostatic state and circadian phase angle). Prior information about the distribution of the trait parameters in the population at large was extracted from psychomotor vigilance test (PVT) performance measurements in 10 subjects who had participated in a laboratory experiment with 88 h of total sleep deprivation. The PVT performance data of 3 additional subjects in this experiment were set aside beforehand for use in prospective computer simulations. The simulations involved updating the subject-specific model parameters every time the next performance measurement became available, and then predicting performance 24 h ahead. Comparison of the predictions to the subjects' actual data revealed that as more data became available for the individuals at hand, the performance predictions became increasingly more accurate and had progressively smaller 95% confidence intervals, as the model parameters converged efficiently to those that best characterized each individual. Even when more challenging simulations were run (mimicking a change in the initial homeostatic state; simulating the data to be sparse), the predictions were still considerably more accurate than would have been achieved by the two-process model alone. Although the work described here is still limited to periods of consolidated wakefulness with stable circadian rhythms, the results obtained thus far indicate that the Bayesian forecasting procedure can successfully overcome some of the major outstanding challenges for biomathematical prediction of cognitive performance in operational settings. Citation: Van Dongen HPA; Mott CG; Huang JK; Mollicone DJ; McKenzie FD; Dinges DF. Optimization of biomathematical model predictions for cognitive performance impairment in individuals: accounting for unknown traits and uncertain states in homeostatic and circadian processes. SLEEP 2007;30(9):1129-1143. PMID:17910385

MoCha: Molecular Characterization of Unknown Pathways.

PubMed

Lobo, Daniel; Hammelman, Jennifer; Levin, Michael

2016-04-01

Automated methods for the reverse-engineering of complex regulatory networks are paving the way for the inference of mechanistic comprehensive models directly from experimental data. These novel methods can infer not only the relations and parameters of the known molecules defined in their input datasets, but also unknown components and pathways identified as necessary by the automated algorithms. Identifying the molecular nature of these unknown components is a crucial step for making testable predictions and experimentally validating the models, yet no specific and efficient tools exist to aid in this process. To this end, we present here MoCha (Molecular Characterization), a tool optimized for the search of unknown proteins and their pathways from a given set of known interacting proteins. MoCha uses the comprehensive dataset of protein-protein interactions provided by the STRING database, which currently includes more than a billion interactions from over 2,000 organisms. MoCha is highly optimized, performing typical searches within seconds. We demonstrate the use of MoCha with the characterization of unknown components from reverse-engineered models from the literature. MoCha is useful for working on network models by hand or as a downstream step of a model inference engine workflow and represents a valuable and efficient tool for the characterization of unknown pathways using known data from thousands of organisms. MoCha and its source code are freely available online under the GPLv3 license.

Structural control and health monitoring of building structures with unknown ground excitations: Experimental investigation

NASA Astrophysics Data System (ADS)

He, Jia; Xu, You-Lin; Zhan, Sheng; Huang, Qin

2017-03-01

When health monitoring system and vibration control system both are required for a building structure, it will be beneficial and cost-effective to integrate these two systems together for creating a smart building structure. Recently, on the basis of extended Kalman filter (EKF), a time-domain integrated approach was proposed for the identification of structural parameters of the controlled buildings with unknown ground excitations. The identified physical parameters and structural state vectors were then utilized to determine the control force for vibration suppression. In this paper, the possibility of establishing such a smart building structure with the function of simultaneous damage detection and vibration suppression was explored experimentally. A five-story shear building structure equipped with three magneto-rheological (MR) dampers was built. Four additional columns were added to the building model, and several damage scenarios were then simulated by symmetrically cutting off these columns in certain stories. Two sets of earthquakes, i.e. Kobe earthquake and Northridge earthquake, were considered as seismic input and assumed to be unknown during the tests. The structural parameters and the unknown ground excitations were identified during the tests by using the proposed identification method with the measured control forces. Based on the identified structural parameters and system states, a switching control law was employed to adjust the current applied to the MR dampers for the purpose of vibration attenuation. The experimental results show that the presented approach is capable of satisfactorily identifying structural damages and unknown excitations on one hand and significantly mitigating the structural vibration on the other hand.

Probabilistic and deterministic aspects of linear estimation in geodesy. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dermanis, A.

1976-01-01

Recent advances in observational techniques related to geodetic work (VLBI, laser ranging) make it imperative that more consideration should be given to modeling problems. Uncertainties in the effect of atmospheric refraction, polar motion and precession-nutation parameters, cannot be dispensed with in the context of centimeter level geodesy. Even physical processes that have generally been previously altogether neglected (station motions) must now be taken into consideration. The problem of modeling functions of time or space, or at least their values at observation points (epochs) is explored. When the nature of the function to be modeled is unknown. The need to include a limited number of terms and to a priori decide upon a specific form may result in a representation which fails to sufficiently approximate the unknown function. An alternative approach of increasing application is the modeling of unknown functions as stochastic processes.

System and method for motor parameter estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luhrs, Bin; Yan, Ting

2014-03-18

A system and method for determining unknown values of certain motor parameters includes a motor input device connectable to an electric motor having associated therewith values for known motor parameters and an unknown value of at least one motor parameter. The motor input device includes a processing unit that receives a first input from the electric motor comprising values for the known motor parameters for the electric motor and receive a second input comprising motor data on a plurality of reference motors, including values for motor parameters corresponding to the known motor parameters of the electric motor and values formore » motor parameters corresponding to the at least one unknown motor parameter value of the electric motor. The processor determines the unknown value of the at least one motor parameter from the first input and the second input and determines a motor management strategy for the electric motor based thereon.« less

Adaptive control of bivalirudin in the cardiac intensive care unit.

PubMed

Zhao, Qi; Edrich, Thomas; Paschalidis, Ioannis Ch

2015-02-01

Bivalirudin is a direct thrombin inhibitor used in the cardiac intensive care unit when heparin is contraindicated due to heparin-induced thrombocytopenia. Since it is not a commonly used drug, clinical experience with its dosing is sparse. In earlier work [1], we developed a dynamic system model that accurately predicts the effect of bivalirudin given dosage over time and patient physiological characteristics. This paper develops adaptive dosage controllers that regulate its effect to desired levels. To that end, and in the case that bivalirudin model parameters are available, we develop a Model Reference Control law. In the case that model parameters are unknown, an indirect Model Reference Adaptive Control scheme is applied to estimate model parameters first and then adapt the controller. Alternatively, direct Model Reference Adaptive Control is applied to adapt the controller directly without estimating model parameters first. Our algorithms are validated using actual patient data from a large hospital in the Boston area.

A Spline Regression Model for Latent Variables

ERIC Educational Resources Information Center

Harring, Jeffrey R.

2014-01-01

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

Monte Carlo sensitivity analysis of unknown parameters in hazardous materials transportation risk assessment.

PubMed

Pet-Armacost, J J; Sepulveda, J; Sakude, M

1999-12-01

The US Department of Transportation was interested in the risks associated with transporting Hydrazine in tanks with and without relief devices. Hydrazine is both highly toxic and flammable, as well as corrosive. Consequently, there was a conflict as to whether a relief device should be used or not. Data were not available on the impact of relief devices on release probabilities or the impact of Hydrazine on the likelihood of fires and explosions. In this paper, a Monte Carlo sensitivity analysis of the unknown parameters was used to assess the risks associated with highway transport of Hydrazine. To help determine whether or not relief devices should be used, fault trees and event trees were used to model the sequences of events that could lead to adverse consequences during transport of Hydrazine. The event probabilities in the event trees were derived as functions of the parameters whose effects were not known. The impacts of these parameters on the risk of toxic exposures, fires, and explosions were analyzed through a Monte Carlo sensitivity analysis and analyzed statistically through an analysis of variance. The analysis allowed the determination of which of the unknown parameters had a significant impact on the risks. It also provided the necessary support to a critical transportation decision even though the values of several key parameters were not known.

Inference regarding multiple structural changes in linear models with endogenous regressors☆

PubMed Central

Hall, Alastair R.; Han, Sanggohn; Boldea, Otilia

2012-01-01

This paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times. It is shown that minimization of a Generalized Method of Moments criterion yields inconsistent estimators of the break fractions, but minimization of the Two Stage Least Squares (2SLS) criterion yields consistent estimators of these parameters. We develop a methodology for estimation and inference of the parameters of the model based on 2SLS. The analysis covers the cases where the reduced form is either stable or unstable. The methodology is illustrated via an application to the New Keynesian Phillips Curve for the US. PMID:23805021

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Murphy, Patrick C.; Klein, Vladislav; Brandon, Jay M.

2001-01-01

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

Mars approach for global sensitivity analysis of differential equation models with applications to dynamics of influenza infection.

PubMed

Lee, Yeonok; Wu, Hulin

2012-01-01

Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.

Assessment of source-specific health effects associated with an unknown number of major sources of multiple air pollutants: a unified Bayesian approach.

PubMed

Park, Eun Sug; Hopke, Philip K; Oh, Man-Suk; Symanski, Elaine; Han, Daikwon; Spiegelman, Clifford H

2014-07-01

There has been increasing interest in assessing health effects associated with multiple air pollutants emitted by specific sources. A major difficulty with achieving this goal is that the pollution source profiles are unknown and source-specific exposures cannot be measured directly; rather, they need to be estimated by decomposing ambient measurements of multiple air pollutants. This estimation process, called multivariate receptor modeling, is challenging because of the unknown number of sources and unknown identifiability conditions (model uncertainty). The uncertainty in source-specific exposures (source contributions) as well as uncertainty in the number of major pollution sources and identifiability conditions have been largely ignored in previous studies. A multipollutant approach that can deal with model uncertainty in multivariate receptor models while simultaneously accounting for parameter uncertainty in estimated source-specific exposures in assessment of source-specific health effects is presented in this paper. The methods are applied to daily ambient air measurements of the chemical composition of fine particulate matter ([Formula: see text]), weather data, and counts of cardiovascular deaths from 1995 to 1997 for Phoenix, AZ, USA. Our approach for evaluating source-specific health effects yields not only estimates of source contributions along with their uncertainties and associated health effects estimates but also estimates of model uncertainty (posterior model probabilities) that have been ignored in previous studies. The results from our methods agreed in general with those from the previously conducted workshop/studies on the source apportionment of PM health effects in terms of number of major contributing sources, estimated source profiles, and contributions. However, some of the adverse source-specific health effects identified in the previous studies were not statistically significant in our analysis, which probably resulted because we incorporated parameter uncertainty in estimated source contributions that has been ignored in the previous studies into the estimation of health effects parameters. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

A Bayesian Retrieval of Greenland Ice Sheet Internal Temperature from Ultra-wideband Software-defined Microwave Radiometer (UWBRAD) Measurements

NASA Astrophysics Data System (ADS)

Duan, Y.; Durand, M. T.; Jezek, K. C.; Yardim, C.; Bringer, A.; Aksoy, M.; Johnson, J. T.

2017-12-01

The ultra-wideband software-defined microwave radiometer (UWBRAD) is designed to provide ice sheet internal temperature product via measuring low frequency microwave emission. Twelve channels ranging from 0.5 to 2.0 GHz are covered by the instrument. A Greenland air-borne demonstration was demonstrated in September 2016, provided first demonstration of Ultra-wideband radiometer observations of geophysical scenes, including ice sheets. Another flight is planned for September 2017 for acquiring measurements in central ice sheet. A Bayesian framework is designed to retrieve the ice sheet internal temperature from simulated UWBRAD brightness temperature (Tb) measurements over Greenland flight path with limited prior information of the ground. A 1-D heat-flow model, the Robin Model, was used to model the ice sheet internal temperature profile with ground information. Synthetic UWBRAD Tb observations was generated via the partially coherent radiation transfer model, which utilizes the Robin model temperature profile and an exponential fit of ice density from Borehole measurement as input, and corrupted with noise. The effective surface temperature, geothermal heat flux, the variance of upper layer ice density, and the variance of fine scale density variation at deeper ice sheet were treated as unknown variables within the retrieval framework. Each parameter is defined with its possible range and set to be uniformly distributed. The Markov Chain Monte Carlo (MCMC) approach is applied to make the unknown parameters randomly walk in the parameter space. We investigate whether the variables can be improved over priors using the MCMC approach and contribute to the temperature retrieval theoretically. UWBRAD measurements near camp century from 2016 was also treated with the MCMC to examine the framework with scattering effect. The fine scale density fluctuation is an important parameter. It is the most sensitive yet highly unknown parameter in the estimation framework. Including the fine scale density fluctuation greatly improved the retrieval results. The ice sheet vertical temperature profile, especially the 10m temperature, can be well retrieved via the MCMC process. Future retrieval work will apply the Bayesian approach to UWBRAD airborne measurements.

Neutrino oscillations and Non-Standard Interactions

NASA Astrophysics Data System (ADS)

Farzan, Yasaman; Tórtola, Mariam

2018-02-01

Current neutrino experiments are measuring the neutrino mixing parameters with an unprecedented accuracy. The upcoming generation of neutrino experiments will be sensitive to subdominant oscillation effects that can give information on the yet-unknown neutrino parameters: the Dirac CP-violating phase, the mass ordering and the octant of θ_{23}. Determining the exact values of neutrino mass and mixing parameters is crucial to test neutrino models and flavor symmetries designed to predict these neutrino parameters. In the first part of this review, we summarize the current status of the neutrino oscillation parameter determination. We consider the most recent data from all solar experiments and the atmospheric data from Super-Kamiokande, IceCube and ANTARES. We also implement the data from the reactor neutrino experiments KamLAND, Daya Bay, RENO and Double Chooz as well as the long baseline neutrino data from MINOS, T2K and NOvA. If in addition to the standard interactions, neutrinos have subdominant yet-unknown Non-Standard Interactions (NSI) with matter fields, extracting the values of these parameters will suffer from new degeneracies and ambiguities. We review such effects and formulate the conditions on the NSI parameters under which the precision measurement of neutrino oscillation parameters can be distorted. Like standard weak interactions, the non-standard interaction can be categorized into two groups: Charged Current (CC) NSI and Neutral Current (NC) NSI. Our focus will be mainly on neutral current NSI because it is possible to build a class of models that give rise to sizeable NC NSI with discernible effects on neutrino oscillation. These models are based on new U(1) gauge symmetry with a gauge boson of mass ≲ 10 MeV. The UV complete model should be of course electroweak invariant which in general implies that along with neutrinos, charged fermions also acquire new interactions on which there are strong bounds. We enumerate the bounds that already exist on the electroweak symmetric models and demonstrate that it is possible to build viable models avoiding all these bounds. In the end, we review methods to test these models and suggest approaches to break the degeneracies in deriving neutrino mass parameters caused by NSI.

Unitarity and predictiveness in new Higgs inflation

NASA Astrophysics Data System (ADS)

Fumagalli, Jacopo; Mooij, Sander; Postma, Marieke

2018-03-01

In new Higgs inflation the Higgs kinetic terms are non-minimally coupled to the Einstein tensor, allowing the Higgs field to play the role of the inflaton. The new interaction is non-renormalizable, and the model only describes physics below some cutoff scale. Even if the unknown UV physics does not affect the tree level inflaton potential significantly, it may still enter at loop level and modify the running of the Standard Model (SM) parameters. This is analogous to what happens in the original model for Higgs inflation. A key difference, though, is that in new Higgs inflation the inflationary predictions are sensitive to this running. Thus the boundary conditions at the EW scale as well as the unknown UV completion may leave a signature on the inflationary parameters. However, this dependence can be evaded if the kinetic terms of the SM fermions and gauge fields are non-minimally coupled to gravity as well. Our approach to determine the model's UV dependence and the connection between low and high scale physics can be used in any particle physics model of inflation.

On the predictiveness of single-field inflationary models

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Patil, Subodh P.; Trott, Michael

2014-06-01

We re-examine the predictiveness of single-field inflationary models and discuss how an unknown UV completion can complicate determining inflationary model parameters from observations, even from precision measurements. Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions. We illustrate this point using the minimal Higgs Inflationary scenario, which is arguably the most predictive single-field model on the market, because its predictions for A S , r and n s are made using only one new free parameter beyond those measured in particle physics experiments, and run up to the inflationary regime. We find that this issue can already have observable effects. At the same time, this UV-parameter dependence in the Renormalization Group allows Higgs Inflation to occur (in principle) for a slightly larger range of Higgs masses. We comment on the origin of the various UV scales that arise at large field values for the SM Higgs, clarifying cut off scale arguments by further developing the formalism of a non-linear realization of SU L (2) × U(1) in curved space. We discuss the interesting fact that, outside of Higgs Inflation, the effect of a non-minimal coupling to gravity, even in the SM, results in a non-linear EFT for the Higgs sector. Finally, we briefly comment on post BICEP2 attempts to modify the Higgs Inflation scenario.

System Identification Applied to Dynamic CFD Simulation and Wind Tunnel Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.; Vicroy, Dan D.

2011-01-01

Demanding aerodynamic modeling requirements for military and civilian aircraft have provided impetus for researchers to improve computational and experimental techniques. Model validation is a key component for these research endeavors so this study is an initial effort to extend conventional time history comparisons by comparing model parameter estimates and their standard errors using system identification methods. An aerodynamic model of an aircraft performing one-degree-of-freedom roll oscillatory motion about its body axes is developed. The model includes linear aerodynamics and deficiency function parameters characterizing an unsteady effect. For estimation of unknown parameters two techniques, harmonic analysis and two-step linear regression, were applied to roll-oscillatory wind tunnel data and to computational fluid dynamics (CFD) simulated data. The model used for this study is a highly swept wing unmanned aerial combat vehicle. Differences in response prediction, parameters estimates, and standard errors are compared and discussed

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Sloppy-model universality class and the Vandermonde matrix.

PubMed

Waterfall, Joshua J; Casey, Fergal P; Gutenkunst, Ryan N; Brown, Kevin S; Myers, Christopher R; Brouwer, Piet W; Elser, Veit; Sethna, James P

2006-10-13

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Parameter Estimation for a Turbulent Buoyant Jet Using Approximate Bayesian Computation

NASA Astrophysics Data System (ADS)

Christopher, Jason D.; Wimer, Nicholas T.; Hayden, Torrey R. S.; Lapointe, Caelan; Grooms, Ian; Rieker, Gregory B.; Hamlington, Peter E.

2016-11-01

Approximate Bayesian Computation (ABC) is a powerful tool that allows sparse experimental or other "truth" data to be used for the prediction of unknown model parameters in numerical simulations of real-world engineering systems. In this presentation, we introduce the ABC approach and then use ABC to predict unknown inflow conditions in simulations of a two-dimensional (2D) turbulent, high-temperature buoyant jet. For this test case, truth data are obtained from a simulation with known boundary conditions and problem parameters. Using spatially-sparse temperature statistics from the 2D buoyant jet truth simulation, we show that the ABC method provides accurate predictions of the true jet inflow temperature. The success of the ABC approach in the present test suggests that ABC is a useful and versatile tool for engineering fluid dynamics research.

Multiple concurrent recursive least squares identification with application to on-line spacecraft mass-property identification

NASA Technical Reports Server (NTRS)

Wilson, Edward (Inventor)

2006-01-01

The present invention is a method for identifying unknown parameters in a system having a set of governing equations describing its behavior that cannot be put into regression form with the unknown parameters linearly represented. In this method, the vector of unknown parameters is segmented into a plurality of groups where each individual group of unknown parameters may be isolated linearly by manipulation of said equations. Multiple concurrent and independent recursive least squares identification of each said group run, treating other unknown parameters appearing in their regression equation as if they were known perfectly, with said values provided by recursive least squares estimation from the other groups, thereby enabling the use of fast, compact, efficient linear algorithms to solve problems that would otherwise require nonlinear solution approaches. This invention is presented with application to identification of mass and thruster properties for a thruster-controlled spacecraft.

Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm

NASA Astrophysics Data System (ADS)

Roozegar, Mehdi; Mahjoob, Mohammad J.; Ayati, Moosa

2017-05-01

This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton-Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.

Multiparameter Estimation in Networked Quantum Sensors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

Multiparameter Estimation in Networked Quantum Sensors

DOE PAGES

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-21

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. Thismore » immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.« less

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2009-01-01

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

Bayesian source term determination with unknown covariance of measurements

NASA Astrophysics Data System (ADS)

Belal, Alkomiet; Tichý, Ondřej; Šmídl, Václav

2017-04-01

Determination of a source term of release of a hazardous material into the atmosphere is a very important task for emergency response. We are concerned with the problem of estimation of the source term in the conventional linear inverse problem, y = Mx, where the relationship between the vector of observations y is described using the source-receptor-sensitivity (SRS) matrix M and the unknown source term x. Since the system is typically ill-conditioned, the problem is recast as an optimization problem minR,B(y - Mx)TR-1(y - Mx) + xTB-1x. The first term minimizes the error of the measurements with covariance matrix R, and the second term is a regularization of the source term. There are different types of regularization arising for different choices of matrices R and B, for example, Tikhonov regularization assumes covariance matrix B as the identity matrix multiplied by scalar parameter. In this contribution, we adopt a Bayesian approach to make inference on the unknown source term x as well as unknown R and B. We assume prior on x to be a Gaussian with zero mean and unknown diagonal covariance matrix B. The covariance matrix of the likelihood R is also unknown. We consider two potential choices of the structure of the matrix R. First is the diagonal matrix and the second is a locally correlated structure using information on topology of the measuring network. Since the inference of the model is intractable, iterative variational Bayes algorithm is used for simultaneous estimation of all model parameters. The practical usefulness of our contribution is demonstrated on an application of the resulting algorithm to real data from the European Tracer Experiment (ETEX). This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis.

PubMed

Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Xin; Chen, Chun Lung Philip

2014-12-01

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.

An adaptive control scheme for a flexible manipulator

NASA Technical Reports Server (NTRS)

Yang, T. C.; Yang, J. C. S.; Kudva, P.

1987-01-01

The problem of controlling a single link flexible manipulator is considered. A self-tuning adaptive control scheme is proposed which consists of a least squares on-line parameter identification of an equivalent linear model followed by a tuning of the gains of a pole placement controller using the parameter estimates. Since the initial parameter values for this model are assumed unknown, the use of arbitrarily chosen initial parameter estimates in the adaptive controller would result in undesirable transient effects. Hence, the initial stage control is carried out with a PID controller. Once the identified parameters have converged, control is transferred to the adaptive controller. Naturally, the relevant issues in this scheme are tests for parameter convergence and minimization of overshoots during control switch-over. To demonstrate the effectiveness of the proposed scheme, simulation results are presented with an analytical nonlinear dynamic model of a single link flexible manipulator.

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 1. Theory

USGS Publications Warehouse

Cooley, Richard L.

1982-01-01

Prior information on the parameters of a groundwater flow model can be used to improve parameter estimates obtained from nonlinear regression solution of a modeling problem. Two scales of prior information can be available: (1) prior information having known reliability (that is, bias and random error structure) and (2) prior information consisting of best available estimates of unknown reliability. A regression method that incorporates the second scale of prior information assumes the prior information to be fixed for any particular analysis to produce improved, although biased, parameter estimates. Approximate optimization of two auxiliary parameters of the formulation is used to help minimize the bias, which is almost always much smaller than that resulting from standard ridge regression. It is shown that if both scales of prior information are available, then a combined regression analysis may be made.

Integrated direct/indirect adaptive robust motion trajectory tracking control of pneumatic cylinders

NASA Astrophysics Data System (ADS)

Meng, Deyuan; Tao, Guoliang; Zhu, Xiaocong

2013-09-01

This paper studies the precision motion trajectory tracking control of a pneumatic cylinder driven by a proportional-directional control valve. An integrated direct/indirect adaptive robust controller is proposed. The controller employs a physical model based indirect-type parameter estimation to obtain reliable estimates of unknown model parameters, and utilises a robust control method with dynamic compensation type fast adaptation to attenuate the effects of parameter estimation errors, unmodelled dynamics and disturbances. Due to the use of projection mapping, the robust control law and the parameter adaption algorithm can be designed separately. Since the system model uncertainties are unmatched, the recursive backstepping technology is adopted to design the robust control law. Extensive comparative experimental results are presented to illustrate the effectiveness of the proposed controller and its performance robustness to parameter variations and sudden disturbances.

Image Restoration for Fluorescence Planar Imaging with Diffusion Model

PubMed Central

Gong, Yuzhu; Li, Yang

2017-01-01

Fluorescence planar imaging (FPI) is failure to capture high resolution images of deep fluorochromes due to photon diffusion. This paper presents an image restoration method to deal with this kind of blurring. The scheme of this method is conceived based on a reconstruction method in fluorescence molecular tomography (FMT) with diffusion model. A new unknown parameter is defined through introducing the first mean value theorem for definite integrals. System matrix converting this unknown parameter to the blurry image is constructed with the elements of depth conversion matrices related to a chosen plane named focal plane. Results of phantom and mouse experiments show that the proposed method is capable of reducing the blurring of FPI image caused by photon diffusion when the depth of focal plane is chosen within a proper interval around the true depth of fluorochrome. This method will be helpful to the estimation of the size of deep fluorochrome. PMID:29279843

Exploring theory space with Monte Carlo reweighting

DOE PAGES

Gainer, James S.; Lykken, Joseph; Matchev, Konstantin T.; ...

2014-10-13

Theories of new physics often involve a large number of unknown parameters which need to be scanned. Additionally, a putative signal in a particular channel may be due to a variety of distinct models of new physics. This makes experimental attempts to constrain the parameter space of motivated new physics models with a high degree of generality quite challenging. We describe how the reweighting of events may allow this challenge to be met, as fully simulated Monte Carlo samples generated for arbitrary benchmark models can be effectively re-used. Specifically, we suggest procedures that allow more efficient collaboration between theorists andmore » experimentalists in exploring large theory parameter spaces in a rigorous way at the LHC.« less

Inverse and forward modeling under uncertainty using MRE-based Bayesian approach

NASA Astrophysics Data System (ADS)

Hou, Z.; Rubin, Y.

2004-12-01

A stochastic inverse approach for subsurface characterization is proposed and applied to shallow vadose zone at a winery field site in north California and to a gas reservoir at the Ormen Lange field site in the North Sea. The approach is formulated in a Bayesian-stochastic framework, whereby the unknown parameters are identified in terms of their statistical moments or their probabilities. Instead of the traditional single-valued estimation /prediction provided by deterministic methods, the approach gives a probability distribution for an unknown parameter. This allows calculating the mean, the mode, and the confidence interval, which is useful for a rational treatment of uncertainty and its consequences. The approach also allows incorporating data of various types and different error levels, including measurements of state variables as well as information such as bounds on or statistical moments of the unknown parameters, which may represent prior information. To obtain minimally subjective prior probabilities required for the Bayesian approach, the principle of Minimum Relative Entropy (MRE) is employed. The approach is tested in field sites for flow parameters identification and soil moisture estimation in the vadose zone and for gas saturation estimation at great depth below the ocean floor. Results indicate the potential of coupling various types of field data within a MRE-based Bayesian formalism for improving the estimation of the parameters of interest.

A spline-based parameter estimation technique for static models of elastic structures

NASA Technical Reports Server (NTRS)

Dutt, P.; Taasan, S.

1986-01-01

The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.

Three-dimensional FEM model of FBGs in PANDA fibers with experimentally determined model parameters

NASA Astrophysics Data System (ADS)

Lindner, Markus; Hopf, Barbara; Koch, Alexander W.; Roths, Johannes

2017-04-01

A 3D-FEM model has been developed to improve the understanding of multi-parameter sensing with Bragg gratings in attached or embedded polarization maintaining fibers. The material properties of the fiber, especially Young's modulus and Poisson's ratio of the fiber's stress applying parts, are crucial for accurate simulations, but are usually not provided by the manufacturers. A methodology is presented to determine the unknown parameters by using experimental characterizations of the fiber and iterative FEM simulations. The resulting 3D-Model is capable of describing the change in birefringence of the free fiber when exposed to longitudinal strain. In future studies the 3D-FEM model will be employed to study the interaction of PANDA fibers with the surrounding materials in which they are embedded.

Backstepping Design of Adaptive Neural Fault-Tolerant Control for MIMO Nonlinear Systems.

PubMed

Gao, Hui; Song, Yongduan; Wen, Changyun

In this paper, an adaptive controller is developed for a class of multi-input and multioutput nonlinear systems with neural networks (NNs) used as a modeling tool. It is shown that all the signals in the closed-loop system with the proposed adaptive neural controller are globally uniformly bounded for any external input in . In our control design, the upper bound of the NN modeling error and the gains of external disturbance are characterized by unknown upper bounds, which is more rational to establish the stability in the adaptive NN control. Filter-based modification terms are used in the update laws of unknown parameters to improve the transient performance. Finally, fault-tolerant control is developed to accommodate actuator failure. An illustrative example applying the adaptive controller to control a rigid robot arm shows the validation of the proposed controller.In this paper, an adaptive controller is developed for a class of multi-input and multioutput nonlinear systems with neural networks (NNs) used as a modeling tool. It is shown that all the signals in the closed-loop system with the proposed adaptive neural controller are globally uniformly bounded for any external input in . In our control design, the upper bound of the NN modeling error and the gains of external disturbance are characterized by unknown upper bounds, which is more rational to establish the stability in the adaptive NN control. Filter-based modification terms are used in the update laws of unknown parameters to improve the transient performance. Finally, fault-tolerant control is developed to accommodate actuator failure. An illustrative example applying the adaptive controller to control a rigid robot arm shows the validation of the proposed controller.

Development of a mathematical model for mechanical transmission of trypanosomes and other pathogens of cattle transmitted by tabanids.

PubMed

Desquesnes, Marc; Biteau-Coroller, Fabienne; Bouyer, Jérémy; Dia, Mamadou Lamine; Foil, Lane

2009-02-01

Mechanical transmission of pathogens by biting insects is a non-specific phenomenon in which pathogens are transmitted from the blood of an infected host to another host during interrupted feeding of the insects. A large range of pathogens can be mechanically transmitted, e.g. hemoparasites, bacteria and viruses. Some pathogens are almost exclusively mechanically transmitted, while others are also cyclically transmitted. For agents transmitted both cyclically and mechanically (mixed transmission), such as certain African pathogenic trypanosomes, the relative impact of mechanical versus cyclical transmission is essentially unknown. We have developed a mathematical model of pathogen transmission by a defined insect population to evaluate the importance of mechanical transmission. Based on a series of experiments aimed at demonstrating mechanical transmission of African trypanosomes by tabanids, the main parameters of the model were either quantified (host parasitaemia, mean individual insect burden, initial prevalence of infection) or estimated (unknown parameters). This model allows us to simulate the evolution of pathogen prevalence under various predictive circumstances, including control measures and could be used to assess the risk of mechanical transmission under field conditions. If adjustments of parameters are provided, this model could be generalized to other pathogenic agents present in the blood of their hosts (Bovine Leukemia virus, Anaplasma, etc.) or other biting insects such as biting muscids (stomoxyines) and hippoboscids.

Advanced Aeroservoelastic Testing and Data Analysis (Les Essais Aeroservoelastiques et l’Analyse des Donnees).

DTIC Science & Technology

1995-11-01

network - based AFS concepts. Neural networks can addition of vanes in each engine exhaust for thrust provide...parameter estimation programs 19-11 8.6 Neural Network Based Methods unknown parameters of the postulated state space model Artificial neural network ...Forward Neural Network the network that the applicability of the recurrent neural and ii) Recurrent Neural Network [117-119]. network to

Parameter estimation for stiff deterministic dynamical systems via ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Arnold, Andrea; Calvetti, Daniela; Somersalo, Erkki

2014-10-01

A commonly encountered problem in numerous areas of applications is to estimate the unknown coefficients of a dynamical system from direct or indirect observations at discrete times of some of the components of the state vector. A related problem is to estimate unobserved components of the state. An egregious example of such a problem is provided by metabolic models, in which the numerous model parameters and the concentrations of the metabolites in tissue are to be estimated from concentration data in the blood. A popular method for addressing similar questions in stochastic and turbulent dynamics is the ensemble Kalman filter (EnKF), a particle-based filtering method that generalizes classical Kalman filtering. In this work, we adapt the EnKF algorithm for deterministic systems in which the numerical approximation error is interpreted as a stochastic drift with variance based on classical error estimates of numerical integrators. This approach, which is particularly suitable for stiff systems where the stiffness may depend on the parameters, allows us to effectively exploit the parallel nature of particle methods. Moreover, we demonstrate how spatial prior information about the state vector, which helps the stability of the computed solution, can be incorporated into the filter. The viability of the approach is shown by computed examples, including a metabolic system modeling an ischemic episode in skeletal muscle, with a high number of unknown parameters.

Evaluation of parameters of color profile models of LCD and LED screens

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The purpose of the research relates to the problem of parametric identification of the color profile model of LCD (liquid crystal display) and LED (light emitting diode) screens. The color profile model of a screen is based on the Grassmann’s Law of additive color mixture. Mathematically the problem is to evaluate unknown parameters (numerical coefficients) of the matrix transformation between different color spaces. Several methods of evaluation of these screen profile coefficients were developed. These methods are based either on processing of some colorimetric measurements or on processing of technical documentation data.

Noise parameter estimation for poisson corrupted images using variance stabilization transforms.

PubMed

Jin, Xiaodan; Xu, Zhenyu; Hirakawa, Keigo

2014-03-01

Noise is present in all images captured by real-world image sensors. Poisson distribution is said to model the stochastic nature of the photon arrival process and agrees with the distribution of measured pixel values. We propose a method for estimating unknown noise parameters from Poisson corrupted images using properties of variance stabilization. With a significantly lower computational complexity and improved stability, the proposed estimation technique yields noise parameters that are comparable in accuracy to the state-of-art methods.

Modeling Hubble Space Telescope flight data by Q-Markov cover identification

NASA Technical Reports Server (NTRS)

Liu, K.; Skelton, R. E.; Sharkey, J. P.

1992-01-01

A state space model for the Hubble Space Telescope under the influence of unknown disturbances in orbit is presented. This model was obtained from flight data by applying the Q-Markov covariance equivalent realization identification algorithm. This state space model guarantees the match of the first Q-Markov parameters and covariance parameters of the Hubble system. The flight data were partitioned into high- and low-frequency components for more efficient Q-Markov cover modeling, to reduce some computational difficulties of the Q-Markov cover algorithm. This identification revealed more than 20 lightly damped modes within the bandwidth of the attitude control system. Comparisons with the analytical (TREETOPS) model are also included.

Explicit least squares system parameter identification for exact differential input/output models

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1993-01-01

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Semiparametric modeling: Correcting low-dimensional model error in parametric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berry, Tyrus, E-mail: thb11@psu.edu; Harlim, John, E-mail: jharlim@psu.edu; Department of Meteorology, the Pennsylvania State University, 503 Walker Building, University Park, PA 16802-5013

2016-03-01

In this paper, a semiparametric modeling approach is introduced as a paradigm for addressing model error arising from unresolved physical phenomena. Our approach compensates for model error by learning an auxiliary dynamical model for the unknown parameters. Practically, the proposed approach consists of the following steps. Given a physics-based model and a noisy data set of historical observations, a Bayesian filtering algorithm is used to extract a time-series of the parameter values. Subsequently, the diffusion forecast algorithm is applied to the retrieved time-series in order to construct the auxiliary model for the time evolving parameters. The semiparametric forecasting algorithm consistsmore » of integrating the existing physics-based model with an ensemble of parameters sampled from the probability density function of the diffusion forecast. To specify initial conditions for the diffusion forecast, a Bayesian semiparametric filtering method that extends the Kalman-based filtering framework is introduced. In difficult test examples, which introduce chaotically and stochastically evolving hidden parameters into the Lorenz-96 model, we show that our approach can effectively compensate for model error, with forecasting skill comparable to that of the perfect model.« less

Robust Adaptive Synchronization of Ring Configured Uncertain Chaotic FitzHugh–Nagumo Neurons under Direction-Dependent Coupling

PubMed Central

Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik

2018-01-01

This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided. PMID:29535622

Extracting scene feature vectors through modeling, volume 3

NASA Technical Reports Server (NTRS)

Berry, J. K.; Smith, J. A.

1976-01-01

The remote estimation of the leaf area index of winter wheat at Finney County, Kansas was studied. The procedure developed consists of three activities: (1) field measurements; (2) model simulations; and (3) response classifications. The first activity is designed to identify model input parameters and develop a model evaluation data set. A stochastic plant canopy reflectance model is employed to simulate reflectance in the LANDSAT bands as a function of leaf area index for two phenological stages. An atmospheric model is used to translate these surface reflectances into simulated satellite radiance. A divergence classifier determines the relative similarity between model derived spectral responses and those of areas with unknown leaf area index. The unknown areas are assigned the index associated with the closest model response. This research demonstrated that the SRVC canopy reflectance model is appropriate for wheat scenes and that broad categories of leaf area index can be inferred from the procedure developed.

ESTIMATION OF CHEMICAL SPECIFIC PARAMETERS WITHIN PHYSIOLOGICALLY BASED PHARMACOKINETIC/PHARMACODYNAMIC MODELS

EPA Science Inventory

While relationships between chemical structure and observed properties or activities (QSAR - quantitative structure activity relationship) can be used to predict the behavior of unknown chemicals, this method is semiempirical in nature relying on high quality experimental data to...

Aerodynamic parameter estimation via Fourier modulating function techniques

NASA Technical Reports Server (NTRS)

Pearson, A. E.

1995-01-01

Parameter estimation algorithms are developed in the frequency domain for systems modeled by input/output ordinary differential equations. The approach is based on Shinbrot's method of moment functionals utilizing Fourier based modulating functions. Assuming white measurement noises for linear multivariable system models, an adaptive weighted least squares algorithm is developed which approximates a maximum likelihood estimate and cannot be biased by unknown initial or boundary conditions in the data owing to a special property attending Shinbrot-type modulating functions. Application is made to perturbation equation modeling of the longitudinal and lateral dynamics of a high performance aircraft using flight-test data. Comparative studies are included which demonstrate potential advantages of the algorithm relative to some well established techniques for parameter identification. Deterministic least squares extensions of the approach are made to the frequency transfer function identification problem for linear systems and to the parameter identification problem for a class of nonlinear-time-varying differential system models.

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

Estimation of beam material random field properties via sensitivity-based model updating using experimental frequency response functions

NASA Astrophysics Data System (ADS)

Machado, M. R.; Adhikari, S.; Dos Santos, J. M. C.; Arruda, J. R. F.

2018-03-01

Structural parameter estimation is affected not only by measurement noise but also by unknown uncertainties which are present in the system. Deterministic structural model updating methods minimise the difference between experimentally measured data and computational prediction. Sensitivity-based methods are very efficient in solving structural model updating problems. Material and geometrical parameters of the structure such as Poisson's ratio, Young's modulus, mass density, modal damping, etc. are usually considered deterministic and homogeneous. In this paper, the distributed and non-homogeneous characteristics of these parameters are considered in the model updating. The parameters are taken as spatially correlated random fields and are expanded in a spectral Karhunen-Loève (KL) decomposition. Using the KL expansion, the spectral dynamic stiffness matrix of the beam is expanded as a series in terms of discretized parameters, which can be estimated using sensitivity-based model updating techniques. Numerical and experimental tests involving a beam with distributed bending rigidity and mass density are used to verify the proposed method. This extension of standard model updating procedures can enhance the dynamic description of structural dynamic models.

Rendezvous with connectivity preservation for multi-robot systems with an unknown leader

NASA Astrophysics Data System (ADS)

Dong, Yi

2018-02-01

This paper studies the leader-following rendezvous problem with connectivity preservation for multi-agent systems composed of uncertain multi-robot systems subject to external disturbances and an unknown leader, both of which are generated by a so-called exosystem with parametric uncertainty. By combining internal model design, potential function technique and adaptive control, two distributed control strategies are proposed to maintain the connectivity of the communication network, to achieve the asymptotic tracking of all the followers to the output of the unknown leader system, as well as to reject unknown external disturbances. It is also worth to mention that the uncertain parameters in the multi-robot systems and exosystem are further allowed to belong to unknown and unbounded sets when applying the second fully distributed control law containing a dynamic gain inspired by high-gain adaptive control or self-tuning regulator.

Design and analysis of adaptive Super-Twisting sliding mode control for a microgyroscope.

PubMed

Feng, Zhilin; Fei, Juntao

2018-01-01

This paper proposes a novel adaptive Super-Twisting sliding mode control for a microgyroscope under unknown model uncertainties and external disturbances. In order to improve the convergence rate of reaching the sliding surface and the accuracy of regulating and trajectory tracking, a high order Super-Twisting sliding mode control strategy is employed, which not only can combine the advantages of the traditional sliding mode control with the Super-Twisting sliding mode control, but also guarantee that the designed control system can reach the sliding surface and equilibrium point in a shorter finite time from any initial state and avoid chattering problems. In consideration of unknown parameters of micro gyroscope system, an adaptive algorithm based on Lyapunov stability theory is designed to estimate the unknown parameters and angular velocity of microgyroscope. Finally, the effectiveness of the proposed scheme is demonstrated by simulation results. The comparative study between adaptive Super-Twisting sliding mode control and conventional sliding mode control demonstrate the superiority of the proposed method.

EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts.

PubMed

Bleka, Øyvind; Storvik, Geir; Gill, Peter

2016-03-01

We have released a software named EuroForMix to analyze STR DNA profiles in a user-friendly graphical user interface. The software implements a model to explain the allelic peak height on a continuous scale in order to carry out weight-of-evidence calculations for profiles which could be from a mixture of contributors. Through a properly parameterized model we are able to do inference on mixture proportions, the peak height properties, stutter proportion and degradation. In addition, EuroForMix includes models for allele drop-out, allele drop-in and sub-population structure. EuroForMix supports two inference approaches for likelihood ratio calculations. The first approach uses maximum likelihood estimation of the unknown parameters. The second approach is Bayesian based which requires prior distributions to be specified for the parameters involved. The user may specify any number of known and unknown contributors in the model, however we find that there is a practical computing time limit which restricts the model to a maximum of four unknown contributors. EuroForMix is the first freely open source, continuous model (accommodating peak height, stutter, drop-in, drop-out, population substructure and degradation), to be reported in the literature. It therefore serves an important purpose to act as an unrestricted platform to compare different solutions that are available. The implementation of the continuous model used in the software showed close to identical results to the R-package DNAmixtures, which requires a HUGIN Expert license to be used. An additional feature in EuroForMix is the ability for the user to adapt the Bayesian inference framework by incorporating their own prior information. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Model-free adaptive sliding mode controller design for generalized projective synchronization of the fractional-order chaotic system via radial basis function neural networks

NASA Astrophysics Data System (ADS)

Wang, L. M.

2017-09-01

A novel model-free adaptive sliding mode strategy is proposed for a generalized projective synchronization (GPS) between two entirely unknown fractional-order chaotic systems subject to the external disturbances. To solve the difficulties from the little knowledge about the master-slave system and to overcome the bad effects of the external disturbances on the generalized projective synchronization, the radial basis function neural networks are used to approach the packaged unknown master system and the packaged unknown slave system (including the external disturbances). Consequently, based on the slide mode technology and the neural network theory, a model-free adaptive sliding mode controller is designed to guarantee asymptotic stability of the generalized projective synchronization error. The main contribution of this paper is that a control strategy is provided for the generalized projective synchronization between two entirely unknown fractional-order chaotic systems subject to the unknown external disturbances, and the proposed control strategy only requires that the master system has the same fractional orders as the slave system. Moreover, the proposed method allows us to achieve all kinds of generalized projective chaos synchronizations by turning the user-defined parameters onto the desired values. Simulation results show the effectiveness of the proposed method and the robustness of the controlled system.

A semi-supervised learning approach for RNA secondary structure prediction.

PubMed

Yonemoto, Haruka; Asai, Kiyoshi; Hamada, Michiaki

2015-08-01

RNA secondary structure prediction is a key technology in RNA bioinformatics. Most algorithms for RNA secondary structure prediction use probabilistic models, in which the model parameters are trained with reliable RNA secondary structures. Because of the difficulty of determining RNA secondary structures by experimental procedures, such as NMR or X-ray crystal structural analyses, there are still many RNA sequences that could be useful for training whose secondary structures have not been experimentally determined. In this paper, we introduce a novel semi-supervised learning approach for training parameters in a probabilistic model of RNA secondary structures in which we employ not only RNA sequences with annotated secondary structures but also ones with unknown secondary structures. Our model is based on a hybrid of generative (stochastic context-free grammars) and discriminative models (conditional random fields) that has been successfully applied to natural language processing. Computational experiments indicate that the accuracy of secondary structure prediction is improved by incorporating RNA sequences with unknown secondary structures into training. To our knowledge, this is the first study of a semi-supervised learning approach for RNA secondary structure prediction. This technique will be useful when the number of reliable structures is limited. Copyright © 2015 Elsevier Ltd. All rights reserved.

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

A simulation of air pollution model parameter estimation using data from a ground-based LIDAR remote sensor

NASA Technical Reports Server (NTRS)

Kibler, J. F.; Suttles, J. T.

1977-01-01

One way to obtain estimates of the unknown parameters in a pollution dispersion model is to compare the model predictions with remotely sensed air quality data. A ground-based LIDAR sensor provides relative pollution concentration measurements as a function of space and time. The measured sensor data are compared with the dispersion model output through a numerical estimation procedure to yield parameter estimates which best fit the data. This overall process is tested in a computer simulation to study the effects of various measurement strategies. Such a simulation is useful prior to a field measurement exercise to maximize the information content in the collected data. Parametric studies of simulated data matched to a Gaussian plume dispersion model indicate the trade offs available between estimation accuracy and data acquisition strategy.

Power maximization of a point absorber wave energy converter using improved model predictive control

NASA Astrophysics Data System (ADS)

Milani, Farideh; Moghaddam, Reihaneh Kardehi

2017-08-01

This paper considers controlling and maximizing the absorbed power of wave energy converters for irregular waves. With respect to physical constraints of the system, a model predictive control is applied. Irregular waves' behavior is predicted by Kalman filter method. Owing to the great influence of controller parameters on the absorbed power, these parameters are optimized by imperialist competitive algorithm. The results illustrate the method's efficiency in maximizing the extracted power in the presence of unknown excitation force which should be predicted by Kalman filter.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Time‐dependent renewal‐model probabilities when date of last earthquake is unknown

USGS Publications Warehouse

Field, Edward H.; Jordan, Thomas H.

2015-01-01

We derive time-dependent, renewal-model earthquake probabilities for the case in which the date of the last event is completely unknown, and compare these with the time-independent Poisson probabilities that are customarily used as an approximation in this situation. For typical parameter values, the renewal-model probabilities exceed Poisson results by more than 10% when the forecast duration exceeds ~20% of the mean recurrence interval. We also derive probabilities for the case in which the last event is further constrained to have occurred before historical record keeping began (the historic open interval), which can only serve to increase earthquake probabilities for typically applied renewal models.We conclude that accounting for the historic open interval can improve long-term earthquake rupture forecasts for California and elsewhere.

The power and robustness of maximum LOD score statistics.

PubMed

Yoo, Y J; Mendell, N R

2008-07-01

The maximum LOD score statistic is extremely powerful for gene mapping when calculated using the correct genetic parameter value. When the mode of genetic transmission is unknown, the maximum of the LOD scores obtained using several genetic parameter values is reported. This latter statistic requires higher critical value than the maximum LOD score statistic calculated from a single genetic parameter value. In this paper, we compare the power of maximum LOD scores based on three fixed sets of genetic parameter values with the power of the LOD score obtained after maximizing over the entire range of genetic parameter values. We simulate family data under nine generating models. For generating models with non-zero phenocopy rates, LOD scores maximized over the entire range of genetic parameters yielded greater power than maximum LOD scores for fixed sets of parameter values with zero phenocopy rates. No maximum LOD score was consistently more powerful than the others for generating models with a zero phenocopy rate. The power loss of the LOD score maximized over the entire range of genetic parameters, relative to the maximum LOD score calculated using the correct genetic parameter value, appeared to be robust to the generating models.

Integrating models to investigate critical phenological overlaps in complex ecological interactions: the mountain pine beetle-fungus symbiosis.

PubMed

Addison, Audrey; Powell, James A; Bentz, Barbara J; Six, Diana L

2015-03-07

The fates of individual species are often tied to synchronization of phenology, however, few methods have been developed for integrating phenological models involving linked species. In this paper, we focus on mountain pine beetle (MPB, Dendroctonus ponderosae) and its two obligate mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. Growth rates of all three partners are driven by temperature, and their idiosyncratic responses affect interactions at important life stage junctures. One critical phase for MPB-fungus symbiosis occurs just before dispersal of teneral (new) adult beetles, when fungi are acquired and transported in specialized structures (mycangia). Before dispersal, fungi must capture sufficient spatial resources within the tree to ensure contact with teneral adults and get packed into mycangia. Mycangial packing occurs at an unknown time during teneral feeding. We adapt thermal models predicting fungal growth and beetle development to predict overlap between the competing fungi and MPB teneral adult feeding windows and emergence. We consider a spectrum of mycangial packing strategies and describe them in terms of explicit functions with unknown parameters. Rates of growth are fixed by laboratory data, the unknown parameters describing various packing strategies, as well as the degree to which mycangial growth is slowed in woody tissues as compared to agar, are determined by maximum likelihood and two years of field observations. At the field location used, the most likely fungus acquisition strategy for MPB was packing mycangia just prior to emergence. Estimated model parameters suggested large differences in the relative growth rates of the two fungi in trees at the study site, with the most likely model estimating that G. clavigera grew approximately twenty-five times faster than O. montium under the bark, which is completely unexpected in comparison with observed fungal growth on agar. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

Performance Analysis for Channel Estimation With 1-Bit ADC and Unknown Quantization Threshold

NASA Astrophysics Data System (ADS)

Stein, Manuel S.; Bar, Shahar; Nossek, Josef A.; Tabrikian, Joseph

2018-05-01

In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with $1$-bit output resolution and an unknown quantization threshold is considered. Single-comparator ADCs are energy-efficient and can be operated at ultra-high sampling rates. For analysis of such systems, a fixed and known quantization threshold is usually assumed. In the symmetric case, i.e., zero hard-limiting offset, it is known that in the low signal-to-noise ratio (SNR) regime the signal processing performance degrades moderately by ${2}/{\\pi}$ ($-1.96$ dB) when comparing to an ideal $\\infty$-bit converter. Due to hardware imperfections, low-complexity $1$-bit ADCs will in practice exhibit an unknown threshold different from zero. Therefore, we study the accuracy which can be obtained with receive data processed by a hard-limiter with unknown quantization level by using asymptotically optimal channel estimation algorithms. To characterize the estimation performance of these nonlinear algorithms, we employ analytic error expressions for different setups while modeling the offset as a nuisance parameter. In the low SNR regime, we establish the necessary condition for a vanishing loss due to missing offset knowledge at the receiver. As an application, we consider the estimation of single-input single-output wireless channels with inter-symbol interference and validate our analysis by comparing the analytic and experimental performance of the studied estimation algorithms. Finally, we comment on the extension to multiple-input multiple-output channel models.

Spatial curvilinear path following control of underactuated AUV with multiple uncertainties.

PubMed

Miao, Jianming; Wang, Shaoping; Zhao, Zhiping; Li, Yuan; Tomovic, Mileta M

2017-03-01

This paper investigates the problem of spatial curvilinear path following control of underactuated autonomous underwater vehicles (AUVs) with multiple uncertainties. Firstly, in order to design the appropriate controller, path following error dynamics model is constructed in a moving Serret-Frenet frame, and the five degrees of freedom (DOFs) dynamic model with multiple uncertainties is established. Secondly, the proposed control law is separated into kinematic controller and dynamic controller via back-stepping technique. In the case of kinematic controller, to overcome the drawback of dependence on the accurate vehicle model that are present in a number of path following control strategies described in the literature, the unknown side-slip angular velocity and attack angular velocity are treated as uncertainties. Whereas in the case of dynamic controller, the model parameters perturbations, unknown external environmental disturbances and the nonlinear hydrodynamic damping terms are treated as lumped uncertainties. Both kinematic and dynamic uncertainties are estimated and compensated by designed reduced-order linear extended state observes (LESOs). Thirdly, feedback linearization (FL) based control law is implemented for the control model using the estimates generated by reduced-order LESOs. For handling the problem of computational complexity inherent in the conventional back-stepping method, nonlinear tracking differentiators (NTDs) are applied to construct derivatives of the virtual control commands. Finally, the closed loop stability for the overall system is established. Simulation and comparative analysis demonstrate that the proposed controller exhibits enhanced performance in the presence of internal parameter variations, external unknown disturbances, unmodeled nonlinear damping terms, and measurement noises. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Finite-time tracking control for multiple non-holonomic mobile robots based on visual servoing

NASA Astrophysics Data System (ADS)

Ou, Meiying; Li, Shihua; Wang, Chaoli

2013-12-01

This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.

An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: Application to real-time phase-contrast flow MRI.

PubMed

Tan, Zhengguo; Hohage, Thorsten; Kalentev, Oleksandr; Joseph, Arun A; Wang, Xiaoqing; Voit, Dirk; Merboldt, K Dietmar; Frahm, Jens

2017-12-01

The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios. Copyright © 2017 John Wiley & Sons, Ltd.

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

PubMed Central

Daunizeau, Jean; Adam, Vincent; Rigoux, Lionel

2014-01-01

This work is in line with an on-going effort tending toward a computational (quantitative and refutable) understanding of human neuro-cognitive processes. Many sophisticated models for behavioural and neurobiological data have flourished during the past decade. Most of these models are partly unspecified (i.e. they have unknown parameters) and nonlinear. This makes them difficult to peer with a formal statistical data analysis framework. In turn, this compromises the reproducibility of model-based empirical studies. This work exposes a software toolbox that provides generic, efficient and robust probabilistic solutions to the three problems of model-based analysis of empirical data: (i) data simulation, (ii) parameter estimation/model selection, and (iii) experimental design optimization. PMID:24465198

Highly adaptive tests for group differences in brain functional connectivity.

PubMed

Kim, Junghi; Pan, Wei

2015-01-01

Resting-state functional magnetic resonance imaging (rs-fMRI) and other technologies have been offering evidence and insights showing that altered brain functional networks are associated with neurological illnesses such as Alzheimer's disease. Exploring brain networks of clinical populations compared to those of controls would be a key inquiry to reveal underlying neurological processes related to such illnesses. For such a purpose, group-level inference is a necessary first step in order to establish whether there are any genuinely disrupted brain subnetworks. Such an analysis is also challenging due to the high dimensionality of the parameters in a network model and high noise levels in neuroimaging data. We are still in the early stage of method development as highlighted by Varoquaux and Craddock (2013) that "there is currently no unique solution, but a spectrum of related methods and analytical strategies" to learn and compare brain connectivity. In practice the important issue of how to choose several critical parameters in estimating a network, such as what association measure to use and what is the sparsity of the estimated network, has not been carefully addressed, largely because the answers are unknown yet. For example, even though the choice of tuning parameters in model estimation has been extensively discussed in the literature, as to be shown here, an optimal choice of a parameter for network estimation may not be optimal in the current context of hypothesis testing. Arbitrarily choosing or mis-specifying such parameters may lead to extremely low-powered tests. Here we develop highly adaptive tests to detect group differences in brain connectivity while accounting for unknown optimal choices of some tuning parameters. The proposed tests combine statistical evidence against a null hypothesis from multiple sources across a range of plausible tuning parameter values reflecting uncertainty with the unknown truth. These highly adaptive tests are not only easy to use, but also high-powered robustly across various scenarios. The usage and advantages of these novel tests are demonstrated on an Alzheimer's disease dataset and simulated data.

Aircraft Engine Thrust Estimator Design Based on GSA-LSSVM

NASA Astrophysics Data System (ADS)

Sheng, Hanlin; Zhang, Tianhong

2017-08-01

In view of the necessity of highly precise and reliable thrust estimator to achieve direct thrust control of aircraft engine, based on support vector regression (SVR), as well as least square support vector machine (LSSVM) and a new optimization algorithm - gravitational search algorithm (GSA), by performing integrated modelling and parameter optimization, a GSA-LSSVM-based thrust estimator design solution is proposed. The results show that compared to particle swarm optimization (PSO) algorithm, GSA can find unknown optimization parameter better and enables the model developed with better prediction and generalization ability. The model can better predict aircraft engine thrust and thus fulfills the need of direct thrust control of aircraft engine.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

Trans-dimensional joint inversion of seabed scattering and reflection data.

PubMed

Steininger, Gavin; Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2013-03-01

This paper examines joint inversion of acoustic scattering and reflection data to resolve seabed interface roughness parameters (spectral strength, exponent, and cutoff) and geoacoustic profiles. Trans-dimensional (trans-D) Bayesian sampling is applied with both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model treated as unknowns. A prior distribution that allows fluid sediment layers over an elastic basement in a trans-D inversion is derived and implemented. Three cases are considered: Scattering-only inversion, joint scattering and reflection inversion, and joint inversion with the trans-D auto-regressive error model. Including reflection data improves the resolution of scattering and geoacoustic parameters. The trans-D auto-regressive model further improves scattering resolution and correctly differentiates between strongly and weakly correlated residual errors.

Removing flicker based on sparse color correspondences in old film restoration

NASA Astrophysics Data System (ADS)

Huang, Xi; Ding, Youdong; Yu, Bing; Xia, Tianran

2018-04-01

In the long history of human civilization, archived film is an indispensable part of it, and using digital method to repair damaged film is also a mainstream trend nowadays. In this paper, we propose a sparse color correspondences based technique to remove fading flicker for old films. Our model, combined with multi frame images to establish a simple correction model, includes three key steps. Firstly, we recover sparse color correspondences in the input frames to build a matrix with many missing entries. Secondly, we present a low-rank matrix factorization approach to estimate the unknown parameters of this model. Finally, we adopt a two-step strategy that divide the estimated parameters into reference frame parameters for color recovery correction and other frame parameters for color consistency correction to remove flicker. Our method combined multi-frames takes continuity of the input sequence into account, and the experimental results show the method can remove fading flicker efficiently.

Auto Regressive Moving Average (ARMA) Modeling Method for Gyro Random Noise Using a Robust Kalman Filter

PubMed Central

Huang, Lei

2015-01-01

To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required. PMID:26437409

Estimating taxonomic diversity, extinction rates, and speciation rates from fossil data using capture-recapture models

USGS Publications Warehouse

Nichols, J.D.; Pollock, K.H.

1983-01-01

Capture-recapture models can be used to estimate parameters of interest from paleobiological data when encouter probabilities are unknown and variable over time. These models also permit estimation of sampling variances and goodness-of-fit tests are available for assessing the fit of data to most models. The authors describe capture-recapture models which should be useful in paleobiological analyses and discuss the assumptions which underlie them. They illustrate these models with examples and discuss aspects of study design.

Bayesian model comparison and parameter inference in systems biology using nested sampling.

PubMed

Pullen, Nick; Morris, Richard J

2014-01-01

Inferring parameters for models of biological processes is a current challenge in systems biology, as is the related problem of comparing competing models that explain the data. In this work we apply Skilling's nested sampling to address both of these problems. Nested sampling is a Bayesian method for exploring parameter space that transforms a multi-dimensional integral to a 1D integration over likelihood space. This approach focuses on the computation of the marginal likelihood or evidence. The ratio of evidences of different models leads to the Bayes factor, which can be used for model comparison. We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results. The effect of missing initial conditions of the variables as well as unknown parameters is investigated. We show how the evidence and the model ranking can change as a function of the available data. Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

Bayesian inference in an item response theory model with a generalized student t link function

NASA Astrophysics Data System (ADS)

Azevedo, Caio L. N.; Migon, Helio S.

2012-10-01

In this paper we introduce a new item response theory (IRT) model with a generalized Student t-link function with unknown degrees of freedom (df), named generalized t-link (GtL) IRT model. In this model we consider only the difficulty parameter in the item response function. GtL is an alternative to the two parameter logit and probit models, since the degrees of freedom (df) play a similar role to the discrimination parameter. However, the behavior of the curves of the GtL is different from those of the two parameter models and the usual Student t link, since in GtL the curve obtained from different df's can cross the probit curves in more than one latent trait level. The GtL model has similar proprieties to the generalized linear mixed models, such as the existence of sufficient statistics and easy parameter interpretation. Also, many techniques of parameter estimation, model fit assessment and residual analysis developed for that models can be used for the GtL model. We develop fully Bayesian estimation and model fit assessment tools through a Metropolis-Hastings step within Gibbs sampling algorithm. We consider a prior sensitivity choice concerning the degrees of freedom. The simulation study indicates that the algorithm recovers all parameters properly. In addition, some Bayesian model fit assessment tools are considered. Finally, a real data set is analyzed using our approach and other usual models. The results indicate that our model fits the data better than the two parameter models.

Numerical weather prediction model tuning via ensemble prediction system

NASA Astrophysics Data System (ADS)

Jarvinen, H.; Laine, M.; Ollinaho, P.; Solonen, A.; Haario, H.

2011-12-01

This paper discusses a novel approach to tune predictive skill of numerical weather prediction (NWP) models. NWP models contain tunable parameters which appear in parameterizations schemes of sub-grid scale physical processes. Currently, numerical values of these parameters are specified manually. In a recent dual manuscript (QJRMS, revised) we developed a new concept and method for on-line estimation of the NWP model parameters. The EPPES ("Ensemble prediction and parameter estimation system") method requires only minimal changes to the existing operational ensemble prediction infra-structure and it seems very cost-effective because practically no new computations are introduced. The approach provides an algorithmic decision making tool for model parameter optimization in operational NWP. In EPPES, statistical inference about the NWP model tunable parameters is made by (i) generating each member of the ensemble of predictions using different model parameter values, drawn from a proposal distribution, and (ii) feeding-back the relative merits of the parameter values to the proposal distribution, based on evaluation of a suitable likelihood function against verifying observations. In the presentation, the method is first illustrated in low-order numerical tests using a stochastic version of the Lorenz-95 model which effectively emulates the principal features of ensemble prediction systems. The EPPES method correctly detects the unknown and wrongly specified parameters values, and leads to an improved forecast skill. Second, results with an atmospheric general circulation model based ensemble prediction system show that the NWP model tuning capacity of EPPES scales up to realistic models and ensemble prediction systems. Finally, a global top-end NWP model tuning exercise with preliminary results is published.

Automated adaptive inference of phenomenological dynamical models.

PubMed

Daniels, Bryan C; Nemenman, Ilya

2015-08-21

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.

Automated adaptive inference of phenomenological dynamical models

PubMed Central

Daniels, Bryan C.; Nemenman, Ilya

2015-01-01

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved. PMID:26293508

Online quantitative analysis of multispectral images of human body tissues

NASA Astrophysics Data System (ADS)

Lisenko, S. A.

2013-08-01

A method is developed for online monitoring of structural and morphological parameters of biological tissues (haemoglobin concentration, degree of blood oxygenation, average diameter of capillaries and the parameter characterising the average size of tissue scatterers), which involves multispectral tissue imaging, image normalisation to one of its spectral layers and determination of unknown parameters based on their stable regression relation with the spectral characteristics of the normalised image. Regression is obtained by simulating numerically the diffuse reflectance spectrum of the tissue by the Monte Carlo method at a wide variation of model parameters. The correctness of the model calculations is confirmed by the good agreement with the experimental data. The error of the method is estimated under conditions of general variability of structural and morphological parameters of the tissue. The method developed is compared with the traditional methods of interpretation of multispectral images of biological tissues, based on the solution of the inverse problem for each pixel of the image in the approximation of different analytical models.

Analysis of a homemade Edison tinfoil phonograph.

PubMed

Sagers, Jason D; McNeese, Andrew R; Lenhart, Richard D; Wilson, Preston S

2012-10-01

Thomas Edison's phonograph was a landmark acoustic invention. In this paper, the phonograph is presented as a tool for education in acoustics. A brief history of the phonograph is outlined and an analogous circuit model that describes its dynamic response is discussed. Microphone and scanning laser Doppler vibrometer (SLDV) measurements were made on a homemade phonograph for model validation and inversion for unknown model parameters. SLDV measurements also conclusively illustrate where model assumptions are violated. The model elements which dominate the dynamic response are discussed.

Forcing Regression through a Given Point Using Any Familiar Computational Routine.

DTIC Science & Technology

1983-03-01

a linear model , Y =a + OX + e ( Model I) then adopt the principle of least squares; and use sample data to estimate the unknown parameters, a and 8...has an expected value of zero indicates that the "average" response is considered linear . If c varies widely, Model I, though conceptually correct, may...relationship is linear from the maximum observed x to x - a, then Model II should be used. To pro- ceed with the customary evaluation of Model I would be

NWP model forecast skill optimization via closure parameter variations

NASA Astrophysics Data System (ADS)

Järvinen, H.; Ollinaho, P.; Laine, M.; Solonen, A.; Haario, H.

2012-04-01

We present results of a novel approach to tune predictive skill of numerical weather prediction (NWP) models. These models contain tunable parameters which appear in parameterizations schemes of sub-grid scale physical processes. The current practice is to specify manually the numerical parameter values, based on expert knowledge. We developed recently a concept and method (QJRMS 2011) for on-line estimation of the NWP model parameters via closure parameter variations. The method called EPPES ("Ensemble prediction and parameter estimation system") utilizes ensemble prediction infra-structure for parameter estimation in a very cost-effective way: practically no new computations are introduced. The approach provides an algorithmic decision making tool for model parameter optimization in operational NWP. In EPPES, statistical inference about the NWP model tunable parameters is made by (i) generating an ensemble of predictions so that each member uses different model parameter values, drawn from a proposal distribution, and (ii) feeding-back the relative merits of the parameter values to the proposal distribution, based on evaluation of a suitable likelihood function against verifying observations. In this presentation, the method is first illustrated in low-order numerical tests using a stochastic version of the Lorenz-95 model which effectively emulates the principal features of ensemble prediction systems. The EPPES method correctly detects the unknown and wrongly specified parameters values, and leads to an improved forecast skill. Second, results with an ensemble prediction system emulator, based on the ECHAM5 atmospheric GCM show that the model tuning capability of EPPES scales up to realistic models and ensemble prediction systems. Finally, preliminary results of EPPES in the context of ECMWF forecasting system are presented.

Estimation of Key Parameters of the Coupled Energy and Water Model by Assimilating Land Surface Data

NASA Astrophysics Data System (ADS)

Abdolghafoorian, A.; Farhadi, L.

2017-12-01

Accurate estimation of land surface heat and moisture fluxes, as well as root zone soil moisture, is crucial in various hydrological, meteorological, and agricultural applications. Field measurements of these fluxes are costly and cannot be readily scaled to large areas relevant to weather and climate studies. Therefore, there is a need for techniques to make quantitative estimates of heat and moisture fluxes using land surface state observations that are widely available from remote sensing across a range of scale. In this work, we applies the variational data assimilation approach to estimate land surface fluxes and soil moisture profile from the implicit information contained Land Surface Temperature (LST) and Soil Moisture (SM) (hereafter the VDA model). The VDA model is focused on the estimation of three key parameters: 1- neutral bulk heat transfer coefficient (CHN), 2- evaporative fraction from soil and canopy (EF), and 3- saturated hydraulic conductivity (Ksat). CHN and EF regulate the partitioning of available energy between sensible and latent heat fluxes. Ksat is one of the main parameters used in determining infiltration, runoff, groundwater recharge, and in simulating hydrological processes. In this study, a system of coupled parsimonious energy and water model will constrain the estimation of three unknown parameters in the VDA model. The profile of SM (LST) at multiple depths is estimated using moisture diffusion (heat diffusion) equation. In this study, the uncertainties of retrieved unknown parameters and fluxes are estimated from the inverse of Hesian matrix of cost function which is computed using the Lagrangian methodology. Analysis of uncertainty provides valuable information about the accuracy of estimated parameters and their correlation and guide the formulation of a well-posed estimation problem. The results of proposed algorithm are validated with a series of experiments using a synthetic data set generated by the simultaneous heat and water (SHAW) model. In addition, the feasibility of extending this algorithm to use remote sensing observations that have low temporal resolution is examined by assimilating the limited number of land surface moisture and temperature observations.

On selecting a prior for the precision parameter of Dirichlet process mixture models

USGS Publications Warehouse

Dorazio, R.M.

2009-01-01

In hierarchical mixture models the Dirichlet process is used to specify latent patterns of heterogeneity, particularly when the distribution of latent parameters is thought to be clustered (multimodal). The parameters of a Dirichlet process include a precision parameter ?? and a base probability measure G0. In problems where ?? is unknown and must be estimated, inferences about the level of clustering can be sensitive to the choice of prior assumed for ??. In this paper an approach is developed for computing a prior for the precision parameter ?? that can be used in the presence or absence of prior information about the level of clustering. This approach is illustrated in an analysis of counts of stream fishes. The results of this fully Bayesian analysis are compared with an empirical Bayes analysis of the same data and with a Bayesian analysis based on an alternative commonly used prior.

A modified Leslie-Gower predator-prey interaction model and parameter identifiability

NASA Astrophysics Data System (ADS)

Tripathi, Jai Prakash; Meghwani, Suraj S.; Thakur, Manoj; Abbas, Syed

2018-01-01

In this work, bifurcation and a systematic approach for estimation of identifiable parameters of a modified Leslie-Gower predator-prey system with Crowley-Martin functional response and prey refuge is discussed. Global asymptotic stability is discussed by applying fluctuation lemma. The system undergoes into Hopf bifurcation with respect to parameters intrinsic growth rate of predators (s) and prey reserve (m). The stability of Hopf bifurcation is also discussed by calculating Lyapunov number. The sensitivity analysis of the considered model system with respect to all variables is performed which also supports our theoretical study. To estimate the unknown parameter from the data, an optimization procedure (pseudo-random search algorithm) is adopted. System responses and phase plots for estimated parameters are also compared with true noise free data. It is found that the system dynamics with true set of parametric values is similar to the estimated parametric values. Numerical simulations are presented to substantiate the analytical findings.

Bayesian inference of physiologically meaningful parameters from body sway measurements.

PubMed

Tietäväinen, A; Gutmann, M U; Keski-Vakkuri, E; Corander, J; Hæggström, E

2017-06-19

The control of the human body sway by the central nervous system, muscles, and conscious brain is of interest since body sway carries information about the physiological status of a person. Several models have been proposed to describe body sway in an upright standing position, however, due to the statistical intractability of the more realistic models, no formal parameter inference has previously been conducted and the expressive power of such models for real human subjects remains unknown. Using the latest advances in Bayesian statistical inference for intractable models, we fitted a nonlinear control model to posturographic measurements, and we showed that it can accurately predict the sway characteristics of both simulated and real subjects. Our method provides a full statistical characterization of the uncertainty related to all model parameters as quantified by posterior probability density functions, which is useful for comparisons across subjects and test settings. The ability to infer intractable control models from sensor data opens new possibilities for monitoring and predicting body status in health applications.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms.

PubMed

Asgharnia, Amirhossein; Shahnazi, Reza; Jamali, Ali

2018-05-11

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

LIBP-Pred: web server for lipid binding proteins using structural network parameters; PDB mining of human cancer biomarkers and drug targets in parasites and bacteria.

PubMed

González-Díaz, Humberto; Munteanu, Cristian R; Postelnicu, Lucian; Prado-Prado, Francisco; Gestal, Marcos; Pazos, Alejandro

2012-03-01

Lipid-Binding Proteins (LIBPs) or Fatty Acid-Binding Proteins (FABPs) play an important role in many diseases such as different types of cancer, kidney injury, atherosclerosis, diabetes, intestinal ischemia and parasitic infections. Thus, the computational methods that can predict LIBPs based on 3D structure parameters became a goal of major importance for drug-target discovery, vaccine design and biomarker selection. In addition, the Protein Data Bank (PDB) contains 3000+ protein 3D structures with unknown function. This list, as well as new experimental outcomes in proteomics research, is a very interesting source to discover relevant proteins, including LIBPs. However, to the best of our knowledge, there are no general models to predict new LIBPs based on 3D structures. We developed new Quantitative Structure-Activity Relationship (QSAR) models based on 3D electrostatic parameters of 1801 different proteins, including 801 LIBPs. We calculated these electrostatic parameters with the MARCH-INSIDE software and they correspond to the entire protein or to specific protein regions named core, inner, middle, and surface. We used these parameters as inputs to develop a simple Linear Discriminant Analysis (LDA) classifier to discriminate 3D structure of LIBPs from other proteins. We implemented this predictor in the web server named LIBP-Pred, freely available at , along with other important web servers of the Bio-AIMS portal. The users can carry out an automatic retrieval of protein structures from PDB or upload their custom protein structural models from their disk created with LOMETS server. We demonstrated the PDB mining option performing a predictive study of 2000+ proteins with unknown function. Interesting results regarding the discovery of new Cancer Biomarkers in humans or drug targets in parasites have been discussed here in this sense.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Structure Elucidation of Unknown Metabolites in Metabolomics by Combined NMR and MS/MS Prediction

DOE PAGES

Boiteau, Rene M.; Hoyt, David W.; Nicora, Carrie D.; ...

2018-01-17

Here, we introduce a cheminformatics approach that combines highly selective and orthogonal structure elucidation parameters; accurate mass, MS/MS (MS 2), and NMR in a single analysis platform to accurately identify unknown metabolites in untargeted studies. The approach starts with an unknown LC-MS feature, and then combines the experimental MS/MS and NMR information of the unknown to effectively filter the false positive candidate structures based on their predicted MS/MS and NMR spectra. We demonstrate the approach on a model mixture and then we identify an uncatalogued secondary metabolite in Arabidopsis thaliana. The NMR/MS 2 approach is well suited for discovery ofmore » new metabolites in plant extracts, microbes, soils, dissolved organic matter, food extracts, biofuels, and biomedical samples, facilitating the identification of metabolites that are not present in experimental NMR and MS metabolomics databases.« less

Structure Elucidation of Unknown Metabolites in Metabolomics by Combined NMR and MS/MS Prediction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boiteau, Rene M.; Hoyt, David W.; Nicora, Carrie D.

Here, we introduce a cheminformatics approach that combines highly selective and orthogonal structure elucidation parameters; accurate mass, MS/MS (MS 2), and NMR in a single analysis platform to accurately identify unknown metabolites in untargeted studies. The approach starts with an unknown LC-MS feature, and then combines the experimental MS/MS and NMR information of the unknown to effectively filter the false positive candidate structures based on their predicted MS/MS and NMR spectra. We demonstrate the approach on a model mixture and then we identify an uncatalogued secondary metabolite in Arabidopsis thaliana. The NMR/MS 2 approach is well suited for discovery ofmore » new metabolites in plant extracts, microbes, soils, dissolved organic matter, food extracts, biofuels, and biomedical samples, facilitating the identification of metabolites that are not present in experimental NMR and MS metabolomics databases.« less

Structure Elucidation of Unknown Metabolites in Metabolomics by Combined NMR and MS/MS Prediction

PubMed Central

Hoyt, David W.; Nicora, Carrie D.; Kinmonth-Schultz, Hannah A.; Ward, Joy K.

2018-01-01

We introduce a cheminformatics approach that combines highly selective and orthogonal structure elucidation parameters; accurate mass, MS/MS (MS2), and NMR into a single analysis platform to accurately identify unknown metabolites in untargeted studies. The approach starts with an unknown LC-MS feature, and then combines the experimental MS/MS and NMR information of the unknown to effectively filter out the false positive candidate structures based on their predicted MS/MS and NMR spectra. We demonstrate the approach on a model mixture, and then we identify an uncatalogued secondary metabolite in Arabidopsis thaliana. The NMR/MS2 approach is well suited to the discovery of new metabolites in plant extracts, microbes, soils, dissolved organic matter, food extracts, biofuels, and biomedical samples, facilitating the identification of metabolites that are not present in experimental NMR and MS metabolomics databases. PMID:29342073

An apodized Kepler periodogram for separating planetary and stellar activity signals

PubMed Central

Gregory, Philip C.

2016-01-01

A new apodized Keplerian (AK) model is proposed for the analysis of precision radial velocity (RV) data to model both planetary and stellar activity (SA) induced RV signals. A symmetrical Gaussian apodization function with unknown width and centre can distinguish planetary signals from SA signals on the basis of the span of the apodization window. The general model for m AK signals includes a linear regression term between RV and the SA diagnostic log (R′hk), as well as an extra Gaussian noise term with unknown standard deviation. The model parameters are explored using a Bayesian fusion Markov chain Monte Carlo code. A differential version of the generalized Lomb–Scargle periodogram that employs a control diagnostic provides an additional way of distinguishing SA signals and helps guide the choice of new periods. Results are reported for a recent international RV blind challenge which included multiple state-of-the-art simulated data sets supported by a variety of SA diagnostics. In the current implementation, the AK method achieved a reduction in SA noise by a factor of approximately 6. Final parameter estimates for the planetary candidates are derived from fits that include AK signals to model the SA components and simple Keplerians to model the planetary candidates. Preliminary results are also reported for AK models augmented by a moving average component that allows for correlations in the residuals. PMID:27346979

Incorporation of prior information on parameters into nonlinear regression groundwater flow models: 2. Applications

USGS Publications Warehouse

Cooley, Richard L.

1983-01-01

This paper investigates factors influencing the degree of improvement in estimates of parameters of a nonlinear regression groundwater flow model by incorporating prior information of unknown reliability. Consideration of expected behavior of the regression solutions and results of a hypothetical modeling problem lead to several general conclusions. First, if the parameters are properly scaled, linearized expressions for the mean square error (MSE) in parameter estimates of a nonlinear model will often behave very nearly as if the model were linear. Second, by using prior information, the MSE in properly scaled parameters can be reduced greatly over the MSE of ordinary least squares estimates of parameters. Third, plots of estimated MSE and the estimated standard deviation of MSE versus an auxiliary parameter (the ridge parameter) specifying the degree of influence of the prior information on regression results can help determine the potential for improvement of parameter estimates. Fourth, proposed criteria can be used to make appropriate choices for the ridge parameter and another parameter expressing degree of overall bias in the prior information. Results of a case study of Truckee Meadows, Reno-Sparks area, Washoe County, Nevada, conform closely to the results of the hypothetical problem. In the Truckee Meadows case, incorporation of prior information did not greatly change the parameter estimates from those obtained by ordinary least squares. However, the analysis showed that both sets of estimates are more reliable than suggested by the standard errors from ordinary least squares.

The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems.

PubMed

White, Andrew; Tolman, Malachi; Thames, Howard D; Withers, Hubert Rodney; Mason, Kathy A; Transtrum, Mark K

2016-12-01

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model's discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system-a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model.

Calibration strategies for a groundwater model in a highly dynamic alpine floodplain

USGS Publications Warehouse

Foglia, L.; Burlando, P.; Hill, Mary C.; Mehl, S.

2004-01-01

Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded and the valley is being investigated to determine environmental flow requirements. The aim of the investigation is the devel-opment of a modelling framework that simulates the dynamics of the ground-water, hydrologic, and ecologic systems. Because of the multi-scale nature of the modelling framework, large-scale models are first developed to provide the boundary conditions for more detailed models of reaches that are of eco-logical importance. We describe here the initial (large-scale) groundwa-ter/surface water model and its calibration in relation to initial and boundary conditions. A MODFLOW-2000 model was constructed to simulate the inter-action of groundwater and surface water and was developed parsimoniously to avoid modelling artefacts and parameter inconsistencies. Model calibration includes two steady-state conditions, with and without recharge to the aquifer from the adjoining hillslopes. Parameters are defined to represent areal re-charge, hydraulic conductivity of the aquifer (up to 5 classes), and streambed hydraulic conductivity. Model performance was investigated following two system representation. The first representation assumed unknown flow input at the northern end of the groundwater domain and unknown lateral inflow. The second representation used simulations of the lateral flow obtained by means of a raster-based, physically oriented and continuous in time rainfall-runoff (R-R) model. Results based on these two representations are compared and discussed.

The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems

PubMed Central

Tolman, Malachi; Thames, Howard D.; Mason, Kathy A.

2016-01-01

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must be included to explain system behaviors. As a consequence, models are often overly complex, with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model become relevant. When this occurs, the model will have a large systematic error and fail to give a good fit to the data. We use a simple hyper-model of model error to quantify a model’s discrepancy and apply it to two models of complex biological processes (EGFR signaling and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system–a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model. PMID:27923060

Application of Novel Lateral Tire Force Sensors to Vehicle Parameter Estimation of Electric Vehicles.

PubMed

Nam, Kanghyun

2015-11-11

This article presents methods for estimating lateral vehicle velocity and tire cornering stiffness, which are key parameters in vehicle dynamics control, using lateral tire force measurements. Lateral tire forces acting on each tire are directly measured by load-sensing hub bearings that were invented and further developed by NSK Ltd. For estimating the lateral vehicle velocity, tire force models considering lateral load transfer effects are used, and a recursive least square algorithm is adapted to identify the lateral vehicle velocity as an unknown parameter. Using the estimated lateral vehicle velocity, tire cornering stiffness, which is an important tire parameter dominating the vehicle's cornering responses, is estimated. For the practical implementation, the cornering stiffness estimation algorithm based on a simple bicycle model is developed and discussed. Finally, proposed estimation algorithms were evaluated using experimental test data.

Extended behavioural modelling of FET and lattice-mismatched HEMT devices

NASA Astrophysics Data System (ADS)

Khawam, Yahya; Albasha, Lutfi

2017-07-01

This study presents an improved large signal model that can be used for high electron mobility transistors (HEMTs) and field effect transistors using measurement-based behavioural modelling techniques. The steps for accurate large and small signal modelling for transistor are also discussed. The proposed DC model is based on the Fager model since it compensates between the number of model's parameters and accuracy. The objective is to increase the accuracy of the drain-source current model with respect to any change in gate or drain voltages. Also, the objective is to extend the improved DC model to account for soft breakdown and kink effect found in some variants of HEMT devices. A hybrid Newton's-Genetic algorithm is used in order to determine the unknown parameters in the developed model. In addition to accurate modelling of a transistor's DC characteristics, the complete large signal model is modelled using multi-bias s-parameter measurements. The way that the complete model is performed is by using a hybrid multi-objective optimisation technique (Non-dominated Sorting Genetic Algorithm II) and local minimum search (multivariable Newton's method) for parasitic elements extraction. Finally, the results of DC modelling and multi-bias s-parameters modelling are presented, and three-device modelling recommendations are discussed.

Control of Systems With Slow Actuators Using Time Scale Separation

NASA Technical Reports Server (NTRS)

Stepanyan, Vehram; Nguyen, Nhan

2009-01-01

This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches.

Quantum Hamiltonian identification from measurement time traces.

PubMed

Zhang, Jun; Sarovar, Mohan

2014-08-22

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this Letter, we consider a setting where system evolution is determined by a parametrized Hamiltonian, and the task is to estimate these parameters from temporal records of a restricted set of system observables (time traces). Based on the notion of system realization from linear systems theory, we develop a constructive algorithm that provides estimates of the unknown parameters directly from these time traces. We illustrate the algorithm and its robustness to measurement noise by applying it to a one-dimensional spin chain model with variable couplings.

Parameter optimization for the visco-hyperelastic constitutive model of tendon using FEM.

PubMed

Tang, C Y; Ng, G Y F; Wang, Z W; Tsui, C P; Zhang, G

2011-01-01

Numerous constitutive models describing the mechanical properties of tendons have been proposed during the past few decades. However, few were widely used owing to the lack of implementation in the general finite element (FE) software, and very few systematic studies have been done on selecting the most appropriate parameters for these constitutive laws. In this work, the visco-hyperelastic constitutive model of the tendon implemented through the use of three-parameter Mooney-Rivlin form and sixty-four-parameter Prony series were firstly analyzed using ANSYS FE software. Afterwards, an integrated optimization scheme was developed by coupling two optimization toolboxes (OPTs) of ANSYS and MATLAB for estimating these unknown constitutive parameters of the tendon. Finally, a group of Sprague-Dawley rat tendons was used to execute experimental and numerical simulation investigation. The simulated results showed good agreement with the experimental data. An important finding revealed that too many Maxwell elements was not necessary for assuring accuracy of the model, which is often neglected in most open literatures. Thus, all these proved that the constitutive parameter optimization scheme was reliable and highly efficient. Furthermore, the approach can be extended to study other tendons or ligaments, as well as any visco-hyperelastic solid materials.

State and Parameter Estimation for a Coupled Ocean--Atmosphere Model

NASA Astrophysics Data System (ADS)

Ghil, M.; Kondrashov, D.; Sun, C.

2006-12-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

Inverse modeling of hydrologic parameters using surface flux and runoff observations in the Community Land Model

NASA Astrophysics Data System (ADS)

Sun, Y.; Hou, Z.; Huang, M.; Tian, F.; Leung, L. Ruby

2013-12-01

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Both deterministic least-square fitting and stochastic Markov-chain Monte Carlo (MCMC)-Bayesian inversion approaches are evaluated by applying them to CLM4 at selected sites with different climate and soil conditions. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find that using model parameters calibrated by the sampling-based stochastic inversion approaches provides significant improvements in the model simulations compared to using default CLM4 parameter values, and that as more information comes in, the predictive intervals (ranges of posterior distributions) of the calibrated parameters become narrower. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.

A vehicle stability control strategy with adaptive neural network sliding mode theory based on system uncertainty approximation

NASA Astrophysics Data System (ADS)

Ji, Xuewu; He, Xiangkun; Lv, Chen; Liu, Yahui; Wu, Jian

2018-06-01

Modelling uncertainty, parameter variation and unknown external disturbance are the major concerns in the development of an advanced controller for vehicle stability at the limits of handling. Sliding mode control (SMC) method has proved to be robust against parameter variation and unknown external disturbance with satisfactory tracking performance. But modelling uncertainty, such as errors caused in model simplification, is inevitable in model-based controller design, resulting in lowered control quality. The adaptive radial basis function network (ARBFN) can effectively improve the control performance against large system uncertainty by learning to approximate arbitrary nonlinear functions and ensure the global asymptotic stability of the closed-loop system. In this paper, a novel vehicle dynamics stability control strategy is proposed using the adaptive radial basis function network sliding mode control (ARBFN-SMC) to learn system uncertainty and eliminate its adverse effects. This strategy adopts a hierarchical control structure which consists of reference model layer, yaw moment control layer, braking torque allocation layer and executive layer. Co-simulation using MATLAB/Simulink and AMESim is conducted on a verified 15-DOF nonlinear vehicle system model with the integrated-electro-hydraulic brake system (I-EHB) actuator in a Sine With Dwell manoeuvre. The simulation results show that ARBFN-SMC scheme exhibits superior stability and tracking performance in different running conditions compared with SMC scheme.

Parameter identifiability of linear dynamical systems

NASA Technical Reports Server (NTRS)

Glover, K.; Willems, J. C.

1974-01-01

It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.

Estimation in SEM: A Concrete Example

ERIC Educational Resources Information Center

Ferron, John M.; Hess, Melinda R.

2007-01-01

A concrete example is used to illustrate maximum likelihood estimation of a structural equation model with two unknown parameters. The fitting function is found for the example, as are the vector of first-order partial derivatives, the matrix of second-order partial derivatives, and the estimates obtained from each iteration of the Newton-Raphson…

Inverse Modeling of Hydrologic Parameters Using Surface Flux and Runoff Observations in the Community Land Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yu; Hou, Zhangshuan; Huang, Maoyi

2013-12-10

This study demonstrates the possibility of inverting hydrologic parameters using surface flux and runoff observations in version 4 of the Community Land Model (CLM4). Previous studies showed that surface flux and runoff calculations are sensitive to major hydrologic parameters in CLM4 over different watersheds, and illustrated the necessity and possibility of parameter calibration. Two inversion strategies, the deterministic least-square fitting and stochastic Markov-Chain Monte-Carlo (MCMC) - Bayesian inversion approaches, are evaluated by applying them to CLM4 at selected sites. The unknowns to be estimated include surface and subsurface runoff generation parameters and vadose zone soil water parameters. We find thatmore » using model parameters calibrated by the least-square fitting provides little improvements in the model simulations but the sampling-based stochastic inversion approaches are consistent - as more information comes in, the predictive intervals of the calibrated parameters become narrower and the misfits between the calculated and observed responses decrease. In general, parameters that are identified to be significant through sensitivity analyses and statistical tests are better calibrated than those with weak or nonlinear impacts on flux or runoff observations. Temporal resolution of observations has larger impacts on the results of inverse modeling using heat flux data than runoff data. Soil and vegetation cover have important impacts on parameter sensitivities, leading to the different patterns of posterior distributions of parameters at different sites. Overall, the MCMC-Bayesian inversion approach effectively and reliably improves the simulation of CLM under different climates and environmental conditions. Bayesian model averaging of the posterior estimates with different reference acceptance probabilities can smooth the posterior distribution and provide more reliable parameter estimates, but at the expense of wider uncertainty bounds.« less

Benefits from bremsstrahlung distribution evaluation to get unknown information from specimen in SEM and TEM

NASA Astrophysics Data System (ADS)

Eggert, F.; Camus, P. P.; Schleifer, M.; Reinauer, F.

2018-01-01

The energy-dispersive X-ray spectrometer (EDS or EDX) is a commonly used device to characterise the composition of investigated material in scanning and transmission electron microscopes (SEM and TEM). One major benefit compared to wavelength-dispersive X-ray spectrometers (WDS) is that EDS systems collect the entire spectrum simultaneously. Therefore, not only are all emitted characteristic X-ray lines in the spectrum, but also the complete bremsstrahlung distribution is included. It is possible to get information about the specimen even from this radiation, which is usually perceived more as a disturbing background. This is possible by using theoretical model knowledge about bremsstrahlung excitation and absorption in the specimen in comparison to the actual measured spectrum. The core aim of this investigation is to present a method for better bremsstrahlung fitting in unknown geometry cases by variation of the geometry parameters and to utilise this knowledge also for characteristic radiation evaluation. A method is described, which allows the parameterisation of the true X-ray absorption conditions during spectrum acquisition. An ‘effective tilt’ angle parameter is determined by evaluation of the bremsstrahlung shape of the measured SEM spectra. It is useful for bremsstrahlung background approximation, with exact calculations of the absorption edges below the characteristic peaks, required for P/B-ZAF model based quantification methods. It can even be used for ZAF based quantification models as a variable input parameter. The analytical results are then much more reliable for the different absorption effects from irregular specimen surfaces because the unknown absorption dependency is considered. Finally, the method is also applied for evaluation of TEM spectra. In this case, the real physical parameter optimisation is with sample thickness (mass thickness), which is influencing the emitted and measured spectrum due to different absorption with TEM measurements. The effects are in the very low energy part of the spectrum, and are much more visible with most recent windowless TEM detectors. The thickness of the sample can be determined in this way from the measured bremsstrahlung spectrum shape.

Assessing Sexual Dicromatism: The Importance of Proper Parameterization in Tetrachromatic Visual Models

PubMed Central

Janisse, Kevyn; Doucet, Stéphanie M.

2017-01-01

Perceptual models of animal vision have greatly contributed to our understanding of animal-animal and plant-animal communication. The receptor-noise model of color contrasts has been central to this research as it quantifies the difference between two colors for any visual system of interest. However, if the properties of the visual system are unknown, assumptions regarding parameter values must be made, generally with unknown consequences. In this study, we conduct a sensitivity analysis of the receptor-noise model using avian visual system parameters to systematically investigate the influence of variation in light environment, photoreceptor sensitivities, photoreceptor densities, and light transmission properties of the ocular media and the oil droplets. We calculated the chromatic contrast of 15 plumage patches to quantify a dichromatism score for 70 species of Galliformes, a group of birds that display a wide range of sexual dimorphism. We found that the photoreceptor densities and the wavelength of maximum sensitivity of the short-wavelength-sensitive photoreceptor 1 (SWS1) can change dichromatism scores by 50% to 100%. In contrast, the light environment, transmission properties of the oil droplets, transmission properties of the ocular media, and the peak sensitivities of the cone photoreceptors had a smaller impact on the scores. By investigating the effect of varying two or more parameters simultaneously, we further demonstrate that improper parameterization could lead to differences between calculated and actual contrasts of more than 650%. Our findings demonstrate that improper parameterization of tetrachromatic visual models can have very large effects on measures of dichromatism scores, potentially leading to erroneous inferences. We urge more complete characterization of avian retinal properties and recommend that researchers either determine whether their species of interest possess an ultraviolet or near-ultraviolet sensitive SWS1 photoreceptor, or present models for both. PMID:28076391

Analysis of condensation on a horizontal cylinder with unknown wall temperature and comparison with the Nusselt model of film condensation

NASA Technical Reports Server (NTRS)

Bahrami, Parviz A.

1996-01-01

Theoretical analysis and numerical computations are performed to set forth a new model of film condensation on a horizontal cylinder. The model is more general than the well-known Nusselt model of film condensation and is designed to encompass all essential features of the Nusselt model. It is shown that a single parameter, constructed explicitly and without specification of the cylinder wall temperature, determines the degree of departure from the Nusselt model, which assumes a known and uniform wall temperature. It is also known that the Nusselt model is reached for very small, as well as very large, values of this parameter. In both limiting cases the cylinder wall temperature assumes a uniform distribution and the Nusselt model is approached. The maximum deviations between the two models is rather small for cases which are representative of cylinder dimensions, materials and conditions encountered in practice.

Methodological issues regarding power of classical test theory (CTT) and item response theory (IRT)-based approaches for the comparison of patient-reported outcomes in two groups of patients - a simulation study

PubMed Central

2010-01-01

Background Patients-Reported Outcomes (PRO) are increasingly used in clinical and epidemiological research. Two main types of analytical strategies can be found for these data: classical test theory (CTT) based on the observed scores and models coming from Item Response Theory (IRT). However, whether IRT or CTT would be the most appropriate method to analyse PRO data remains unknown. The statistical properties of CTT and IRT, regarding power and corresponding effect sizes, were compared. Methods Two-group cross-sectional studies were simulated for the comparison of PRO data using IRT or CTT-based analysis. For IRT, different scenarios were investigated according to whether items or person parameters were assumed to be known, to a certain extent for item parameters, from good to poor precision, or unknown and therefore had to be estimated. The powers obtained with IRT or CTT were compared and parameters having the strongest impact on them were identified. Results When person parameters were assumed to be unknown and items parameters to be either known or not, the power achieved using IRT or CTT were similar and always lower than the expected power using the well-known sample size formula for normally distributed endpoints. The number of items had a substantial impact on power for both methods. Conclusion Without any missing data, IRT and CTT seem to provide comparable power. The classical sample size formula for CTT seems to be adequate under some conditions but is not appropriate for IRT. In IRT, it seems important to take account of the number of items to obtain an accurate formula. PMID:20338031

Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification.

PubMed

Zhao, Xuefeng; Raghavan, Madhavan L; Lu, Jia

2011-05-01

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eightply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains.

PubMed

Dettmer, Jan; Dosso, Stan E

2012-10-01

This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.

EmpiriciSN: Re-sampling Observed Supernova/Host Galaxy Populations Using an XD Gaussian Mixture Model

NASA Astrophysics Data System (ADS)

Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.

2017-06-01

We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of a subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.

EmpiriciSN: Re-sampling Observed Supernova/Host Galaxy Populations Using an XD Gaussian Mixture Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holoien, Thomas W. -S.; Marshall, Philip J.; Wechsler, Risa H.

We describe two new open-source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program that uses Gaussian mixtures to perform density estimation of noisy data using extreme deconvolution (XD) algorithms. Additionally, it has functionality not available in other XD tools. It allows the user to select between the AstroML and Bovy et al. fitting methods and is compatible with scikit-learn machine learning algorithms. Most crucially, it allows the user to condition a model based on the known values of amore » subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model that is conditioned on known values of other parameters. EmpiriciSN is an exemplary application of this functionality, which can be used to fit an XDGMM model to observed supernova/host data sets and predict likely supernova parameters using a model conditioned on observed host properties. It is primarily intended to simulate realistic supernovae for LSST data simulations based on empirical galaxy properties.« less

A Robust Deconvolution Method based on Transdimensional Hierarchical Bayesian Inference

NASA Astrophysics Data System (ADS)

Kolb, J.; Lekic, V.

2012-12-01

Analysis of P-S and S-P conversions allows us to map receiver side crustal and lithospheric structure. This analysis often involves deconvolution of the parent wave field from the scattered wave field as a means of suppressing source-side complexity. A variety of deconvolution techniques exist including damped spectral division, Wiener filtering, iterative time-domain deconvolution, and the multitaper method. All of these techniques require estimates of noise characteristics as input parameters. We present a deconvolution method based on transdimensional Hierarchical Bayesian inference in which both noise magnitude and noise correlation are used as parameters in calculating the likelihood probability distribution. Because the noise for P-S and S-P conversion analysis in terms of receiver functions is a combination of both background noise - which is relatively easy to characterize - and signal-generated noise - which is much more difficult to quantify - we treat measurement errors as an known quantity, characterized by a probability density function whose mean and variance are model parameters. This transdimensional Hierarchical Bayesian approach has been successfully used previously in the inversion of receiver functions in terms of shear and compressional wave speeds of an unknown number of layers [1]. In our method we used a Markov chain Monte Carlo (MCMC) algorithm to find the receiver function that best fits the data while accurately assessing the noise parameters. In order to parameterize the receiver function we model the receiver function as an unknown number of Gaussians of unknown amplitude and width. The algorithm takes multiple steps before calculating the acceptance probability of a new model, in order to avoid getting trapped in local misfit minima. Using both observed and synthetic data, we show that the MCMC deconvolution method can accurately obtain a receiver function as well as an estimate of the noise parameters given the parent and daughter components. Furthermore, we demonstrate that this new approach is far less susceptible to generating spurious features even at high noise levels. Finally, the method yields not only the most-likely receiver function, but also quantifies its full uncertainty. [1] Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301

A Bayesian Framework for Coupled Estimation of Key Unknown Parameters of Land Water and Energy Balance Equations

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

The land surface is a key component of climate system. It controls the partitioning of available energy at the surface between sensible and latent heat, and partitioning of available water between evaporation and runoff. Water and energy cycle are intrinsically coupled through evaporation, which represents a heat exchange as latent heat flux. Accurate estimation of fluxes of heat and moisture are of significant importance in many fields such as hydrology, climatology and meteorology. In this study we develop and apply a Bayesian framework for estimating the key unknown parameters of terrestrial water and energy balance equations (i.e. moisture and heat diffusion) and their uncertainty in land surface models. These equations are coupled through flux of evaporation. The estimation system is based on the adjoint method for solving a least-squares optimization problem. The cost function consists of aggregated errors on state (i.e. moisture and temperature) with respect to observation and parameters estimation with respect to prior values over the entire assimilation period. This cost function is minimized with respect to parameters to identify models of sensible heat, latent heat/evaporation and drainage and runoff. Inverse of Hessian of the cost function is an approximation of the posterior uncertainty of parameter estimates. Uncertainty of estimated fluxes is estimated by propagating the uncertainty for linear and nonlinear function of key parameters through the method of First Order Second Moment (FOSM). Uncertainty analysis is used in this method to guide the formulation of a well-posed estimation problem. Accuracy of the method is assessed at point scale using surface energy and water fluxes generated by the Simultaneous Heat and Water (SHAW) model at the selected AmeriFlux stations. This method can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements of surface moisture and temperature states

Discrete-time switching periodic adaptive control for time-varying parameters with unknown periodicity

NASA Astrophysics Data System (ADS)

Yu, Miao; Huang, Deqing; Yang, Wanqiu

2018-06-01

In this paper, we address the problem of unknown periodicity for a class of discrete-time nonlinear parametric systems without assuming any growth conditions on the nonlinearities. The unknown periodicity hides in the parametric uncertainties, which is difficult to estimate with existing techniques. By incorporating a logic-based switching mechanism, we identify the period and bound of unknown parameter simultaneously. Lyapunov-based analysis is given to demonstrate that a finite number of switchings can guarantee the asymptotic tracking for the nonlinear parametric systems. The simulation result also shows the efficacy of the proposed switching periodic adaptive control approach.

Methods for parameter identification in oscillatory networks and application to cortical and thalamic 600 Hz activity.

PubMed

Leistritz, L; Suesse, T; Haueisen, J; Hilgenfeld, B; Witte, H

2006-01-01

Directed information transfer in the human brain occurs presumably by oscillations. As of yet, most approaches for the analysis of these oscillations are based on time-frequency or coherence analysis. The present work concerns the modeling of cortical 600 Hz oscillations, localized within the Brodmann Areas 3b and 1 after stimulation of the nervus medianus, by means of coupled differential equations. This approach leads to the so-called parameter identification problem, where based on a given data set, a set of unknown parameters of a system of ordinary differential equations is determined by special optimization procedures. Some suitable algorithms for this task are presented in this paper. Finally an oscillatory network model is optimally fitted to the data taken from ten volunteers.

Determination of Phobos' rotational parameters by an inertial frame bundle block adjustment

NASA Astrophysics Data System (ADS)

Burmeister, Steffi; Willner, Konrad; Schmidt, Valentina; Oberst, Jürgen

2018-01-01

A functional model for a bundle block adjustment in the inertial reference frame was developed, implemented and tested. This approach enables the determination of rotation parameters of planetary bodies on the basis of photogrammetric observations. Tests with a self-consistent synthetic data set showed that the implementation converges reliably toward the expected values of the introduced unknown parameters of the adjustment, e.g., spin pole orientation, and that it can cope with typical observational errors in the data. We applied the model to a data set of Phobos using images from the Mars Express and the Viking mission. With Phobos being in a locked rotation, we computed a forced libration amplitude of 1.14^circ ± 0.03^circ together with a control point network of 685 points.

Differential flatness properties and adaptive control of the hypothalamic-pituitary-adrenal axis model

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos

2016-12-01

It is shown that the model of the hypothalamic-pituitary-adrenal gland axis is a differentially flat one and this permits to transform it to the so-called linear canonical form. For the new description of the system's dynamics the transformed control inputs contain unknown terms which depend on the system's parameters. To identify these terms an adaptive fuzzy approximator is used in the control loop. Thus an adaptive fuzzy control scheme is implemented in which the unknown or unmodeled system dynamics is approximated by neurofuzzy networks and next this information is used by a feedback controller that makes the state variables (CRH - corticotropin releasing hormone, adenocortocotropic hormone - ACTH, cortisol) of the hypothalamic-pituitary-adrenal gland axis model converge to the desirable levels (setpoints). This adaptive control scheme is exclusively implemented with the use of output feedback, while the state vector elements which are not directly measured are estimated with the use of a state observer that operates in the control loop. The learning rate of the adaptive fuzzy system is suitably computed from Lyapunov analysis, so as to assure that both the learning procedure for the unknown system's parameters, the dynamics of the observer and the dynamics of the control loop will remain stable. The performed Lyapunov stability analysis depends on two Riccati equations, one associated with the feedback controller and one associated with the state observer. Finally, it is proven that for the control scheme that comprises the feedback controller, the state observer and the neurofuzzy approximator, an H-infinity tracking performance can be succeeded.

GLRT-based array receivers for the detection of a known signal with unknown parameters corrupted by noncircular interferences

NASA Astrophysics Data System (ADS)

Chevalier, Pascal; Oukaci, Abdelkader; Delmas, Jean-Pierre

2011-12-01

The detection of a known signal with unknown parameters in the presence of noise plus interferences (called total noise) whose covariance matrix is unknown is an important problem which has received much attention these last decades for applications such as radar, satellite localization or time acquisition in radio communications. However, most of the available receivers assume a second order (SO) circular (or proper) total noise and become suboptimal in the presence of SO noncircular (or improper) interferences, potentially present in the previous applications. The scarce available receivers which take the potential SO noncircularity of the total noise into account have been developed under the restrictive condition of a known signal with known parameters or under the assumption of a random signal. For this reason, following a generalized likelihood ratio test (GLRT) approach, the purpose of this paper is to introduce and to analyze the performance of different array receivers for the detection of a known signal, with different sets of unknown parameters, corrupted by an unknown noncircular total noise. To simplify the study, we limit the analysis to rectilinear known useful signals for which the baseband signal is real, which concerns many applications.

Modeling and analysis of the space shuttle nose-gear tire with semianalytic finite elements

NASA Technical Reports Server (NTRS)

Kim, Kyun O.; Noor, Ahmed K.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The Space Shuttle Orbiter nose gear tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynominals in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell. Numerical results of the Space Shuttle Orbiter nose gear tire model are compared with experimental measurements of the tire subjected to inflation loading.

Simulation-based Extraction of Key Material Parameters from Atomic Force Microscopy

NASA Astrophysics Data System (ADS)

Alsafi, Huseen; Peninngton, Gray

Models for the atomic force microscopy (AFM) tip and sample interaction contain numerous material parameters that are often poorly known. This is especially true when dealing with novel material systems or when imaging samples that are exposed to complicated interactions with the local environment. In this work we use Monte Carlo methods to extract sample material parameters from the experimental AFM analysis of a test sample. The parameterized theoretical model that we use is based on the Virtual Environment for Dynamic AFM (VEDA) [1]. The extracted material parameters are then compared with the accepted values for our test sample. Using this procedure, we suggest a method that can be used to successfully determine unknown material properties in novel and complicated material systems. We acknowledge Fisher Endowment Grant support from the Jess and Mildred Fisher College of Science and Mathematics,Towson University.

Application of Novel Lateral Tire Force Sensors to Vehicle Parameter Estimation of Electric Vehicles

PubMed Central

Nam, Kanghyun

2015-01-01

This article presents methods for estimating lateral vehicle velocity and tire cornering stiffness, which are key parameters in vehicle dynamics control, using lateral tire force measurements. Lateral tire forces acting on each tire are directly measured by load-sensing hub bearings that were invented and further developed by NSK Ltd. For estimating the lateral vehicle velocity, tire force models considering lateral load transfer effects are used, and a recursive least square algorithm is adapted to identify the lateral vehicle velocity as an unknown parameter. Using the estimated lateral vehicle velocity, tire cornering stiffness, which is an important tire parameter dominating the vehicle’s cornering responses, is estimated. For the practical implementation, the cornering stiffness estimation algorithm based on a simple bicycle model is developed and discussed. Finally, proposed estimation algorithms were evaluated using experimental test data. PMID:26569246

A linked simulation-optimization model for solving the unknown groundwater pollution source identification problems.

PubMed

Ayvaz, M Tamer

2010-09-20

This study proposes a linked simulation-optimization model for solving the unknown groundwater pollution source identification problems. In the proposed model, MODFLOW and MT3DMS packages are used to simulate the flow and transport processes in the groundwater system. These models are then integrated with an optimization model which is based on the heuristic harmony search (HS) algorithm. In the proposed simulation-optimization model, the locations and release histories of the pollution sources are treated as the explicit decision variables and determined through the optimization model. Also, an implicit solution procedure is proposed to determine the optimum number of pollution sources which is an advantage of this model. The performance of the proposed model is evaluated on two hypothetical examples for simple and complex aquifer geometries, measurement error conditions, and different HS solution parameter sets. Identified results indicated that the proposed simulation-optimization model is an effective way and may be used to solve the inverse pollution source identification problems. Copyright (c) 2010 Elsevier B.V. All rights reserved.

Error analysis in inverse scatterometry. I. Modeling.

PubMed

Al-Assaad, Rayan M; Byrne, Dale M

2007-02-01

Scatterometry is an optical technique that has been studied and tested in recent years in semiconductor fabrication metrology for critical dimensions. Previous work presented an iterative linearized method to retrieve surface-relief profile parameters from reflectance measurements upon diffraction. With the iterative linear solution model in this work, rigorous models are developed to represent the random and deterministic or offset errors in scatterometric measurements. The propagation of different types of error from the measurement data to the profile parameter estimates is then presented. The improvement in solution accuracies is then demonstrated with theoretical and experimental data by adjusting for the offset errors. In a companion paper (in process) an improved optimization method is presented to account for unknown offset errors in the measurements based on the offset error model.

A novel super-resolution camera model

NASA Astrophysics Data System (ADS)

Shao, Xiaopeng; Wang, Yi; Xu, Jie; Wang, Lin; Liu, Fei; Luo, Qiuhua; Chen, Xiaodong; Bi, Xiangli

2015-05-01

Aiming to realize super resolution(SR) to single image and video reconstruction, a super resolution camera model is proposed for the problem that the resolution of the images obtained by traditional cameras behave comparatively low. To achieve this function we put a certain driving device such as piezoelectric ceramics in the camera. By controlling the driving device, a set of continuous low resolution(LR) images can be obtained and stored instantaneity, which reflect the randomness of the displacements and the real-time performance of the storage very well. The low resolution image sequences have different redundant information and some particular priori information, thus it is possible to restore super resolution image factually and effectively. The sample method is used to derive the reconstruction principle of super resolution, which analyzes the possible improvement degree of the resolution in theory. The super resolution algorithm based on learning is used to reconstruct single image and the variational Bayesian algorithm is simulated to reconstruct the low resolution images with random displacements, which models the unknown high resolution image, motion parameters and unknown model parameters in one hierarchical Bayesian framework. Utilizing sub-pixel registration method, a super resolution image of the scene can be reconstructed. The results of 16 images reconstruction show that this camera model can increase the image resolution to 2 times, obtaining images with higher resolution in currently available hardware levels.

Observational support for the current sheet catastrophe model of substorm current disruption

NASA Technical Reports Server (NTRS)

Burkhart, G. R.; Lopez, R. E.; Dusenbery, P. B.; Speiser, T. W.

1992-01-01

The principles of the current sheet catastrophe models are briefly reviewed, and observations of some of the signatures predicted by the theory are presented. The data considered here include AMPTE/CCE observations of fifteen current sheet disruption events. According to the model proposed here, the root cause of the current disruption is some process, as yet unknown, that leads to an increase in the k sub A parameter. Possible causes for the increase in k sub A are discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tuo, Rui; Wu, C. F. Jeff

Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

Seabed roughness parameters from joint backscatter and reflection inversion at the Malta Plateau.

PubMed

Steininger, Gavin; Holland, Charles W; Dosso, Stan E; Dettmer, Jan

2013-09-01

This paper presents estimates of seabed roughness and geoacoustic parameters and uncertainties on the Malta Plateau, Mediterranean Sea, by joint Bayesian inversion of mono-static backscatter and spherical wave reflection-coefficient data. The data are modeled using homogeneous fluid sediment layers overlying an elastic basement. The scattering model assumes a randomly rough water-sediment interface with a von Karman roughness power spectrum. Scattering and reflection data are inverted simultaneously using a population of interacting Markov chains to sample roughness and geoacoustic parameters as well as residual error parameters. Trans-dimensional sampling is applied to treat the number of sediment layers and the order (zeroth or first) of an autoregressive error model (to represent potential residual correlation) as unknowns. Results are considered in terms of marginal posterior probability profiles and distributions, which quantify the effective data information content to resolve scattering/geoacoustic structure. Results indicate well-defined scattering (roughness) parameters in good agreement with existing measurements, and a multi-layer sediment profile over a high-speed (elastic) basement, consistent with independent knowledge of sand layers over limestone.

Classification of longitudinal data through a semiparametric mixed-effects model based on lasso-type estimators.

PubMed

Arribas-Gil, Ana; De la Cruz, Rolando; Lebarbier, Emilie; Meza, Cristian

2015-06-01

We propose a classification method for longitudinal data. The Bayes classifier is classically used to determine a classification rule where the underlying density in each class needs to be well modeled and estimated. This work is motivated by a real dataset of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. The proposed model, which is a semiparametric linear mixed-effects model (SLMM), is a particular case of the semiparametric nonlinear mixed-effects class of models (SNMM) in which finite dimensional (fixed effects and variance components) and infinite dimensional (an unknown function) parameters have to be estimated. In SNMM's maximum likelihood estimation is performed iteratively alternating parametric and nonparametric procedures. However, if one can make the assumption that the random effects and the unknown function interact in a linear way, more efficient estimation methods can be used. Our contribution is the proposal of a unified estimation procedure based on a penalized EM-type algorithm. The Expectation and Maximization steps are explicit. In this latter step, the unknown function is estimated in a nonparametric fashion using a lasso-type procedure. A simulation study and an application on real data are performed. © 2015, The International Biometric Society.

Consistent Parameter and Transfer Function Estimation using Context Free Grammars

NASA Astrophysics Data System (ADS)

Klotz, Daniel; Herrnegger, Mathew; Schulz, Karsten

2017-04-01

This contribution presents a method for the inference of transfer functions for rainfall-runoff models. Here, transfer functions are defined as parametrized (functional) relationships between a set of spatial predictors (e.g. elevation, slope or soil texture) and model parameters. They are ultimately used for estimation of consistent, spatially distributed model parameters from a limited amount of lumped global parameters. Additionally, they provide a straightforward method for parameter extrapolation from one set of basins to another and can even be used to derive parameterizations for multi-scale models [see: Samaniego et al., 2010]. Yet, currently an actual knowledge of the transfer functions is often implicitly assumed. As a matter of fact, for most cases these hypothesized transfer functions can rarely be measured and often remain unknown. Therefore, this contribution presents a general method for the concurrent estimation of the structure of transfer functions and their respective (global) parameters. Note, that by consequence an estimation of the distributed parameters of the rainfall-runoff model is also undertaken. The method combines two steps to achieve this. The first generates different possible transfer functions. The second then estimates the respective global transfer function parameters. The structural estimation of the transfer functions is based on the context free grammar concept. Chomsky first introduced context free grammars in linguistics [Chomsky, 1956]. Since then, they have been widely applied in computer science. But, to the knowledge of the authors, they have so far not been used in hydrology. Therefore, the contribution gives an introduction to context free grammars and shows how they can be constructed and used for the structural inference of transfer functions. This is enabled by new methods from evolutionary computation, such as grammatical evolution [O'Neill, 2001], which make it possible to exploit the constructed grammar as a search space for equations. The parametrization of the transfer functions is then achieved through a second optimization routine. The contribution explores different aspects of the described procedure through a set of experiments. These experiments can be divided into three categories: (1) The inference of transfer functions from directly measurable parameters; (2) The estimation of global parameters for given transfer functions from runoff data; and (3) The estimation of sets of completely unknown transfer functions from runoff data. The conducted tests reveal different potentials and limits of the procedure. In concrete it is shown that example (1) and (2) work remarkably well. Example (3) is much more dependent on the setup. In general, it can be said that in that case much more data is needed to derive transfer function estimations, even for simple models and setups. References: - Chomsky, N. (1956): Three Models for the Description of Language. IT IRETr. 2(3), p 113-124 - O'Neil, M. (2001): Grammatical Evolution. IEEE ToEC, Vol.5, No. 4 - Samaniego, L.; Kumar, R.; Attinger, S. (2010): Multiscale parameter regionalization of a grid-based hydrologic model at the mesoscale. WWR, Vol. 46, W05523, doi:10.1029/2008WR007327

Complete synchronization of uncertain chaotic systems via a single proportional adaptive controller: A comparative study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahmad, Israr, E-mail: iak-2000plus@yahoo.com; Saaban, Azizan Bin, E-mail: azizan.s@uum.edu.my; Ibrahim, Adyda Binti, E-mail: adyda@uum.edu.my

This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.

A new moving strategy for the sequential Monte Carlo approach in optimizing the hydrological model parameters

NASA Astrophysics Data System (ADS)

Zhu, Gaofeng; Li, Xin; Ma, Jinzhu; Wang, Yunquan; Liu, Shaomin; Huang, Chunlin; Zhang, Kun; Hu, Xiaoli

2018-04-01

Sequential Monte Carlo (SMC) samplers have become increasing popular for estimating the posterior parameter distribution with the non-linear dependency structures and multiple modes often present in hydrological models. However, the explorative capabilities and efficiency of the sampler depends strongly on the efficiency in the move step of SMC sampler. In this paper we presented a new SMC sampler entitled the Particle Evolution Metropolis Sequential Monte Carlo (PEM-SMC) algorithm, which is well suited to handle unknown static parameters of hydrologic model. The PEM-SMC sampler is inspired by the works of Liang and Wong (2001) and operates by incorporating the strengths of the genetic algorithm, differential evolution algorithm and Metropolis-Hasting algorithm into the framework of SMC. We also prove that the sampler admits the target distribution to be a stationary distribution. Two case studies including a multi-dimensional bimodal normal distribution and a conceptual rainfall-runoff hydrologic model by only considering parameter uncertainty and simultaneously considering parameter and input uncertainty show that PEM-SMC sampler is generally superior to other popular SMC algorithms in handling the high dimensional problems. The study also indicated that it may be important to account for model structural uncertainty by using multiplier different hydrological models in the SMC framework in future study.

An improved state-parameter analysis of ecosystem models using data assimilation

USGS Publications Warehouse

Chen, M.; Liu, S.; Tieszen, L.L.; Hollinger, D.Y.

2008-01-01

Much of the effort spent in developing data assimilation methods for carbon dynamics analysis has focused on estimating optimal values for either model parameters or state variables. The main weakness of estimating parameter values alone (i.e., without considering state variables) is that all errors from input, output, and model structure are attributed to model parameter uncertainties. On the other hand, the accuracy of estimating state variables may be lowered if the temporal evolution of parameter values is not incorporated. This research develops a smoothed ensemble Kalman filter (SEnKF) by combining ensemble Kalman filter with kernel smoothing technique. SEnKF has following characteristics: (1) to estimate simultaneously the model states and parameters through concatenating unknown parameters and state variables into a joint state vector; (2) to mitigate dramatic, sudden changes of parameter values in parameter sampling and parameter evolution process, and control narrowing of parameter variance which results in filter divergence through adjusting smoothing factor in kernel smoothing algorithm; (3) to assimilate recursively data into the model and thus detect possible time variation of parameters; and (4) to address properly various sources of uncertainties stemming from input, output and parameter uncertainties. The SEnKF is tested by assimilating observed fluxes of carbon dioxide and environmental driving factor data from an AmeriFlux forest station located near Howland, Maine, USA, into a partition eddy flux model. Our analysis demonstrates that model parameters, such as light use efficiency, respiration coefficients, minimum and optimum temperatures for photosynthetic activity, and others, are highly constrained by eddy flux data at daily-to-seasonal time scales. The SEnKF stabilizes parameter values quickly regardless of the initial values of the parameters. Potential ecosystem light use efficiency demonstrates a strong seasonality. Results show that the simultaneous parameter estimation procedure significantly improves model predictions. Results also show that the SEnKF can dramatically reduce the variance in state variables stemming from the uncertainty of parameters and driving variables. The SEnKF is a robust and effective algorithm in evaluating and developing ecosystem models and in improving the understanding and quantification of carbon cycle parameters and processes. ?? 2008 Elsevier B.V.

Dual Rate Adaptive Control for an Industrial Heat Supply Process Using Signal Compensation Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chai, Tianyou; Jia, Yao; Wang, Hong

The industrial heat supply process (HSP) is a highly nonlinear cascaded process which uses a steam valve opening as its control input, the steam flow-rate as its inner loop output and the supply water temperature as its outer loop output. The relationship between the heat exchange rate and the model parameters, such as steam density, entropy, and fouling correction factor and heat exchange efficiency are unknown and nonlinear. Moreover, these model parameters vary in line with steam pressure, ambient temperature and the residuals caused by the quality variations of the circulation water. When the steam pressure and the ambient temperaturemore » are of high values and are subjected to frequent external random disturbances, the supply water temperature and the steam flow-rate would interact with each other and fluctuate a lot. This is also true when the process exhibits unknown characteristic variations of the process dynamics caused by the unexpected changes of the heat exchange residuals. As a result, it is difficult to control the supply water temperature and the rates of changes of steam flow-rate well inside their targeted ranges. In this paper, a novel compensation signal based dual rate adaptive controller is developed by representing the unknown variations of dynamics as unmodeled dynamics. In the proposed controller design, such a compensation signal is constructed and added onto the control signal obtained from the linear deterministic model based feedback control design. Such a compensation signal aims at eliminating the unmodeled dynamics and the rate of changes of the currently sample unmodeled dynamics. A successful industrial application is carried out, where it has been shown that both the supply water temperature and the rate of the changes of the steam flow-rate can be controlled well inside their targeted ranges when the process is subjected to unknown variations of its dynamics.« less

A Fast Surrogate-facilitated Data-driven Bayesian Approach to Uncertainty Quantification of a Regional Groundwater Flow Model with Structural Error

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Ye, M.; Liang, F.

2016-12-01

Due to simplification and/or misrepresentation of the real aquifer system, numerical groundwater flow and solute transport models are usually subject to model structural error. During model calibration, the hydrogeological parameters may be overly adjusted to compensate for unknown structural error. This may result in biased predictions when models are used to forecast aquifer response to new forcing. In this study, we extend a fully Bayesian method [Xu and Valocchi, 2015] to calibrate a real-world, regional groundwater flow model. The method uses a data-driven error model to describe model structural error and jointly infers model parameters and structural error. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models. The surrogate models are constructed using machine learning techniques to emulate the response simulated by the computationally expensive groundwater model. We demonstrate in the real-world case study that explicitly accounting for model structural error yields parameter posterior distributions that are substantially different from those derived by the classical Bayesian calibration that does not account for model structural error. In addition, the Bayesian with error model method gives significantly more accurate prediction along with reasonable credible intervals.

Adaptive control of nonlinear uncertain active suspension systems with prescribed performance.

PubMed

Huang, Yingbo; Na, Jing; Wu, Xing; Liu, Xiaoqin; Guo, Yu

2015-01-01

This paper proposes adaptive control designs for vehicle active suspension systems with unknown nonlinear dynamics (e.g., nonlinear spring and piece-wise linear damper dynamics). An adaptive control is first proposed to stabilize the vertical vehicle displacement and thus to improve the ride comfort and to guarantee other suspension requirements (e.g., road holding and suspension space limitation) concerning the vehicle safety and mechanical constraints. An augmented neural network is developed to online compensate for the unknown nonlinearities, and a novel adaptive law is developed to estimate both NN weights and uncertain model parameters (e.g., sprung mass), where the parameter estimation error is used as a leakage term superimposed on the classical adaptations. To further improve the control performance and simplify the parameter tuning, a prescribed performance function (PPF) characterizing the error convergence rate, maximum overshoot and steady-state error is used to propose another adaptive control. The stability for the closed-loop system is proved and particular performance requirements are analyzed. Simulations are included to illustrate the effectiveness of the proposed control schemes. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Hiereachical Bayesian Model for Combining Geochemical and Geophysical Data for Environmental Applications Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong

2013-05-01

Development of a hierarchical Bayesian model to estimate the spatiotemporal distribution of aqueous geochemical parameters associated with in-situ bioremediation using surface spectral induced polarization (SIP) data and borehole geochemical measurements collected during a bioremediation experiment at a uranium-contaminated site near Rifle, Colorado. The SIP data are first inverted for Cole-Cole parameters including chargeability, time constant, resistivity at the DC frequency and dependence factor, at each pixel of two-dimensional grids using a previously developed stochastic method. Correlations between the inverted Cole-Cole parameters and the wellbore-based groundwater chemistry measurements indicative of key metabolic processes within the aquifer (e.g. ferrous iron, sulfate, uranium)more » were established and used as a basis for petrophysical model development. The developed Bayesian model consists of three levels of statistical sub-models: 1) data model, providing links between geochemical and geophysical attributes, 2) process model, describing the spatial and temporal variability of geochemical properties in the subsurface system, and 3) parameter model, describing prior distributions of various parameters and initial conditions. The unknown parameters are estimated using Markov chain Monte Carlo methods. By combining the temporally distributed geochemical data with the spatially distributed geophysical data, we obtain the spatio-temporal distribution of ferrous iron, sulfate and sulfide, and their associated uncertainity information. The obtained results can be used to assess the efficacy of the bioremediation treatment over space and time and to constrain reactive transport models.« less

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Lofberg, Johan; Brenner, Martin J.

2006-01-01

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

Optimization methods have been used in groundwater modeling as well as for the planning and management of groundwater systems. This paper reviews and evaluates the various optimization methods that have been used for solving the inverse problem of parameter identification (estimation), experimental design, and groundwater planning and management. Various model selection criteria are discussed, as well as criteria used for model discrimination. The inverse problem of parameter identification concerns the optimal determination of model parameters using water-level observations. In general, the optimal experimental design seeks to find sampling strategies for the purpose of estimating the unknown model parameters. A typical objective of optimal conjunctive-use planning of surface water and groundwater is to minimize the operational costs of meeting water demand. The optimization methods include mathematical programming techniques such as linear programming, quadratic programming, dynamic programming, stochastic programming, nonlinear programming, and the global search algorithms such as genetic algorithms, simulated annealing, and tabu search. Emphasis is placed on groundwater flow problems as opposed to contaminant transport problems. A typical two-dimensional groundwater flow problem is used to explain the basic formulations and algorithms that have been used to solve the formulated optimization problems.

LFlGRB: Luminosity function of long gamma-ray bursts

NASA Astrophysics Data System (ADS)

Paul, Debdutta

2018-04-01

LFlGRB models the luminosity function (LF) of long Gamma Ray Bursts (lGRBs) by using a sample of Swift and Fermi lGRBs to re-derive the parameters of the Yonetoku correlation and self-consistently estimate pseudo-redshifts of all the bursts with unknown redshifts. The GRB formation rate is modeled as the product of the cosmic star formation rate and a GRB formation efficiency for a given stellar mass.

Capture-recapture studies for multiple strata including non-markovian transitions

USGS Publications Warehouse

Brownie, C.; Hines, J.E.; Nichols, J.D.; Pollock, K.H.; Hestbeck, J.B.

1993-01-01

We consider capture-recapture studies where release and recapture data are available from each of a number of strata on every capture occasion. Strata may, for example, be geographic locations or physiological states. Movement of animals among strata occurs with unknown probabilities, and estimation of these unknown transition probabilities is the objective. We describe a computer routine for carrying out the analysis under a model that assumes Markovian transitions and under reduced parameter versions of this model. We also introduce models that relax the Markovian assumption and allow 'memory' to operate (i.e., allow dependence of the transition probabilities on the previous state). For these models, we sugg st an analysis based on a conditional likelihood approach. Methods are illustrated with data from a large study on Canada geese (Branta canadensis) banded in three geographic regions. The assumption of Markovian transitions is rejected convincingly for these data, emphasizing the importance of the more general models that allow memory.

Spacecraft Stabilization and Control for Capture of Non-Cooperative Space Objects

NASA Technical Reports Server (NTRS)

Joshi, Suresh; Kelkar, Atul G.

2014-01-01

This paper addresses stabilization and control issues in autonomous capture and manipulation of non-cooperative space objects such as asteroids, space debris, and orbital spacecraft in need of servicing. Such objects are characterized by unknown mass-inertia properties, unknown rotational motion, and irregular shapes, which makes it a challenging control problem. The problem is further compounded by the presence of inherent nonlinearities, signi cant elastic modes with low damping, and parameter uncertainties in the spacecraft. Robust dissipativity-based control laws are presented and are shown to provide global asymptotic stability in spite of model uncertainties and nonlinearities. It is shown that robust stabilization can be accomplished via model-independent dissipativity-based controllers using thrusters alone, while stabilization with attitude and position control can be accomplished using thrusters and torque actuators.

Calibration and LOD/LOQ estimation of a chemiluminescent hybridization assay for residual DNA in recombinant protein drugs expressed in E. coli using a four-parameter logistic model.

PubMed

Lee, K R; Dipaolo, B; Ji, X

2000-06-01

Calibration is the process of fitting a model based on reference data points (x, y), then using the model to estimate an unknown x based on a new measured response, y. In DNA assay, x is the concentration, and y is the measured signal volume. A four-parameter logistic model was used frequently for calibration of immunoassay when the response is optical density for enzyme-linked immunosorbent assay (ELISA) or adjusted radioactivity count for radioimmunoassay (RIA). Here, it is shown that the same model or a linearized version of the curve are equally useful for the calibration of a chemiluminescent hybridization assay for residual DNA in recombinant protein drugs and calculation of performance measures of the assay.

On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed; Karami-Mollaee, Ali

2018-06-01

Chaotic systems demonstrate complex behaviour in their state variables and their parameters, which generate some challenges and consequences. This paper presents a new synchronisation scheme based on integral sliding mode control (ISMC) method on a class of complex chaotic systems with complex unknown parameters. Synchronisation between corresponding states of a class of complex chaotic systems and also convergence of the errors of the system parameters to zero point are studied. The designed feedback control vector and complex unknown parameter vector are analytically achieved based on the Lyapunov stability theory. Moreover, the effectiveness of the proposed methodology is verified by synchronisation of the Chen complex system and the Lorenz complex systems as the leader and the follower chaotic systems, respectively. In conclusion, some numerical simulations related to the synchronisation methodology is given to illustrate the effectiveness of the theoretical discussions.

Parameter Estimation and Model Selection in Computational Biology

PubMed Central

Lillacci, Gabriele; Khammash, Mustafa

2010-01-01

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection. PMID:20221262

Joint Bayesian Estimation of Quasar Continua and the Lyα Forest Flux Probability Distribution Function

NASA Astrophysics Data System (ADS)

Eilers, Anna-Christina; Hennawi, Joseph F.; Lee, Khee-Gan

2017-08-01

We present a new Bayesian algorithm making use of Markov Chain Monte Carlo sampling that allows us to simultaneously estimate the unknown continuum level of each quasar in an ensemble of high-resolution spectra, as well as their common probability distribution function (PDF) for the transmitted Lyα forest flux. This fully automated PDF regulated continuum fitting method models the unknown quasar continuum with a linear principal component analysis (PCA) basis, with the PCA coefficients treated as nuisance parameters. The method allows one to estimate parameters governing the thermal state of the intergalactic medium (IGM), such as the slope of the temperature-density relation γ -1, while marginalizing out continuum uncertainties in a fully Bayesian way. Using realistic mock quasar spectra created from a simplified semi-numerical model of the IGM, we show that this method recovers the underlying quasar continua to a precision of ≃ 7 % and ≃ 10 % at z = 3 and z = 5, respectively. Given the number of principal component spectra, this is comparable to the underlying accuracy of the PCA model itself. Most importantly, we show that we can achieve a nearly unbiased estimate of the slope γ -1 of the IGM temperature-density relation with a precision of +/- 8.6 % at z = 3 and +/- 6.1 % at z = 5, for an ensemble of ten mock high-resolution quasar spectra. Applying this method to real quasar spectra and comparing to a more realistic IGM model from hydrodynamical simulations would enable precise measurements of the thermal and cosmological parameters governing the IGM, albeit with somewhat larger uncertainties, given the increased flexibility of the model.

Efficient calibration for imperfect computer models

DOE PAGES

Tuo, Rui; Wu, C. F. Jeff

2015-12-01

Many computer models contain unknown parameters which need to be estimated using physical observations. Furthermore, the calibration method based on Gaussian process models may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the L 2 calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Here, numerical examples show that the proposed method outperforms the existing ones.

Determining Hypocentral Parameters for Local Earthquakes in 1-D Using a Genetic Algorithm and Two-point ray tracing

NASA Astrophysics Data System (ADS)

Kim, W.; Hahm, I.; Ahn, S. J.; Lim, D. H.

2005-12-01

This paper introduces a powerful method for determining hypocentral parameters for local earthquakes in 1-D using a genetic algorithm (GA) and two-point ray tracing. Using existing algorithms to determine hypocentral parameters is difficult, because these parameters can vary based on initial velocity models. We developed a new method to solve this problem by applying a GA to an existing algorithm, HYPO-71 (Lee and Larh, 1975). The original HYPO-71 algorithm was modified by applying two-point ray tracing and a weighting factor with respect to the takeoff angle at the source to reduce errors from the ray path and hypocenter depth. Artificial data, without error, were generated by computer using two-point ray tracing in a true model, in which velocity structure and hypocentral parameters were known. The accuracy of the calculated results was easily determined by comparing calculated and actual values. We examined the accuracy of this method for several cases by changing the true and modeled layer numbers and thicknesses. The computational results show that this method determines nearly exact hypocentral parameters without depending on initial velocity models. Furthermore, accurate and nearly unique hypocentral parameters were obtained, although the number of modeled layers and thicknesses differed from those in the true model. Therefore, this method can be a useful tool for determining hypocentral parameters in regions where reliable local velocity values are unknown. This method also provides the basic a priori information for 3-D studies. KEY -WORDS: hypocentral parameters, genetic algorithm (GA), two-point ray tracing

SU-E-J-150: Four-Dimensional Cone-Beam CT Algorithm by Extraction of Physical and Motion Parameter of Mobile Targets Retrospective to Image Reconstruction with Motion Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ali, I; Ahmad, S; Alsbou, N

Purpose: To develop 4D-cone-beam CT (CBCT) algorithm by motion modeling that extracts actual length, CT numbers level and motion amplitude of a mobile target retrospective to image reconstruction by motion modeling. Methods: The algorithm used three measurable parameters: apparent length and blurred CT number distribution of a mobile target obtained from CBCT images to determine actual length, CT-number value of the stationary target, and motion amplitude. The predictions of this algorithm were tested with mobile targets that with different well-known sizes made from tissue-equivalent gel which was inserted into a thorax phantom. The phantom moved sinusoidally in one-direction to simulatemore » respiratory motion using eight amplitudes ranging 0–20mm. Results: Using this 4D-CBCT algorithm, three unknown parameters were extracted that include: length of the target, CT number level, speed or motion amplitude for the mobile targets retrospective to image reconstruction. The motion algorithms solved for the three unknown parameters using measurable apparent length, CT number level and gradient for a well-defined mobile target obtained from CBCT images. The motion model agreed with measured apparent lengths which were dependent on the actual target length and motion amplitude. The gradient of the CT number distribution of the mobile target is dependent on the stationary CT number level, actual target length and motion amplitude. Motion frequency and phase did not affect the elongation and CT number distribution of the mobile target and could not be determined. Conclusion: A 4D-CBCT motion algorithm was developed to extract three parameters that include actual length, CT number level and motion amplitude or speed of mobile targets directly from reconstructed CBCT images without prior knowledge of the stationary target parameters. This algorithm provides alternative to 4D-CBCT without requirement to motion tracking and sorting of the images into different breathing phases which has potential applications in diagnostic CT imaging and radiotherapy.« less

Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay

NASA Astrophysics Data System (ADS)

Torkamani, Shahab; Butcher, Eric A.

2013-07-01

The stochastic estimation of parameters and states in linear and nonlinear time-delayed vibratory systems with distributed delay is explored. The approach consists of first employing a continuous time approximation to approximate the delayed integro-differential system with a large set of ordinary differential equations having stochastic excitations. Then the problem of state and parameter estimation in the resulting stochastic ordinary differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman-Bucy filter to the augmented filtering problem, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states. Similarly, the upper bound of the distributed delay can also be estimated by the proposed technique. As an illustrative example to a practical problem in vibrations, the parameter, delay upper bound, and state estimation from noise-corrupted measurements in a distributed force model widely used for modeling machine tool vibrations in the turning operation is investigated.

Enhanced Engine Performance During Emergency Operation Using a Model-Based Engine Control Architecture

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2016-01-01

This paper discusses the design and application of model-based engine control (MBEC) for use during emergency operation of the aircraft. The MBEC methodology is applied to the Commercial Modular Aero-Propulsion System Simulation 40k (CMAPSS40k) and features an optimal tuner Kalman Filter (OTKF) to estimate unmeasured engine parameters, which can then be used for control. During an emergency scenario, normally-conservative engine operating limits may be relaxed to increase the performance of the engine and overall survivability of the aircraft; this comes at the cost of additional risk of an engine failure. The MBEC architecture offers the advantage of estimating key engine parameters that are not directly measureable. Estimating the unknown parameters allows for tighter control over these parameters, and on the level of risk the engine will operate at. This will allow the engine to achieve better performance than possible when operating to more conservative limits on a related, measurable parameter.

Enhanced Engine Performance During Emergency Operation Using a Model-Based Engine Control Architecture

NASA Technical Reports Server (NTRS)

Csank, Jeffrey T.; Connolly, Joseph W.

2015-01-01

This paper discusses the design and application of model-based engine control (MBEC) for use during emergency operation of the aircraft. The MBEC methodology is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (CMAPSS40,000) and features an optimal tuner Kalman Filter (OTKF) to estimate unmeasured engine parameters, which can then be used for control. During an emergency scenario, normally-conservative engine operating limits may be relaxed to increase the performance of the engine and overall survivability of the aircraft; this comes at the cost of additional risk of an engine failure. The MBEC architecture offers the advantage of estimating key engine parameters that are not directly measureable. Estimating the unknown parameters allows for tighter control over these parameters, and on the level of risk the engine will operate at. This will allow the engine to achieve better performance than possible when operating to more conservative limits on a related, measurable parameter.

ShinyKGode: an interactive application for ODE parameter inference using gradient matching.

PubMed

Wandy, Joe; Niu, Mu; Giurghita, Diana; Daly, Rónán; Rogers, Simon; Husmeier, Dirk

2018-07-01

Mathematical modelling based on ordinary differential equations (ODEs) is widely used to describe the dynamics of biological systems, particularly in systems and pathway biology. Often the kinetic parameters of these ODE systems are unknown and have to be inferred from the data. Approximate parameter inference methods based on gradient matching (which do not require performing computationally expensive numerical integration of the ODEs) have been getting popular in recent years, but many implementations are difficult to run without expert knowledge. Here, we introduce ShinyKGode, an interactive web application to perform fast parameter inference on ODEs using gradient matching. ShinyKGode can be used to infer ODE parameters on simulated and observed data using gradient matching. Users can easily load their own models in Systems Biology Markup Language format, and a set of pre-defined ODE benchmark models are provided in the application. Inferred parameters are visualized alongside diagnostic plots to assess convergence. The R package for ShinyKGode can be installed through the Comprehensive R Archive Network (CRAN). Installation instructions, as well as tutorial videos and source code are available at https://joewandy.github.io/shinyKGode. Supplementary data are available at Bioinformatics online.

Efficient hierarchical trans-dimensional Bayesian inversion of magnetotelluric data

NASA Astrophysics Data System (ADS)

Xiang, Enming; Guo, Rongwen; Dosso, Stan E.; Liu, Jianxin; Dong, Hao; Ren, Zhengyong

2018-06-01

This paper develops an efficient hierarchical trans-dimensional (trans-D) Bayesian algorithm to invert magnetotelluric (MT) data for subsurface geoelectrical structure, with unknown geophysical model parameterization (the number of conductivity-layer interfaces) and data-error models parameterized by an auto-regressive (AR) process to account for potential error correlations. The reversible-jump Markov-chain Monte Carlo algorithm, which adds/removes interfaces and AR parameters in birth/death steps, is applied to sample the trans-D posterior probability density for model parameterization, model parameters, error variance and AR parameters, accounting for the uncertainties of model dimension and data-error statistics in the uncertainty estimates of the conductivity profile. To provide efficient sampling over the multiple subspaces of different dimensions, advanced proposal schemes are applied. Parameter perturbations are carried out in principal-component space, defined by eigen-decomposition of the unit-lag model covariance matrix, to minimize the effect of inter-parameter correlations and provide effective perturbation directions and length scales. Parameters of new layers in birth steps are proposed from the prior, instead of focused distributions centred at existing values, to improve birth acceptance rates. Parallel tempering, based on a series of parallel interacting Markov chains with successively relaxed likelihoods, is applied to improve chain mixing over model dimensions. The trans-D inversion is applied in a simulation study to examine the resolution of model structure according to the data information content. The inversion is also applied to a measured MT data set from south-central Australia.

Improved mapping of radio sources from VLBI data by least-square fit

NASA Technical Reports Server (NTRS)

Rodemich, E. R.

1985-01-01

A method is described for producing improved mapping of radio sources from Very Long Base Interferometry (VLBI) data. The method described is more direct than existing Fourier methods, is often more accurate, and runs at least as fast. The visibility data is modeled here, as in existing methods, as a function of the unknown brightness distribution and the unknown antenna gains and phases. These unknowns are chosen so that the resulting function values are as near as possible to the observed values. If researchers use the radio mapping source deviation to measure the closeness of this fit to the observed values, they are led to the problem of minimizing a certain function of all the unknown parameters. This minimization problem cannot be solved directly, but it can be attacked by iterative methods which we show converge automatically to the minimum with no user intervention. The resulting brightness distribution will furnish the best fit to the data among all brightness distributions of given resolution.

Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, Ralph C.

1994-01-01

A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural flaws through nondestructive evaluation techniques. The presence and excitation of patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear. As a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, well-posedness and approximations results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for systems excitations and data collection.

Nonlinear robust controller design for multi-robot systems with unknown payloads

NASA Technical Reports Server (NTRS)

Song, Y. D.; Anderson, J. N.; Homaifar, A.; Lai, H. Y.

1992-01-01

This work is concerned with the control problem of a multi-robot system handling a payload with unknown mass properties. Force constraints at the grasp points are considered. Robust control schemes are proposed that cope with the model uncertainty and achieve asymptotic path tracking. To deal with the force constraints, a strategy for optimally sharing the task is suggested. This strategy basically consists of two steps. The first detects the robots that need help and the second arranges that help. It is shown that the overall system is not only robust to uncertain payload parameters, but also satisfies the force constraints.

The log-periodic-AR(1)-GARCH(1,1) model for financial crashes

NASA Astrophysics Data System (ADS)

Gazola, L.; Fernandes, C.; Pizzinga, A.; Riera, R.

2008-02-01

This paper intends to meet recent claims for the attainment of more rigorous statistical methodology within the econophysics literature. To this end, we consider an econometric approach to investigate the outcomes of the log-periodic model of price movements, which has been largely used to forecast financial crashes. In order to accomplish reliable statistical inference for unknown parameters, we incorporate an autoregressive dynamic and a conditional heteroskedasticity structure in the error term of the original model, yielding the log-periodic-AR(1)-GARCH(1,1) model. Both the original and the extended models are fitted to financial indices of U. S. market, namely S&P500 and NASDAQ. Our analysis reveal two main points: (i) the log-periodic-AR(1)-GARCH(1,1) model has residuals with better statistical properties and (ii) the estimation of the parameter concerning the time of the financial crash has been improved.

Identifiability Results for Several Classes of Linear Compartment Models.

PubMed

Meshkat, Nicolette; Sullivant, Seth; Eisenberg, Marisa

2015-08-01

Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.

An algebraic aspect of Pareto mixture parameter estimation using censored sample: A Bayesian approach.

PubMed

Saleem, Muhammad; Sharif, Kashif; Fahmi, Aliya

2018-04-27

Applications of Pareto distribution are common in reliability, survival and financial studies. In this paper, A Pareto mixture distribution is considered to model a heterogeneous population comprising of two subgroups. Each of two subgroups is characterized by the same functional form with unknown distinct shape and scale parameters. Bayes estimators have been derived using flat and conjugate priors using squared error loss function. Standard errors have also been derived for the Bayes estimators. An interesting feature of this study is the preparation of components of Fisher Information matrix.

Parameter estimation of qubit states with unknown phase parameter

NASA Astrophysics Data System (ADS)

Suzuki, Jun

2015-02-01

We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean square errors (MSEs) when estimating relevant parameters with separable measurements based on known precision bounds; the symmetric logarithmic derivative (SLD) Cramér-Rao (CR) bound and Hayashi-Gill-Massar (HGM) bound. We investigate the optimal measurement which attains the HGM bound and discuss its properties. We show that the HGM bound for relevant parameters can be attained asymptotically by using some fraction of given n quantum states to estimate the phase parameter. We also discuss the Holevo bound which can be attained asymptotically by a collective measurement.

A validation procedure for a LADAR system radiometric simulation model

NASA Astrophysics Data System (ADS)

Leishman, Brad; Budge, Scott; Pack, Robert

2007-04-01

The USU LadarSIM software package is a ladar system engineering tool that has recently been enhanced to include the modeling of the radiometry of Ladar beam footprints. This paper will discuss our validation of the radiometric model and present a practical approach to future validation work. In order to validate complicated and interrelated factors affecting radiometry, a systematic approach had to be developed. Data for known parameters were first gathered then unknown parameters of the system were determined from simulation test scenarios. This was done in a way to isolate as many unknown variables as possible, then build on the previously obtained results. First, the appropriate voltage threshold levels of the discrimination electronics were set by analyzing the number of false alarms seen in actual data sets. With this threshold set, the system noise was then adjusted to achieve the appropriate number of dropouts. Once a suitable noise level was found, the range errors of the simulated and actual data sets were compared and studied. Predicted errors in range measurements were analyzed using two methods: first by examining the range error of a surface with known reflectivity and second by examining the range errors for specific detectors with known responsivities. This provided insight into the discrimination method and receiver electronics used in the actual system.

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison w/ LIS Satellite Data

NASA Technical Reports Server (NTRS)

Koshak, William; Krider, E. Philip; Murray, Natalie; Boccippio, Dennis

2007-01-01

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

Uncertainty quantification and propagation in dynamic models using ambient vibration measurements, application to a 10-story building

NASA Astrophysics Data System (ADS)

Behmanesh, Iman; Yousefianmoghadam, Seyedsina; Nozari, Amin; Moaveni, Babak; Stavridis, Andreas

2018-07-01

This paper investigates the application of Hierarchical Bayesian model updating for uncertainty quantification and response prediction of civil structures. In this updating framework, structural parameters of an initial finite element (FE) model (e.g., stiffness or mass) are calibrated by minimizing error functions between the identified modal parameters and the corresponding parameters of the model. These error functions are assumed to have Gaussian probability distributions with unknown parameters to be determined. The estimated parameters of error functions represent the uncertainty of the calibrated model in predicting building's response (modal parameters here). The focus of this paper is to answer whether the quantified model uncertainties using dynamic measurement at building's reference/calibration state can be used to improve the model prediction accuracies at a different structural state, e.g., damaged structure. Also, the effects of prediction error bias on the uncertainty of the predicted values is studied. The test structure considered here is a ten-story concrete building located in Utica, NY. The modal parameters of the building at its reference state are identified from ambient vibration data and used to calibrate parameters of the initial FE model as well as the error functions. Before demolishing the building, six of its exterior walls were removed and ambient vibration measurements were also collected from the structure after the wall removal. These data are not used to calibrate the model; they are only used to assess the predicted results. The model updating framework proposed in this paper is applied to estimate the modal parameters of the building at its reference state as well as two damaged states: moderate damage (removal of four walls) and severe damage (removal of six walls). Good agreement is observed between the model-predicted modal parameters and those identified from vibration tests. Moreover, it is shown that including prediction error bias in the updating process instead of commonly-used zero-mean error function can significantly reduce the prediction uncertainties.

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework

PubMed Central

Sun, Mingzhu; Xu, Hui; Zeng, Xingjuan; Zhao, Xin

2017-01-01

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation. PMID:28225811

Automated numerical simulation of biological pattern formation based on visual feedback simulation framework.

PubMed

Sun, Mingzhu; Xu, Hui; Zeng, Xingjuan; Zhao, Xin

2017-01-01

There are various fantastic biological phenomena in biological pattern formation. Mathematical modeling using reaction-diffusion partial differential equation systems is employed to study the mechanism of pattern formation. However, model parameter selection is both difficult and time consuming. In this paper, a visual feedback simulation framework is proposed to calculate the parameters of a mathematical model automatically based on the basic principle of feedback control. In the simulation framework, the simulation results are visualized, and the image features are extracted as the system feedback. Then, the unknown model parameters are obtained by comparing the image features of the simulation image and the target biological pattern. Considering two typical applications, the visual feedback simulation framework is applied to fulfill pattern formation simulations for vascular mesenchymal cells and lung development. In the simulation framework, the spot, stripe, labyrinthine patterns of vascular mesenchymal cells, the normal branching pattern and the branching pattern lacking side branching for lung branching are obtained in a finite number of iterations. The simulation results indicate that it is easy to achieve the simulation targets, especially when the simulation patterns are sensitive to the model parameters. Moreover, this simulation framework can expand to other types of biological pattern formation.

Determination of power system component parameters using nonlinear dead beat estimation method

NASA Astrophysics Data System (ADS)

Kolluru, Lakshmi

Power systems are considered the most complex man-made wonders in existence today. In order to effectively supply the ever increasing demands of the consumers, power systems are required to remain stable at all times. Stability and monitoring of these complex systems are achieved by strategically placed computerized control centers. State and parameter estimation is an integral part of these facilities, as they deal with identifying the unknown states and/or parameters of the systems. Advancements in measurement technologies and the introduction of phasor measurement units (PMU) provide detailed and dynamic information of all measurements. Accurate availability of dynamic measurements provides engineers the opportunity to expand and explore various possibilities in power system dynamic analysis/control. This thesis discusses the development of a parameter determination algorithm for nonlinear power systems, using dynamic data obtained from local measurements. The proposed algorithm was developed by observing the dead beat estimator used in state space estimation of linear systems. The dead beat estimator is considered to be very effective as it is capable of obtaining the required results in a fixed number of steps. The number of steps required is related to the order of the system and the number of parameters to be estimated. The proposed algorithm uses the idea of dead beat estimator and nonlinear finite difference methods to create an algorithm which is user friendly and can determine the parameters fairly accurately and effectively. The proposed algorithm is based on a deterministic approach, which uses dynamic data and mathematical models of power system components to determine the unknown parameters. The effectiveness of the algorithm is tested by implementing it to identify the unknown parameters of a synchronous machine. MATLAB environment is used to create three test cases for dynamic analysis of the system with assumed known parameters. Faults are introduced in the virtual test systems and the dynamic data obtained in each case is analyzed and recorded. Ideally, actual measurements are to be provided to the algorithm. As the measurements are not readily available the data obtained from simulations is fed into the determination algorithm as inputs. The obtained results are then compared to the original (or assumed) values of the parameters. The results obtained suggest that the algorithm is able to determine the parameters of a synchronous machine when crisp data is available.

An Enhanced Box-Wing Solar Radiation pressure model for BDS and initial results

NASA Astrophysics Data System (ADS)

Zhao, Qunhe; Wang, Xiaoya; Hu, Xiaogong; Guo, Rui; Shang, Lin; Tang, Chengpan; Shao, Fan

2016-04-01

Solar radiation pressure forces are the largest non-gravitational perturbations acting on GNSS satellites, which is difficult to be accurately modeled due to the complicated and changing satellite attitude and unknown surface material characteristics. By the end of 2015, there are more than 50 stations of the Multi-GNSS Experiment(MGEX) set-up by the IGS. The simple box-plate model relies on coarse assumptions about the dimensions and optical properties of the satellite due to lack of more detailed information. So, a physical model based on BOX-WING model is developed, which is more sophisticated and more detailed physical structure has been taken into account, then calculating pressure forces according to the geometric relations between light rays and surfaces. All the MGEX stations and IGS core stations had been processed for precise orbit determination tests with GPS and BDS observations. Calculation range covers all the two kinds of Eclipsing and non-eclipsing periods in 2015, and we adopted the un-differential observation mode and more accurate values of satellite phase centers. At first, we tried nine parameters model, and then eliminated the parameters with strong correlation between them, came into being five parameters of the model. Five parameters were estimated, such as solar scale, y-bias, three material coefficients of solar panel, x-axis and z-axis panels. Initial results showed that, in the period of yaw-steering mode, use of Enhanced ADBOXW model results in small improvement for IGSO and MEO satellites, and the Root-Mean-Square(RMS) error value of one-day arc orbit decreased by about 10%~30% except for C08 and C14. The new model mainly improved the along track acceleration, up to 30% while in the radial track was not obvious. The Satellite Laser Ranging(SLR) validation showed, however, that this model had higher prediction accuracy in the period of orbit-normal mode, compared to GFZ multi-GNSS orbit products, as well with relative post-processing results. Because of the system bias and unknown reasons, GEO satellites had bad results, when after adding some Chinese regional stations, there had an obviously improvement of the orbit precision. This model can be used as a priori model to help build experience models for the later works.

State, Parameter, and Unknown Input Estimation Problems in Active Automotive Safety Applications

NASA Astrophysics Data System (ADS)

Phanomchoeng, Gridsada

A variety of driver assistance systems such as traction control, electronic stability control (ESC), rollover prevention and lane departure avoidance systems are being developed by automotive manufacturers to reduce driver burden, partially automate normal driving operations, and reduce accidents. The effectiveness of these driver assistance systems can be significant enhanced if the real-time values of several vehicle parameters and state variables, namely tire-road friction coefficient, slip angle, roll angle, and rollover index, can be known. Since there are no inexpensive sensors available to measure these variables, it is necessary to estimate them. However, due to the significant nonlinear dynamics in a vehicle, due to unknown and changing plant parameters, and due to the presence of unknown input disturbances, the design of estimation algorithms for this application is challenging. This dissertation develops a new approach to observer design for nonlinear systems in which the nonlinearity has a globally (or locally) bounded Jacobian. The developed approach utilizes a modified version of the mean value theorem to express the nonlinearity in the estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). A number of illustrative examples are presented to show that the developed approach is less conservative and more useful than the standard Lipschitz assumption based nonlinear observer. The developed nonlinear observer is utilized for estimation of slip angle, longitudinal vehicle velocity, and vehicle roll angle. In order to predict and prevent vehicle rollovers in tripped situations, it is necessary to estimate the vertical tire forces in the presence of unknown road disturbance inputs. An approach to estimate unknown disturbance inputs in nonlinear systems using dynamic model inversion and a modified version of the mean value theorem is presented. The developed theory is used to estimate vertical tire forces and predict tripped rollovers in situations involving road bumps, potholes, and lateral unknown force inputs. To estimate the tire-road friction coefficients at each individual tire of the vehicle, algorithms to estimate longitudinal forces and slip ratios at each tire are proposed. Subsequently, tire-road friction coefficients are obtained using recursive least squares parameter estimators that exploit the relationship between longitudinal force and slip ratio at each tire. The developed approaches are evaluated through simulations with industry standard software, CARSIM, with experimental tests on a Volvo XC90 sport utility vehicle and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed approaches can reliably estimate the vehicle parameters and state variables needed for effective ESC and rollover prevention applications.

Bayesian statistics and Monte Carlo methods

NASA Astrophysics Data System (ADS)

Koch, K. R.

2018-03-01

The Bayesian approach allows an intuitive way to derive the methods of statistics. Probability is defined as a measure of the plausibility of statements or propositions. Three rules are sufficient to obtain the laws of probability. If the statements refer to the numerical values of variables, the so-called random variables, univariate and multivariate distributions follow. They lead to the point estimation by which unknown quantities, i.e. unknown parameters, are computed from measurements. The unknown parameters are random variables, they are fixed quantities in traditional statistics which is not founded on Bayes' theorem. Bayesian statistics therefore recommends itself for Monte Carlo methods, which generate random variates from given distributions. Monte Carlo methods, of course, can also be applied in traditional statistics. The unknown parameters, are introduced as functions of the measurements, and the Monte Carlo methods give the covariance matrix and the expectation of these functions. A confidence region is derived where the unknown parameters are situated with a given probability. Following a method of traditional statistics, hypotheses are tested by determining whether a value for an unknown parameter lies inside or outside the confidence region. The error propagation of a random vector by the Monte Carlo methods is presented as an application. If the random vector results from a nonlinearly transformed vector, its covariance matrix and its expectation follow from the Monte Carlo estimate. This saves a considerable amount of derivatives to be computed, and errors of the linearization are avoided. The Monte Carlo method is therefore efficient. If the functions of the measurements are given by a sum of two or more random vectors with different multivariate distributions, the resulting distribution is generally not known. TheMonte Carlo methods are then needed to obtain the covariance matrix and the expectation of the sum.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Development of a Rational Modeling Approach for the Design, and Optimization of the Multifiltration Unit. Volume 1

NASA Technical Reports Server (NTRS)

Hand, David W.; Crittenden, John C.; Ali, Anisa N.; Bulloch, John L.; Hokanson, David R.; Parrem, David L.

1996-01-01

This thesis includes the development and verification of an adsorption model for analysis and optimization of the adsorption processes within the International Space Station multifiltration beds. The fixed bed adsorption model includes multicomponent equilibrium and both external and intraparticle mass transfer resistances. Single solute isotherm parameters were used in the multicomponent equilibrium description to predict the competitive adsorption interactions occurring during the adsorption process. The multicomponent equilibrium description used the Fictive Component Analysis to describe adsorption in unknown background matrices. Multicomponent isotherms were used to validate the multicomponent equilibrium description. Column studies were used to develop and validate external and intraparticle mass transfer parameter correlations for compounds of interest. The fixed bed model was verified using a shower and handwash ersatz water which served as a surrogate to the actual shower and handwash wastewater.

Bayesian estimation of a source term of radiation release with approximately known nuclide ratios

NASA Astrophysics Data System (ADS)

Tichý, Ondřej; Šmídl, Václav; Hofman, Radek

2016-04-01

We are concerned with estimation of a source term in case of an accidental release from a known location, e.g. a power plant. Usually, the source term of an accidental release of radiation comprises of a mixture of nuclide. The gamma dose rate measurements do not provide a direct information on the source term composition. However, physical properties of respective nuclide (deposition properties, decay half-life) can be used when uncertain information on nuclide ratios is available, e.g. from known reactor inventory. The proposed method is based on linear inverse model where the observation vector y arise as a linear combination y = Mx of a source-receptor-sensitivity (SRS) matrix M and the source term x. The task is to estimate the unknown source term x. The problem is ill-conditioned and further regularization is needed to obtain a reasonable solution. In this contribution, we assume that nuclide ratios of the release is known with some degree of uncertainty. This knowledge is used to form the prior covariance matrix of the source term x. Due to uncertainty in the ratios the diagonal elements of the covariance matrix are considered to be unknown. Positivity of the source term estimate is guaranteed by using multivariate truncated Gaussian distribution. Following Bayesian approach, we estimate all parameters of the model from the data so that y, M, and known ratios are the only inputs of the method. Since the inference of the model is intractable, we follow the Variational Bayes method yielding an iterative algorithm for estimation of all model parameters. Performance of the method is studied on simulated 6 hour power plant release where 3 nuclide are released and 2 nuclide ratios are approximately known. The comparison with method with unknown nuclide ratios will be given to prove the usefulness of the proposed approach. This research is supported by EEA/Norwegian Financial Mechanism under project MSMT-28477/2014 Source-Term Determination of Radionuclide Releases by Inverse Atmospheric Dispersion Modelling (STRADI).

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake.

PubMed

Grandjean, Thomas R B; Chappell, Michael J; Yates, James W T; Evans, Neil D

2014-05-01

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available. Copyright © 2013. Published by Elsevier Ireland Ltd.

Mesoscopic modeling and parameter estimation of a lithium-ion battery based on LiFePO4/graphite

NASA Astrophysics Data System (ADS)

Jokar, Ali; Désilets, Martin; Lacroix, Marcel; Zaghib, Karim

2018-03-01

A novel numerical model for simulating the behavior of lithium-ion batteries based on LiFePO4(LFP)/graphite is presented. The model is based on the modified Single Particle Model (SPM) coupled to a mesoscopic approach for the LFP electrode. The model comprises one representative spherical particle as the graphite electrode, and N LFP units as the positive electrode. All the SPM equations are retained to model the negative electrode performance. The mesoscopic model rests on non-equilibrium thermodynamic conditions and uses a non-monotonic open circuit potential for each unit. A parameter estimation study is also carried out to identify all the parameters needed for the model. The unknown parameters are the solid diffusion coefficient of the negative electrode (Ds,n), reaction-rate constant of the negative electrode (Kn), negative and positive electrode porosity (εn&εn), initial State-Of-Charge of the negative electrode (SOCn,0), initial partial composition of the LFP units (yk,0), minimum and maximum resistance of the LFP units (Rmin&Rmax), and solution resistance (Rcell). The results show that the mesoscopic model can simulate successfully the electrochemical behavior of lithium-ion batteries at low and high charge/discharge rates. The model also describes adequately the lithiation/delithiation of the LFP particles, however, it is computationally expensive compared to macro-based models.

Non-cavitating propeller noise modeling and inversion

NASA Astrophysics Data System (ADS)

Kim, Dongho; Lee, Keunhwa; Seong, Woojae

2014-12-01

Marine propeller is the dominant exciter of the hull surface above it causing high level of noise and vibration in the ship structure. Recent successful developments have led to non-cavitating propeller designs and thus present focus is the non-cavitating characteristics of propeller such as hydrodynamic noise and its induced hull excitation. In this paper, analytic source model of propeller non-cavitating noise, described by longitudinal quadrupoles and dipoles, is suggested based on the propeller hydrodynamics. To find the source unknown parameters, the multi-parameter inversion technique is adopted using the pressure data obtained from the model scale experiment and pressure field replicas calculated by boundary element method. The inversion results show that the proposed source model is appropriate in modeling non-cavitating propeller noise. The result of this study can be utilized in the prediction of propeller non-cavitating noise and hull excitation at various stages in design and analysis.

Kron-Branin modelling of ultra-short pulsed signal microelectrode

NASA Astrophysics Data System (ADS)

Xu, Zhifei; Ravelo, Blaise; Liu, Yang; Zhao, Lu; Delaroche, Fabien; Vurpillot, Francois

2018-06-01

An uncommon circuit modelling of microelectrode for ultra-short signal propagation is developed. The proposed model is based on the Tensorial Analysis of Network (TAN) using the Kron-Branin (KB) formalism. The systemic graph topology equivalent to the considered structure problem is established by assuming as unknown variables the branch currents. The TAN mathematical solution is determined after the KB characteristic matrix identification. The TAN can integrate various structure physical parameters. As proof of concept, via hole ended microelectrodes implemented on Kapton substrate were designed, fabricated and tested. The 0.1-MHz-to-6-GHz S-parameter KB model, simulation and measurement are in good agreement. In addition, time-domain analyses with nanosecond duration pulse signals were carried out to predict the microelectrode signal integrity. The modelled microstrip electrode is usually integrated in the atom probe tomography. The proposed unfamiliar KB method is particularly beneficial with respect to the computation speed and adaptability to various structures.

Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics.

PubMed

Sokoloski, Sacha

2017-09-01

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

2008-05-15

We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

Chaotic dynamics in the (47171) Lempo triple system

NASA Astrophysics Data System (ADS)

Correia, Alexandre C. M.

2018-05-01

We investigate the dynamics of the (47171) Lempo triple system, also known by 1999 TC36. We derive a full 3D N-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution for the Lempo system is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of the Lempo system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.

Identifying quantum phase transitions with adversarial neural networks

NASA Astrophysics Data System (ADS)

Huembeli, Patrick; Dauphin, Alexandre; Wittek, Peter

2018-04-01

The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. Traditionally, physicists have to identify the relevant order parameters for the classification of the different phases. We here follow a radically different approach: we address this problem with a state-of-the-art deep learning technique, adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. This method has the advantage that the input of the algorithm can be directly the ground state without any ad hoc feature engineering. Furthermore, the dimension of the parameter space is unrestricted. More specifically, the input data set contains both labeled and unlabeled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the Su-Schrieffer-Heeger model with disorder. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phase boundaries are complex such as the many-body localization problem or the Bose glass phase.

Hierarchial mark-recapture models: a framework for inference about demographic processes

USGS Publications Warehouse

Link, W.A.; Barker, R.J.

2004-01-01

The development of sophisticated mark-recapture models over the last four decades has provided fundamental tools for the study of wildlife populations, allowing reliable inference about population sizes and demographic rates based on clearly formulated models for the sampling processes. Mark-recapture models are now routinely described by large numbers of parameters. These large models provide the next challenge to wildlife modelers: the extraction of signal from noise in large collections of parameters. Pattern among parameters can be described by strong, deterministic relations (as in ultrastructural models) but is more flexibly and credibly modeled using weaker, stochastic relations. Trend in survival rates is not likely to be manifest by a sequence of values falling precisely on a given parametric curve; rather, if we could somehow know the true values, we might anticipate a regression relation between parameters and explanatory variables, in which true value equals signal plus noise. Hierarchical models provide a useful framework for inference about collections of related parameters. Instead of regarding parameters as fixed but unknown quantities, we regard them as realizations of stochastic processes governed by hyperparameters. Inference about demographic processes is based on investigation of these hyperparameters. We advocate the Bayesian paradigm as a natural, mathematically and scientifically sound basis for inference about hierarchical models. We describe analysis of capture-recapture data from an open population based on hierarchical extensions of the Cormack-Jolly-Seber model. In addition to recaptures of marked animals, we model first captures of animals and losses on capture, and are thus able to estimate survival probabilities w (i.e., the complement of death or permanent emigration) and per capita growth rates f (i.e., the sum of recruitment and immigration rates). Covariation in these rates, a feature of demographic interest, is explicitly described in the model.

Optimization of a Thermodynamic Model Using a Dakota Toolbox Interface

NASA Astrophysics Data System (ADS)

Cyrus, J.; Jafarov, E. E.; Schaefer, K. M.; Wang, K.; Clow, G. D.; Piper, M.; Overeem, I.

2016-12-01

Scientific modeling of the Earth physical processes is an important driver of modern science. The behavior of these scientific models is governed by a set of input parameters. It is crucial to choose accurate input parameters that will also preserve the corresponding physics being simulated in the model. In order to effectively simulate real world processes the models output data must be close to the observed measurements. To achieve this optimal simulation, input parameters are tuned until we have minimized the objective function, which is the error between the simulation model outputs and the observed measurements. We developed an auxiliary package, which serves as a python interface between the user and DAKOTA. The package makes it easy for the user to conduct parameter space explorations, parameter optimizations, as well as sensitivity analysis while tracking and storing results in a database. The ability to perform these analyses via a Python library also allows the users to combine analysis techniques, for example finding an approximate equilibrium with optimization then immediately explore the space around it. We used the interface to calibrate input parameters for the heat flow model, which is commonly used in permafrost science. We performed optimization on the first three layers of the permafrost model, each with two thermal conductivity coefficients input parameters. Results of parameter space explorations indicate that the objective function not always has a unique minimal value. We found that gradient-based optimization works the best for the objective functions with one minimum. Otherwise, we employ more advanced Dakota methods such as genetic optimization and mesh based convergence in order to find the optimal input parameters. We were able to recover 6 initially unknown thermal conductivity parameters within 2% accuracy of their known values. Our initial tests indicate that the developed interface for the Dakota toolbox could be used to perform analysis and optimization on a `black box' scientific model more efficiently than using just Dakota.

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Structural Identifiability of Dynamic Systems Biology Models

PubMed Central

Villaverde, Alejandro F.

2016-01-01

A powerful way of gaining insight into biological systems is by creating a nonlinear differential equation model, which usually contains many unknown parameters. Such a model is called structurally identifiable if it is possible to determine the values of its parameters from measurements of the model outputs. Structural identifiability is a prerequisite for parameter estimation, and should be assessed before exploiting a model. However, this analysis is seldom performed due to the high computational cost involved in the necessary symbolic calculations, which quickly becomes prohibitive as the problem size increases. In this paper we show how to analyse the structural identifiability of a very general class of nonlinear models by extending methods originally developed for studying observability. We present results about models whose identifiability had not been previously determined, report unidentifiabilities that had not been found before, and show how to modify those unidentifiable models to make them identifiable. This method helps prevent problems caused by lack of identifiability analysis, which can compromise the success of tasks such as experiment design, parameter estimation, and model-based optimization. The procedure is called STRIKE-GOLDD (STRuctural Identifiability taKen as Extended-Generalized Observability with Lie Derivatives and Decomposition), and it is implemented in a MATLAB toolbox which is available as open source software. The broad applicability of this approach facilitates the analysis of the increasingly complex models used in systems biology and other areas. PMID:27792726

System parameter identification from projection of inverse analysis

NASA Astrophysics Data System (ADS)

Liu, K.; Law, S. S.; Zhu, X. Q.

2017-05-01

The output of a system due to a change of its parameters is often approximated with the sensitivity matrix from the first order Taylor series. The system output can be measured in practice, but the perturbation in the system parameters is usually not available. Inverse sensitivity analysis can be adopted to estimate the unknown system parameter perturbation from the difference between the observation output data and corresponding analytical output data calculated from the original system model. The inverse sensitivity analysis is re-visited in this paper with improvements based on the Principal Component Analysis on the analytical data calculated from the known system model. The identification equation is projected into a subspace of principal components of the system output, and the sensitivity of the inverse analysis is improved with an iterative model updating procedure. The proposed method is numerical validated with a planar truss structure and dynamic experiments with a seven-storey planar steel frame. Results show that it is robust to measurement noise, and the location and extent of stiffness perturbation can be identified with better accuracy compared with the conventional response sensitivity-based method.

Quantification of the impact of precipitation spatial distribution uncertainty on predictive uncertainty of a snowmelt runoff model

NASA Astrophysics Data System (ADS)

Jacquin, A. P.

2012-04-01

This study is intended to quantify the impact of uncertainty about precipitation spatial distribution on predictive uncertainty of a snowmelt runoff model. This problem is especially relevant in mountain catchments with a sparse precipitation observation network and relative short precipitation records. The model analysed is a conceptual watershed model operating at a monthly time step. The model divides the catchment into five elevation zones, where the fifth zone corresponds to the catchment's glaciers. Precipitation amounts at each elevation zone i are estimated as the product between observed precipitation at a station and a precipitation factor FPi. If other precipitation data are not available, these precipitation factors must be adjusted during the calibration process and are thus seen as parameters of the model. In the case of the fifth zone, glaciers are seen as an inexhaustible source of water that melts when the snow cover is depleted.The catchment case study is Aconcagua River at Chacabuquito, located in the Andean region of Central Chile. The model's predictive uncertainty is measured in terms of the output variance of the mean squared error of the Box-Cox transformed discharge, the relative volumetric error, and the weighted average of snow water equivalent in the elevation zones at the end of the simulation period. Sobol's variance decomposition (SVD) method is used for assessing the impact of precipitation spatial distribution, represented by the precipitation factors FPi, on the models' predictive uncertainty. In the SVD method, the first order effect of a parameter (or group of parameters) indicates the fraction of predictive uncertainty that could be reduced if the true value of this parameter (or group) was known. Similarly, the total effect of a parameter (or group) measures the fraction of predictive uncertainty that would remain if the true value of this parameter (or group) was unknown, but all the remaining model parameters could be fixed. In this study, first order and total effects of the group of precipitation factors FP1- FP4, and the precipitation factor FP5, are calculated separately. First order and total effects of the group FP1- FP4 are much higher than first order and total effects of the factor FP5, which are negligible This situation is due to the fact that the actual value taken by FP5 does not have much influence in the contribution of the glacier zone to the catchment's output discharge, mainly limited by incident solar radiation. In addition to this, first order effects indicate that, in average, nearly 25% of predictive uncertainty could be reduced if the true values of the precipitation factors FPi could be known, but no information was available on the appropriate values for the remaining model parameters. Finally, the total effects of the precipitation factors FP1- FP4 are close to 41% in average, implying that even if the appropriate values for the remaining model parameters could be fixed, predictive uncertainty would be still quite high if the spatial distribution of precipitation remains unknown. Acknowledgements: This research was funded by FONDECYT, Research Project 1110279.

Global 3ν oscillation analysis: Status of unknown parameters and future systematic challenges for ORCA and PINGU

NASA Astrophysics Data System (ADS)

Capozzi, Francesco; Lisi, Eligio; Marrone, Antonio

2016-04-01

Within the standard 3ν oscillation framework, we illustrate the status of currently unknown oscillation parameters: the θ23 octant, the mass hierarchy (normal or inverted), and the possible CP-violating phase δ, as derived by a (preliminary) global analysis of oscillation data available in 2015. We then discuss some challenges that will be faced by future, high-statistics analyses of spectral data, starting with one-dimensional energy spectra in reactor experiments, and concluding with two-dimensional energy-angle spectra in large-volume atmospheric experiments. It is shown that systematic uncertainties in the spectral shapes can noticeably affect the prospective sensitivities to unknown oscillation parameters, in particular to the mass hierarchy.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Reason, emotion and decision-making: risk and reward computation with feeling.

PubMed

Quartz, Steven R

2009-05-01

Many models of judgment and decision-making posit distinct cognitive and emotional contributions to decision-making under uncertainty. Cognitive processes typically involve exact computations according to a cost-benefit calculus, whereas emotional processes typically involve approximate, heuristic processes that deliver rapid evaluations without mental effort. However, it remains largely unknown what specific parameters of uncertain decision the brain encodes, the extent to which these parameters correspond to various decision-making frameworks, and their correspondence to emotional and rational processes. Here, I review research suggesting that emotional processes encode in a precise quantitative manner the basic parameters of financial decision theory, indicating a reorientation of emotional and cognitive contributions to risky choice.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

PubMed

Vernon, Ian; Liu, Junli; Goldstein, Michael; Rowe, James; Topping, Jen; Lindsey, Keith

2018-01-02

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

Market-Based Coordination of Thermostatically Controlled Loads—Part II: Unknown Parameters and Case Studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Sen; Zhang, Wei; Lian, Jianming

This two-part paper considers the coordination of a population of Thermostatically Controlled Loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the bidding and market clearing strategy to motivate self-interested users to realize efficient energy allocation subject to a peak power constraint. The companion paper (Part I) formulates the problem and proposes a load coordination framework using the mechanism design approach. To address the unknown parameters, Part II of this paper presents a joint state and parameter estimation framework based on the expectation maximization algorithm. The overall framework is then validated using real-world weather data andmore » price data, and is compared with other approaches in terms of aggregated power response. Simulation results indicate that our coordination framework can effectively improve the efficiency of the power grid operations and reduce power congestion at key times.« less

Genetic algorithm based input selection for a neural network function approximator with applications to SSME health monitoring

NASA Technical Reports Server (NTRS)

Peck, Charles C.; Dhawan, Atam P.; Meyer, Claudia M.

1991-01-01

A genetic algorithm is used to select the inputs to a neural network function approximator. In the application considered, modeling critical parameters of the space shuttle main engine (SSME), the functional relationship between measured parameters is unknown and complex. Furthermore, the number of possible input parameters is quite large. Many approaches have been used for input selection, but they are either subjective or do not consider the complex multivariate relationships between parameters. Due to the optimization and space searching capabilities of genetic algorithms they were employed to systematize the input selection process. The results suggest that the genetic algorithm can generate parameter lists of high quality without the explicit use of problem domain knowledge. Suggestions for improving the performance of the input selection process are also provided.

Spectrophotometric properties of Moon's and Mars's surfaces exploration by shadow mechanism

NASA Astrophysics Data System (ADS)

Morozhenko, Alexandr; Vidmachenko, Anatolij; Kostogryz, Nadiia

2015-03-01

Typically, to analyze the data of the phase dependence of brightness atmosphereless celestial bodies one use some modification of the shadow mechanism involving the coherent mechanism. There are several modification of B.Hapke [2] model divided into two groups by the number of unknown parameters: the first one with 4 parameters [3,4] and the second one with up to 10 unknown parameters [1] providing a good agreement of observations and calculations in several wavelengths. However, they are complicated by analysing of the colorindex C(α) dependence and photometric contrast of details with phase K(α) and on the disk (μ o = cos i). We have got good agreement between observed and calculated values of C(α) = U(α)-I(α), K(α), K(muo) for Moon and Mars with a minimum number of unknown parameters [4]. We used an empirical dependence of single scattering albedo (ω) and particle semi-transparency(æ): æ = (1-ω)n. Assuming that [χ (0°)/χ(5°)] = χ (5°)/χ (0°)], where χ(α) is scattering function, using the phase dependence of brightness and opposition effect in a single wavelength, we have defined ω,χ(α),g (particle packing factor), and the first term expansion of χ(α) in a series of Legendre polynomials x1. Good agreement between calculated and observed data of C(α) = U(α)-I(α) for the light and dark parts of the lunar surface and the integral disk reached at n ~ 0,25, g = 0,4 (porosity 0,91), x1 = -0,93, ω = 0,137 at λ = 359nm and 0,394 at λ = 1064nm;, for Mars with n ~ 0,25,g = 0,6 (porosity 0,84), x1 ~ 0, ω = 0,210 at λ = 359nm and ω = 0,784 at λ = 730nm. 1. Bowell E., Hapke B., Domingue D., Lumme K., et al. Applications of photometric models to asteroids, in Asteroids II. Tucson: Univ. Arizona Press. p.524-556. (1989) 2. Hapke B. A theoretical function for the lunar surface, J.Geophys.Res. 68, No.15., 4571-4586(1963). 3. Irwine W. M., The shadowing effect in diffuse reflection, J.Geophys.Res. 71,No.12, 2931-2937(1966). 4. Morozhenko A. V., Yanovitskij E.G., An optical model of the Martian surface in the visible region of spectrum, Astronomy Reports 48, No.4, 795-809(1971).

Friction Compensation for Enhancing Transparency of a Teleoperator with Compliant Transmission

PubMed Central

Mahvash, Mohsen; Okamura, Allison

2009-01-01

This article presents a model-based compensator for canceling friction in the tendon-driven joints of a haptic-feedback teleoperator. Unlike position-tracking systems, a teleoperator involves an unknown environment force that prevents the use of tracking position error as a feedback to the compensator. Thus, we use a model-based feedforward friction compensator to cancel the friction forces. We provide conditions for selecting compensator parameters to ensure passivity of the teleoperator and demonstrate performance experimentally. PMID:20514151

Nonparametric Transfer Function Models

PubMed Central

Liu, Jun M.; Chen, Rong; Yao, Qiwei

2009-01-01

In this paper a class of nonparametric transfer function models is proposed to model nonlinear relationships between ‘input’ and ‘output’ time series. The transfer function is smooth with unknown functional forms, and the noise is assumed to be a stationary autoregressive-moving average (ARMA) process. The nonparametric transfer function is estimated jointly with the ARMA parameters. By modeling the correlation in the noise, the transfer function can be estimated more efficiently. The parsimonious ARMA structure improves the estimation efficiency in finite samples. The asymptotic properties of the estimators are investigated. The finite-sample properties are illustrated through simulations and one empirical example. PMID:20628584

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

NASA Astrophysics Data System (ADS)

Kolev, M.; Nawrocki, S.; Zubik-Kowal, B.

2013-06-01

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.

Distributed adaptive asymptotically consensus tracking control of uncertain Euler-Lagrange systems under directed graph condition.

PubMed

Wang, Wei; Wen, Changyun; Huang, Jiangshuai; Fan, Huijin

2017-11-01

In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The Approximate Bayesian Computation methods in the localization of the atmospheric contamination source

NASA Astrophysics Data System (ADS)

Kopka, P.; Wawrzynczak, A.; Borysiewicz, M.

2015-09-01

In many areas of application, a central problem is a solution to the inverse problem, especially estimation of the unknown model parameters to model the underlying dynamics of a physical system precisely. In this situation, the Bayesian inference is a powerful tool to combine observed data with prior knowledge to gain the probability distribution of searched parameters. We have applied the modern methodology named Sequential Approximate Bayesian Computation (S-ABC) to the problem of tracing the atmospheric contaminant source. The ABC is technique commonly used in the Bayesian analysis of complex models and dynamic system. Sequential methods can significantly increase the efficiency of the ABC. In the presented algorithm, the input data are the on-line arriving concentrations of released substance registered by distributed sensor network from OVER-LAND ATMOSPHERIC DISPERSION (OLAD) experiment. The algorithm output are the probability distributions of a contamination source parameters i.e. its particular location, release rate, speed and direction of the movement, start time and duration. The stochastic approach presented in this paper is completely general and can be used in other fields where the parameters of the model bet fitted to the observable data should be found.

SU-E-J-252: A Motion Algorithm to Extract Physical and Motion Parameters of a Mobile Target in Cone-Beam Computed Tomographic Imaging Retrospective to Image Reconstruction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ali, I; Ahmad, S; Alsbou, N

Purpose: A motion algorithm was developed to extract actual length, CT-numbers and motion amplitude of a mobile target imaged with cone-beam-CT (CBCT) retrospective to image-reconstruction. Methods: The motion model considered a mobile target moving with a sinusoidal motion and employed three measurable parameters: apparent length, CT number level and gradient of a mobile target obtained from CBCT images to extract information about the actual length and CT number value of the stationary target and motion amplitude. The algorithm was verified experimentally with a mobile phantom setup that has three targets with different sizes manufactured from homogenous tissue-equivalent gel material embeddedmore » into a thorax phantom. The phantom moved sinusoidal in one-direction using eight amplitudes (0–20mm) and a frequency of 15-cycles-per-minute. The model required imaging parameters such as slice thickness, imaging time. Results: This motion algorithm extracted three unknown parameters: length of the target, CT-number-level, motion amplitude for a mobile target retrospective to CBCT image reconstruction. The algorithm relates three unknown parameters to measurable apparent length, CT-number-level and gradient for well-defined mobile targets obtained from CBCT images. The motion model agreed with measured apparent lengths which were dependent on actual length of the target and motion amplitude. The cumulative CT-number for a mobile target was dependent on CT-number-level of the stationary target and motion amplitude. The gradient of the CT-distribution of mobile target is dependent on the stationary CT-number-level, actual target length along the direction of motion, and motion amplitude. Motion frequency and phase did not affect the elongation and CT-number distributions of mobile targets when imaging time included several motion cycles. Conclusion: The motion algorithm developed in this study has potential applications in diagnostic CT imaging and radiotherapy to extract actual length, size and CT-numbers distorted by motion in CBCT imaging. The model provides further information about motion of the target.« less

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

PubMed

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

NASA Astrophysics Data System (ADS)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

Stability of neutrino parameters and self-complementarity relation with varying SUSY breaking scale

NASA Astrophysics Data System (ADS)

Singh, K. Sashikanta; Roy, Subhankar; Singh, N. Nimai

2018-03-01

The scale at which supersymmetry (SUSY) breaks (ms) is still unknown. The present article, following a top-down approach, endeavors to study the effect of varying ms on the radiative stability of the observational parameters associated with the neutrino mixing. These parameters get additional contributions in the minimal supersymmetric model (MSSM). A variation in ms will influence the bounds for which the Standard Model (SM) and MSSM work and hence, will account for the different radiative contributions received from both sectors, respectively, while running the renormalization group equations (RGE). The present work establishes the invariance of the self complementarity relation among the three mixing angles, θ13+θ12≈θ23 against the radiative evolution. A similar result concerning the mass ratio, m2:m1 is also found to be valid. In addition to varying ms, the work incorporates a range of different seesaw (SS) scales and tries to see how the latter affects the parameters.

Design of experiment for earth rotation and baseline parameter determination from very long baseline interferometry

NASA Technical Reports Server (NTRS)

Dermanis, A.

1977-01-01

The possibility of recovering earth rotation and network geometry (baseline) parameters are emphasized. The numerical simulated experiments performed are set up in an environment where station coordinates vary with respect to inertial space according to a simulated earth rotation model similar to the actual but unknown rotation of the earth. The basic technique of VLBI and its mathematical model are presented. The parametrization of earth rotation chosen is described and the resulting model is linearized. A simple analysis of the geometry of the observations leads to some useful hints on achieving maximum sensitivity of the observations with respect to the parameters considered. The basic philosophy for the simulation of data and their analysis through standard least squares adjustment techniques is presented. A number of characteristic network designs based on present and candidate station locations are chosen. The results of the simulations for each design are presented together with a summary of the conclusions.

ESTIMATION OF CONSTANT AND TIME-VARYING DYNAMIC PARAMETERS OF HIV INFECTION IN A NONLINEAR DIFFERENTIAL EQUATION MODEL.

PubMed

Liang, Hua; Miao, Hongyu; Wu, Hulin

2010-03-01

Modeling viral dynamics in HIV/AIDS studies has resulted in deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper, we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies. We applied the proposed techniques to estimate the key HIV viral dynamic parameters for two individual AIDS patients treated with antiretroviral therapies. We demonstrate that HIV viral dynamics can be well characterized and quantified for individual patients. As a result, personalized treatment decision based on viral dynamic models is possible.

Three-dimensional whole-brain perfusion quantification using pseudo-continuous arterial spin labeling MRI at multiple post-labeling delays: accounting for both arterial transit time and impulse response function.

PubMed

Qin, Qin; Huang, Alan J; Hua, Jun; Desmond, John E; Stevens, Robert D; van Zijl, Peter C M

2014-02-01

Measurement of the cerebral blood flow (CBF) with whole-brain coverage is challenging in terms of both acquisition and quantitative analysis. In order to fit arterial spin labeling-based perfusion kinetic curves, an empirical three-parameter model which characterizes the effective impulse response function (IRF) is introduced, which allows the determination of CBF, the arterial transit time (ATT) and T(1,eff). The accuracy and precision of the proposed model were compared with those of more complicated models with four or five parameters through Monte Carlo simulations. Pseudo-continuous arterial spin labeling images were acquired on a clinical 3-T scanner in 10 normal volunteers using a three-dimensional multi-shot gradient and spin echo scheme at multiple post-labeling delays to sample the kinetic curves. Voxel-wise fitting was performed using the three-parameter model and other models that contain two, four or five unknown parameters. For the two-parameter model, T(1,eff) values close to tissue and blood were assumed separately. Standard statistical analysis was conducted to compare these fitting models in various brain regions. The fitted results indicated that: (i) the estimated CBF values using the two-parameter model show appreciable dependence on the assumed T(1,eff) values; (ii) the proposed three-parameter model achieves the optimal balance between the goodness of fit and model complexity when compared among the models with explicit IRF fitting; (iii) both the two-parameter model using fixed blood T1 values for T(1,eff) and the three-parameter model provide reasonable fitting results. Using the proposed three-parameter model, the estimated CBF (46 ± 14 mL/100 g/min) and ATT (1.4 ± 0.3 s) values averaged from different brain regions are close to the literature reports; the estimated T(1,eff) values (1.9 ± 0.4 s) are higher than the tissue T1 values, possibly reflecting a contribution from the microvascular arterial blood compartment. Copyright © 2013 John Wiley & Sons, Ltd.

Optimized tuner selection for engine performance estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L. (Inventor); Garg, Sanjay (Inventor)

2013-01-01

A methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented. This technique specifically addresses the underdetermined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine which seeks to minimize the theoretical mean-squared estimation error. Theoretical Kalman filter estimation error bias and variance values are derived at steady-state operating conditions, and the tuner selection routine is applied to minimize these values. The new methodology yields an improvement in on-line engine performance estimation accuracy.

Lyapunov function-based control laws for revolute robot arms - Tracking control, robustness, and adaptive control

NASA Technical Reports Server (NTRS)

Wen, John T.; Kreutz-Delgado, Kenneth; Bayard, David S.

1992-01-01

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to a recently proposed energy-like Liapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates (i.e., certainty equivalence adaptation).

Adaptive control based on retrospective cost optimization

NASA Technical Reports Server (NTRS)

Bernstein, Dennis S. (Inventor); Santillo, Mario A. (Inventor)

2012-01-01

A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.

A neuroeconomic theory of rational addiction and nonlinear time-perception.

PubMed

Takahashi, Taiki

2011-01-01

Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal cognition corresponds to the degree of irrationality (i.e., Prelec's "decreasing impatience" parameter of temporal discounting) and (ii) rationality in addicts is controlled by a nondimensionalization parameter of the logarithmic time-perception function. Furthermore, the present theory illustrates the possibility that addictive drugs increase impulsivity via dopaminergic neuroadaptation without increasing irrationality. Future directions in the application of the model to studies in neuroeconomics are discussed.

Interacting Winds in Eclipsing Symbiotic Systems - The Case Study of EG Andromedae

NASA Astrophysics Data System (ADS)

Calabrò, Emanuele

2014-03-01

We report the mathematical representation of the so called eccentric eclipse model, whose numerical solutions can be used to obtain the physical parameters of a quiescent eclipsing symbiotic system. Indeed the nebular region produced by the collision of the stellar winds should be shifted to the orbital axis because of the orbital motion of the system. This mechanism is not negligible, and it led us to modify the classical concept of an eclipse. The orbital elements obtained from spectroscopy and photometry of the symbiotic EG Andromedae were used to test the eccentric eclipse model. Consistent values for the unknown orbital elements of this symbiotic were obtained. The physical parameters are in agreement with those obtained by means of other simulations for this system.

The contribution of NOAA/CMDL ground-based measurements to understanding long-term stratospheric changes

NASA Astrophysics Data System (ADS)

Montzka, S. A.; Butler, J. H.; Dutton, G.; Thompson, T. M.; Hall, B.; Mondeel, D. J.; Elkins, J. W.

2005-05-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

Study the Seasonal Variability of Plankton and Forage Fish in the Gulf of Khambhat Using Npzfd Model

NASA Astrophysics Data System (ADS)

Kumar, V.; Kumar, S.

2016-02-01

Numerical modelling of marine ecology exploits several assumptions and it is indeed quite challenging to include marine ecological phenomena into a mathematical framework with too many unknown parameters. The governing ordinary differential equations represent the interaction of the biological and chemical processes in a marine environment. The key concern in the development of a numerical models are parameterizations based on output, viz., mathematical modelling of ecological system mainly depends on parameters and its variations. Almost, all constituents of each trophic level of marine food web are depended on phytoplankton, which are mostly influenced by initial slope of P-I curve and nutrient stock in the study domain. Whereas, the earlier plankton dynamic models rarely include a compartment of small fish and as an agent in zooplankton mortality, which is most important for the modelling of higher trophic level of marine species. A compartment of forage fish in the modelling of plankton dynamics has been given more realistic mortality rates of plankton, viz., they feed upon phytoplankton and zooplankton. The inclusion of an additional compartment increases complexity of earlier plankton dynamics model as it introduces additional unknown parameters, which has been specified for performing the numerical simulations.As a case study we applied our analysis to explain the aquatic ecology of Gulf of Khambhat (19o 48' N - 22o20' N, 65o E - 72o40' E), west coast of India, which has rich bio-diversity and a high productive area in the form of plankton and forage fish. It has elevated turbidity and varying geography location, viz., one of the regions among world's ocean with high biological productivity.The model presented in this study is able to bring out the essential features of the observed data; that includes the bimodal oscillations in the observed data, monthly mean chlorophyll-a in the SeaWiFs/MODIS Aqua data and in-situ data of plankton. The additional compartment of forage fish and detritus in NPZFD model represents a major structural difference from the earlier NPZ model.

Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review.

PubMed

Bodgi, Larry; Canet, Aurélien; Pujo-Menjouet, Laurent; Lesne, Annick; Victor, Jean-Marc; Foray, Nicolas

2016-04-07

Cell survival is conventionally defined as the capability of irradiated cells to produce colonies. It is quantified by the clonogenic assays that consist in determining the number of colonies resulting from a known number of irradiated cells. Several mathematical models were proposed to describe the survival curves, notably from the target theory. The Linear-Quadratic (LQ) model, which is to date the most frequently used model in radiobiology and radiotherapy, dominates all the other models by its robustness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and β, on which it is based, predicts the occurrence of post-irradiation tissue reactions. However, the biological interpretation of these parameters is still unknown. Throughout this review, we revisit and discuss historically, mathematically and biologically, the different models of the radiation action by providing clues for resolving the enigma of the LQ model. Copyright © 2016 Elsevier Ltd. All rights reserved.

A physiologically based model for tramadol pharmacokinetics in horses.

PubMed

Abbiati, Roberto Andrea; Cagnardi, Petra; Ravasio, Giuliano; Villa, Roberto; Manca, Davide

2017-09-21

This work proposes an application of a minimal complexity physiologically based pharmacokinetic model to predict tramadol concentration vs time profiles in horses. Tramadol is an opioid analgesic also used for veterinary treatments. Researchers and medical doctors can profit from the application of mathematical models as supporting tools to optimize the pharmacological treatment of animal species. The proposed model is based on physiology but adopts the minimal compartmental architecture necessary to describe the experimental data. The model features a system of ordinary differential equations, where most of the model parameters are either assigned or individualized for a given horse, using literature data and correlations. Conversely, residual parameters, whose value is unknown, are regressed exploiting experimental data. The model proved capable of simulating pharmacokinetic profiles with accuracy. In addition, it provides further insights on un-observable tramadol data, as for instance tramadol concentration in the liver or hepatic metabolism and renal excretion extent. Copyright © 2017 Elsevier Ltd. All rights reserved.

An evaluation of the predictive capabilities of CTRW and MRMT

NASA Astrophysics Data System (ADS)

Fiori, Aldo; Zarlenga, Antonio; Gotovac, Hrvoje; Jankovic, Igor; Cvetkovic, Vladimir; Dagan, Gedeon

2016-04-01

The prediction capability of two approximate models of non-Fickian transport in highly heterogeneous aquifers is checked by comparison with accurate numerical simulations, for mean uniform flow of velocity U. The two models considered are the MRMT (Multi Rate Mass Transfer) and CTRW (Continuous Time Random Walk) models. Both circumvent the need to solve the flow and transport equations by using proxy models, which provide the BTC μ(x,t) depending on a vector a of unknown 5 parameters. Although underlain by different conceptualisations, the two models have a similar mathematical structure. The proponents of the models suggest using field transport experiments at a small scale to calibrate a, toward predicting transport at larger scale. The strategy was tested with the aid of accurate numerical simulations in two and three dimensions from the literature. First, the 5 parameter values were calibrated by using the simulated μ at a control plane close to the injection one and subsequently using these same parameters for predicting μ at further 10 control planes. It is found that the two methods perform equally well, though the parameters identification is nonunique, with a large set of parameters providing similar fitting. Also, errors in the determination of the mean eulerian velocity may lead to significant shifts of the predicted BTC. It is found that the simulated BTCs satisfy Markovianity: they can be found as n-fold convolutions of a "kernel", in line with the models' main assumption.

Domain Derivatives in Dielectric Rough Surface Scattering

DTIC Science & Technology

2015-01-01

and require the gradient of the objective function in the unknown model parameter vector at each stage of iteration. For large N, finite...differencing becomes numerically intensive, and an efficient alternative is domain differentiation in which the full gradient is obtained by solving a single...derivative calculation of the gradient for a locally perturbed dielectric interface. The method is non-variational, and algebraic in nature in that it

Quiet breathing in hindlimb casted mice.

PubMed

Receno, Candace N; Roffo, Katelynn E; Mickey, Marisa C; DeRuisseau, Keith C; DeRuisseau, Lara R

2018-06-07

The hindlimb casting model was developed to study skeletal muscle reloading following a period of unloading. It is unknown if ventilation parameters of mice are affected by the casting model. We tested the hypothesis that hindlimb casted mice have similar ventilatory patterns compared to mice with the casts removed. Male CD-1 mice underwent 14 days of hindlimb immobilization via plaster casting. Breathing parameters were obtained utilizing unrestrained barometric plethysmography (UBP). Breathing traces were analyzed with Ponemah software for breathing frequency, tidal volume (TV), and minute ventilation (MV). Frequency, TV and MV did not show any differences in quiet breathing patterns during or post-casting in mice. Thus, the hindlimb casting model does not complicate breathing during and after casting and should not interfere with the unloading and reloading of skeletal muscle. Copyright © 2018 Elsevier B.V. All rights reserved.

Tune-stabilized, non-scaling, fixed-field, alternating gradient accelerator

DOEpatents

Johnstone, Carol J [Warrenville, IL

2011-02-01

A FFAG is a particle accelerator having turning magnets with a linear field gradient for confinement and a large edge angle to compensate for acceleration. FODO cells contain focus magnets and defocus magnets that are specified by a number of parameters. A set of seven equations, called the FFAG equations relate the parameters to one another. A set of constraints, call the FFAG constraints, constrain the FFAG equations. Selecting a few parameters, such as injection momentum, extraction momentum, and drift distance reduces the number of unknown parameters to seven. Seven equations with seven unknowns can be solved to yield the values for all the parameters and to thereby fully specify a FFAG.

New techniques for the analysis of manual control systems. [mathematical models of human operator behavior

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.

A flowsheet model of a well-mixed fluidized bed dryer: Applications in controllability assessment and optimization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langrish, T.A.G.; Harvey, A.C.

2000-01-01

A model of a well-mixed fluidized-bed dryer within a process flowsheeting package (SPEEDUP{trademark}) has been developed and applied to a parameter sensitivity study, a steady-state controllability analysis and an optimization study. This approach is more general and would be more easily applied to a complex flowsheet than one which relied on stand-alone dryer modeling packages. The simulation has shown that industrial data may be fitted to the model outputs with sensible values of unknown parameters. For this case study, the parameter sensitivity study has found that the heat loss from the dryer and the critical moisture content of the materialmore » have the greatest impact on the dryer operation at the current operating point. An optimization study has demonstrated the dominant effect of the heat loss from the dryer on the current operating cost and the current operating conditions, and substantial cost savings (around 50%) could be achieved with a well-insulated and airtight dryer, for the specific case studied here.« less

Novel prescribed performance neural control of a flexible air-breathing hypersonic vehicle with unknown initial errors.

PubMed

Bu, Xiangwei; Wu, Xiaoyan; Zhu, Fujing; Huang, Jiaqi; Ma, Zhen; Zhang, Rui

2015-11-01

A novel prescribed performance neural controller with unknown initial errors is addressed for the longitudinal dynamic model of a flexible air-breathing hypersonic vehicle (FAHV) subject to parametric uncertainties. Different from traditional prescribed performance control (PPC) requiring that the initial errors have to be known accurately, this paper investigates the tracking control without accurate initial errors via exploiting a new performance function. A combined neural back-stepping and minimal learning parameter (MLP) technology is employed for exploring a prescribed performance controller that provides robust tracking of velocity and altitude reference trajectories. The highlight is that the transient performance of velocity and altitude tracking errors is satisfactory and the computational load of neural approximation is low. Finally, numerical simulation results from a nonlinear FAHV model demonstrate the efficacy of the proposed strategy. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A mathematical model for HIV and hepatitis C co-infection and its assessment from a statistical perspective.

PubMed

Castro Sanchez, Amparo Yovanna; Aerts, Marc; Shkedy, Ziv; Vickerman, Peter; Faggiano, Fabrizio; Salamina, Guiseppe; Hens, Niel

2013-03-01

The hepatitis C virus (HCV) and the human immunodeficiency virus (HIV) are a clear threat for public health, with high prevalences especially in high risk groups such as injecting drug users. People with HIV infection who are also infected by HCV suffer from a more rapid progression to HCV-related liver disease and have an increased risk for cirrhosis and liver cancer. Quantifying the impact of HIV and HCV co-infection is therefore of great importance. We propose a new joint mathematical model accounting for co-infection with the two viruses in the context of injecting drug users (IDUs). Statistical concepts and methods are used to assess the model from a statistical perspective, in order to get further insights in: (i) the comparison and selection of optional model components, (ii) the unknown values of the numerous model parameters, (iii) the parameters to which the model is most 'sensitive' and (iv) the combinations or patterns of values in the high-dimensional parameter space which are most supported by the data. Data from a longitudinal study of heroin users in Italy are used to illustrate the application of the proposed joint model and its statistical assessment. The parameters associated with contact rates (sharing syringes) and the transmission rates per syringe-sharing event are shown to play a major role. Copyright © 2013 Elsevier B.V. All rights reserved.

Inertial parameter identification using contact force information for an unknown object captured by a space manipulator

NASA Astrophysics Data System (ADS)

Chu, Zhongyi; Ma, Ye; Hou, Yueyang; Wang, Fengwen

2017-02-01

This paper presents a novel identification method for the intact inertial parameters of an unknown object in space captured by a manipulator in a space robotic system. With strong dynamic and kinematic coupling existing in the robotic system, the inertial parameter identification of the unknown object is essential for the ideal control strategy based on changes in the attitude and trajectory of the space robot via capturing operations. Conventional studies merely refer to the principle and theory of identification, and an error analysis process of identification is deficient for a practical scenario. To solve this issue, an analysis of the effect of errors on identification is illustrated first, and the accumulation of measurement or estimation errors causing poor identification precision is demonstrated. Meanwhile, a modified identification equation incorporating the contact force, as well as the force/torque of the end-effector, is proposed to weaken the accumulation of errors and improve the identification accuracy. Furthermore, considering a severe disturbance condition caused by various measured noises, the hybrid immune algorithm, Recursive Least Squares and Affine Projection Sign Algorithm (RLS-APSA), is employed to decode the modified identification equation to ensure a stable identification property. Finally, to verify the validity of the proposed identification method, the co-simulation of ADAMS-MATLAB is implemented by multi-degree of freedom models of a space robotic system, and the numerical results show a precise and stable identification performance, which is able to guarantee the execution of aerospace operations and prevent failed control strategies.

Nowcasting sunshine number using logistic modeling

NASA Astrophysics Data System (ADS)

Brabec, Marek; Badescu, Viorel; Paulescu, Marius

2013-04-01

In this paper, we present a formalized approach to statistical modeling of the sunshine number, binary indicator of whether the Sun is covered by clouds introduced previously by Badescu (Theor Appl Climatol 72:127-136, 2002). Our statistical approach is based on Markov chain and logistic regression and yields fully specified probability models that are relatively easily identified (and their unknown parameters estimated) from a set of empirical data (observed sunshine number and sunshine stability number series). We discuss general structure of the model and its advantages, demonstrate its performance on real data and compare its results to classical ARIMA approach as to a competitor. Since the model parameters have clear interpretation, we also illustrate how, e.g., their inter-seasonal stability can be tested. We conclude with an outlook to future developments oriented to construction of models allowing for practically desirable smooth transition between data observed with different frequencies and with a short discussion of technical problems that such a goal brings.

Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution

NASA Astrophysics Data System (ADS)

Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.

2017-12-01

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.

PARTICLE FILTERING WITH SEQUENTIAL PARAMETER LEARNING FOR NONLINEAR BOLD fMRI SIGNALS.

PubMed

Xia, Jing; Wang, Michelle Yongmei

Analyzing the blood oxygenation level dependent (BOLD) effect in the functional magnetic resonance imaging (fMRI) is typically based on recent ground-breaking time series analysis techniques. This work represents a significant improvement over existing approaches to system identification using nonlinear hemodynamic models. It is important for three reasons. First, instead of using linearized approximations of the dynamics, we present a nonlinear filtering based on the sequential Monte Carlo method to capture the inherent nonlinearities in the physiological system. Second, we simultaneously estimate the hidden physiological states and the system parameters through particle filtering with sequential parameter learning to fully take advantage of the dynamic information of the BOLD signals. Third, during the unknown static parameter learning, we employ the low-dimensional sufficient statistics for efficiency and avoiding potential degeneration of the parameters. The performance of the proposed method is validated using both the simulated data and real BOLD fMRI data.

Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.

PubMed

Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik

2014-01-01

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

A unifying view of synchronization for data assimilation in complex nonlinear networks

NASA Astrophysics Data System (ADS)

Abarbanel, Henry D. I.; Shirman, Sasha; Breen, Daniel; Kadakia, Nirag; Rey, Daniel; Armstrong, Eve; Margoliash, Daniel

2017-12-01

Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network. This allows the validation (or invalidation) of the model as a representation of the dynamical processes producing the observations. Once the model has been tested against new data, it may be utilized as a predictor of responses to innovative stimuli or forcing. We describe a general framework for the tasks involved in the "inverse" problem of determining properties of a model built to represent measured output from physical, biological, or other processes when the measurements are noisy, the model has errors, and the state of the model is unknown when measurements begin. This framework is called statistical data assimilation and is the best one can do in estimating model properties through the use of the conditional probability distributions of the model state variables, conditioned on observations. There is a very broad arena of applications of the methods described. These include numerical weather prediction, properties of nonlinear electrical circuitry, and determining the biophysical properties of functional networks of neurons. Illustrative examples will be given of (1) estimating the connectivity among neurons with known dynamics in a network of unknown connectivity, and (2) estimating the biophysical properties of individual neurons in vitro taken from a functional network underlying vocalization in songbirds.

Integrated survival analysis using an event-time approach in a Bayesian framework

USGS Publications Warehouse

Walsh, Daniel P.; Dreitz, VJ; Heisey, Dennis M.

2015-01-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Integrated survival analysis using an event-time approach in a Bayesian framework.

PubMed

Walsh, Daniel P; Dreitz, Victoria J; Heisey, Dennis M

2015-02-01

Event-time or continuous-time statistical approaches have been applied throughout the biostatistical literature and have led to numerous scientific advances. However, these techniques have traditionally relied on knowing failure times. This has limited application of these analyses, particularly, within the ecological field where fates of marked animals may be unknown. To address these limitations, we developed an integrated approach within a Bayesian framework to estimate hazard rates in the face of unknown fates. We combine failure/survival times from individuals whose fates are known and times of which are interval-censored with information from those whose fates are unknown, and model the process of detecting animals with unknown fates. This provides the foundation for our integrated model and permits necessary parameter estimation. We provide the Bayesian model, its derivation, and use simulation techniques to investigate the properties and performance of our approach under several scenarios. Lastly, we apply our estimation technique using a piece-wise constant hazard function to investigate the effects of year, age, chick size and sex, sex of the tending adult, and nesting habitat on mortality hazard rates of the endangered mountain plover (Charadrius montanus) chicks. Traditional models were inappropriate for this analysis because fates of some individual chicks were unknown due to failed radio transmitters. Simulations revealed biases of posterior mean estimates were minimal (≤ 4.95%), and posterior distributions behaved as expected with RMSE of the estimates decreasing as sample sizes, detection probability, and survival increased. We determined mortality hazard rates for plover chicks were highest at <5 days old and were lower for chicks with larger birth weights and/or whose nest was within agricultural habitats. Based on its performance, our approach greatly expands the range of problems for which event-time analyses can be used by eliminating the need for having completely known fate data.

Efficient Ensemble State-Parameters Estimation Techniques in Ocean Ecosystem Models: Application to the North Atlantic

NASA Astrophysics Data System (ADS)

El Gharamti, M.; Bethke, I.; Tjiputra, J.; Bertino, L.

2016-02-01

Given the recent strong international focus on developing new data assimilation systems for biological models, we present in this comparative study the application of newly developed state-parameters estimation tools to an ocean ecosystem model. It is quite known that the available physical models are still too simple compared to the complexity of the ocean biology. Furthermore, various biological parameters remain poorly unknown and hence wrong specifications of such parameters can lead to large model errors. Standard joint state-parameters augmentation technique using the ensemble Kalman filter (Stochastic EnKF) has been extensively tested in many geophysical applications. Some of these assimilation studies reported that jointly updating the state and the parameters might introduce significant inconsistency especially for strongly nonlinear models. This is usually the case for ecosystem models particularly during the period of the spring bloom. A better handling of the estimation problem is often carried out by separating the update of the state and the parameters using the so-called Dual EnKF. The dual filter is computationally more expensive than the Joint EnKF but is expected to perform more accurately. Using a similar separation strategy, we propose a new EnKF estimation algorithm in which we apply a one-step-ahead smoothing to the state. The new state-parameters estimation scheme is derived in a consistent Bayesian filtering framework and results in separate update steps for the state and the parameters. Unlike the classical filtering path, the new scheme starts with an update step and later a model propagation step is performed. We test the performance of the new smoothing-based schemes against the standard EnKF in a one-dimensional configuration of the Norwegian Earth System Model (NorESM) in the North Atlantic. We use nutrients profile (up to 2000 m deep) data and surface partial CO2 measurements from Mike weather station (66o N, 2o E) to estimate different biological parameters of phytoplanktons and zooplanktons. We analyze the performance of the filters in terms of complexity and accuracy of the state and parameters estimates.

Analysis of aircraft tires via semianalytic finite elements

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Kim, Kyun O.; Tanner, John A.

1990-01-01

A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.

Direct Adaptive Control of Systems with Actuator Failures: State of the Art and Continuing Challenges

NASA Technical Reports Server (NTRS)

Tao, Gang; Joshi, Suresh M.

2008-01-01

In this paper, the problem of controlling systems with failures and faults is introduced, and an overview of recent work on direct adaptive control for compensation of uncertain actuator failures is presented. Actuator failures may be characterized by some unknown system inputs being stuck at some unknown (fixed or varying) values at unknown time instants, that cannot be influenced by the control signals. The key task of adaptive compensation is to design the control signals in such a manner that the remaining actuators can automatically and seamlessly take over for the failed ones, and achieve desired stability and asymptotic tracking. A certain degree of redundancy is necessary to accomplish failure compensation. The objective of adaptive control design is to effectively use the available actuation redundancy to handle failures without the knowledge of the failure patterns, parameters, and time of occurrence. This is a challenging problem because failures introduce large uncertainties in the dynamic structure of the system, in addition to parametric uncertainties and unknown disturbances. The paper addresses some theoretical issues in adaptive actuator failure compensation: actuator failure modeling, redundant actuation requirements, plant-model matching, error system dynamics, adaptation laws, and stability, tracking, and performance analysis. Adaptive control designs can be shown to effectively handle uncertain actuator failures without explicit failure detection. Some open technical challenges and research problems in this important research area are discussed.

Efficient Bayesian experimental design for contaminant source identification

NASA Astrophysics Data System (ADS)

Zhang, J.; Zeng, L.

2013-12-01

In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameter identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from indirect concentration measurements in identifying unknown source parameters such as the release time, strength and location. In this approach, the sampling location that gives the maximum relative entropy is selected as the optimal one. Once the sampling location is determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown source parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. Compared with the traditional optimal design, which is based on the Gaussian linear assumption, the method developed in this study can cope with arbitrary nonlinearity. It can be used to assist in groundwater monitor network design and identification of unknown contaminant sources. Contours of the expected information gain. The optimal observing location corresponds to the maximum value. Posterior marginal probability densities of unknown parameters, the thick solid black lines are for the designed location. For comparison, other 7 lines are for randomly chosen locations. The true values are denoted by vertical lines. It is obvious that the unknown parameters are estimated better with the desinged location.

Reciprocating and Screw Compressor semi-empirical models for establishing minimum energy performance standards

NASA Astrophysics Data System (ADS)

Javed, Hassan; Armstrong, Peter

2015-08-01

The efficiency bar for a Minimum Equipment Performance Standard (MEPS) generally aims to minimize energy consumption and life cycle cost of a given chiller type and size category serving a typical load profile. Compressor type has a significant chiller performance impact. Performance of screw and reciprocating compressors is expressed in terms of pressure ratio and speed for a given refrigerant and suction density. Isentropic efficiency for a screw compressor is strongly affected by under- and over-compression (UOC) processes. The theoretical simple physical UOC model involves a compressor-specific (but sometimes unknown) volume index parameter and the real gas properties of the refrigerant used. Isentropic efficiency is estimated by the UOC model and a bi-cubic, used to account for flow, friction and electrical losses. The unknown volume index, a smoothing parameter (to flatten the UOC model peak) and bi-cubic coefficients are identified by curve fitting to minimize an appropriate residual norm. Chiller performance maps are produced for each compressor type by selecting optimized sub-cooling and condenser fan speed options in a generic component-based chiller model. SEER is the sum of hourly load (from a typical building in the climate of interest) and specific power for the same hourly conditions. An empirical UAE cooling load model, scalable to any equipment capacity, is used to establish proposed UAE MEPS. Annual electricity use and cost, determined from SEER and annual cooling load, and chiller component cost data are used to find optimal chiller designs and perform life-cycle cost comparison between screw and reciprocating compressor-based chillers. This process may be applied to any climate/load model in order to establish optimized MEPS for any country and/or region.

Numerical slope stability simulations of chasma walls in Valles Marineris/Mars using a distinct element method (dem).

NASA Astrophysics Data System (ADS)

Imre, B.

2003-04-01

NUMERICAL SLOPE STABILITY SIMULATIONS OF CHASMA WALLS IN VALLES MARINERIS/MARS USING A DISTINCT ELEMENT METHOD (DEM). B. Imre (1) (1) German Aerospace Center, Berlin Adlershof, bernd.imre@gmx.net The 8- to 10-km depths of Valles Marineris (VM) offer excellent views into the upper Martian crust. Layering, fracturing, lithology, stratigraphy and the content of volatiles have influenced the evolution of the Valles Marineris wallslopes. But these parameters also reflect the development of VM and its wall slopes. The scope of this work is to gain understanding in these parameters by back-simulating the development of wall slopes. For that purpose, the two dimensional Particle Flow Code PFC2D has been chosen (ITASCA, version 2.00-103). PFC2D is a distinct element code for numerical modelling of movements and interactions of assemblies of arbitrarily sized circular particles. Particles may be bonded together to represent a solid material. Movements of particles are unlimited. That is of importance because results of open systems with numerous unknown variables are non-unique and therefore highly path dependent. This DEM allows the simulation of whole development paths of VM walls what makes confirmation of the model more complete (e.g. Oreskes et al., Science 263, 1994). To reduce the number of unknown variables a proper (that means as simple as possible) field-site had to be selected. The northern wall of eastern Candor Chasma has been chosen. This wall is up to 8-km high and represents a significant outcrop of the upper Martian crust. It is quite uncomplex, well-aligned and of simple morphology. Currently the work on the model is at the stage of performing the parameter study. Results will be presented via poster by the EGS-Meeting.

Real-Time Robust Adaptive Modeling and Scheduling for an Electronic Commerce Server

NASA Astrophysics Data System (ADS)

Du, Bing; Ruan, Chun

With the increasing importance and pervasiveness of Internet services, it is becoming a challenge for the proliferation of electronic commerce services to provide performance guarantees under extreme overload. This paper describes a real-time optimization modeling and scheduling approach for performance guarantee of electronic commerce servers. We show that an electronic commerce server may be simulated as a multi-tank system. A robust adaptive server model is subject to unknown additive load disturbances and uncertain model matching. Overload control techniques are based on adaptive admission control to achieve timing guarantees. We evaluate the performance of the model using a complex simulation that is subjected to varying model parameters and massive overload.

Complexity-aware simple modeling.

PubMed

Gómez-Schiavon, Mariana; El-Samad, Hana

2018-02-26

Mathematical models continue to be essential for deepening our understanding of biology. On one extreme, simple or small-scale models help delineate general biological principles. However, the parsimony of detail in these models as well as their assumption of modularity and insulation make them inaccurate for describing quantitative features. On the other extreme, large-scale and detailed models can quantitatively recapitulate a phenotype of interest, but have to rely on many unknown parameters, making them often difficult to parse mechanistically and to use for extracting general principles. We discuss some examples of a new approach-complexity-aware simple modeling-that can bridge the gap between the small-scale and large-scale approaches. Copyright © 2018 Elsevier Ltd. All rights reserved.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

A method for testing whether model predictions fall within a prescribed factor of true values, with an application to pesticide leaching

USGS Publications Warehouse

Parrish, Rudolph S.; Smith, Charles N.

1990-01-01

A quantitative method is described for testing whether model predictions fall within a specified factor of true values. The technique is based on classical theory for confidence regions on unknown population parameters and can be related to hypothesis testing in both univariate and multivariate situations. A capability index is defined that can be used as a measure of predictive capability of a model, and its properties are discussed. The testing approach and the capability index should facilitate model validation efforts and permit comparisons among competing models. An example is given for a pesticide leaching model that predicts chemical concentrations in the soil profile.

Back analysis of geomechanical parameters in underground engineering using artificial bee colony.

PubMed

Zhu, Changxing; Zhao, Hongbo; Zhao, Ming

2014-01-01

Accurate geomechanical parameters are critical in tunneling excavation, design, and supporting. In this paper, a displacements back analysis based on artificial bee colony (ABC) algorithm is proposed to identify geomechanical parameters from monitored displacements. ABC was used as global optimal algorithm to search the unknown geomechanical parameters for the problem with analytical solution. To the problem without analytical solution, optimal back analysis is time-consuming, and least square support vector machine (LSSVM) was used to build the relationship between unknown geomechanical parameters and displacement and improve the efficiency of back analysis. The proposed method was applied to a tunnel with analytical solution and a tunnel without analytical solution. The results show the proposed method is feasible.

An improved method for nonlinear parameter estimation: a case study of the Rössler model

NASA Astrophysics Data System (ADS)

He, Wen-Ping; Wang, Liu; Jiang, Yun-Di; Wan, Shi-Quan

2016-08-01

Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.

A Bayesian approach for parameter estimation and prediction using a computationally intensive model

DOE PAGES

Higdon, Dave; McDonnell, Jordan D.; Schunck, Nicolas; ...

2015-02-05

Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based modelmore » $$\\eta (\\theta )$$, where θ denotes the uncertain, best input setting. Hence the statistical model is of the form $$y=\\eta (\\theta )+\\epsilon ,$$ where $$\\epsilon $$ accounts for measurement, and possibly other, error sources. When nonlinearity is present in $$\\eta (\\cdot )$$, the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model $$\\eta (\\cdot )$$. This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. Lastly, we also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.« less

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Miller, Brad A.; Howard, Samuel A.

2008-01-01

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Estimation of object motion parameters from noisy images.

PubMed

Broida, T J; Chellappa, R

1986-01-01

An approach is presented for the estimation of object motion parameters based on a sequence of noisy images. The problem considered is that of a rigid body undergoing unknown rotational and translational motion. The measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points. By modeling the object dynamics as a function of time, estimates of the model parameters (including motion parameters) can be extracted from the data using recursive and/or batch techniques. This permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images. Some assumptions regarding object structure are presently made. Results are presented for a recursive estimation procedure: the case considered here is that of a sequence of one dimensional images of a two dimensional object. Thus, the object moves in one transverse dimension, and in depth, preserving the fundamental ambiguity of the central projection image model (loss of depth information). An iterated extended Kalman filter is used for the recursive solution. Noise levels of 5-10 percent of the object image size are used. Approximate Cramer-Rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level. This approach may be of use in situations where it is difficult to resolve large numbers of object match points, but relatively long sequences of images (10 to 20 or more) are available.

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions

PubMed Central

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation. PMID:26150807

Bottom-up modeling approach for the quantitative estimation of parameters in pathogen-host interactions.

PubMed

Lehnert, Teresa; Timme, Sandra; Pollmächer, Johannes; Hünniger, Kerstin; Kurzai, Oliver; Figge, Marc Thilo

2015-01-01

Opportunistic fungal pathogens can cause bloodstream infection and severe sepsis upon entering the blood stream of the host. The early immune response in human blood comprises the elimination of pathogens by antimicrobial peptides and innate immune cells, such as neutrophils or monocytes. Mathematical modeling is a predictive method to examine these complex processes and to quantify the dynamics of pathogen-host interactions. Since model parameters are often not directly accessible from experiment, their estimation is required by calibrating model predictions with experimental data. Depending on the complexity of the mathematical model, parameter estimation can be associated with excessively high computational costs in terms of run time and memory. We apply a strategy for reliable parameter estimation where different modeling approaches with increasing complexity are used that build on one another. This bottom-up modeling approach is applied to an experimental human whole-blood infection assay for Candida albicans. Aiming for the quantification of the relative impact of different routes of the immune response against this human-pathogenic fungus, we start from a non-spatial state-based model (SBM), because this level of model complexity allows estimating a priori unknown transition rates between various system states by the global optimization method simulated annealing. Building on the non-spatial SBM, an agent-based model (ABM) is implemented that incorporates the migration of interacting cells in three-dimensional space. The ABM takes advantage of estimated parameters from the non-spatial SBM, leading to a decreased dimensionality of the parameter space. This space can be scanned using a local optimization approach, i.e., least-squares error estimation based on an adaptive regular grid search, to predict cell migration parameters that are not accessible in experiment. In the future, spatio-temporal simulations of whole-blood samples may enable timely stratification of sepsis patients by distinguishing hyper-inflammatory from paralytic phases in immune dysregulation.

On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation

PubMed Central

DiStefano, Joseph

2014-01-01

Parameter identifiability problems can plague biomodelers when they reach the quantification stage of development, even for relatively simple models. Structural identifiability (SI) is the primary question, usually understood as knowing which of P unknown biomodel parameters p 1,…, pi,…, pP are-and which are not-quantifiable in principle from particular input-output (I-O) biodata. It is not widely appreciated that the same database also can provide quantitative information about the structurally unidentifiable (not quantifiable) subset, in the form of explicit algebraic relationships among unidentifiable pi. Importantly, this is a first step toward finding what else is needed to quantify particular unidentifiable parameters of interest from new I–O experiments. We further develop, implement and exemplify novel algorithms that address and solve the SI problem for a practical class of ordinary differential equation (ODE) systems biology models, as a user-friendly and universally-accessible web application (app)–COMBOS. Users provide the structural ODE and output measurement models in one of two standard forms to a remote server via their web browser. COMBOS provides a list of uniquely and non-uniquely SI model parameters, and–importantly-the combinations of parameters not individually SI. If non-uniquely SI, it also provides the maximum number of different solutions, with important practical implications. The behind-the-scenes symbolic differential algebra algorithms are based on computing Gröbner bases of model attributes established after some algebraic transformations, using the computer-algebra system Maxima. COMBOS was developed for facile instructional and research use as well as modeling. We use it in the classroom to illustrate SI analysis; and have simplified complex models of tumor suppressor p53 and hormone regulation, based on explicit computation of parameter combinations. It’s illustrated and validated here for models of moderate complexity, with and without initial conditions. Built-in examples include unidentifiable 2 to 4-compartment and HIV dynamics models. PMID:25350289

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

PubMed Central

Liebermeister, Wolfram; Klipp, Edda

2006-01-01

Background Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. Results We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. Conclusion Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases. PMID:17173669

Heterogeneous Multi-Robot Multi-Sensor Platform for Intruder Detection

DTIC Science & Technology

2009-09-15

propagation model, with variance τi: si ~ N(b0i + b1i *logDi, τ i). The initial parameters (b0i, b1i, τ i ) of the model are unknown, and the training...that the advantage of MOO-learned mode would become more significant over time compared with the other mode. 1 2 3 4 5 6 7 0 0.05 0.1 0.15 0.2...nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II,” in Parallel Problem Solving from Nature (PPSN VI), M. Schoenauer

Computational methods for inverse problems in geophysics: inversion of travel time observations

USGS Publications Warehouse

Pereyra, V.; Keller, H.B.; Lee, W.H.K.

1980-01-01

General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.

Minimal Unified Resolution to R_{K^{(*)}} and R(D^{(*)}) Anomalies with Lepton Mixing.

PubMed

Choudhury, Debajyoti; Kundu, Anirban; Mandal, Rusa; Sinha, Rahul

2017-10-13

It is a challenging task to explain, in terms of a simple and compelling new physics scenario, the intriguing discrepancies between the standard model expectations and the data for the neutral-current observables R_{K} and R_{K^{*}}, as well as the charged-current observables R(D) and R(D^{*}). We show that this can be achieved in an effective theory with only two unknown parameters. In addition, this class of models predicts some interesting signatures in the context of both B decays as well as high-energy collisions.

Thawing of ice in porous space of building materials: Experimental monitoring and computational modelling

NASA Astrophysics Data System (ADS)

Kočí, Jan; Maděra, Jiří; Kočí, Václav; Hlaváčová, Zuzana; Černý, Robert

2017-11-01

A simple laboratory experiment for the determination of thermal response of a studied sample during thawing is described in the paper. The sample made of autoclaved aerated concrete was partially water saturated and frozen. Then, the temperature development during thawing was recorded, allowing to identify the time scale of the phase change process taking place inside the sample. The experimental data was then used in the inverse analysis, in order to find unknown parameters of the smoothed effective specific heat capacity model.

Dust in Extragalactic Reflection Nebulae

NASA Astrophysics Data System (ADS)

Lee, Chris H.; Hodges-Kluck, Edmund J.

2017-08-01

Observational evidence for extragalactic dust has been recently found in the form of UV extragalactic reflection nebulae around edge-on spiral galaxies, but the nature of the dust is largely unknown. To derive dust parameters, UV fluxes from the spacecrafts GALEX and Swift have been compared with model UV halo SEDs, which have been created from galaxy template spectra and a silicate-graphite dust model. The model contains two free parameters, which are fractional composition and maximum grain size. These analyses have been done for a sample of 8 nearby edge-on spiral galaxies with bright UV halos, where the dust properties can be spatially resolved, such as inside and outside of galactic winds or as a function of height from the galactic disc. The dust properties give insight into how dust is expelled from the galactic disc, which can also be applied to understanding gaseous outflows from the galaxies as well.

Unresolved Galaxy Classifier for ESA/Gaia mission: Support Vector Machines approach

NASA Astrophysics Data System (ADS)

Bellas-Velidis, Ioannis; Kontizas, Mary; Dapergolas, Anastasios; Livanou, Evdokia; Kontizas, Evangelos; Karampelas, Antonios

A software package Unresolved Galaxy Classifier (UGC) is being developed for the ground-based pipeline of ESA's Gaia mission. It aims to provide an automated taxonomic classification and specific parameters estimation analyzing Gaia BP/RP instrument low-dispersion spectra of unresolved galaxies. The UGC algorithm is based on a supervised learning technique, the Support Vector Machines (SVM). The software is implemented in Java as two separate modules. An offline learning module provides functions for SVM-models training. Once trained, the set of models can be repeatedly applied to unknown galaxy spectra by the pipeline's application module. A library of galaxy models synthetic spectra, simulated for the BP/RP instrument, is used to train and test the modules. Science tests show a very good classification performance of UGC and relatively good regression performance, except for some of the parameters. Possible approaches to improve the performance are discussed.

Recipe for potassium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Izutani, Natsuko

2012-11-12

I investigate favorable conditions for producing potassium (K). Observations show [K/Fe] > 0 at low metallicities, while zero-metal supernova models show low [K/Fe] (< 0). Theoretically, it is natural that the odd-Z element, potassium decreases with lower metallicity, and thus, the observation should imply new and unknown sites for potassium. In this proceedings, I calculate proton-rich nucleosynthesis with three parameters, the initial Y{sub e} (from 0.51 to 0.60), the initial density {rho}{sub max} (10{sup 7}, 10{sup 8}, and 10{sup 9} [g/cm{sup 3}]), and the e-fold time {tau} for the density (0.01, 0.1, and 1.0 [sec]). Among 90 models I havemore » calculated, only 26 models show [K/Fe] > 0, and they all have {rho}{sub max} = 10{sup 9}[g/cm{sup 3}]. I discuss parameter dependence of [K/Fe].« less

Spatiotemporal Bayesian analysis of Lyme disease in New York state, 1990-2000.

PubMed

Chen, Haiyan; Stratton, Howard H; Caraco, Thomas B; White, Dennis J

2006-07-01

Mapping ordinarily increases our understanding of nontrivial spatial and temporal heterogeneities in disease rates. However, the large number of parameters required by the corresponding statistical models often complicates detailed analysis. This study investigates the feasibility of a fully Bayesian hierarchical regression approach to the problem and identifies how it outperforms two more popular methods: crude rate estimates (CRE) and empirical Bayes standardization (EBS). In particular, we apply a fully Bayesian approach to the spatiotemporal analysis of Lyme disease incidence in New York state for the period 1990-2000. These results are compared with those obtained by CRE and EBS in Chen et al. (2005). We show that the fully Bayesian regression model not only gives more reliable estimates of disease rates than the other two approaches but also allows for tractable models that can accommodate more numerous sources of variation and unknown parameters.

Controller design for a class of nonlinear MIMO coupled system using multiple models and second level adaptation.

PubMed

Pandey, Vinay Kumar; Kar, Indrani; Mahanta, Chitralekha

2017-07-01

In this paper, an adaptive control method using multiple models with second level adaptation is proposed for a class of nonlinear multi-input multi-output (MIMO) coupled systems. Multiple estimation models are used to tune the unknown parameters at the first level. The second level adaptation provides a single parameter vector for the controller. A feedback linearization technique is used to design a state feedback control. The efficacy of the designed controller is validated by conducting real time experiment on a laboratory setup of twin rotor MIMO system (TRMS). The TRMS setup is discussed in detail and the experiments were performed for regulation and tracking problem for pitch and yaw control using different reference signals. An Extended Kalman Filter (EKF) has been used to observe the unavailable states of the TRMS. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

On the estimation algorithm used in adaptive performance optimization of turbofan engines

NASA Technical Reports Server (NTRS)

Espana, Martin D.; Gilyard, Glenn B.

1993-01-01

The performance seeking control algorithm is designed to continuously optimize the performance of propulsion systems. The performance seeking control algorithm uses a nominal model of the propulsion system and estimates, in flight, the engine deviation parameters characterizing the engine deviations with respect to nominal conditions. In practice, because of measurement biases and/or model uncertainties, the estimated engine deviation parameters may not reflect the engine's actual off-nominal condition. This factor has a necessary impact on the overall performance seeking control scheme exacerbated by the open-loop character of the algorithm. The effects produced by unknown measurement biases over the estimation algorithm are evaluated. This evaluation allows for identification of the most critical measurements for application of the performance seeking control algorithm to an F100 engine. An equivalence relation between the biases and engine deviation parameters stems from an observability study; therefore, it is undecided whether the estimated engine deviation parameters represent the actual engine deviation or whether they simply reflect the measurement biases. A new algorithm, based on the engine's (steady-state) optimization model, is proposed and tested with flight data. When compared with previous Kalman filter schemes, based on local engine dynamic models, the new algorithm is easier to design and tune and it reduces the computational burden of the onboard computer.

Reconstruction of Atmospheric Tracer Releases with Optimal Resolution Features: Concentration Data Assimilation

NASA Astrophysics Data System (ADS)

Singh, Sarvesh Kumar; Turbelin, Gregory; Issartel, Jean-Pierre; Kumar, Pramod; Feiz, Amir Ali

2015-04-01

The fast growing urbanization, industrialization and military developments increase the risk towards the human environment and ecology. This is realized in several past mortality incidents, for instance, Chernobyl nuclear explosion (Ukraine), Bhopal gas leak (India), Fukushima-Daichi radionuclide release (Japan), etc. To reduce the threat and exposure to the hazardous contaminants, a fast and preliminary identification of unknown releases is required by the responsible authorities for the emergency preparedness and air quality analysis. Often, an early detection of such contaminants is pursued by a distributed sensor network. However, identifying the origin and strength of unknown releases following the sensor reported concentrations is a challenging task. This requires an optimal strategy to integrate the measured concentrations with the predictions given by the atmospheric dispersion models. This is an inverse problem. The measured concentrations are insufficient and atmospheric dispersion models suffer from inaccuracy due to the lack of process understanding, turbulence uncertainties, etc. These lead to a loss of information in the reconstruction process and thus, affect the resolution, stability and uniqueness of the retrieved source. An additional well known issue is the numerical artifact arisen at the measurement locations due to the strong concentration gradient and dissipative nature of the concentration. Thus, assimilation techniques are desired which can lead to an optimal retrieval of the unknown releases. In general, this is facilitated within the Bayesian inference and optimization framework with a suitable choice of a priori information, regularization constraints, measurement and background error statistics. An inversion technique is introduced here for an optimal reconstruction of unknown releases using limited concentration measurements. This is based on adjoint representation of the source-receptor relationship and utilization of a weight function which exhibits a priori information about the unknown releases apparent to the monitoring network. The properties of the weight function provide an optimal data resolution and model resolution to the retrieved source estimates. The retrieved source estimates are proved theoretically to be stable against the random measurement errors and their reliability can be interpreted in terms of the distribution of the weight functions. Further, the same framework can be extended for the identification of the point type releases by utilizing the maximum of the retrieved source estimates. The inversion technique has been evaluated with the several diffusion experiments, like, Idaho low wind diffusion experiment (1974), IIT Delhi tracer experiment (1991), European Tracer Experiment (1994), Fusion Field Trials (2007), etc. In case of point release experiments, the source parameters are mostly retrieved close to the true source parameters with least error. Primarily, the proposed technique overcomes two major difficulties incurred in the source reconstruction: (i) The initialization of the source parameters as required by the optimization based techniques. The converged solution depends on their initialization. (ii) The statistical knowledge about the measurement and background errors as required by the Bayesian inference based techniques. These are hypothetically assumed in case of no prior knowledge.

Regularized Semiparametric Estimation for Ordinary Differential Equations

PubMed Central

Li, Yun; Zhu, Ji; Wang, Naisyin

2015-01-01

Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this paper, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the non-regularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare-lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results. PMID:26392639

Effective connectivity: Influence, causality and biophysical modeling

PubMed Central

Valdes-Sosa, Pedro A.; Roebroeck, Alard; Daunizeau, Jean; Friston, Karl

2011-01-01

This is the final paper in a Comments and Controversies series dedicated to “The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution”. We argue that discovering effective connectivity depends critically on state-space models with biophysically informed observation and state equations. These models have to be endowed with priors on unknown parameters and afford checks for model Identifiability. We consider the similarities and differences among Dynamic Causal Modeling, Granger Causal Modeling and other approaches. We establish links between past and current statistical causal modeling, in terms of Bayesian dependency graphs and Wiener–Akaike–Granger–Schweder influence measures. We show that some of the challenges faced in this field have promising solutions and speculate on future developments. PMID:21477655

Adaptive Heat Engine.

PubMed

Allahverdyan, A E; Babajanyan, S G; Martirosyan, N H; Melkikh, A V

2016-07-15

A major limitation of many heat engines is that their functioning demands on-line control and/or an external fitting between the environmental parameters (e.g., temperatures of thermal baths) and internal parameters of the engine. We study a model for an adaptive heat engine, where-due to feedback from the functional part-the engine's structure adapts to given thermal baths. Hence, no on-line control and no external fitting are needed. The engine can employ unknown resources; it can also adapt to results of its own functioning that make the bath temperatures closer. We determine resources of adaptation and relate them to the prior information available about the environment.

Nonlinear adaptive control system design with asymptotically stable parameter estimation error

NASA Astrophysics Data System (ADS)

Mishkov, Rumen; Darmonski, Stanislav

2018-01-01

The paper presents a new general method for nonlinear adaptive system design with asymptotic stability of the parameter estimation error. The advantages of the approach include asymptotic unknown parameter estimation without persistent excitation and capability to directly control the estimates transient response time. The method proposed modifies the basic parameter estimation dynamics designed via a known nonlinear adaptive control approach. The modification is based on the generalised prediction error, a priori constraints with a hierarchical parameter projection algorithm, and the stable data accumulation concepts. The data accumulation principle is the main tool for achieving asymptotic unknown parameter estimation. It relies on the parametric identifiability system property introduced. Necessary and sufficient conditions for exponential stability of the data accumulation dynamics are derived. The approach is applied in a nonlinear adaptive speed tracking vector control of a three-phase induction motor.

A pharmacokinetic model of filgrastim and pegfilgrastim application in normal mice and those with cyclophosphamide-induced granulocytopaenia.

PubMed

Scholz, M; Ackermann, M; Engel, C; Emmrich, F; Loeffler, M; Kamprad, M

2009-12-01

Recombinant human granulocyte colony-stimulating factor (rhG-CSF) is widely used as treatment for granulocytopaenia during cytotoxic chemotherapy; however, optimal scheduling of this pharmaceutical is unknown. Biomathematical models can help to pre-select optimal application schedules but precise pharmacokinetic properties of the pharmaceuticals are required at first. In this study, we have aimed to construct a pharmacokinetic model of G-CSF derivatives filgrastim and pegfilgrastim in mice. Healthy CD-1 mice and those with cyclophosphamide-induced granulocytopaenia were studied after administration of filgrastim and pegfilgrastim in different dosing and timing schedules. Close meshed time series of granulocytes and G-CSF plasma concentrations were determined. An ordinary differential equations model of pharmacokinetics was constructed on the basis of known mechanisms of drug distribution and degradation. Predictions of the model fit well with all experimental data for both filgrastim and pegfilgrastim. We obtained a unique parameter setting for all experimental scenarios. Differences in pharmacokinetics between filgrastim and pegfilgrastim can be explained by different estimates of model parameters rather than by different model mechanisms. Parameter estimates with respect to distribution and clearance of the drug derivatives are in agreement with qualitative experimental results. Dynamics of filgrastim and pegfilgrastim plasma levels can be explained by the same pharmacokinetic model but different model parameters. Beause of a strong clearance mechanism mediated by granulocytes, granulocytotic and granulocytopaenic conditions must be studied simultaneously to construct a reliable model. The pharmacokinetic model will be extended to a murine model of granulopoiesis under chemotherapy and G-CSF application.

Exponential parameter and tracking error convergence guarantees for adaptive controllers without persistency of excitation

NASA Astrophysics Data System (ADS)

Chowdhary, Girish; Mühlegg, Maximilian; Johnson, Eric

2014-08-01

In model reference adaptive control (MRAC) the modelling uncertainty is often assumed to be parameterised with time-invariant unknown ideal parameters. The convergence of parameters of the adaptive element to these ideal parameters is beneficial, as it guarantees exponential stability, and makes an online learned model of the system available. Most MRAC methods, however, require persistent excitation of the states to guarantee that the adaptive parameters converge to the ideal values. Enforcing PE may be resource intensive and often infeasible in practice. This paper presents theoretical analysis and illustrative examples of an adaptive control method that leverages the increasing ability to record and process data online by using specifically selected and online recorded data concurrently with instantaneous data for adaptation. It is shown that when the system uncertainty can be modelled as a combination of known nonlinear bases, simultaneous exponential tracking and parameter error convergence can be guaranteed if the system states are exciting over finite intervals such that rich data can be recorded online; PE is not required. Furthermore, the rate of convergence is directly proportional to the minimum singular value of the matrix containing online recorded data. Consequently, an online algorithm to record and forget data is presented and its effects on the resulting switched closed-loop dynamics are analysed. It is also shown that when radial basis function neural networks (NNs) are used as adaptive elements, the method guarantees exponential convergence of the NN parameters to a compact neighbourhood of their ideal values without requiring PE. Flight test results on a fixed-wing unmanned aerial vehicle demonstrate the effectiveness of the method.

Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation.

PubMed

Sun, Zhijian; Zhang, Guoqing; Lu, Yu; Zhang, Weidong

2018-01-01

This paper studies the leader-follower formation control of underactuated surface vehicles with model uncertainties and environmental disturbances. A parameter estimation and upper bound estimation based sliding mode control scheme is proposed to solve the problem of the unknown plant parameters and environmental disturbances. For each of these leader-follower formation systems, the dynamic equations of position and attitude are analyzed using coordinate transformation with the aid of the backstepping technique. All the variables are guaranteed to be uniformly ultimately bounded stable in the closed-loop system, which is proven by the distribution design Lyapunov function synthesis. The main advantages of this approach are that: first, parameter estimation based sliding mode control can enhance the robustness of the closed-loop system in presence of model uncertainties and environmental disturbances; second, a continuous function is developed to replace the signum function in the design of sliding mode scheme, which devotes to reduce the chattering of the control system. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

The general linear inverse problem - Implication of surface waves and free oscillations for earth structure.

NASA Technical Reports Server (NTRS)

Wiggins, R. A.

1972-01-01

The discrete general linear inverse problem reduces to a set of m equations in n unknowns. There is generally no unique solution, but we can find k linear combinations of parameters for which restraints are determined. The parameter combinations are given by the eigenvectors of the coefficient matrix. The number k is determined by the ratio of the standard deviations of the observations to the allowable standard deviations in the resulting solution. Various linear combinations of the eigenvectors can be used to determine parameter resolution and information distribution among the observations. Thus we can determine where information comes from among the observations and exactly how it constraints the set of possible models. The application of such analyses to surface-wave and free-oscillation observations indicates that (1) phase, group, and amplitude observations for any particular mode provide basically the same type of information about the model; (2) observations of overtones can enhance the resolution considerably; and (3) the degree of resolution has generally been overestimated for many model determinations made from surface waves.

Inferring the parameters of a Markov process from snapshots of the steady state

NASA Astrophysics Data System (ADS)

Dettmer, Simon L.; Berg, Johannes

2018-02-01

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous configurations. We apply the method to non-equilibrium models from statistical physics and theoretical biology, including the asymmetric simple exclusion process (ASEP), the kinetic Ising model, and replicator dynamics.

Estimation of Complex Permittivity of Composite Multilayer Material at Microwave Frequency Using Waveguide Measurements

NASA Technical Reports Server (NTRS)

Deshpande, Manohar D.; Dudley, Kenneth

2003-01-01

A simple method is presented to estimate the complex dielectric constants of individual layers of a multilayer composite material. Using the MatLab Optimization Tools simple MatLab scripts are written to search for electric properties of individual layers so as to match the measured and calculated S-parameters. A single layer composite material formed by using materials such as Bakelite, Nomex Felt, Fiber Glass, Woven Composite B and G, Nano Material #0, Cork, Garlock, of different thicknesses are tested using the present approach. Assuming the thicknesses of samples unknown, the present approach is shown to work well in estimating the dielectric constants and the thicknesses. A number of two layer composite materials formed by various combinations of above individual materials are tested using the present approach. However, the present approach could not provide estimate values close to their true values when the thicknesses of individual layers were assumed to be unknown. This is attributed to the difficulty in modelling the presence of airgaps between the layers while doing the measurement of S-parameters. A few examples of three layer composites are also presented.

Bayesian inversions of a dynamic vegetation model in four European grassland sites

NASA Astrophysics Data System (ADS)

Minet, J.; Laloy, E.; Tychon, B.; François, L.

2015-01-01

Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB dynamic vegetation model (DVM) with ten unknown parameters, using the DREAM(ZS) Markov chain Monte Carlo (MCMC) sampler. We compare model inversions considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a~priori or jointly inferred with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root-mean-square error (RMSE) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19 g C m-2 day-1, 1.04 to 1.56 g C m-2 day-1, and 0.50 to 1.28 mm day-1, respectively. In validation, mismatches between measured and simulated data are larger, but still with Nash-Sutcliffe efficiency scores above 0.5 for three out of the four sites. Although measurement errors associated with eddy covariance data are known to be heteroscedastic, we showed that assuming a classical linear heteroscedastic model of the residual errors in the inversion do not fully remove heteroscedasticity. Since the employed heteroscedastic error model allows for larger deviations between simulated and measured data as the magnitude of the measured data increases, this error model expectedly lead to poorer data fitting compared to inversions considering a constant variance of the residual errors. Furthermore, sampling the residual error variances along with model parameters results in overall similar model parameter posterior distributions as those obtained by fixing these variances beforehand, while slightly improving model performance. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides model behaviour, difference between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics. Lastly, the possibility of finding a common set of parameters among the four experimental sites is discussed.

Groundwater Pollution Source Identification using Linked ANN-Optimization Model

NASA Astrophysics Data System (ADS)

Ayaz, Md; Srivastava, Rajesh; Jain, Ashu

2014-05-01

Groundwater is the principal source of drinking water in several parts of the world. Contamination of groundwater has become a serious health and environmental problem today. Human activities including industrial and agricultural activities are generally responsible for this contamination. Identification of groundwater pollution source is a major step in groundwater pollution remediation. Complete knowledge of pollution source in terms of its source characteristics is essential to adopt an effective remediation strategy. Groundwater pollution source is said to be identified completely when the source characteristics - location, strength and release period - are known. Identification of unknown groundwater pollution source is an ill-posed inverse problem. It becomes more difficult for real field conditions, when the lag time between the first reading at observation well and the time at which the source becomes active is not known. We developed a linked ANN-Optimization model for complete identification of an unknown groundwater pollution source. The model comprises two parts- an optimization model and an ANN model. Decision variables of linked ANN-Optimization model contain source location and release period of pollution source. An objective function is formulated using the spatial and temporal data of observed and simulated concentrations, and then minimized to identify the pollution source parameters. In the formulation of the objective function, we require the lag time which is not known. An ANN model with one hidden layer is trained using Levenberg-Marquardt algorithm to find the lag time. Different combinations of source locations and release periods are used as inputs and lag time is obtained as the output. Performance of the proposed model is evaluated for two and three dimensional case with error-free and erroneous data. Erroneous data was generated by adding uniformly distributed random error (error level 0-10%) to the analytically computed concentration values. The main advantage of the proposed model is that it requires only upper half of the breakthrough curve and is capable of predicting source parameters when the lag time is not known. Linking of ANN model with proposed optimization model reduces the dimensionality of the decision variables of the optimization model by one and hence complexity of optimization model is reduced. The results show that our proposed linked ANN-Optimization model is able to predict the source parameters for the error-free data accurately. The proposed model was run several times to obtain the mean, standard deviation and interval estimate of the predicted parameters for observations with random measurement errors. It was observed that mean values as predicted by the model were quite close to the exact values. An increasing trend was observed in the standard deviation of the predicted values with increasing level of measurement error. The model appears to be robust and may be efficiently utilized to solve the inverse pollution source identification problem.

Joint probabilistic determination of earthquake location and velocity structure: application to local and regional events

NASA Astrophysics Data System (ADS)

Beucler, E.; Haugmard, M.; Mocquet, A.

2016-12-01

The most widely used inversion schemes to locate earthquakes are based on iterative linearized least-squares algorithms and using an a priori knowledge of the propagation medium. When a small amount of observations is available for moderate events for instance, these methods may lead to large trade-offs between outputs and both the velocity model and the initial set of hypocentral parameters. We present a joint structure-source determination approach using Bayesian inferences. Monte-Carlo continuous samplings, using Markov chains, generate models within a broad range of parameters, distributed according to the unknown posterior distributions. The non-linear exploration of both the seismic structure (velocity and thickness) and the source parameters relies on a fast forward problem using 1-D travel time computations. The a posteriori covariances between parameters (hypocentre depth, origin time and seismic structure among others) are computed and explicitly documented. This method manages to decrease the influence of the surrounding seismic network geometry (sparse and/or azimuthally inhomogeneous) and a too constrained velocity structure by inferring realistic distributions on hypocentral parameters. Our algorithm is successfully used to accurately locate events of the Armorican Massif (western France), which is characterized by moderate and apparently diffuse local seismicity.

Rational selection of experimental readout and intervention sites for reducing uncertainties in computational model predictions.

PubMed

Flassig, Robert J; Migal, Iryna; der Zalm, Esther van; Rihko-Struckmann, Liisa; Sundmacher, Kai

2015-01-16

Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort. In this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts. Having data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.

Effective model approach to the dense state of QCD matter

NASA Astrophysics Data System (ADS)

Fukushima, Kenji

2011-12-01

The first-principle approach to the dense state of QCD matter, i.e. the lattice-QCD simulation at finite baryon density, is not under theoretical control for the moment. The effective model study based on QCD symmetries is a practical alternative. However the model parameters that are fixed by hadronic properties in the vacuum may have unknown dependence on the baryon chemical potential. We propose a new prescription to constrain the effective model parameters by the matching condition with the thermal Statistical Model. In the transitional region where thermal quantities blow up in the Statistical Model, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from hadrons and resonances. We use the Polyakov-loop coupled Nambu-Jona-Lasinio (PNJL) model as an effective description in the quark side and show how the matching condition is satisfied by a simple ansäatz on the Polyakov loop potential. Our results favor a phase diagram with the chiral phase transition located at slightly higher temperature than deconfinement which stays close to the chemical freeze-out points.

Calibration of 3D ALE finite element model from experiments on friction stir welding of lap joints

NASA Astrophysics Data System (ADS)

Fourment, Lionel; Gastebois, Sabrina; Dubourg, Laurent

2016-10-01

In order to support the design of such a complex process like Friction Stir Welding (FSW) for the aeronautic industry, numerical simulation software requires (1) developing an efficient and accurate Finite Element (F.E.) formulation that allows predicting welding defects, (2) properly modeling the thermo-mechanical complexity of the FSW process and (3) calibrating the F.E. model from accurate measurements from FSW experiments. This work uses a parallel ALE formulation developed in the Forge® F.E. code to model the different possible defects (flashes and worm holes), while pin and shoulder threads are modeled by a new friction law at the tool / material interface. FSW experiments require using a complex tool with scroll on shoulder, which is instrumented for providing sensitive thermal data close to the joint. Calibration of unknown material thermal coefficients, constitutive equations parameters and friction model from measured forces, torques and temperatures is carried out using two F.E. models, Eulerian and ALE, to reach a satisfactory agreement assessed by the proper sensitivity of the simulation to process parameters.

Systems identification using a modified Newton-Raphson method: A FORTRAN program

NASA Technical Reports Server (NTRS)

Taylor, L. W., Jr.; Iliff, K. W.

1972-01-01

A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

Mapping land water and energy balance relations through conditional sampling of remote sensing estimates of atmospheric forcing and surface states

NASA Astrophysics Data System (ADS)

Farhadi, Leila; Entekhabi, Dara; Salvucci, Guido

2016-04-01

In this study, we develop and apply a mapping estimation capability for key unknown parameters that link the surface water and energy balance equations. The method is applied to the Gourma region in West Africa. The accuracy of the estimation method at point scale was previously examined using flux tower data. In this study, the capability is scaled to be applicable with remotely sensed data products and hence allow mapping. Parameters of the system are estimated through a process that links atmospheric forcing (precipitation and incident radiation), surface states, and unknown parameters. Based on conditional averaging of land surface temperature and moisture states, respectively, a single objective function is posed that measures moisture and temperature-dependent errors solely in terms of observed forcings and surface states. This objective function is minimized with respect to parameters to identify evapotranspiration and drainage models and estimate water and energy balance flux components. The uncertainty of the estimated parameters (and associated statistical confidence limits) is obtained through the inverse of Hessian of the objective function, which is an approximation of the covariance matrix. This calibration-free method is applied to the mesoscale region of Gourma in West Africa using multiplatform remote sensing data. The retrievals are verified against tower-flux field site data and physiographic characteristics of the region. The focus is to find the functional form of the evaporative fraction dependence on soil moisture, a key closure function for surface and subsurface heat and moisture dynamics, using remote sensing data.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries.

PubMed

McGarry, Matthew; Nauleau, Pierre; Apostolakis, Iason; Konofagou, Elisa

2017-11-07

Accurate arterial stiffness measurement would improve diagnosis and monitoring for many diseases. Atherosclerotic plaques and aneurysms are expected to involve focal changes in vessel wall properties; therefore, a method to image the stiffness variation would be a valuable clinical tool. The pulse wave inverse problem (PWIP) fits unknown parameters from a computational model of arterial pulse wave propagation to ultrasound-based measurements of vessel wall displacements by minimizing the difference between the model and measured displacements. The PWIP has been validated in phantoms, and this study presents the first in vivo demonstration. The common carotid arteries of five healthy volunteers were imaged five times in a single session with repositioning of the probe and subject between each scan. The 1D finite difference computational model used in the PWIP spanned from the start of the transducer to the carotid bifurcation, where a resistance outlet boundary condition was applied to approximately model the downstream reflection of the pulse wave. Unknown parameters that were estimated by the PWIP included a 10-segment linear piecewise compliance distribution and 16 discrete cosine transformation coefficients for each of the inlet boundary conditions. Input data was selected to include pulse waves resulting from the primary pulse and dicrotic notch. The recovered compliance maps indicate that the compliance increases close to the bifurcation, and the variability of the average pulse wave velocity estimated through the PWIP is on the order of 11%, which is similar to that of the conventional processing technique which tracks the wavefront arrival time (13%). Copyright © 2017 Elsevier Ltd. All rights reserved.

An offline approach for output-only Bayesian identification of stochastic nonlinear systems using unscented Kalman filtering

NASA Astrophysics Data System (ADS)

Erazo, Kalil; Nagarajaiah, Satish

2017-06-01

In this paper an offline approach for output-only Bayesian identification of stochastic nonlinear systems is presented. The approach is based on a re-parameterization of the joint posterior distribution of the parameters that define a postulated state-space stochastic model class. In the re-parameterization the state predictive distribution is included, marginalized, and estimated recursively in a state estimation step using an unscented Kalman filter, bypassing state augmentation as required by existing online methods. In applications expectations of functions of the parameters are of interest, which requires the evaluation of potentially high-dimensional integrals; Markov chain Monte Carlo is adopted to sample the posterior distribution and estimate the expectations. The proposed approach is suitable for nonlinear systems subjected to non-stationary inputs whose realization is unknown, and that are modeled as stochastic processes. Numerical verification and experimental validation examples illustrate the effectiveness and advantages of the approach, including: (i) an increased numerical stability with respect to augmented-state unscented Kalman filtering, avoiding divergence of the estimates when the forcing input is unmeasured; (ii) the ability to handle arbitrary prior and posterior distributions. The experimental validation of the approach is conducted using data from a large-scale structure tested on a shake table. It is shown that the approach is robust to inherent modeling errors in the description of the system and forcing input, providing accurate prediction of the dynamic response when the excitation history is unknown.

Quantity Competition in a Differentiated Duopoly

NASA Astrophysics Data System (ADS)

Ferreira, Fernanda A.; Ferreira, Flávio; Ferreira, Miguel; Pinto, Alberto A.

In this paper, we consider a Stackelberg duopoly competition with differentiated goods, linear and symmetric demand and with unknown costs. In our model, the two firms play a non-cooperative game with two stages: in a first stage, firm F 1 chooses the quantity, q 1, that is going to produce; in the second stage, firm F 2 observes the quantity q 1 produced by firm F 1 and chooses its own quantity q 2. Firms choose their output levels in order to maximise their profits. We suppose that each firm has two different technologies, and uses one of them following a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the variations of the expected profits with the parameters of the model, namely with the parameters of the probability distributions, and with the parameters of the demand and differentiation.

Quantification of Skeletal Blood Flow and Fluoride Metabolism in Rats using PET in a Pre-Clinical Stress Fracture Model

PubMed Central

Tomlinson, Ryan E.; Silva, Matthew J.; Shoghi, Kooresh I.

2013-01-01

Purpose Blood flow is an important factor in bone production and repair, but its role in osteogenesis induced by mechanical loading is unknown. Here, we present techniques for evaluating blood flow and fluoride metabolism in a pre-clinical stress fracture model of osteogenesis in rats. Procedures Bone formation was induced by forelimb compression in adult rats. 15O water and 18F fluoride PET imaging were used to evaluate blood flow and fluoride kinetics 7 days after loading. 15O water was modeled using a one-compartment, two-parameter model, while a two-compartment, three-parameter model was used to model 18F fluoride. Input functions were created from the heart, and a stochastic search algorithm was implemented to provide initial parameter values in conjunction with a Levenberg–Marquardt optimization algorithm. Results Loaded limbs are shown to have a 26% increase in blood flow rate, 113% increase in fluoride flow rate, 133% increase in fluoride flux, and 13% increase in fluoride incorporation into bone as compared to non-loaded limbs (p < 0.05 for all results). Conclusions The results shown here are consistent with previous studies, confirming this technique is suitable for evaluating the vascular response and mineral kinetics of osteogenic mechanical loading. PMID:21785919

On how to avoid input and structural uncertainties corrupt the inference of hydrological parameters using a Bayesian framework

NASA Astrophysics Data System (ADS)

Hernández, Mario R.; Francés, Félix

2015-04-01

One phase of the hydrological models implementation process, significantly contributing to the hydrological predictions uncertainty, is the calibration phase in which values of the unknown model parameters are tuned by optimizing an objective function. An unsuitable error model (e.g. Standard Least Squares or SLS) introduces noise into the estimation of the parameters. The main sources of this noise are the input errors and the hydrological model structural deficiencies. Thus, the biased calibrated parameters cause the divergence model phenomenon, where the errors variance of the (spatially and temporally) forecasted flows far exceeds the errors variance in the fitting period, and provoke the loss of part or all of the physical meaning of the modeled processes. In other words, yielding a calibrated hydrological model which works well, but not for the right reasons. Besides, an unsuitable error model yields a non-reliable predictive uncertainty assessment. Hence, with the aim of prevent all these undesirable effects, this research focuses on the Bayesian joint inference (BJI) of both the hydrological and error model parameters, considering a general additive (GA) error model that allows for correlation, non-stationarity (in variance and bias) and non-normality of model residuals. As hydrological model, it has been used a conceptual distributed model called TETIS, with a particular split structure of the effective model parameters. Bayesian inference has been performed with the aid of a Markov Chain Monte Carlo (MCMC) algorithm called Dream-ZS. MCMC algorithm quantifies the uncertainty of the hydrological and error model parameters by getting the joint posterior probability distribution, conditioned on the observed flows. The BJI methodology is a very powerful and reliable tool, but it must be used correctly this is, if non-stationarity in errors variance and bias is modeled, the Total Laws must be taken into account. The results of this research show that the application of BJI with a GA error model outperforms the hydrological parameters robustness (diminishing the divergence model phenomenon) and improves the reliability of the streamflow predictive distribution, in respect of the results of a bad error model as SLS. Finally, the most likely prediction in a validation period, for both BJI+GA and SLS error models shows a similar performance.

Inverse modelling for real-time estimation of radiological consequences in the early stage of an accidental radioactivity release.

PubMed

Pecha, Petr; Šmídl, Václav

2016-11-01

A stepwise sequential assimilation algorithm is proposed based on an optimisation approach for recursive parameter estimation and tracking of radioactive plume propagation in the early stage of a radiation accident. Predictions of the radiological situation in each time step of the plume propagation are driven by an existing short-term meteorological forecast and the assimilation procedure manipulates the model parameters to match the observations incoming concurrently from the terrain. Mathematically, the task is a typical ill-posed inverse problem of estimating the parameters of the release. The proposed method is designated as a stepwise re-estimation of the source term release dynamics and an improvement of several input model parameters. It results in a more precise determination of the adversely affected areas in the terrain. The nonlinear least-squares regression methodology is applied for estimation of the unknowns. The fast and adequately accurate segmented Gaussian plume model (SGPM) is used in the first stage of direct (forward) modelling. The subsequent inverse procedure infers (re-estimates) the values of important model parameters from the actual observations. Accuracy and sensitivity of the proposed method for real-time forecasting of the accident propagation is studied. First, a twin experiment generating noiseless simulated "artificial" observations is studied to verify the minimisation algorithm. Second, the impact of the measurement noise on the re-estimated source release rate is examined. In addition, the presented method can be used as a proposal for more advanced statistical techniques using, e.g., importance sampling. Copyright © 2016 Elsevier Ltd. All rights reserved.

Analyzing crash frequency in freeway tunnels: A correlated random parameters approach.

PubMed

Hou, Qinzhong; Tarko, Andrew P; Meng, Xianghai

2018-02-01

The majority of past road safety studies focused on open road segments while only a few focused on tunnels. Moreover, the past tunnel studies produced some inconsistent results about the safety effects of the traffic patterns, the tunnel design, and the pavement conditions. The effects of these conditions therefore remain unknown, especially for freeway tunnels in China. The study presented in this paper investigated the safety effects of these various factors utilizing a four-year period (2009-2012) of data as well as three models: 1) a random effects negative binomial model (RENB), 2) an uncorrelated random parameters negative binomial model (URPNB), and 3) a correlated random parameters negative binomial model (CRPNB). Of these three, the results showed that the CRPNB model provided better goodness-of-fit and offered more insights into the factors that contribute to tunnel safety. The CRPNB was not only able to allocate the part of the otherwise unobserved heterogeneity to the individual model parameters but also was able to estimate the cross-correlations between these parameters. Furthermore, the study results showed that traffic volume, tunnel length, proportion of heavy trucks, curvature, and pavement rutting were associated with higher frequencies of traffic crashes, while the distance to the tunnel wall, distance to the adjacent tunnel, distress ratio, International Roughness Index (IRI), and friction coefficient were associated with lower crash frequencies. In addition, the effects of the heterogeneity of the proportion of heavy trucks, the curvature, the rutting depth, and the friction coefficient were identified and their inter-correlations were analyzed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Material parameter estimation with terahertz time-domain spectroscopy.

PubMed

Dorney, T D; Baraniuk, R G; Mittleman, D M

2001-07-01

Imaging systems based on terahertz (THz) time-domain spectroscopy offer a range of unique modalities owing to the broad bandwidth, subpicosecond duration, and phase-sensitive detection of the THz pulses. Furthermore, the possibility exists for combining spectroscopic characterization or identification with imaging because the radiation is broadband in nature. To achieve this, we require novel methods for real-time analysis of THz waveforms. This paper describes a robust algorithm for extracting material parameters from measured THz waveforms. Our algorithm simultaneously obtains both the thickness and the complex refractive index of an unknown sample under certain conditions. In contrast, most spectroscopic transmission measurements require knowledge of the sample's thickness for an accurate determination of its optical parameters. Our approach relies on a model-based estimation, a gradient descent search, and the total variation measure. We explore the limits of this technique and compare the results with literature data for optical parameters of several different materials.

Modeling of feed-forward control using the partial least squares regression method in the tablet compression process.

PubMed

Hattori, Yusuke; Otsuka, Makoto

2017-05-30

In the pharmaceutical industry, the implementation of continuous manufacturing has been widely promoted in lieu of the traditional batch manufacturing approach. More specially, in recent years, the innovative concept of feed-forward control has been introduced in relation to process analytical technology. In the present study, we successfully developed a feed-forward control model for the tablet compression process by integrating data obtained from near-infrared (NIR) spectra and the physical properties of granules. In the pharmaceutical industry, batch manufacturing routinely allows for the preparation of granules with the desired properties through the manual control of process parameters. On the other hand, continuous manufacturing demands the automatic determination of these process parameters. Here, we proposed the development of a control model using the partial least squares regression (PLSR) method. The most significant feature of this method is the use of dataset integrating both the NIR spectra and the physical properties of the granules. Using our model, we determined that the properties of products, such as tablet weight and thickness, need to be included as independent variables in the PLSR analysis in order to predict unknown process parameters. Copyright © 2017 Elsevier B.V. All rights reserved.

A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

PubMed

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Generation Mechanism of Alternans in Luo-Rudy Model

NASA Astrophysics Data System (ADS)

Kitajima, Hiroyuki; Ioka, Eri; Yazawa, Toru

Electrical alternans is the alternating amplitude from beat to beat in the action potential of the cardiac cell. It has been associated with ventricular arrhythmias in many clinical studies; however, its dynamical mechanisms remain unknown. The reason is that we do not have realistic network models of the heart system. Recently, Yazawa clarified the network structure of the heart and the central nerve system in the crustacean heart. In this study, we construct a simple model of the heart system based on Yazawa’s experimental data. Using this model, we clarify that two parameters (the conductance of sodium ions and free concentration of potassium ions in the extracellular compartment) play the key roles of generating alternans. In particular, we clarify that the inactivation gate of the time-independent potassium channel is the most important parameter. Moreover, interaction between the membrane potential and potassium ionic currents is significant for generating alternate rhythms. This result indicates that if the muscle cell has problems such as channelopathies, there is great risk of generating alternans.

Parameter identification of piezoelectric hysteresis model based on improved artificial bee colony algorithm

NASA Astrophysics Data System (ADS)

Wang, Geng; Zhou, Kexin; Zhang, Yeming

2018-04-01

The widely used Bouc-Wen hysteresis model can be utilized to accurately simulate the voltage-displacement curves of piezoelectric actuators. In order to identify the unknown parameters of the Bouc-Wen model, an improved artificial bee colony (IABC) algorithm is proposed in this paper. A guiding strategy for searching the current optimal position of the food source is proposed in the method, which can help balance the local search ability and global exploitation capability. And the formula for the scout bees to search for the food source is modified to increase the convergence speed. Some experiments were conducted to verify the effectiveness of the IABC algorithm. The results show that the identified hysteresis model agreed well with the actual actuator response. Moreover, the identification results were compared with the standard particle swarm optimization (PSO) method, and it can be seen that the search performance in convergence rate of the IABC algorithm is better than that of the standard PSO method.

Quantitative composition determination at the atomic level using model-based high-angle annular dark field scanning transmission electron microscopy.

PubMed

Martinez, G T; Rosenauer, A; De Backer, A; Verbeeck, J; Van Aert, S

2014-02-01

High angle annular dark field scanning transmission electron microscopy (HAADF STEM) images provide sample information which is sensitive to the chemical composition. The image intensities indeed scale with the mean atomic number Z. To some extent, chemically different atomic column types can therefore be visually distinguished. However, in order to quantify the atomic column composition with high accuracy and precision, model-based methods are necessary. Therefore, an empirical incoherent parametric imaging model can be used of which the unknown parameters are determined using statistical parameter estimation theory (Van Aert et al., 2009, [1]). In this paper, it will be shown how this method can be combined with frozen lattice multislice simulations in order to evolve from a relative toward an absolute quantification of the composition of single atomic columns with mixed atom types. Furthermore, the validity of the model assumptions are explored and discussed. © 2013 Published by Elsevier B.V. All rights reserved.

A new method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao

2015-01-01

Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.

Poroelastic Modeling as a Proof of Concept for Modular Representation of Coupled Geophysical Processes

NASA Astrophysics Data System (ADS)

Walker, R. L., II; Knepley, M.; Aminzadeh, F.

2017-12-01

We seek to use the tools provided by the Portable, Extensible Toolkit for Scientific Computation (PETSc) to represent a multiphysics problem in a form that decouples the element definition from the fully coupled equation through the use of pointwise functions that imitate the strong form of the governing equation. This allows allows individual physical processes to be expressed as independent kernels that may be then coupled with the existing finite element framework, PyLith, and capitalizes upon the flexibility offered by the solver, data management, and time stepping algorithms offered by PETSc. To demonstrate a characteristic example of coupled geophysical simulation devised in this manner, we present a model of a synthetic poroelastic environment, with and without the consideration of inertial effects, with fluid initially represented as a single phase. Matrix displacement and fluid pressure serve as the desired unknowns, with the option for various model parameters represented as dependent variables of the central unknowns. While independent of PyLith, this model also serves to showcase the adaptability of physics kernels for synthetic forward modeling. In addition, we seek to expand the base case to demonstrate the impact of modeling fluid as single phase compressible versus a single incompressible phase. As a goal, we also seek to include multiphase fluid modeling, as well as capillary effects.

Extension of the lod score: the mod score.

PubMed

Clerget-Darpoux, F

2001-01-01

In 1955 Morton proposed the lod score method both for testing linkage between loci and for estimating the recombination fraction between them. If a disease is controlled by a gene at one of these loci, the lod score computation requires the prior specification of an underlying model that assigns the probabilities of genotypes from the observed phenotypes. To address the case of linkage studies for diseases with unknown mode of inheritance, we suggested (Clerget-Darpoux et al., 1986) extending the lod score function to a so-called mod score function. In this function, the variables are both the recombination fraction and the disease model parameters. Maximizing the mod score function over all these parameters amounts to maximizing the probability of marker data conditional on the disease status. Under the absence of linkage, the mod score conforms to a chi-square distribution, with extra degrees of freedom in comparison to the lod score function (MacLean et al., 1993). The mod score is asymptotically maximum for the true disease model (Clerget-Darpoux and Bonaïti-Pellié, 1992; Hodge and Elston, 1994). Consequently, the power to detect linkage through mod score will be highest when the space of models where the maximization is performed includes the true model. On the other hand, one must avoid overparametrization of the model space. For example, when the approach is applied to affected sibpairs, only two constrained disease model parameters should be used (Knapp et al., 1994) for the mod score maximization. It is also important to emphasize the existence of a strong correlation between the disease gene location and the disease model. Consequently, there is poor resolution of the location of the susceptibility locus when the disease model at this locus is unknown. Of course, this is true regardless of the statistics used. The mod score may also be applied in a candidate gene strategy to model the potential effect of this gene in the disease. Since, however, it ignores the information provided both by disease segregation and by linkage disequilibrium between the marker alleles and the functional disease alleles, its power of discrimination between genetic models is weak. The MASC method (Clerget-Darpoux et al., 1988) has been designed to address more efficiently the objectives of a candidate gene approach.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Selle, J.E.

A modification was made to the Kaufman method of calculating binary phase diagrams to permit calculation of intra-rare earth diagrams. Atomic volumes for all phases, real or hypothetical, are necessary to determine interaction parameters for calculation of complete diagrams. The procedures used to determine unknown atomic volumes are describes. Also, procedures are described for determining lattice stability parameters for unknown transformations. Results are presented on the calculation of intra-rare earth diagrams between both trivalent and divalent rare earths. 13 refs., 36 figs., 11 tabs.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

NASA Astrophysics Data System (ADS)

Miyata, Y.; Suzuki, T.; Takechi, M.; Urano, H.; Ide, S.

2015-07-01

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichlet and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.

An Adaptive Moving Target Imaging Method for Bistatic Forward-Looking SAR Using Keystone Transform and Optimization NLCS.

PubMed

Li, Zhongyu; Wu, Junjie; Huang, Yulin; Yang, Haiguang; Yang, Jianyu

2017-01-23

Bistatic forward-looking SAR (BFSAR) is a kind of bistatic synthetic aperture radar (SAR) system that can image forward-looking terrain in the flight direction of an aircraft. Until now, BFSAR imaging theories and methods for a stationary scene have been researched thoroughly. However, for moving-target imaging with BFSAR, the non-cooperative movement of the moving target induces some new issues: (I) large and unknown range cell migration (RCM) (including range walk and high-order RCM); (II) the spatial-variances of the Doppler parameters (including the Doppler centroid and high-order Doppler) are not only unknown, but also nonlinear for different point-scatterers. In this paper, we put forward an adaptive moving-target imaging method for BFSAR. First, the large and unknown range walk is corrected by applying keystone transform over the whole received echo, and then, the relationships among the unknown high-order RCM, the nonlinear spatial-variances of the Doppler parameters, and the speed of the mover, are established. After that, using an optimization nonlinear chirp scaling (NLCS) technique, not only can the unknown high-order RCM be accurately corrected, but also the nonlinear spatial-variances of the Doppler parameters can be balanced. At last, a high-order polynomial filter is applied to compress the whole azimuth data of the moving target. Numerical simulations verify the effectiveness of the proposed method.

Slope Estimation in Noisy Piecewise Linear Functions✩

PubMed Central

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2014-01-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure. PMID:25419020

Slope Estimation in Noisy Piecewise Linear Functions.

PubMed

Ingle, Atul; Bucklew, James; Sethares, William; Varghese, Tomy

2015-03-01

This paper discusses the development of a slope estimation algorithm called MAPSlope for piecewise linear data that is corrupted by Gaussian noise. The number and locations of slope change points (also known as breakpoints) are assumed to be unknown a priori though it is assumed that the possible range of slope values lies within known bounds. A stochastic hidden Markov model that is general enough to encompass real world sources of piecewise linear data is used to model the transitions between slope values and the problem of slope estimation is addressed using a Bayesian maximum a posteriori approach. The set of possible slope values is discretized, enabling the design of a dynamic programming algorithm for posterior density maximization. Numerical simulations are used to justify choice of a reasonable number of quantization levels and also to analyze mean squared error performance of the proposed algorithm. An alternating maximization algorithm is proposed for estimation of unknown model parameters and a convergence result for the method is provided. Finally, results using data from political science, finance and medical imaging applications are presented to demonstrate the practical utility of this procedure.

Predicting uncertainty in future marine ice sheet volume using Bayesian statistical methods

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

The marine ice instability can trigger rapid retreat of marine ice streams. Recent observations suggest that marine ice systems in West Antarctica have begun retreating. However, unknown ice dynamics, computationally intensive mathematical models, and uncertain parameters in these models make predicting retreat rate and ice volume difficult. In this work, we fuse current observational data with ice stream/shelf models to develop probabilistic predictions of future grounded ice sheet volume. Given observational data (e.g., thickness, surface elevation, and velocity) and a forward model that relates uncertain parameters (e.g., basal friction and basal topography) to these observations, we use a Bayesian framework to define a posterior distribution over the parameters. A stochastic predictive model then propagates uncertainties in these parameters to uncertainty in a particular quantity of interest (QoI)---here, the volume of grounded ice at a specified future time. While the Bayesian approach can in principle characterize the posterior predictive distribution of the QoI, the computational cost of both the forward and predictive models makes this effort prohibitively expensive. To tackle this challenge, we introduce a new Markov chain Monte Carlo method that constructs convergent approximations of the QoI target density in an online fashion, yielding accurate characterizations of future ice sheet volume at significantly reduced computational cost.Our second goal is to attribute uncertainty in these Bayesian predictions to uncertainties in particular parameters. Doing so can help target data collection, for the purpose of constraining the parameters that contribute most strongly to uncertainty in the future volume of grounded ice. For instance, smaller uncertainties in parameters to which the QoI is highly sensitive may account for more variability in the prediction than larger uncertainties in parameters to which the QoI is less sensitive. We use global sensitivity analysis to help answer this question, and make the computation of sensitivity indices computationally tractable using a combination of polynomial chaos and Monte Carlo techniques.

Adaptive control based on an on-line parameter estimation of an upper limb exoskeleton.

PubMed

Riani, Akram; Madani, Tarek; Hadri, Abdelhafid El; Benallegue, Abdelaziz

2017-07-01

This paper presents an adaptive control strategy for an upper-limb exoskeleton based on an on-line dynamic parameter estimator. The objective is to improve the control performance of this system that plays a critical role in assisting patients for shoulder, elbow and wrist joint movements. In general, the dynamic parameters of the human limb are unknown and differ from a person to another, which degrade the performances of the exoskeleton-human control system. For this reason, the proposed control scheme contains a supplementary loop based on a new efficient on-line estimator of the dynamic parameters. Indeed, the latter is acting upon the parameter adaptation of the controller to ensure the performances of the system in the presence of parameter uncertainties and perturbations. The exoskeleton used in this work is presented and a physical model of the exoskeleton interacting with a 7 Degree of Freedom (DoF) upper limb model is generated using the SimMechanics library of MatLab/Simulink. To illustrate the effectiveness of the proposed approach, an example of passive rehabilitation movements is performed using multi-body dynamic simulation. The aims is to maneuver the exoskeleton that drive the upper limb to track desired trajectories in the case of the passive arm movements.

A Bayesian method for inferring transmission chains in a partially observed epidemic.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef M.; Ray, Jaideep

2008-10-01

We present a Bayesian approach for estimating transmission chains and rates in the Abakaliki smallpox epidemic of 1967. The epidemic affected 30 individuals in a community of 74; only the dates of appearance of symptoms were recorded. Our model assumes stochastic transmission of the infections over a social network. Distinct binomial random graphs model intra- and inter-compound social connections, while disease transmission over each link is treated as a Poisson process. Link probabilities and rate parameters are objects of inference. Dates of infection and recovery comprise the remaining unknowns. Distributions for smallpox incubation and recovery periods are obtained from historicalmore » data. Using Markov chain Monte Carlo, we explore the joint posterior distribution of the scalar parameters and provide an expected connectivity pattern for the social graph and infection pathway.« less

Original analytic solution of a half-bridge modelled as a statically indeterminate system

NASA Astrophysics Data System (ADS)

Oanta, Emil M.; Panait, Cornel; Raicu, Alexandra; Barhalescu, Mihaela

2016-12-01

The paper presents an original computer based analytical model of a half-bridge belonging to a circular settling tank. The primary unknown is computed using the force method, the coefficients of the canonical equation being calculated using either the discretization of the bending moment diagram in trapezoids, or using the relations specific to the polygons. A second algorithm based on the method of initial parameters is also presented. Analyzing the new solution we came to the conclusion that most of the computer code developed for other model may be reused. The results are useful to evaluate the behavior of the structure and to compare with the results of the finite element models.

Bayesian inversions of a dynamic vegetation model at four European grassland sites

NASA Astrophysics Data System (ADS)

Minet, J.; Laloy, E.; Tychon, B.; Francois, L.

2015-05-01

Eddy covariance data from four European grassland sites are used to probabilistically invert the CARAIB (CARbon Assimilation In the Biosphere) dynamic vegetation model (DVM) with 10 unknown parameters, using the DREAM(ZS) (DiffeRential Evolution Adaptive Metropolis) Markov chain Monte Carlo (MCMC) sampler. We focus on comparing model inversions, considering both homoscedastic and heteroscedastic eddy covariance residual errors, with variances either fixed a priori or jointly inferred together with the model parameters. Agreements between measured and simulated data during calibration are comparable with previous studies, with root mean square errors (RMSEs) of simulated daily gross primary productivity (GPP), ecosystem respiration (RECO) and evapotranspiration (ET) ranging from 1.73 to 2.19, 1.04 to 1.56 g C m-2 day-1 and 0.50 to 1.28 mm day-1, respectively. For the calibration period, using a homoscedastic eddy covariance residual error model resulted in a better agreement between measured and modelled data than using a heteroscedastic residual error model. However, a model validation experiment showed that CARAIB models calibrated considering heteroscedastic residual errors perform better. Posterior parameter distributions derived from using a heteroscedastic model of the residuals thus appear to be more robust. This is the case even though the classical linear heteroscedastic error model assumed herein did not fully remove heteroscedasticity of the GPP residuals. Despite the fact that the calibrated model is generally capable of fitting the data within measurement errors, systematic bias in the model simulations are observed. These are likely due to model inadequacies such as shortcomings in the photosynthesis modelling. Besides the residual error treatment, differences between model parameter posterior distributions among the four grassland sites are also investigated. It is shown that the marginal distributions of the specific leaf area and characteristic mortality time parameters can be explained by site-specific ecophysiological characteristics.

A Particle Smoother with Sequential Importance Resampling for soil hydraulic parameter estimation: A lysimeter experiment

NASA Astrophysics Data System (ADS)

Montzka, Carsten; Hendricks Franssen, Harrie-Jan; Moradkhani, Hamid; Pütz, Thomas; Han, Xujun; Vereecken, Harry

2013-04-01

An adequate description of soil hydraulic properties is essential for a good performance of hydrological forecasts. So far, several studies showed that data assimilation could reduce the parameter uncertainty by considering soil moisture observations. However, these observations and also the model forcings were recorded with a specific measurement error. It seems a logical step to base state updating and parameter estimation on observations made at multiple time steps, in order to reduce the influence of outliers at single time steps given measurement errors and unknown model forcings. Such outliers could result in erroneous state estimation as well as inadequate parameters. This has been one of the reasons to use a smoothing technique as implemented for Bayesian data assimilation methods such as the Ensemble Kalman Filter (i.e. Ensemble Kalman Smoother). Recently, an ensemble-based smoother has been developed for state update with a SIR particle filter. However, this method has not been used for dual state-parameter estimation. In this contribution we present a Particle Smoother with sequentially smoothing of particle weights for state and parameter resampling within a time window as opposed to the single time step data assimilation used in filtering techniques. This can be seen as an intermediate variant between a parameter estimation technique using global optimization with estimation of single parameter sets valid for the whole period, and sequential Monte Carlo techniques with estimation of parameter sets evolving from one time step to another. The aims are i) to improve the forecast of evaporation and groundwater recharge by estimating hydraulic parameters, and ii) to reduce the impact of single erroneous model inputs/observations by a smoothing method. In order to validate the performance of the proposed method in a real world application, the experiment is conducted in a lysimeter environment.

qPIPSA: Relating enzymatic kinetic parameters and interaction fields

PubMed Central

Gabdoulline, Razif R; Stein, Matthias; Wade, Rebecca C

2007-01-01

Background The simulation of metabolic networks in quantitative systems biology requires the assignment of enzymatic kinetic parameters. Experimentally determined values are often not available and therefore computational methods to estimate these parameters are needed. It is possible to use the three-dimensional structure of an enzyme to perform simulations of a reaction and derive kinetic parameters. However, this is computationally demanding and requires detailed knowledge of the enzyme mechanism. We have therefore sought to develop a general, simple and computationally efficient procedure to relate protein structural information to enzymatic kinetic parameters that allows consistency between the kinetic and structural information to be checked and estimation of kinetic constants for structurally and mechanistically similar enzymes. Results We describe qPIPSA: quantitative Protein Interaction Property Similarity Analysis. In this analysis, molecular interaction fields, for example, electrostatic potentials, are computed from the enzyme structures. Differences in molecular interaction fields between enzymes are then related to the ratios of their kinetic parameters. This procedure can be used to estimate unknown kinetic parameters when enzyme structural information is available and kinetic parameters have been measured for related enzymes or were obtained under different conditions. The detailed interaction of the enzyme with substrate or cofactors is not modeled and is assumed to be similar for all the proteins compared. The protein structure modeling protocol employed ensures that differences between models reflect genuine differences between the protein sequences, rather than random fluctuations in protein structure. Conclusion Provided that the experimental conditions and the protein structural models refer to the same protein state or conformation, correlations between interaction fields and kinetic parameters can be established for sets of related enzymes. Outliers may arise due to variation in the importance of different contributions to the kinetic parameters, such as protein stability and conformational changes. The qPIPSA approach can assist in the validation as well as estimation of kinetic parameters, and provide insights into enzyme mechanism. PMID:17919319

Precision and accuracy in smFRET based structural studies—A benchmark study of the Fast-Nano-Positioning System

NASA Astrophysics Data System (ADS)

Nagy, Julia; Eilert, Tobias; Michaelis, Jens

2018-03-01

Modern hybrid structural analysis methods have opened new possibilities to analyze and resolve flexible protein complexes where conventional crystallographic methods have reached their limits. Here, the Fast-Nano-Positioning System (Fast-NPS), a Bayesian parameter estimation-based analysis method and software, is an interesting method since it allows for the localization of unknown fluorescent dye molecules attached to macromolecular complexes based on single-molecule Förster resonance energy transfer (smFRET) measurements. However, the precision, accuracy, and reliability of structural models derived from results based on such complex calculation schemes are oftentimes difficult to evaluate. Therefore, we present two proof-of-principle benchmark studies where we use smFRET data to localize supposedly unknown positions on a DNA as well as on a protein-nucleic acid complex. Since we use complexes where structural information is available, we can compare Fast-NPS localization to the existing structural data. In particular, we compare different dye models and discuss how both accuracy and precision can be optimized.

A motion algorithm to extract physical and motion parameters of mobile targets from cone-beam computed tomographic images.

PubMed

Alsbou, Nesreen; Ahmad, Salahuddin; Ali, Imad

2016-05-17

A motion algorithm has been developed to extract length, CT number level and motion amplitude of a mobile target from cone-beam CT (CBCT) images. The algorithm uses three measurable parameters: Apparent length and blurred CT number distribution of a mobile target obtained from CBCT images to determine length, CT-number value of the stationary target, and motion amplitude. The predictions of this algorithm are tested with mobile targets having different well-known sizes that are made from tissue-equivalent gel which is inserted into a thorax phantom. The phantom moves sinusoidally in one-direction to simulate respiratory motion using eight amplitudes ranging 0-20 mm. Using this motion algorithm, three unknown parameters are extracted that include: Length of the target, CT number level, speed or motion amplitude for the mobile targets from CBCT images. The motion algorithm solves for the three unknown parameters using measured length, CT number level and gradient for a well-defined mobile target obtained from CBCT images. The motion model agrees with the measured lengths which are dependent on the target length and motion amplitude. The gradient of the CT number distribution of the mobile target is dependent on the stationary CT number level, the target length and motion amplitude. Motion frequency and phase do not affect the elongation and CT number distribution of the mobile target and could not be determined. A motion algorithm has been developed to extract three parameters that include length, CT number level and motion amplitude or speed of mobile targets directly from reconstructed CBCT images without prior knowledge of the stationary target parameters. This algorithm provides alternative to 4D-CBCT without requirement of motion tracking and sorting of the images into different breathing phases. The motion model developed here works well for tumors that have simple shapes, high contrast relative to surrounding tissues and move nearly in regular motion pattern that can be approximated with a simple sinusoidal function. This algorithm has potential applications in diagnostic CT imaging and radiotherapy in terms of motion management.

Closing the loop: modelling of heart failure progression from health to end-stage using a meta-analysis of left ventricular pressure-volume loops.

PubMed

Warriner, David R; Brown, Alistair G; Varma, Susheel; Sheridan, Paul J; Lawford, Patricia; Hose, David R; Al-Mohammad, Abdallah; Shi, Yubing

2014-01-01

The American Heart Association (AHA)/American College of Cardiology (ACC) guidelines for the classification of heart failure (HF) are descriptive but lack precise and objective measures which would assist in categorising such patients. Our aim was two fold, firstly to demonstrate quantitatively the progression of HF through each stage using a meta-analysis of existing left ventricular (LV) pressure-volume (PV) loop data and secondly use the LV PV loop data to create stage specific HF models. A literature search yielded 31 papers with PV data, representing over 200 patients in different stages of HF. The raw pressure and volume data were extracted from the papers using a digitising software package and the means were calculated. The data demonstrated that, as HF progressed, stroke volume (SV), ejection fraction (EF%) decreased while LV volumes increased. A 2-element lumped parameter model was employed to model the mean loops and the error was calculated between the loops, demonstrating close fit between the loops. The only parameter that was consistently and statistically different across all the stages was the elastance (Emax). For the first time, the authors have created a visual and quantitative representation of the AHA/ACC stages of LVSD-HF, from normal to end-stage. The study demonstrates that robust, load-independent and reproducible parameters, such as elastance, can be used to categorise and model HF, complementing the existing classification. The modelled PV loops establish previously unknown physiological parameters for each AHA/ACC stage of LVSD-HF, such as LV elastance and highlight that it this parameter alone, in lumped parameter models, that determines the severity of HF. Such information will enable cardiovascular modellers with an interest in HF, to create more accurate models of the heart as it fails.

A Novel Approach to Implement Takagi-Sugeno Fuzzy Models.

PubMed

Chang, Chia-Wen; Tao, Chin-Wang

2017-09-01

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

Nonlinear adaptive formation control for a class of autonomous holonomic planetary exploration rovers

NASA Astrophysics Data System (ADS)

Ganji, Farid

This dissertation presents novel nonlinear adaptive formation controllers for a heterogeneous group of holonomic planetary exploration rovers navigating over flat terrains with unknown soil types and surface conditions. A leader-follower formation control architecture is employed. In the first part, using a point-mass model for robots and a Coulomb-viscous friction model for terrain resistance, direct adaptive control laws and a formation speed-adaptation strategy are developed for formation navigation over unknown and changing terrain in the presence of actuator saturation. On-line estimates of terrain frictional parameters compensate for unknown terrain resistance and its variations. In saturation events over difficult terrain, the formation speed is reduced based on the speed of the slowest saturated robot, using internal fleet communication and a speed-adaptation strategy, so that the formation error stays bounded and small. A formal proof for asymptotic stability of the formation system in non-saturated conditions is given. The performance of robot controllers are verified using a modular 3-robot formation simulator. Simulations show that the formation errors reduce to zero asymptotically under non-saturated conditions as is guaranteed by the theoretical proof. In the second part, the proposed adaptive control methodology is extended for formation control of a class of omnidirectional rovers with three independently-driven universal holonomic rigid wheels, where the rovers' rigid-body dynamics, drive-system electromechanical characteristics, and wheel-ground interaction mechanics are incorporated. Holonomic rovers have the ability to move simultaneously and independently in translation and rotation, rendering great maneuverability and agility, which makes them suitable for formation navigation. Novel nonlinear adaptive control laws are designed for the input voltages of the three wheel-drive motors. The motion resistance, which is due to the sinkage of rover wheels in soft planetary terrain, is modeled using classical terramechanics theory. The unknown system parameters for adaptive estimation pertain to the rolling resistance forces and scrubbing resistance torques at the wheel-terrain interfaces. Novel terramechanical formulas for terrain resistance forces and torques are derived via considering the universal holonomic wheels as rigid toroidal wheels moving forward and/or sideways as well as turning on soft ground. The asymptotic stability of the formation control system is rigorously proved using Lyapunov's direct method.

A global search inversion for earthquake kinematic rupture history: Application to the 2000 western Tottori, Japan earthquake

USGS Publications Warehouse

Piatanesi, A.; Cirella, A.; Spudich, P.; Cocco, M.

2007-01-01

We present a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. To account for the actual rupture complexity, the fault parameters are spatially variable peak slip velocity, slip direction, rupture time and risetime. The unknown parameters are given at the nodes of the subfaults, whereas the parameters within a subfault are allowed to vary through a bilinear interpolation of the nodal values. The forward modeling is performed with a discrete wave number technique, whose Green's functions include the complete response of the vertically varying Earth structure. During the first stage, an algorithm based on the heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of parameter space. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some synthetic tests to show the effectiveness of the method and its robustness to uncertainty of the adopted crustal model. Finally, we apply this inverse technique to the well recorded 2000 western Tottori, Japan, earthquake (Mw 6.6); we confirm that the rupture process is characterized by large slip (3-4 m) at very shallow depths but, differently from previous studies, we imaged a new slip patch (2-2.5 m) located deeper, between 14 and 18 km depth. Copyright 2007 by the American Geophysical Union.

Polarimetric subspace target detector for SAR data based on the Huynen dihedral model

NASA Astrophysics Data System (ADS)

Larson, Victor J.; Novak, Leslie M.

1995-06-01

Two new polarimetric subspace target detectors are developed based on a dihedral signal model for bright peaks within a spatially extended target signature. The first is a coherent dihedral target detector based on the exact Huynen model for a dihedral. The second is a noncoherent dihedral target detector based on the Huynen model with an extra unknown phase term. Expressions for these polarimetric subspace target detectors are developed for both additive Gaussian clutter and more general additive spherically invariant random vector clutter including the K-distribution. For the case of Gaussian clutter with unknown clutter parameters, constant false alarm rate implementations of these polarimetric subspace target detectors are developed. The performance of these dihedral detectors is demonstrated with real millimeter-wave fully polarimetric SAR data. The coherent dihedral detector which is developed with a more accurate description of a dihedral offers no performance advantage over the noncoherent dihedral detector which is computationally more attractive. The dihedral detectors do a better job of separating a set of tactical military targets from natural clutter compared to a detector that assumes no knowledge about the polarimetric structure of the target signal.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

The geostatistical approach for structural and stratigraphic framework analysis of offshore NW Bonaparte Basin, Australia

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wahid, Ali, E-mail: ali.wahid@live.com; Salim, Ahmed Mohamed Ahmed, E-mail: mohamed.salim@petronas.com.my; Yusoff, Wan Ismail Wan, E-mail: wanismail-wanyusoff@petronas.com.my

2016-02-01

Geostatistics or statistical approach is based on the studies of temporal and spatial trend, which depend upon spatial relationships to model known information of variable(s) at unsampled locations. The statistical technique known as kriging was used for petrophycial and facies analysis, which help to assume spatial relationship to model the geological continuity between the known data and the unknown to produce a single best guess of the unknown. Kriging is also known as optimal interpolation technique, which facilitate to generate best linear unbiased estimation of each horizon. The idea is to construct a numerical model of the lithofacies and rockmore » properties that honor available data and further integrate with interpreting seismic sections, techtonostratigraphy chart with sea level curve (short term) and regional tectonics of the study area to find the structural and stratigraphic growth history of the NW Bonaparte Basin. By using kriging technique the models were built which help to estimate different parameters like horizons, facies, and porosities in the study area. The variograms were used to determine for identification of spatial relationship between data which help to find the depositional history of the North West (NW) Bonaparte Basin.« less

Structure-activity relationships for serotonin transporter and dopamine receptor selectivity.

PubMed

Agatonovic-Kustrin, Snezana; Davies, Paul; Turner, Joseph V

2009-05-01

Antipsychotic medications have a diverse pharmacology with affinity for serotonergic, dopaminergic, adrenergic, histaminergic and cholinergic receptors. Their clinical use now also includes the treatment of mood disorders, thought to be mediated by serotonergic receptor activity. The aim of our study was to characterise the molecular properties of antipsychotic agents, and to develop a model that would indicate molecular specificity for the dopamine (D(2)) receptor and the serotonin (5-HT) transporter. Back-propagation artificial neural networks (ANNs) were trained on a dataset of 47 ligands categorically assigned antidepressant or antipsychotic utility. The structure of each compound was encoded with 63 calculated molecular descriptors. ANN parameters including hidden neurons and input descriptors were optimised based on sensitivity analyses, with optimum models containing between four and 14 descriptors. Predicted binding preferences were in excellent agreement with clinical antipsychotic or antidepressant utility. Validated models were further tested by use of an external prediction set of five drugs with unknown mechanism of action. The SAR models developed revealed the importance of simple molecular characteristics for differential binding to the D(2) receptor and the 5-HT transporter. These included molecular size and shape, solubility parameters, hydrogen donating potential, electrostatic parameters, stereochemistry and presence of nitrogen. The developed models and techniques employed are expected to be useful in the rational design of future therapeutic agents.

Calibration-induced uncertainty of the EPIC model to estimate climate change impact on global maize yield

NASA Astrophysics Data System (ADS)

Xiong, Wei; Skalský, Rastislav; Porter, Cheryl H.; Balkovič, Juraj; Jones, James W.; Yang, Di

2016-09-01

Understanding the interactions between agricultural production and climate is necessary for sound decision-making in climate policy. Gridded and high-resolution crop simulation has emerged as a useful tool for building this understanding. Large uncertainty exists in this utilization, obstructing its capacity as a tool to devise adaptation strategies. Increasing focus has been given to sources of uncertainties for climate scenarios, input-data, and model, but uncertainties due to model parameter or calibration are still unknown. Here, we use publicly available geographical data sets as input to the Environmental Policy Integrated Climate model (EPIC) for simulating global-gridded maize yield. Impacts of climate change are assessed up to the year 2099 under a climate scenario generated by HadEM2-ES under RCP 8.5. We apply five strategies by shifting one specific parameter in each simulation to calibrate the model and understand the effects of calibration. Regionalizing crop phenology or harvest index appears effective to calibrate the model for the globe, but using various values of phenology generates pronounced difference in estimated climate impact. However, projected impacts of climate change on global maize production are consistently negative regardless of the parameter being adjusted. Different values of model parameter result in a modest uncertainty at global level, with difference of the global yield change less than 30% by the 2080s. The uncertainty subjects to decrease if applying model calibration or input data quality control. Calibration has a larger effect at local scales, implying the possible types and locations for adaptation.

Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

PubMed Central

Dräger, Andreas; Kronfeld, Marcel; Ziller, Michael J; Supper, Jochen; Planatscher, Hannes; Magnus, Jørgen B; Oldiges, Marco; Kohlbacher, Oliver; Zell, Andreas

2009-01-01

Background To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem. Results We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis. Conclusion A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings. PMID:19144170

Constraining sterile neutrinos with AMANDA and IceCube atmospheric neutrino data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Esmaili, Arman; Peres, O.L.G.; Halzen, Francis, E-mail: aesmaili@ifi.unicamp.br, E-mail: halzen@icecube.wisc.edu, E-mail: orlando@ifi.unicamp.br

2012-11-01

We demonstrate that atmospheric neutrino data accumulated with the AMANDA and the partially deployed IceCube experiments constrain the allowed parameter space for a hypothesized fourth sterile neutrino beyond the reach of a combined analysis of all other experiments, for Δm{sup 2}{sub 41}∼<1 eV{sup 2}. Although the IceCube data wins the statistics in the analysis, the advantage of a combined analysis of AMANDA and IceCube data is the partial remedy of yet unknown instrumental systematic uncertainties. We also illustrate the sensitivity of the completed IceCube detector, that is now taking data, to the parameter space of 3+1 model.

Procedures and results related to the direct determination of gravity anomalies from satellite and terrestrial gravity data

NASA Technical Reports Server (NTRS)

Rapp, R. H.

1974-01-01

The equations needed for the incorporation of gravity anomalies as unknown parameters in an orbit determination program are described. These equations were implemented in the Geodyn computer program which was used to process optical satellite observations. The arc dependent parameter unknowns, 184 unknown 15 deg and coordinates of 7 tracking stations were considered. Up to 39 arcs (5 to 7 days) involving 10 different satellites, were processed. An anomaly solution from the satellite data and a combination solution with 15 deg terrestrial anomalies were made. The limited data samples indicate that the method works. The 15 deg anomalies from various solutions and the potential coefficients implied by the different solutions are reported.

Predicting minimum uncertainties in the inversion of ocean color geophysical parameters based on Cramer-Rao bounds.

PubMed

Jay, Sylvain; Guillaume, Mireille; Chami, Malik; Minghelli, Audrey; Deville, Yannick; Lafrance, Bruno; Serfaty, Véronique

2018-01-22

We present an analytical approach based on Cramer-Rao Bounds (CRBs) to investigate the uncertainties in estimated ocean color parameters resulting from the propagation of uncertainties in the bio-optical reflectance modeling through the inversion process. Based on given bio-optical and noise probabilistic models, CRBs can be computed efficiently for any set of ocean color parameters and any sensor configuration, directly providing the minimum estimation variance that can be possibly attained by any unbiased estimator of any targeted parameter. Here, CRBs are explicitly developed using (1) two water reflectance models corresponding to deep and shallow waters, resp., and (2) four probabilistic models describing the environmental noises observed within four Sentinel-2 MSI, HICO, Sentinel-3 OLCI and MODIS images, resp. For both deep and shallow waters, CRBs are shown to be consistent with the experimental estimation variances obtained using two published remote-sensing methods, while not requiring one to perform any inversion. CRBs are also used to investigate to what extent perfect a priori knowledge on one or several geophysical parameters can improve the estimation of remaining unknown parameters. For example, using pre-existing knowledge of bathymetry (e.g., derived from LiDAR) within the inversion is shown to greatly improve the retrieval of bottom cover for shallow waters. Finally, CRBs are shown to provide valuable information on the best estimation performances that may be achieved with the MSI, HICO, OLCI and MODIS configurations for a variety of oceanic, coastal and inland waters. CRBs are thus demonstrated to be an informative and efficient tool to characterize minimum uncertainties in inverted ocean color geophysical parameters.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

Finite element method (FEM) model of the mechanical stress on phospholipid membranes from shock waves produced in nanosecond electric pulses (nsEP)

NASA Astrophysics Data System (ADS)

Barnes, Ronald; Roth, Caleb C.; Shadaram, Mehdi; Beier, Hope; Ibey, Bennett L.

2015-03-01

The underlying mechanism(s) responsible for nanoporation of phospholipid membranes by nanosecond pulsed electric fields (nsEP) remains unknown. The passage of a high electric field through a conductive medium creates two primary contributing factors that may induce poration: the electric field interaction at the membrane and the shockwave produced from electrostriction of a polar submersion medium exposed to an electric field. Previous work has focused on the electric field interaction at the cell membrane, through such models as the transport lattice method. Our objective is to model the shock wave cell membrane interaction induced from the density perturbation formed at the rising edge of a high voltage pulse in a polar liquid resulting in a shock wave propagating away from the electrode toward the cell membrane. Utilizing previous data from cell membrane mechanical parameters, and nsEP generated shockwave parameters, an acoustic shock wave model based on the Helmholtz equation for sound pressure was developed and coupled to a cell membrane model with finite-element modeling in COMSOL. The acoustic structure interaction model was developed to illustrate the harmonic membrane displacements and stresses resulting from shockwave and membrane interaction based on Hooke's law. Poration is predicted by utilizing membrane mechanical breakdown parameters including cortical stress limits and hydrostatic pressure gradients.

Use of an anaerobic sequencing batch reactor for parameter estimation in modelling of anaerobic digestion.

PubMed

Batstone, D J; Torrijos, M; Ruiz, C; Schmidt, J E

2004-01-01

The model structure in anaerobic digestion has been clarified following publication of the IWA Anaerobic Digestion Model No. 1 (ADM1). However, parameter values are not well known, and uncertainty and variability in the parameter values given is almost unknown. Additionally, platforms for identification of parameters, namely continuous-flow laboratory digesters, and batch tests suffer from disadvantages such as long run times, and difficulty in defining initial conditions, respectively. Anaerobic sequencing batch reactors (ASBRs) are sequenced into fill-react-settle-decant phases, and offer promising possibilities for estimation of parameters, as they are by nature, dynamic in behaviour, and allow repeatable behaviour to establish initial conditions, and evaluate parameters. In this study, we estimated parameters describing winery wastewater (most COD as ethanol) degradation using data from sequencing operation, and validated these parameters using unsequenced pulses of ethanol and acetate. The model used was the ADM1, with an extension for ethanol degradation. Parameter confidence spaces were found by non-linear, correlated analysis of the two main Monod parameters; maximum uptake rate (k(m)), and half saturation concentration (K(S)). These parameters could be estimated together using only the measured acetate concentration (20 points per cycle). From interpolating the single cycle acetate data to multiple cycles, we estimate that a practical "optimal" identifiability could be achieved after two cycles for the acetate parameters, and three cycles for the ethanol parameters. The parameters found performed well in the short term, and represented the pulses of acetate and ethanol (within 4 days of the winery-fed cycles) very well. The main discrepancy was poor prediction of pH dynamics, which could be due to an unidentified buffer with an overall influence the same as a weak base (possibly CaCO3). Based on this work, ASBR systems are effective for parameter estimation, especially for comparative wastewater characterisation. The main disadvantages are heavy computational requirements for multiple cycles, and difficulty in establishing the correct biomass concentration in the reactor, though the last is also a disadvantage for continuous fixed film reactors, and especially, batch tests.

Developing a methodology for the inverse estimation of root architectural parameters from field based sampling schemes

NASA Astrophysics Data System (ADS)

Morandage, Shehan; Schnepf, Andrea; Vanderborght, Jan; Javaux, Mathieu; Leitner, Daniel; Laloy, Eric; Vereecken, Harry

2017-04-01

Root traits are increasingly important in breading of new crop varieties. E.g., longer and fewer lateral roots are suggested to improve drought resistance of wheat. Thus, detailed root architectural parameters are important. However, classical field sampling of roots only provides more aggregated information such as root length density (coring), root counts per area (trenches) or root arrival curves at certain depths (rhizotubes). We investigate the possibility of obtaining the information about root system architecture of plants using field based classical root sampling schemes, based on sensitivity analysis and inverse parameter estimation. This methodology was developed based on a virtual experiment where a root architectural model was used to simulate root system development in a field, parameterized for winter wheat. This information provided the ground truth which is normally unknown in a real field experiment. The three sampling schemes coring, trenching, and rhizotubes where virtually applied to and aggregated information computed. Morris OAT global sensitivity analysis method was then performed to determine the most sensitive parameters of root architecture model for the three different sampling methods. The estimated means and the standard deviation of elementary effects of a total number of 37 parameters were evaluated. Upper and lower bounds of the parameters were obtained based on literature and published data of winter wheat root architectural parameters. Root length density profiles of coring, arrival curve characteristics observed in rhizotubes, and root counts in grids of trench profile method were evaluated statistically to investigate the influence of each parameter using five different error functions. Number of branches, insertion angle inter-nodal distance, and elongation rates are the most sensitive parameters and the parameter sensitivity varies slightly with the depth. Most parameters and their interaction with the other parameters show highly nonlinear effect to the model output. The most sensitive parameters will be subject to inverse estimation from the virtual field sampling data using DREAMzs algorithm. The estimated parameters can then be compared with the ground truth in order to determine the suitability of the sampling schemes to identify specific traits or parameters of the root growth model.

A user-friendly one-dimensional model for wet volcanic plumes

USGS Publications Warehouse

Mastin, Larry G.

2007-01-01

This paper presents a user-friendly graphically based numerical model of one-dimensional steady state homogeneous volcanic plumes that calculates and plots profiles of upward velocity, plume density, radius, temperature, and other parameters as a function of height. The model considers effects of water condensation and ice formation on plume dynamics as well as the effect of water added to the plume at the vent. Atmospheric conditions may be specified through input parameters of constant lapse rates and relative humidity, or by loading profiles of actual atmospheric soundings. To illustrate the utility of the model, we compare calculations with field-based estimates of plume height (∼9 km) and eruption rate (>∼4 × 105 kg/s) during a brief tephra eruption at Mount St. Helens on 8 March 2005. Results show that the atmospheric conditions on that day boosted plume height by 1–3 km over that in a standard dry atmosphere. Although the eruption temperature was unknown, model calculations most closely match the observations for a temperature that is below magmatic but above 100°C.

An adaptive state of charge estimation approach for lithium-ion series-connected battery system

NASA Astrophysics Data System (ADS)

Peng, Simin; Zhu, Xuelai; Xing, Yinjiao; Shi, Hongbing; Cai, Xu; Pecht, Michael

2018-07-01

Due to the incorrect or unknown noise statistics of a battery system and its cell-to-cell variations, state of charge (SOC) estimation of a lithium-ion series-connected battery system is usually inaccurate or even divergent using model-based methods, such as extended Kalman filter (EKF) and unscented Kalman filter (UKF). To resolve this problem, an adaptive unscented Kalman filter (AUKF) based on a noise statistics estimator and a model parameter regulator is developed to accurately estimate the SOC of a series-connected battery system. An equivalent circuit model is first built based on the model parameter regulator that illustrates the influence of cell-to-cell variation on the battery system. A noise statistics estimator is then used to attain adaptively the estimated noise statistics for the AUKF when its prior noise statistics are not accurate or exactly Gaussian. The accuracy and effectiveness of the SOC estimation method is validated by comparing the developed AUKF and UKF when model and measurement statistics noises are inaccurate, respectively. Compared with the UKF and EKF, the developed method shows the highest SOC estimation accuracy.

Dynamic model predicting overweight, obesity, and extreme obesity prevalence trends.

PubMed

Thomas, Diana M; Weedermann, Marion; Fuemmeler, Bernard F; Martin, Corby K; Dhurandhar, Nikhil V; Bredlau, Carl; Heymsfield, Steven B; Ravussin, Eric; Bouchard, Claude

2014-02-01

Obesity prevalence in the United States appears to be leveling, but the reasons behind the plateau remain unknown. Mechanistic insights can be provided from a mathematical model. The objective of this study is to model known multiple population parameters associated with changes in body mass index (BMI) classes and to establish conditions under which obesity prevalence will plateau. A differential equation system was developed that predicts population-wide obesity prevalence trends. The model considers both social and nonsocial influences on weight gain, incorporates other known parameters affecting obesity trends, and allows for country specific population growth. The dynamic model predicts that: obesity prevalence is a function of birthrate and the probability of being born in an obesogenic environment; obesity prevalence will plateau independent of current prevention strategies; and the US prevalence of overweight, obesity, and extreme obesity will plateau by about 2030 at 28%, 32%, and 9% respectively. The US prevalence of obesity is stabilizing and will plateau, independent of current preventative strategies. This trend has important implications in accurately evaluating the impact of various anti-obesity strategies aimed at reducing obesity prevalence. Copyright © 2013 The Obesity Society.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Reconstructing high-dimensional two-photon entangled states via compressive sensing

PubMed Central

Tonolini, Francesco; Chan, Susan; Agnew, Megan; Lindsay, Alan; Leach, Jonathan

2014-01-01

Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction procedures can become prohibitively time-consuming. Compressive sensing, a procedure for solving inverse problems by incorporating prior knowledge about the form of the solution, provides an attractive alternative to the problem of high-dimensional quantum state characterisation. Using a modified version of compressive sensing that incorporates the principles of singular value thresholding, we reconstruct the density matrix of a high-dimensional two-photon entangled system. The dimension of each photon is equal to d = 17, corresponding to a system of 83521 unknown real parameters. Accurate reconstruction is achieved with approximately 2500 measurements, only 3% of the total number of unknown parameters in the state. The algorithm we develop is fast, computationally inexpensive, and applicable to a wide range of quantum states, thus demonstrating compressive sensing as an effective technique for measuring the state of large-scale quantum systems. PMID:25306850

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

PubMed

Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

2018-01-01

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models

NASA Astrophysics Data System (ADS)

Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.

2012-02-01

This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stroeer, Alexander; Veitch, John

The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme-mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals ''out of the box'', handling the total number of signals as an additional unknown parameter beside the unknownmore » parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.« less

Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

NASA Astrophysics Data System (ADS)

Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

2018-01-01

To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Relaxation limit of a compressible gas-liquid model with well-reservoir interaction

NASA Astrophysics Data System (ADS)

Solem, Susanne; Evje, Steinar

2017-02-01

This paper deals with the relaxation limit of a two-phase compressible gas-liquid model which contains a pressure-dependent well-reservoir interaction term of the form q (P_r - P) where q>0 is the rate of the pressure-dependent influx/efflux of gas, P is the (unknown) wellbore pressure, and P_r is the (known) surrounding reservoir pressure. The model can be used to study gas-kick flow scenarios relevant for various wellbore operations. One extreme case is when the wellbore pressure P is largely dictated by the surrounding reservoir pressure P_r. Formally, this model is obtained by deriving the limiting system as the relaxation parameter q in the full model tends to infinity. The main purpose of this work is to understand to what extent this case can be represented by a well-defined mathematical model for a fixed global time T>0. Well-posedness of the full model has been obtained in Evje (SIAM J Math Anal 45(2):518-546, 2013). However, as the estimates for the full model are dependent on the relaxation parameter q, new estimates must be obtained for the equilibrium model to ensure existence of solutions. By means of appropriate a priori assumptions and some restrictions on the model parameters, necessary estimates (low order and higher order) are obtained. These estimates that depend on the global time T together with smallness assumptions on the initial data are then used to obtain existence of solutions in suitable Sobolev spaces.

Assessment of the accuracy of plasma shape reconstruction by the Cauchy condition surface method in JT-60SA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyata, Y.; Suzuki, T.; Takechi, M.

2015-07-15

For the purpose of stable plasma equilibrium control and detailed analysis, it is essential to reconstruct an accurate plasma boundary on the poloidal cross section in tokamak devices. The Cauchy condition surface (CCS) method is a numerical approach for calculating the spatial distribution of the magnetic flux outside a hypothetical surface and reconstructing the plasma boundary from the magnetic measurements located outside the plasma. The accuracy of the plasma shape reconstruction has been assessed by comparing the CCS method and an equilibrium calculation in JT-60SA with a high elongation and triangularity of plasma shape. The CCS, on which both Dirichletmore » and Neumann conditions are unknown, is defined as a hypothetical surface located inside the real plasma region. The accuracy of the plasma shape reconstruction is sensitive to the CCS free parameters such as the number of unknown parameters and the shape in JT-60SA. It is found that the optimum number of unknown parameters and the size of the CCS that minimizes errors in the reconstructed plasma shape are in proportion to the plasma size. Furthermore, it is shown that the accuracy of the plasma shape reconstruction is greatly improved using the optimum number of unknown parameters and shape of the CCS, and the reachable reconstruction errors in plasma shape and locations of strike points are within the target ranges in JT-60SA.« less

The application of the pilot points in groundwater numerical inversion model

NASA Astrophysics Data System (ADS)

Hu, Bin; Teng, Yanguo; Cheng, Lirong

2015-04-01

Numerical inversion simulation of groundwater has been widely applied in groundwater. Compared to traditional forward modeling, inversion model has more space to study. Zones and inversing modeling cell by cell are conventional methods. Pilot points is a method between them. The traditional inverse modeling method often uses software dividing the model into several zones with a few parameters needed to be inversed. However, distribution is usually too simple for modeler and result of simulation deviation. Inverse cell by cell will get the most actual parameter distribution in theory, but it need computational complexity greatly and quantity of survey data for geological statistical simulation areas. Compared to those methods, pilot points distribute a set of points throughout the different model domains for parameter estimation. Property values are assigned to model cells by Kriging to ensure geological units within the parameters of heterogeneity. It will reduce requirements of simulation area geological statistics and offset the gap between above methods. Pilot points can not only save calculation time, increase fitting degree, but also reduce instability of numerical model caused by numbers of parameters and other advantages. In this paper, we use pilot point in a field which structure formation heterogeneity and hydraulics parameter was unknown. We compare inversion modeling results of zones and pilot point methods. With the method of comparative analysis, we explore the characteristic of pilot point in groundwater inversion model. First, modeler generates an initial spatially correlated field given a geostatistical model by the description of the case site with the software named Groundwater Vistas 6. Defining Kriging to obtain the value of the field functions over the model domain on the basis of their values at measurement and pilot point locations (hydraulic conductivity), then we assign pilot points to the interpolated field which have been divided into 4 zones. And add range of disturbance values to inversion targets to calculate the value of hydraulic conductivity. Third, after inversion calculation (PEST), the interpolated field will minimize an objective function measuring the misfit between calculated and measured data. It's an optimization problem to find the optimum value of parameters. After the inversion modeling, the following major conclusion can be found out: (1) In a field structure formation is heterogeneity, the results of pilot point method is more real: better fitting result of parameters, more stable calculation of numerical simulation (stable residual distribution). Compared to zones, it is better of reflecting the heterogeneity of study field. (2) Pilot point method ensures that each parameter is sensitive and not entirely dependent on other parameters. Thus it guarantees the relative independence and authenticity of parameters evaluation results. However, it costs more time to calculate than zones. Key words: groundwater; pilot point; inverse model; heterogeneity; hydraulic conductivity

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

NASA Astrophysics Data System (ADS)

Hassanabadi, Amir Hossein; Shafiee, Masoud; Puig, Vicenc

2018-01-01

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H∞ performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.

Kinetic analysis of non-isothermal solid-state reactions: multi-stage modeling without assumptions in the reaction mechanism.

PubMed

Pomerantsev, Alexey L; Kutsenova, Alla V; Rodionova, Oxana Ye

2017-02-01

A novel non-linear regression method for modeling non-isothermal thermogravimetric data is proposed. Experiments for several heating rates are analyzed simultaneously. The method is applicable to complex multi-stage processes when the number of stages is unknown. Prior knowledge of the type of kinetics is not required. The main idea is a consequent estimation of parameters when the overall model is successively changed from one level of modeling to another. At the first level, the Avrami-Erofeev functions are used. At the second level, the Sestak-Berggren functions are employed with the goal to broaden the overall model. The method is tested using both simulated and real-world data. A comparison of the proposed method with a recently published 'model-free' deconvolution method is presented.

Model Calibration with Censored Data

DOE PAGES

Cao, Fang; Ba, Shan; Brenneman, William A.; ...

2017-06-28

Here, the purpose of model calibration is to make the model predictions closer to reality. The classical Kennedy-O'Hagan approach is widely used for model calibration, which can account for the inadequacy of the computer model while simultaneously estimating the unknown calibration parameters. In many applications, the phenomenon of censoring occurs when the exact outcome of the physical experiment is not observed, but is only known to fall within a certain region. In such cases, the Kennedy-O'Hagan approach cannot be used directly, and we propose a method to incorporate the censoring information when performing model calibration. The method is applied tomore » study the compression phenomenon of liquid inside a bottle. The results show significant improvement over the traditional calibration methods, especially when the number of censored observations is large.« less

Unification of Intercontinental Height Systems based on the Fixed Geodetic Boundary Value Problem - A Case Study in Spherical Approximation

NASA Astrophysics Data System (ADS)

Grombein, T.; Seitz, K.; Heck, B.

2013-12-01

In general, national height reference systems are related to individual vertical datums defined by specific tide gauges. The discrepancy of these vertical datums causes height system biases that range in an order of 1-2 m at a global scale. Continental height systems can be connected by spirit leveling and gravity measurements along the leveling lines as performed for the definition of the European Vertical Reference Frame. In order to unify intercontinental height systems, an indirect connection is needed. For this purpose, global geopotential models derived from recent satellite missions like GOCE provide an important contribution. However, to achieve a highly-precise solution, a combination with local terrestrial gravity data is indispensable. Such combinations result in the solution of a Geodetic Boundary Value Problem (GBVP). In contrast to previous studies, mostly related to the traditional (scalar) free GBVP, the present paper discusses the use of the fixed GBVP for height system unification, where gravity disturbances instead of gravity anomalies are applied as boundary values. The basic idea of our approach is a conversion of measured gravity anomalies to gravity disturbances, where unknown datum parameters occur that can be associated with height system biases. In this way, the fixed GBVP can be extended by datum parameters for each datum zone. By evaluating the GBVP at GNSS/leveling benchmarks, the unknown datum parameters can be estimated in a least squares adjustment. Beside the developed theory, we present numerical results of a case study based on the spherical fixed GBVP and boundary values simulated by the use of the global geopotential model EGM2008. In a further step, the impact of approximations like linearization as well as topographic and ellipsoidal effects is taken into account by suitable reduction and correction terms.

Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination

PubMed Central

Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos

2010-01-01

The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093

Species-Independent Modeling of High-Frequency Ultrasound Backscatter in Hyaline Cartilage.

PubMed

Männicke, Nils; Schöne, Martin; Liukkonen, Jukka; Fachet, Dominik; Inkinen, Satu; Malo, Markus K; Oelze, Michael L; Töyräs, Juha; Jurvelin, Jukka S; Raum, Kay

2016-06-01

Apparent integrated backscatter (AIB) is a common ultrasound parameter used to assess cartilage matrix degeneration. However, the specific contributions of chondrocytes, proteoglycan and collagen to AIB remain unknown. To reveal these relationships, this work examined biopsies and cross sections of human, ovine and bovine cartilage with 40-MHz ultrasound biomicroscopy. Site-matched estimates of collagen concentration, proteoglycan concentration, collagen orientation and cell number density were employed in quasi-least-squares linear regression analyses to model AIB. A positive correlation (R(2) = 0.51, p < 10(-4)) between AIB and a combination model of cell number density and collagen concentration was obtained for collagen orientations approximately perpendicular (>70°) to the sound beam direction. These findings indicate causal relationships between AIB and cartilage structural parameters and could aid in more sophisticated future interpretations of ultrasound backscatter. Copyright © 2016 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Delta-Isobar Production in the Hard Photodisintegration of a Deuteron

NASA Astrophysics Data System (ADS)

Granados, Carlos; Sargsian, Misak

2010-02-01

Hard photodisintegration of the deuteron in delta-isobar production channels is proposed as a useful process in identifying the quark structure of hadrons and of hadronic interactions at large momentum and energy transfer. The reactions are modeled using the hard re scattering model, HRM, following previous works on hard breakup of a nucleon nucleon (NN) system in light nuclei. Here,quantitative predictions through the HRM require the numerical input of fits of experimental NN hard elastic scattering cross sections. Because of the lack of data in hard NN scattering into δ-isobar channels, the cross section of the corresponding photodisintegration processes cannot be predicted in the same way. Instead, the corresponding NN scattering process is modeled through the quark interchange mechanism, QIM, leaving an unknown normalization parameter. The observables of interest are ratios of differential cross sections of δ-isobar production channels to NN breakup in deuteron photodisintegration. Both entries in these ratios are derived through the HRM and QIM so that normalization parameters cancel out and numerical predictions can be obtained. )

Distributed parameter estimation in unreliable sensor networks via broadcast gossip algorithms.

PubMed

Wang, Huiwei; Liao, Xiaofeng; Wang, Zidong; Huang, Tingwen; Chen, Guo

2016-01-01

In this paper, we present an asynchronous algorithm to estimate the unknown parameter under an unreliable network which allows new sensors to join and old sensors to leave, and can tolerate link failures. Each sensor has access to partially informative measurements when it is awakened. In addition, the proposed algorithm can avoid the interference among messages and effectively reduce the accumulated measurement and quantization errors. Based on the theory of stochastic approximation, we prove that our proposed algorithm almost surely converges to the unknown parameter. Finally, we present a numerical example to assess the performance and the communication cost of the algorithm. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adaptive exponential synchronization of complex-valued Cohen-Grossberg neural networks with known and unknown parameters.

PubMed

Hu, Jin; Zeng, Chunna

2017-02-01

The complex-valued Cohen-Grossberg neural network is a special kind of complex-valued neural network. In this paper, the synchronization problem of a class of complex-valued Cohen-Grossberg neural networks with known and unknown parameters is investigated. By using Lyapunov functionals and the adaptive control method based on parameter identification, some adaptive feedback schemes are proposed to achieve synchronization exponentially between the drive and response systems. The results obtained in this paper have extended and improved some previous works on adaptive synchronization of Cohen-Grossberg neural networks. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

The comparative immunology of wild and laboratory mice, Mus musculus domesticus

PubMed Central

Abolins, Stephen; King, Elizabeth C.; Lazarou, Luke; Weldon, Laura; Hughes, Louise; Drescher, Paul; Raynes, John G.; Hafalla, Julius C. R.; Viney, Mark E.; Riley, Eleanor M.

2017-01-01

The laboratory mouse is the workhorse of immunology, used as a model of mammalian immune function, but how well immune responses of laboratory mice reflect those of free-living animals is unknown. Here we comprehensively characterize serological, cellular and functional immune parameters of wild mice and compare them with laboratory mice, finding that wild mouse cellular immune systems are, comparatively, in a highly activated (primed) state. Associations between immune parameters and infection suggest that high level pathogen exposure drives this activation. Moreover, wild mice have a population of highly activated myeloid cells not present in laboratory mice. By contrast, in vitro cytokine responses to pathogen-associated ligands are generally lower in cells from wild mice, probably reflecting the importance of maintaining immune homeostasis in the face of intense antigenic challenge in the wild. These data provide a comprehensive basis for validating (or not) laboratory mice as a useful and relevant immunological model system. PMID:28466840

A sensitive search for unknown spectral emission lines in the diffuse X-ray background with XMM-Newton

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gewering-Peine, A.; Horns, D.; Schmitt, J.H.M.M., E-mail: alexander.gewering-peine@desy.de, E-mail: dieter.horns@desy.de, E-mail: jschmitt@hs.uni-hamburg.de

The Standard Model of particle physics can be extended to include sterile (right-handed) neutrinos or axions to solve the dark matter problem. Depending upon the mixing angle between active and sterile neutrinos, the latter have the possibility to decay into monoenergetic active neutrinos and photons in the keV-range while axions can couple to two photons. We have used data taken with the X-ray telescope XMM-Newton for the search of line emissions. We used pointings with high exposures and expected dark matter column densities with respect to the dark matter halo of the Milky Way. The posterior predictive p-value analysis hasmore » been applied to locate parameter space regions which favour additional emission lines. In addition, upper limits of the parameter space of the models have been generated such that the preexisting limits have been significantly improved.« less

The interaction of host genetics and disease processes in chronic livestock disease: a simulation model of ovine footrot.

PubMed

Russell, V N L; Green, L E; Bishop, S C; Medley, G F

2013-03-01

A stochastic, individual-based, simulation model of footrot in a flock of 200 ewes was developed that included flock demography, disease processes, host genetic variation for traits influencing infection and disease processes, and bacterial contamination of the environment. Sensitivity analyses were performed using ANOVA to examine the contribution of unknown parameters to outcome variation. The infection rate and bacterial death rate were the most significant factors determining the observed prevalence of footrot, as well as the heritability of resistance. The dominance of infection parameters in determining outcomes implies that observational data cannot be used to accurately estimate the strength of genetic control of underlying traits describing the infection process, i.e. resistance. Further work will allow us to address the potential for genetic selection to control ovine footrot. Copyright © 2012 Elsevier B.V. All rights reserved.

An efficient recursive least square-based condition monitoring approach for a rail vehicle suspension system

NASA Astrophysics Data System (ADS)

Liu, X. Y.; Alfi, S.; Bruni, S.

2016-06-01

A model-based condition monitoring strategy for the railway vehicle suspension is proposed in this paper. This approach is based on recursive least square (RLS) algorithm focusing on the deterministic 'input-output' model. RLS has Kalman filtering feature and is able to identify the unknown parameters from a noisy dynamic system by memorising the correlation properties of variables. The identification of suspension parameter is achieved by machine learning of the relationship between excitation and response in a vehicle dynamic system. A fault detection method for the vertical primary suspension is illustrated as an instance of this condition monitoring scheme. Simulation results from the rail vehicle dynamics software 'ADTreS' are utilised as 'virtual measurements' considering a trailer car of Italian ETR500 high-speed train. The field test data from an E464 locomotive are also employed to validate the feasibility of this strategy for the real application. Results of the parameter identification performed indicate that estimated suspension parameters are consistent or approximate with the reference values. These results provide the supporting evidence that this fault diagnosis technique is capable of paving the way for the future vehicle condition monitoring system.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

A hybrid Pade-Galerkin technique for differential equations

NASA Technical Reports Server (NTRS)

Geer, James F.; Andersen, Carl M.

1993-01-01

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Optical diagnosis of malaria infection in human plasma using Raman spectroscopy

NASA Astrophysics Data System (ADS)

Bilal, Muhammad; Saleem, Muhammad; Amanat, Samina Tufail; Shakoor, Huma Abdul; Rashid, Rashad; Mahmood, Arshad; Ahmed, Mushtaq

2015-01-01

We present the prediction of malaria infection in human plasma using Raman spectroscopy. Raman spectra of malaria-infected samples are compared with those of healthy and dengue virus infected ones for disease recognition. Raman spectra were acquired using a laser at 532 nm as an excitation source and 10 distinct spectral signatures that statistically differentiated malaria from healthy and dengue-infected cases were found. A multivariate regression model has been developed that utilized Raman spectra of 20 malaria-infected, 10 non-malarial with fever, 10 healthy, and 6 dengue-infected samples to optically predict the malaria infection. The model yields the correlation coefficient r2 value of 0.981 between the predicted values and clinically known results of trainee samples, and the root mean square error in cross validation was found to be 0.09; both these parameters validated the model. The model was further blindly tested for 30 unknown suspected samples and found to be 86% accurate compared with the clinical results, with the inaccuracy due to three samples which were predicted in the gray region. Standard deviation and root mean square error in prediction for unknown samples were found to be 0.150 and 0.149, which are accepted for the clinical validation of the model.

Coupled wake boundary layer model of windfarms

NASA Astrophysics Data System (ADS)

Stevens, Richard; Gayme, Dennice; Meneveau, Charles

2014-11-01

We present a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a windfarm. The model couples the traditional, industry-standard wake expansion/superposition approach with a top-down model for the overall windfarm boundary layer structure. Wake models capture the effect of turbine positioning, while the top-down approach represents the interaction between the windturbine wakes and the atmospheric boundary layer. Each portion of the CWBL model requires specification of a parameter that is unknown a-priori. The wake model requires the wake expansion rate, whereas the top-down model requires the effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion rate is obtained by matching the mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing is determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We show that the CWBL model predictions compare more favorably with large eddy simulation results than those made with either the wake or top-down model in isolation and that the model can be applied successfully to the Horns Rev and Nysted windfarms. The `Fellowships for Young Energy Scientists' (YES!) of the Foundation for Fundamental Research on Matter supported by NWO, and NSF Grant #1243482.

A flexible model for correlated medical costs, with application to medical expenditure panel survey data.

PubMed

Chen, Jinsong; Liu, Lei; Shih, Ya-Chen T; Zhang, Daowen; Severini, Thomas A

2016-03-15

We propose a flexible model for correlated medical cost data with several appealing features. First, the mean function is partially linear. Second, the distributional form for the response is not specified. Third, the covariance structure of correlated medical costs has a semiparametric form. We use extended generalized estimating equations to simultaneously estimate all parameters of interest. B-splines are used to estimate unknown functions, and a modification to Akaike information criterion is proposed for selecting knots in spline bases. We apply the model to correlated medical costs in the Medical Expenditure Panel Survey dataset. Simulation studies are conducted to assess the performance of our method. Copyright © 2015 John Wiley & Sons, Ltd.

Constructing a cosmological model-independent Hubble diagram of type Ia supernovae with cosmic chronometers

NASA Astrophysics Data System (ADS)

Li, Zhengxiang; Gonzalez, J. E.; Yu, Hongwei; Zhu, Zong-Hong; Alcaniz, J. S.

2016-02-01

We apply two methods, i.e., the Gaussian processes and the nonparametric smoothing procedure, to reconstruct the Hubble parameter H (z ) as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of passively evolving galaxies. These reconstructions enable us to derive the luminosity distance to a certain redshift z , calibrate the light-curve fitting parameters accounting for the (unknown) intrinsic magnitude of type Ia supernova (SNe Ia), and construct cosmological model-independent Hubble diagrams of SNe Ia. In order to test the compatibility between the reconstructed functions of H (z ), we perform a statistical analysis considering the latest SNe Ia sample, the so-called joint light-curve compilation. We find that, for the Gaussian processes, the reconstructed functions of Hubble parameter versus redshift, and thus the following analysis on SNe Ia calibrations and cosmological implications, are sensitive to prior mean functions. However, for the nonparametric smoothing method, the reconstructed functions are not dependent on initial guess models, and consistently require high values of H0, which are in excellent agreement with recent measurements of this quantity from Cepheids and other local distance indicators.

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

Synchronization between uncertain nonidentical networks with quantum chaotic behavior

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2016-11-01

Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.

A Localized Ensemble Kalman Smoother

NASA Technical Reports Server (NTRS)

Butala, Mark D.

2012-01-01

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

Decentralized adaptive control

NASA Technical Reports Server (NTRS)

Oh, B. J.; Jamshidi, M.; Seraji, H.

1988-01-01

A decentralized adaptive control is proposed to stabilize and track the nonlinear, interconnected subsystems with unknown parameters. The adaptation of the controller gain is derived by using model reference adaptive control theory based on Lyapunov's direct method. The adaptive gains consist of sigma, proportional, and integral combination of the measured and reference values of the corresponding subsystem. The proposed control is applied to the joint control of a two-link robot manipulator, and the performance in computer simulation corresponds with what is expected in theoretical development.

Determining Crust and Upper Mantle Structure by Bayesian Joint Inversion of Receiver Functions and Surface Wave Dispersion at a Single Station: Preparation for Data from the InSight Mission

NASA Astrophysics Data System (ADS)

Jia, M.; Panning, M. P.; Lekic, V.; Gao, C.

2017-12-01

The InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will deploy a geophysical station on Mars in 2018. Using seismology to explore the interior structure of the Mars is one of the main targets, and as part of the mission, we will use 3-component seismic data to constrain the crust and upper mantle structure including P and S wave velocities and densities underneath the station. We will apply a reversible jump Markov chain Monte Carlo algorithm in the transdimensional hierarchical Bayesian inversion framework, in which the number of parameters in the model space and the noise level of the observed data are also treated as unknowns in the inversion process. Bayesian based methods produce an ensemble of models which can be analyzed to quantify uncertainties and trade-offs of the model parameters. In order to get better resolution, we will simultaneously invert three different types of seismic data: receiver functions, surface wave dispersion (SWD), and ZH ratios. Because the InSight mission will only deliver a single seismic station to Mars, and both the source location and the interior structure will be unknown, we will jointly invert the ray parameter in our approach. In preparation for this work, we first verify our approach by using a set of synthetic data. We find that SWD can constrain the absolute value of velocities while receiver functions constrain the discontinuities. By joint inversion, the velocity structure in the crust and upper mantle is well recovered. Then, we apply our approach to real data from an earth-based seismic station BFO located in Black Forest Observatory in Germany, as already used in a demonstration study for single station location methods. From the comparison of the results, our hierarchical treatment shows its advantage over the conventional method in which the noise level of observed data is fixed as a prior.

Estimating stage-specific daily survival probabilities of nests when nest age is unknown

USGS Publications Warehouse

Stanley, T.R.

2004-01-01

Estimation of daily survival probabilities of nests is common in studies of avian populations. Since the introduction of Mayfield's (1961, 1975) estimator, numerous models have been developed to relax Mayfield's assumptions and account for biologically important sources of variation. Stanley (2000) presented a model for estimating stage-specific (e.g. incubation stage, nestling stage) daily survival probabilities of nests that conditions on “nest type” and requires that nests be aged when they are found. Because aging nests typically requires handling the eggs, there may be situations where nests can not or should not be aged and the Stanley (2000) model will be inapplicable. Here, I present a model for estimating stage-specific daily survival probabilities that conditions on nest stage for active nests, thereby obviating the need to age nests when they are found. Specifically, I derive the maximum likelihood function for the model, evaluate the model's performance using Monte Carlo simulations, and provide software for estimating parameters (along with an example). For sample sizes as low as 50 nests, bias was small and confidence interval coverage was close to the nominal rate, especially when a reduced-parameter model was used for estimation.

The uniqueness of the solution of cone-like inversion models for halo CMEs

NASA Astrophysics Data System (ADS)

Zhao, X. P.

2006-12-01

Most of elliptic halo CMEs are believed to be formed by the Thompson scattering of the photospheric light by the 3-D cone-like shell of the CME plasma. To obtain the real propagation direction and angular width of the halo CMEs, such cone-like inversion models as the circular cone, the elliptic cone and the ice-cream cone models have been suggested recently. Because the number of given parameters that are used to characterize 2-D elliptic halo CMEs observed by one spacecraft are less than the number of unknown parameters that are used to characterize the 3-D elliptic cone model, the solution of the elliptic cone model is not unique. Since it is difficult to determine whether or not an observed halo CME is formed by an circular cone or elliptic cone shell, the solution of circular cone model may often be not unique too. To fix the problem of the uniqueness of the solution of various 3-D cone-like inversion models, this work tries to develop the algorithm for using the data from multi-spacecraft, such as the STEREO A and B, and the Solar Sentinels.

A new approach to estimate parameters of speciation models with application to apes.

PubMed

Becquet, Celine; Przeworski, Molly

2007-10-01

How populations diverge and give rise to distinct species remains a fundamental question in evolutionary biology, with important implications for a wide range of fields, from conservation genetics to human evolution. A promising approach is to estimate parameters of simple speciation models using polymorphism data from multiple loci. Existing methods, however, make a number of assumptions that severely limit their applicability, notably, no gene flow after the populations split and no intralocus recombination. To overcome these limitations, we developed a new Markov chain Monte Carlo method to estimate parameters of an isolation-migration model. The approach uses summaries of polymorphism data at multiple loci surveyed in a pair of diverging populations or closely related species and, importantly, allows for intralocus recombination. To illustrate its potential, we applied it to extensive polymorphism data from populations and species of apes, whose demographic histories are largely unknown. The isolation-migration model appears to provide a reasonable fit to the data. It suggests that the two chimpanzee species became reproductively isolated in allopatry approximately 850 Kya, while Western and Central chimpanzee populations split approximately 440 Kya but continued to exchange migrants. Similarly, Eastern and Western gorillas and Sumatran and Bornean orangutans appear to have experienced gene flow since their splits approximately 90 and over 250 Kya, respectively.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Licatta, Angelo; Griffin, Devon

2007-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Griffin, Devon

2008-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

Proton-pump inhibitor use does not affect semen quality in subfertile men.

PubMed

Keihani, Sorena; Craig, James R; Zhang, Chong; Presson, Angela P; Myers, Jeremy B; Brant, William O; Aston, Kenneth I; Emery, Benjamin R; Jenkins, Timothy G; Carrell, Douglas T; Hotaling, James M

2018-01-01

Proton-pump inhibitors (PPIs) are among the most widely used drugs worldwide. PPI use has recently been linked to adverse changes in semen quality in healthy men; however, the effects of PPI use on semen parameters remain largely unknown specifically in cases with male factor infertility. We examined whether PPI use was associated with detrimental effects on semen parameters in a large population of subfertile men. We retrospectively reviewed data from 12 257 subfertile men who had visited our fertility clinic from 2003 to 2013. Patients who reported using any PPIs for >3 months before semen sample collection were included; 7698 subfertile men taking no medication served as controls. Data were gathered on patient age, medication use, and conventional semen parameters; patients taking any known spermatotoxic medication were excluded. Linear mixed-effect regression models were used to test the effect of PPI use on semen parameters adjusting for age. A total of 248 patients (258 samples) used PPIs for at least 3 months before semen collection. In regression models, PPI use (either as the only medication or when used in combination with other nonspermatotoxic medications) was not associated with statistically significant changes in semen parameters. To our knowledge, this is the largest study to compare PPI use with semen parameters in subfertile men. Using PPIs was not associated with detrimental effects on semen quality in this retrospective study.

CONSTRAINTS FROM ASYMMETRIC HEATING: INVESTIGATING THE EPSILON AURIGAE DISK

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pearson, Richard L. III; Stencel, Robert E., E-mail: richard.pearson@du.edu, E-mail: robert.stencel@du.edu

2015-01-01

Epsilon Aurigae is a long-period eclipsing binary that likely contains an F0Ia star and a circumstellar disk enshrouding a hidden companion, assumed to be a main-sequence B star. High uncertainty in its parallax has kept the evolutionary status of the system in question and, hence, the true nature of each component. This unknown, as well as the absence of solid state spectral features in the infrared, requires an investigation of a wide parameter space by means of both analytic and Monte Carlo radiative transfer (MCRT) methods. The first MCRT models of epsilon Aurigae that include all three system components aremore » presented here. We seek additional system parameter constraints by melding analytic approximations with MCRT outputs (e.g., dust temperatures) on a first-order level. The MCRT models investigate the effects of various parameters on the disk-edge temperatures; these include two distances, three particle size distributions, three compositions, and two disk masses, resulting in 36 independent models. Specifically, the MCRT temperatures permit analytic calculations of effective heating and cooling curves along the disk edge. These are used to calculate representative observed fluxes and corresponding temperatures. This novel application of thermal properties provides the basis for utilization of other binary systems containing disks. We find degeneracies in the model fits for the various parameter sets. However, the results show a preference for a carbon disk with particle size distributions ≥10 μm. Additionally, a linear correlation between the MCRT noon and basal temperatures serves as a tool for effectively eliminating portions of the parameter space.« less

A 3D interactive method for estimating body segmental parameters in animals: application to the turning and running performance of Tyrannosaurus rex.

PubMed

Hutchinson, John R; Ng-Thow-Hing, Victor; Anderson, Frank C

2007-06-21

We developed a method based on interactive B-spline solids for estimating and visualizing biomechanically important parameters for animal body segments. Although the method is most useful for assessing the importance of unknowns in extinct animals, such as body contours, muscle bulk, or inertial parameters, it is also useful for non-invasive measurement of segmental dimensions in extant animals. Points measured directly from bodies or skeletons are digitized and visualized on a computer, and then a B-spline solid is fitted to enclose these points, allowing quantification of segment dimensions. The method is computationally fast enough so that software implementations can interactively deform the shape of body segments (by warping the solid) or adjust the shape quantitatively (e.g., expanding the solid boundary by some percentage or a specific distance beyond measured skeletal coordinates). As the shape changes, the resulting changes in segment mass, center of mass (CM), and moments of inertia can be recomputed immediately. Volumes of reduced or increased density can be embedded to represent lungs, bones, or other structures within the body. The method was validated by reconstructing an ostrich body from a fleshed and defleshed carcass and comparing the estimated dimensions to empirically measured values from the original carcass. We then used the method to calculate the segmental masses, centers of mass, and moments of inertia for an adult Tyrannosaurus rex, with measurements taken directly from a complete skeleton. We compare these results to other estimates, using the model to compute the sensitivities of unknown parameter values based upon 30 different combinations of trunk, lung and air sac, and hindlimb dimensions. The conclusion that T. rex was not an exceptionally fast runner remains strongly supported by our models-the main area of ambiguity for estimating running ability seems to be estimating fascicle lengths, not body dimensions. Additionally, the craniad position of the CM in all of our models reinforces the notion that T. rex did not stand or move with extremely columnar, elephantine limbs. It required some flexion in the limbs to stand still, but how much flexion depends directly on where its CM is assumed to lie. Finally we used our model to test an unsolved problem in dinosaur biomechanics: how fast a huge biped like T. rex could turn. Depending on the assumptions, our whole body model integrated with a musculoskeletal model estimates that turning 45 degrees on one leg could be achieved slowly, in about 1-2s.

Self-Learning Variable Structure Control for a Class of Sensor-Actuator Systems

PubMed Central

Chen, Sanfeng; Li, Shuai; Liu, Bo; Lou, Yuesheng; Liang, Yongsheng

2012-01-01

Variable structure strategy is widely used for the control of sensor-actuator systems modeled by Euler-Lagrange equations. However, accurate knowledge on the model structure and model parameters are often required for the control design. In this paper, we consider model-free variable structure control of a class of sensor-actuator systems, where only the online input and output of the system are available while the mathematic model of the system is unknown. The problem is formulated from an optimal control perspective and the implicit form of the control law are analytically obtained by using the principle of optimality. The control law and the optimal cost function are explicitly solved iteratively. Simulations demonstrate the effectiveness and the efficiency of the proposed method. PMID:22778633

A Bayesian-Based Novel Methodology to Generate Reliable Site Response Mapping Sensitive to Data Uncertainties

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Goto, H.

2017-12-01

The 2011 off the Pacific coast of Tohoku earthquake caused severe damage in many areas further inside the mainland because of site-amplification. Furukawa district in Miyagi Prefecture, Japan recorded significant spatial differences in ground motion even at sub-kilometer scales. The site responses in the damage zone far exceeded the levels in the hazard maps. A reason why the mismatch occurred is that mapping follow only the mean value at the measurement locations with no regard to the data uncertainties and thus are not always reliable. Our research objective is to develop a methodology to incorporate data uncertainties in mapping and propose a reliable map. The methodology is based on a hierarchical Bayesian modeling of normally-distributed site responses in space where the mean (μ), site-specific variance (σ2) and between-sites variance(s2) parameters are treated as unknowns with a prior distribution. The observation data is artificially created site responses with varying means and variances for 150 seismic events across 50 locations in one-dimensional space. Spatially auto-correlated random effects were added to the mean (μ) using a conditionally autoregressive (CAR) prior. The inferences on the unknown parameters are done using Markov Chain Monte Carlo methods from the posterior distribution. The goal is to find reliable estimates of μ sensitive to uncertainties. During initial trials, we observed that the tau (=1/s2) parameter of CAR prior controls the μ estimation. Using a constraint, s = 1/(k×σ), five spatial models with varying k-values were created. We define reliability to be measured by the model likelihood and propose the maximum likelihood model to be highly reliable. The model with maximum likelihood was selected using a 5-fold cross-validation technique. The results show that the maximum likelihood model (μ*) follows the site-specific mean at low uncertainties and converges to the model-mean at higher uncertainties (Fig.1). This result is highly significant as it successfully incorporates the effect of data uncertainties in mapping. This novel approach can be applied to any research field using mapping techniques. The methodology is now being applied to real records from a very dense seismic network in Furukawa district, Miyagi Prefecture, Japan to generate a reliable map of the site responses.

Genetic Parameter Estimates for Metabolizing Two Common Pharmaceuticals in Swine.

PubMed

Howard, Jeremy T; Ashwell, Melissa S; Baynes, Ronald E; Brooks, James D; Yeatts, James L; Maltecca, Christian

2018-01-01

In livestock, the regulation of drugs used to treat livestock has received increased attention and it is currently unknown how much of the phenotypic variation in drug metabolism is due to the genetics of an animal. Therefore, the objective of the study was to determine the amount of phenotypic variation in fenbendazole and flunixin meglumine drug metabolism due to genetics. The population consisted of crossbred female and castrated male nursery pigs ( n = 198) that were sired by boars represented by four breeds. The animals were spread across nine batches. Drugs were administered intravenously and blood collected a minimum of 10 times over a 48 h period. Genetic parameters for the parent drug and metabolite concentration within each drug were estimated based on pharmacokinetics (PK) parameters or concentrations across time utilizing a random regression model. The PK parameters were estimated using a non-compartmental analysis. The PK model included fixed effects of sex and breed of sire along with random sire and batch effects. The random regression model utilized Legendre polynomials and included a fixed population concentration curve, sex, and breed of sire effects along with a random sire deviation from the population curve and batch effect. The sire effect included the intercept for all models except for the fenbendazole metabolite (i.e., intercept and slope). The mean heritability across PK parameters for the fenbendazole and flunixin meglumine parent drug (metabolite) was 0.15 (0.18) and 0.31 (0.40), respectively. For the parent drug (metabolite), the mean heritability across time was 0.27 (0.60) and 0.14 (0.44) for fenbendazole and flunixin meglumine, respectively. The errors surrounding the heritability estimates for the random regression model were smaller compared to estimates obtained from PK parameters. Across both the PK and plasma drug concentration across model, a moderate heritability was estimated. The model that utilized the plasma drug concentration across time resulted in estimates with a smaller standard error compared to models that utilized PK parameters. The current study found a low to moderate proportion of the phenotypic variation in metabolizing fenbendazole and flunixin meglumine that was explained by genetics in the current study.

Genetic Parameter Estimates for Metabolizing Two Common Pharmaceuticals in Swine

PubMed Central

Howard, Jeremy T.; Ashwell, Melissa S.; Baynes, Ronald E.; Brooks, James D.; Yeatts, James L.; Maltecca, Christian

2018-01-01

In livestock, the regulation of drugs used to treat livestock has received increased attention and it is currently unknown how much of the phenotypic variation in drug metabolism is due to the genetics of an animal. Therefore, the objective of the study was to determine the amount of phenotypic variation in fenbendazole and flunixin meglumine drug metabolism due to genetics. The population consisted of crossbred female and castrated male nursery pigs (n = 198) that were sired by boars represented by four breeds. The animals were spread across nine batches. Drugs were administered intravenously and blood collected a minimum of 10 times over a 48 h period. Genetic parameters for the parent drug and metabolite concentration within each drug were estimated based on pharmacokinetics (PK) parameters or concentrations across time utilizing a random regression model. The PK parameters were estimated using a non-compartmental analysis. The PK model included fixed effects of sex and breed of sire along with random sire and batch effects. The random regression model utilized Legendre polynomials and included a fixed population concentration curve, sex, and breed of sire effects along with a random sire deviation from the population curve and batch effect. The sire effect included the intercept for all models except for the fenbendazole metabolite (i.e., intercept and slope). The mean heritability across PK parameters for the fenbendazole and flunixin meglumine parent drug (metabolite) was 0.15 (0.18) and 0.31 (0.40), respectively. For the parent drug (metabolite), the mean heritability across time was 0.27 (0.60) and 0.14 (0.44) for fenbendazole and flunixin meglumine, respectively. The errors surrounding the heritability estimates for the random regression model were smaller compared to estimates obtained from PK parameters. Across both the PK and plasma drug concentration across model, a moderate heritability was estimated. The model that utilized the plasma drug concentration across time resulted in estimates with a smaller standard error compared to models that utilized PK parameters. The current study found a low to moderate proportion of the phenotypic variation in metabolizing fenbendazole and flunixin meglumine that was explained by genetics in the current study. PMID:29487615

Reconstructing Mammalian Sleep Dynamics with Data Assimilation

PubMed Central

Sedigh-Sarvestani, Madineh; Schiff, Steven J.; Gluckman, Bruce J.

2012-01-01

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies. PMID:23209396

Modeling of protein electrophoresis in silica colloidal crystals having brush layers of polyacrylamide

PubMed Central

Birdsall, Robert E.; Koshel, Brooke M.; Hua, Yimin; Ratnayaka, Saliya N.; Wirth, Mary J.

2013-01-01

Sieving of proteins in silica colloidal crystals of mm dimensions is characterized for particle diameters of nominally 350 and 500 nm, where the colloidal crystals are chemically modified with a brush layer of polyacrylamide. A model is developed that relates the reduced electrophoretic mobility to the experimentally measurable porosity. The model fits the data with no adjustable parameters for the case of silica colloidal crystals packed in capillaries, for which independent measurements of the pore radii were made from flow data. The model also fits the data for electrophoresis in a highly ordered colloidal crystal formed in a channel, where the unknown pore radius was used as a fitting parameter. Plate heights as small as 0.4 μm point to the potential for miniaturized separations. Band broadening increases as the pore radius approaches the protein radius, indicating that the main contribution to broadening is the spatial heterogeneity of the pore radius. The results quantitatively support the notion that sieving occurs for proteins in silica colloidal crystals, and facilitate design of new separations that would benefit from miniaturization. PMID:23229163

Development and Implementation of the DTOPLATS-MP land surface model over the Continental US at 30 meters

NASA Astrophysics Data System (ADS)

Chaney, N.; Wood, E. F.

2014-12-01

The increasing accessibility of high-resolution land data (< 100 m) and high performance computing allows improved parameterizations of subgrid hydrologic processes in macroscale land surface models. Continental scale fully distributed modeling at these spatial scales is possible; however, its practicality for operational use is still unknown due to uncertainties in input data, model parameters, and storage requirements. To address these concerns, we propose a modeling framework that provides the spatial detail of a fully distributed model yet maintains the benefits of a semi-distributed model. In this presentation we will introduce DTOPLATS-MP, a coupling between the NOAH-MP land surface model and the Dynamic TOPMODEL hydrologic model. This new model captures a catchment's spatial heterogeneity by clustering high-resolution land datasets (soil, topography, and land cover) into hundreds of hydrologic similar units (HSUs). A prior DEM analysis defines the connections between each HSU. At each time step, the 1D land surface model updates each HSU; the HSUs then interact laterally via the subsurface and surface. When compared to the fully distributed form of the model, this framework allows a significant decrease in computation and storage while providing most of the same information and enabling parameter transferability. As a proof of concept, we will show how this new modeling framework can be run over CONUS at a 30-meter spatial resolution. For each catchment in the WBD HUC-12 dataset, the model is run between 2002 and 2012 using available high-resolution continental scale land and meteorological datasets over CONUS (dSSURGO, NLCD, NED, and NCEP Stage IV). For each catchment, the model is run with 1000 model parameter sets obtained from a Latin hypercube sample. This exercise will illustrate the feasibility of running the model operationally at continental scales while accounting for model parameter uncertainty.

Commercial absorption chiller models for evaluation of control strategies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koeppel, E.A.; Klein, S.A.; Mitchell, J.W.

1995-08-01

A steady-state computer simulation model of a direct fired double-effect water-lithium bromide absorption chiller in the parallel-flow configuration was developed from first principles. Unknown model parameters such as heat transfer coefficients were determined by matching the model`s calculated state points and coefficient of performance (COP) against nominal full-load operating data and COPs obtained from a manufacturer`s catalog. The model compares favorably with the manufacturer`s performance ratings for varying water circuit (chilled and cooling) temperatures at full load conditions and for chiller part-load performance. The model was used (1) to investigate the effect of varying the water circuit flow rates withmore » the chiller load and (2) to optimize chiller part-load performance with respect to the distribution and flow of the weak solution.« less

Advanced Computational Framework for Environmental Management ZEM, Version 1.x

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vesselinov, Velimir V.; O'Malley, Daniel; Pandey, Sachin

2016-11-04

Typically environmental management problems require analysis of large and complex data sets originating from concurrent data streams with different data collection frequencies and pedigree. These big data sets require on-the-fly integration into a series of models with different complexity for various types of model analyses where the data are applied as soft and hard model constraints. This is needed to provide fast iterative model analyses based on the latest available data to guide decision-making. Furthermore, the data and model are associated with uncertainties. The uncertainties are probabilistic (e.g. measurement errors) and non-probabilistic (unknowns, e.g. alternative conceptual models characterizing site conditions).more » To address all of these issues, we have developed an integrated framework for real-time data and model analyses for environmental decision-making called ZEM. The framework allows for seamless and on-the-fly integration of data and modeling results for robust and scientifically-defensible decision-making applying advanced decision analyses tools such as Bayesian- Information-Gap Decision Theory (BIG-DT). The framework also includes advanced methods for optimization that are capable of dealing with a large number of unknown model parameters, and surrogate (reduced order) modeling capabilities based on support vector regression techniques. The framework is coded in Julia, a state-of-the-art high-performance programing language (http://julialang.org). The ZEM framework is open-source and can be applied to any environmental management site. The framework will be open-source and released under GPL V3 license.« less

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Inverting multiple suites of thermal indicator data to constrain the heat flow history: A case study from east Kalimantan, Indonesia

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mudford, B.S.

1996-12-31

The determination of an appropriate thermal history in an exploration area is of fundamental importance when attempting to understand the evolution of the petroleum system. In this talk we present the results of a single-well modelling study in which bottom hole temperature data, vitrinite reflectance data and three different biomarker ratio datasets were available to constrain the modelling. Previous modelling studies using biomarker ratios have been hampered by the wide variety of published kinetic parameters for biomarker evolution. Generally, these parameters have been determined either from measurements in the laboratory and extrapolation to the geological setting, or from downhole measurementsmore » where the heat flow history is assumed to be known. In the first case serious errors can arise because the heating rate is being extrapolated over many orders of magnitude, while in the second case errors can arise if the assumed heat flow history is incorrect. To circumvent these problems we carried out a parameter optimization in which the heat flow history was treated as an unknown in addition to the biomarker ratio kinetic parameters. This method enabled the heat flow history for the area to be determined together with appropriate kinetic parameters for the three measured biomarker ratios. Within the resolution of the data, the heat flow since the early Miocene has been relatively constant at levels required to yield good agreement between predicted and measured subsurface temperatures.« less

Inverting multiple suites of thermal indicator data to constrain the heat flow history: A case study from east Kalimantan, Indonesia

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mudford, B.S.

1996-01-01

The determination of an appropriate thermal history in an exploration area is of fundamental importance when attempting to understand the evolution of the petroleum system. In this talk we present the results of a single-well modelling study in which bottom hole temperature data, vitrinite reflectance data and three different biomarker ratio datasets were available to constrain the modelling. Previous modelling studies using biomarker ratios have been hampered by the wide variety of published kinetic parameters for biomarker evolution. Generally, these parameters have been determined either from measurements in the laboratory and extrapolation to the geological setting, or from downhole measurementsmore » where the heat flow history is assumed to be known. In the first case serious errors can arise because the heating rate is being extrapolated over many orders of magnitude, while in the second case errors can arise if the assumed heat flow history is incorrect. To circumvent these problems we carried out a parameter optimization in which the heat flow history was treated as an unknown in addition to the biomarker ratio kinetic parameters. This method enabled the heat flow history for the area to be determined together with appropriate kinetic parameters for the three measured biomarker ratios. Within the resolution of the data, the heat flow since the early Miocene has been relatively constant at levels required to yield good agreement between predicted and measured subsurface temperatures.« less

The continuum fusion theory of signal detection applied to a bi-modal fusion problem

NASA Astrophysics Data System (ADS)

Schaum, A.

2011-05-01

A new formalism has been developed that produces detection algorithms for model-based problems, in which one or more parameter values is unknown. Continuum Fusion can be used to generate different flavors of algorithm for any composite hypothesis testing problem. The methodology is defined by a fusion logic that can be translated into max/min conditions. Here it is applied to a simple sensor fusion model, but one for which the generalized likelihood ratio test is intractable. By contrast, a fusion-based response to the same problem can be devised that is solvable in closed form and represents a good approximation to the GLR test.

Transmission probabilities and durations of immunity for three pathogenic group B Streptococcus serotypes

PubMed Central

Percha, Bethany; Newman, M. E. J.; Foxman, Betsy

2012-01-01

Group B Streptococcus (GBS) remains a major cause of neonatal sepsis and is an emerging cause of invasive bacterial infections. The 9 known serotypes vary in virulence, and there is little cross-immunity. Key parameters for planning an effective vaccination strategy, such as average length of immunity and transmission probabilities by serotype, are unknown. We simulated GBS spread in a population using a computational model with parameters derived from studies of GBS sexual transmission in a college dormitory. Here we provide estimates of the duration of immunity relative to the transmission probabilities for the 3 GBS serotypes most associated with invasive disease: Ia, III, and V. We also place upper limits on the durations of immunity for serotype Ia (570 days), III (1125 days) and V (260 days). Better transmission estimates are required to establish the epidemiological parameters of GBS infection and determine the best vaccination strategies to prevent GBS disease. PMID:21605704

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Applications of laser ranging and VLBI observations for selenodetic control

NASA Technical Reports Server (NTRS)

Fajemirokun, F. A.

1971-01-01

The observation equations necessary to utilize lunar laser ranging and very long baseline interferometry measurements were developed for the establishment of a primary control network on the moon. The network consists of coordinates of moon points in the selenodetic Cartesian coordinate system, which is fixed to the lunar body, oriented along the three principal axes of inertia of the moon, and centered at the lunar center of mass. The observation equations derived are based on a general model in which the unknown parameters included: the selenodetic Cartesian coordinates, the geocentric coordinates of earth stations, parameters of the orientation of the selenodetic coordinate system with respect to a fixed celestial system, the parameters of the orientation of the average terrestrial coordinate system with respect to a fixed celestial coordinate system, and the geocentric coordinates of the center of mass of the moon, given by a lunar ephemeris.

Analytical Incorporation of Velocity Parameters into Ice Sheet Elevation Change Rate Computations

NASA Astrophysics Data System (ADS)

Nagarajan, S.; Ahn, Y.; Teegavarapu, R. S. V.

2014-12-01

NASA, ESA and various other agencies have been collecting laser, optical and RADAR altimetry data through various missions to study the elevation changes of the Cryosphere. The laser altimetry collected by various airborne and spaceborne missions provides multi-temporal coverage of Greenland and Antarctica since 1993 to now. Though these missions have increased the data coverage, considering the dynamic nature of the ice surface, it is still sparse both spatially and temporally for accurate elevation change detection studies. The temporal and spatial gaps are usually filled by interpolation techniques. This presentation will demonstrate a method to improve the temporal interpolation. Considering the accuracy, repeat coverage and spatial distribution, the laser scanning data has been widely used to compute elevation change rate of Greenland and Antarctica ice sheets. A major problem with these approaches is non-consideration of ice sheet velocity dynamics into change rate computations. Though the correlation between velocity and elevation change rate have been noticed by Hurkmans et al., 2012, the corrections for velocity changes were applied after computing elevation change rates by assuming linear or higher polynomial relationship. This research will discuss the possibilities of parameterizing ice sheet dynamics as unknowns (dX and dY) in the adjustment mathematical model that computes elevation change (dZ) rates. It is a simultaneous computation of changes in all three directions of the ice surface. Also, the laser points between two time epochs in a crossover area have different distribution and count. Therefore, a registration method that does not require point-to-point correspondence is required to recover the unknown elevation and velocity parameters. This research will experiment the possibilities of registering multi-temporal datasets using volume minimization algorithm, which determines the unknown dX, dY and dZ that minimizes the volume between two or more time-epoch point clouds. In order to make use of other existing data as well as to constrain the adjustment, InSAR velocity will be used as initial values for the parameters dX and dY. The presentation will discuss the results of analytical incorporation of parameters and the volume based registration method for a test site in Greenland.

Mass properties measurement system dynamics

NASA Technical Reports Server (NTRS)

Doty, Keith L.

1993-01-01

The MPMS mechanism possess two revolute degrees-of-freedom and allows the user to measure the mass, center of gravity, and the inertia tensor of an unknown mass. The dynamics of the Mass Properties Measurement System (MPMS) from the Lagrangian approach to illustrate the dependency of the motion on the unknown parameters.

Robust Decision-making Applied to Model Selection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hemez, Francois M.

2012-08-06

The scientific and engineering communities are relying more and more on numerical models to simulate ever-increasingly complex phenomena. Selecting a model, from among a family of models that meets the simulation requirements, presents a challenge to modern-day analysts. To address this concern, a framework is adopted anchored in info-gap decision theory. The framework proposes to select models by examining the trade-offs between prediction accuracy and sensitivity to epistemic uncertainty. The framework is demonstrated on two structural engineering applications by asking the following question: Which model, of several numerical models, approximates the behavior of a structure when parameters that define eachmore » of those models are unknown? One observation is that models that are nominally more accurate are not necessarily more robust, and their accuracy can deteriorate greatly depending upon the assumptions made. It is posited that, as reliance on numerical models increases, establishing robustness will become as important as demonstrating accuracy.« less

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

NASA Astrophysics Data System (ADS)

Pulkkinen, Aki; Cox, Ben T.; Arridge, Simon R.; Kaipio, Jari P.; Tarvainen, Tanja

2016-03-01

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

Adaptive control of stochastic linear systems with unknown parameters. M.S. Thesis

NASA Technical Reports Server (NTRS)

Ku, R. T.

1972-01-01

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

1r2dinv: A finite-difference model for inverse analysis of two dimensional linear or radial groundwater flow

USGS Publications Warehouse

Bohling, Geoffrey C.; Butler, J.J.

2001-01-01

We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, 1r2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg-Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface. ?? 2001 Elsevier Science Ltd. All rights reserved.

Uncertainty quantification of overpressure buildup through inverse modeling of compaction processes in sedimentary basins

NASA Astrophysics Data System (ADS)

Colombo, Ivo; Porta, Giovanni M.; Ruffo, Paolo; Guadagnini, Alberto

2017-03-01

This study illustrates a procedure conducive to a preliminary risk analysis of overpressure development in sedimentary basins characterized by alternating depositional events of sandstone and shale layers. The approach rests on two key elements: (1) forward modeling of fluid flow and compaction, and (2) application of a model-complexity reduction technique based on a generalized polynomial chaos expansion (gPCE). The forward model considers a one-dimensional vertical compaction processes. The gPCE model is then used in an inverse modeling context to obtain efficient model parameter estimation and uncertainty quantification. The methodology is applied to two field settings considered in previous literature works, i.e. the Venture Field (Scotian Shelf, Canada) and the Navarin Basin (Bering Sea, Alaska, USA), relying on available porosity and pressure information for model calibration. It is found that the best result is obtained when porosity and pressure data are considered jointly in the model calibration procedure. Uncertainty propagation from unknown input parameters to model outputs, such as pore pressure vertical distribution, is investigated and quantified. This modeling strategy enables one to quantify the relative importance of key phenomena governing the feedback between sediment compaction and fluid flow processes and driving the buildup of fluid overpressure in stratified sedimentary basins characterized by the presence of low-permeability layers. The results here illustrated (1) allow for diagnosis of the critical role played by the parameters of quantitative formulations linking porosity and permeability in compacted shales and (2) provide an explicit and detailed quantification of the effects of their uncertainty in field settings.

Systematic wavelength selection for improved multivariate spectral analysis

DOEpatents

Thomas, Edward V.; Robinson, Mark R.; Haaland, David M.

1995-01-01

Methods and apparatus for determining in a biological material one or more unknown values of at least one known characteristic (e.g. the concentration of an analyte such as glucose in blood or the concentration of one or more blood gas parameters) with a model based on a set of samples with known values of the known characteristics and a multivariate algorithm using several wavelength subsets. The method includes selecting multiple wavelength subsets, from the electromagnetic spectral region appropriate for determining the known characteristic, for use by an algorithm wherein the selection of wavelength subsets improves the model's fitness of the determination for the unknown values of the known characteristic. The selection process utilizes multivariate search methods that select both predictive and synergistic wavelengths within the range of wavelengths utilized. The fitness of the wavelength subsets is determined by the fitness function F=.function.(cost, performance). The method includes the steps of: (1) using one or more applications of a genetic algorithm to produce one or more count spectra, with multiple count spectra then combined to produce a combined count spectrum; (2) smoothing the count spectrum; (3) selecting a threshold count from a count spectrum to select these wavelength subsets which optimize the fitness function; and (4) eliminating a portion of the selected wavelength subsets. The determination of the unknown values can be made: (1) noninvasively and in vivo; (2) invasively and in vivo; or (3) in vitro.

Data and Model Uncertainties associated with Biogeochemical Groundwater Remediation and their impact on Decision Analysis

NASA Astrophysics Data System (ADS)

Pandey, S.; Vesselinov, V. V.; O'Malley, D.; Karra, S.; Hansen, S. K.

2016-12-01

Models and data are used to characterize the extent of contamination and remediation, both of which are dependent upon the complex interplay of processes ranging from geochemical reactions, microbial metabolism, and pore-scale mixing to heterogeneous flow and external forcings. Characterization is wrought with important uncertainties related to the model itself (e.g. conceptualization, model implementation, parameter values) and the data used for model calibration (e.g. sparsity, measurement errors). This research consists of two primary components: (1) Developing numerical models that incorporate the complex hydrogeology and biogeochemistry that drive groundwater contamination and remediation; (2) Utilizing novel techniques for data/model-based analyses (such as parameter calibration and uncertainty quantification) to aid in decision support for optimal uncertainty reduction related to characterization and remediation of contaminated sites. The reactive transport models are developed using PFLOTRAN and are capable of simulating a wide range of biogeochemical and hydrologic conditions that affect the migration and remediation of groundwater contaminants under diverse field conditions. Data/model-based analyses are achieved using MADS, which utilizes Bayesian methods and Information Gap theory to address the data/model uncertainties discussed above. We also use these tools to evaluate different models, which vary in complexity, in order to weigh and rank models based on model accuracy (in representation of existing observations), model parsimony (everything else being equal, models with smaller number of model parameters are preferred), and model robustness (related to model predictions of unknown future states). These analyses are carried out on synthetic problems, but are directly related to real-world problems; for example, the modeled processes and data inputs are consistent with the conditions at the Los Alamos National Laboratory contamination sites (RDX and Chromium).

Regolith thermal property inversion in the LUNAR-A heat-flow experiment

NASA Astrophysics Data System (ADS)

Hagermann, A.; Tanaka, S.; Yoshida, S.; Fujimura, A.; Mizutani, H.

2001-11-01

In 2003, two penetrators of the LUNAR--A mission of ISAS will investigate the internal structure of the Moon by conducting seismic and heat--flow experiments. Heat-flow is the product of thermal gradient tial T / tial z, and thermal conductivity λ of the lunar regolith. For measuring the thermal conductivity (or dissusivity), each penetrator will carry five thermal property sensors, consisting of small disc heaters. The thermal response Ts(t) of the heater itself to the constant known power supply of approx. 50 mW serves as the data for the subsequent data interpretation. Horai et al. (1991) found a forward analytical solution to the problem of determining the thermal inertia λ ρ c of the regolith for constant thermal properties and a simplyfied geometry. In the inversion, the problem of deriving the unknown thermal properties of a medium from known heat sources and temperatures is an Identification Heat Conduction Problem (IDHCP), an ill--posed inverse problem. Assuming that thermal conductivity λ and heat capacity ρ c are linear functions of temperature (which is reasonable in most cases), one can apply a Kirchhoff transformation to linearize the heat conduction equation, which minimizes computing time. Then the error functional, i.e. the difference between the measured temperature response of the heater and the predicted temperature response, can be minimized, thus solving for thermal dissusivity κ = λ / (ρ c), wich will complete the set of parameters needed for a detailed description of thermal properties of the lunar regolith. Results of model calculations will be presented, in which synthetic data and calibration data are used to invert the unknown thermal diffusivity of the unknown medium by means of a modified Newton Method. Due to the ill-posedness of the problem, the number of parameters to be solved for should be limited. As the model calculations reveal, a homogeneous regolith allows for a fast and accurate inversion.

Orbit Determination and Maneuver Detection Using Event Representation with Thrust-Fourier-Coefficients

NASA Astrophysics Data System (ADS)

Lubey, D.; Ko, H.; Scheeres, D.

The classical orbit determination (OD) method of dealing with unknown maneuvers is to restart the OD process with post-maneuver observations. However, it is also possible to continue the OD process through such unknown maneuvers by representing those unknown maneuvers with an appropriate event representation. It has been shown in previous work (Ko & Scheeres, JGCD 2014) that any maneuver performed by a satellite transitioning between two arbitrary orbital states can be represented as an equivalent maneuver connecting those two states using Thrust-Fourier-Coefficients (TFCs). Event representation using TFCs rigorously provides a unique control law that can generate the desired secular behavior for a given unknown maneuver. This paper presents applications of this representation approach to orbit prediction and maneuver detection problem across unknown maneuvers. The TFCs are appended to a sequential filter as an adjoint state to compensate unknown perturbing accelerations and the modified filter estimates the satellite state and thrust coefficients by processing OD across the time of an unknown maneuver. This modified sequential filter with TFCs is capable of fitting tracking data and maintaining an OD solution in the presence of unknown maneuvers. Also, the modified filter is found effective in detecting a sudden change in TFC values which indicates a maneuver. In order to illustrate that the event representation approach with TFCs is robust and sufficiently general to be easily adjustable, different types of measurement data are processed with the filter in a realistic LEO setting. Further, cases with mis-modeling of non-gravitational force are included in our study to verify the versatility and efficiency of our presented algorithm. Simulation results show that the modified sequential filter with TFCs can detect and estimate the orbit and thrust parameters in the presence of unknown maneuvers with or without measurement data during maneuvers. With no measurement data during maneuvers, the modified filter with TFCs uses an existing pre-maneuver orbit solution to compute a post-maneuver orbit solution by forcing TFCs to compensate for an unknown maneuver. With observation data available during maneuvers, maneuver start time and stop time is determined

Advective transport in heterogeneous aquifers: Are proxy models predictive?

NASA Astrophysics Data System (ADS)

Fiori, A.; Zarlenga, A.; Gotovac, H.; Jankovic, I.; Volpi, E.; Cvetkovic, V.; Dagan, G.

2015-12-01

We examine the prediction capability of two approximate models (Multi-Rate Mass Transfer (MRMT) and Continuous Time Random Walk (CTRW)) of non-Fickian transport, by comparison with accurate 2-D and 3-D numerical simulations. Both nonlocal in time approaches circumvent the need to solve the flow and transport equations by using proxy models to advection, providing the breakthrough curves (BTC) at control planes at any x, depending on a vector of five unknown parameters. Although underlain by different mechanisms, the two models have an identical structure in the Laplace Transform domain and have the Markovian property of independent transitions. We show that also the numerical BTCs enjoy the Markovian property. Following the procedure recommended in the literature, along a practitioner perspective, we first calibrate the parameters values by a best fit with the numerical BTC at a control plane at x1, close to the injection plane, and subsequently use it for prediction at further control planes for a few values of σY2≤8. Due to a similar structure and Markovian property, the two methods perform equally well in matching the numerical BTC. The identified parameters are generally not unique, making their identification somewhat arbitrary. The inverse Gaussian model and the recently developed Multi-Indicator Model (MIM), which does not require any fitting as it relates the BTC to the permeability structure, are also discussed. The application of the proxy models for prediction requires carrying out transport field tests of large plumes for a long duration.

Three-dimensional cinematography with control object of unknown shape.

PubMed

Dapena, J; Harman, E A; Miller, J A

1982-01-01

A technique for reconstruction of three-dimensional (3D) motion which involves a simple filming procedure but allows the deduction of coordinates in large object volumes was developed. Internal camera parameters are calculated from measurements of the film images of two calibrated crosses while external camera parameters are calculated from the film images of points in a control object of unknown shape but at least one known length. The control object, which includes the volume in which the activity is to take place, is formed by a series of poles placed at unknown locations, each carrying two targets. From the internal and external camera parameters, and from locations of the images of point in the films of the two cameras, 3D coordinates of the point can be calculated. Root mean square errors of the three coordinates of points in a large object volume (5m x 5m x 1.5m) were 15 mm, 13 mm, 13 mm and 6 mm, and relative errors in lengths averaged 0.5%, 0.7% and 0.5%, respectively.

Sensitivity of predicted scaling and permeability in Enhanced Geothermal Systems to Thermodynamic Data and Activity Models

NASA Astrophysics Data System (ADS)

Hingerl, Ferdinand F.; Wagner, Thomas; Kulik, Dmitrii A.; Kosakowski, Georg; Driesner, Thomas; Thomsen, Kaj

2010-05-01

A consortium of research groups from ETH Zurich, EPF Lausanne, the Paul Scherrer Institut and the University of Bonn collaborates in a comprehensive program of basic research on key aspects of the Enhanced Geothermal Systems (EGSs). As part of this GEOTHERM project (www.geotherm.ethz.ch), we concentrate on the fundamental investigation of thermodynamic models suitable for describing fluid-rock interactions at geothermal conditions. Predictions of the fluid-rock interaction in EGS still face several major challenges. Slight variations in the input thermodynamic and kinetic parameters may result in significant differences in the predicted mineral solubilities and stable assemblage. Realistic modeling of mineral precipitation in turn has implications onto our understanding of the permeability evolution of the geothermal reservoir, as well as the scaling in technical installations. In order to reasonably model an EGS, thermodynamic databases and activity models must be tailored to geothermal conditions. We therefore implemented in GEMS code the Pitzer formalism, which is the standard model used for computing thermodynamic excess properties of brines at elevated temperatures and pressures. This model, however, depends on a vast amount of interaction parameters, which are to a substantial extend unknown. Furthermore, a high order polynomial temperature interpolation makes extrapolation unreliable if not impossible. As an alternative we additionally implemented the EUNIQUAC activity model. EUNIQUAC requires fewer empirical fit parameters (only binary interaction parameters needed) and uses simpler and more stable temperature and pressure extrapolations. This results in an increase in computation speed, which is of crucial importance when performing coupled long term simulations of geothermal reservoirs. To achieve better performance under geothermal conditions, we are currently partly reformulating EUNIQUAC and refitting the existing parameter set. First results of the Pitzer-EUNIQUAC benchmark applied to relevant aqueous solutions at elevated temperature, pressure and ionic strength will be presented.

Structural identifiability of cyclic graphical models of biological networks with latent variables.

PubMed

Wang, Yulin; Lu, Na; Miao, Hongyu

2016-06-13

Graphical models have long been used to describe biological networks for a variety of important tasks such as the determination of key biological parameters, and the structure of graphical model ultimately determines whether such unknown parameters can be unambiguously obtained from experimental observations (i.e., the identifiability problem). Limited by resources or technical capacities, complex biological networks are usually partially observed in experiment, which thus introduces latent variables into the corresponding graphical models. A number of previous studies have tackled the parameter identifiability problem for graphical models such as linear structural equation models (SEMs) with or without latent variables. However, the limited resolution and efficiency of existing approaches necessarily calls for further development of novel structural identifiability analysis algorithms. An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of symbolic polynomials, and then converts these symbolic equations to binary matrices (called identifiability matrix). Several matrix operations are introduced for identifiability matrix reduction with system equivalency maintained. Based on the reduced identifiability matrices, the structural identifiability of each parameter is determined. A number of benchmark models are used to verify the validity of the proposed approach. Finally, the network module for influenza A virus replication is employed as a real example to illustrate the application of the proposed approach in practice. The proposed approach can deal with cyclic networks with latent variables. The key advantage is that it intentionally avoids symbolic computation and is thus highly efficient. Also, this method is capable of determining the identifiability of each single parameter and is thus of higher resolution in comparison with many existing approaches. Overall, this study provides a basis for systematic examination and refinement of graphical models of biological networks from the identifiability point of view, and it has a significant potential to be extended to more complex network structures or high-dimensional systems.

Transformation to equivalent dimensions—a new methodology to study earthquake clustering

NASA Astrophysics Data System (ADS)

Lasocki, Stanislaw

2014-05-01

A seismic event is represented by a point in a parameter space, quantified by the vector of parameter values. Studies of earthquake clustering involve considering distances between such points in multidimensional spaces. However, the metrics of earthquake parameters are different, hence the metric in a multidimensional parameter space cannot be readily defined. The present paper proposes a solution of this metric problem based on a concept of probabilistic equivalence of earthquake parameters. Under this concept the lengths of parameter intervals are equivalent if the probability for earthquakes to take values from either interval is the same. Earthquake clustering is studied in an equivalent rather than the original dimensions space, where the equivalent dimension (ED) of a parameter is its cumulative distribution function. All transformed parameters are of linear scale in [0, 1] interval and the distance between earthquakes represented by vectors in any ED space is Euclidean. The unknown, in general, cumulative distributions of earthquake parameters are estimated from earthquake catalogues by means of the model-free non-parametric kernel estimation method. Potential of the transformation to EDs is illustrated by two examples of use: to find hierarchically closest neighbours in time-space and to assess temporal variations of earthquake clustering in a specific 4-D phase space.

Kumaraswamy autoregressive moving average models for double bounded environmental data

NASA Astrophysics Data System (ADS)

Bayer, Fábio Mariano; Bayer, Débora Missio; Pumi, Guilherme

2017-12-01

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval (a,b) following the Kumaraswamy distribution. The Kumaraswamy family of distribution is widely applied in many areas, especially hydrology and related fields. Classical examples are time series representing rates and proportions observed over time. In the proposed KARMA model, the median is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and a link function. We introduce the new class of models and discuss conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. An application to environmental real data is presented and discussed.

A Nonlinear Interactions Approximation Model for Large-Eddy Simulation

NASA Astrophysics Data System (ADS)

Haliloglu, Mehmet U.; Akhavan, Rayhaneh

2003-11-01

A new approach to LES modelling is proposed based on direct approximation of the nonlinear terms \\overlineu_iuj in the filtered Navier-Stokes equations, instead of the subgrid-scale stress, τ_ij. The proposed model, which we call the Nonlinear Interactions Approximation (NIA) model, uses graded filters and deconvolution to parameterize the local interactions across the LES cutoff, and a Smagorinsky eddy viscosity term to parameterize the distant interactions. A dynamic procedure is used to determine the unknown eddy viscosity coefficient, rendering the model free of adjustable parameters. The proposed NIA model has been applied to LES of turbulent channel flows at Re_τ ≈ 210 and Re_τ ≈ 570. The results show good agreement with DNS not only for the mean and resolved second-order turbulence statistics but also for the full (resolved plus subgrid) Reynolds stress and turbulence intensities.

Accounting for Parameter Uncertainty in Complex Atmospheric Models, With an Application to Greenhouse Gas Emissions Evaluation

NASA Astrophysics Data System (ADS)

Swallow, B.; Rigby, M. L.; Rougier, J.; Manning, A.; Thomson, D.; Webster, H. N.; Lunt, M. F.; O'Doherty, S.

2016-12-01

In order to understand underlying processes governing environmental and physical phenomena, a complex mathematical model is usually required. However, there is an inherent uncertainty related to the parameterisation of unresolved processes in these simulators. Here, we focus on the specific problem of accounting for uncertainty in parameter values in an atmospheric chemical transport model. Systematic errors introduced by failing to account for these uncertainties have the potential to have a large effect on resulting estimates in unknown quantities of interest. One approach that is being increasingly used to address this issue is known as emulation, in which a large number of forward runs of the simulator are carried out, in order to approximate the response of the output to changes in parameters. However, due to the complexity of some models, it is often unfeasible to run large numbers of training runs that is usually required for full statistical emulators of the environmental processes. We therefore present a simplified model reduction method for approximating uncertainties in complex environmental simulators without the need for very large numbers of training runs. We illustrate the method through an application to the Met Office's atmospheric transport model NAME. We show how our parameter estimation framework can be incorporated into a hierarchical Bayesian inversion, and demonstrate the impact on estimates of UK methane emissions, using atmospheric mole fraction data. We conclude that accounting for uncertainties in the parameterisation of complex atmospheric models is vital if systematic errors are to be minimized and all relevant uncertainties accounted for. We also note that investigations of this nature can prove extremely useful in highlighting deficiencies in the simulator that might otherwise be missed.

LiDAR-IMU Time Delay Calibration Based on Iterative Closest Point and Iterated Sigma Point Kalman Filter.

PubMed

Liu, Wanli

2017-03-08

The time delay calibration between Light Detection and Ranging (LiDAR) and Inertial Measurement Units (IMUs) is an essential prerequisite for its applications. However, the correspondences between LiDAR and IMU measurements are usually unknown, and thus cannot be computed directly for the time delay calibration. In order to solve the problem of LiDAR-IMU time delay calibration, this paper presents a fusion method based on iterative closest point (ICP) and iterated sigma point Kalman filter (ISPKF), which combines the advantages of ICP and ISPKF. The ICP algorithm can precisely determine the unknown transformation between LiDAR-IMU; and the ISPKF algorithm can optimally estimate the time delay calibration parameters. First of all, the coordinate transformation from the LiDAR frame to the IMU frame is realized. Second, the measurement model and time delay error model of LiDAR and IMU are established. Third, the methodology of the ICP and ISPKF procedure is presented for LiDAR-IMU time delay calibration. Experimental results are presented that validate the proposed method and demonstrate the time delay error can be accurately calibrated.

Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation

NASA Technical Reports Server (NTRS)

Simon, Donald L.; Garg, Sanjay

2011-01-01

An emerging approach in the field of aircraft engine controls and system health management is the inclusion of real-time, onboard models for the inflight estimation of engine performance variations. This technology, typically based on Kalman-filter concepts, enables the estimation of unmeasured engine performance parameters that can be directly utilized by controls, prognostics, and health-management applications. A challenge that complicates this practice is the fact that an aircraft engine s performance is affected by its level of degradation, generally described in terms of unmeasurable health parameters such as efficiencies and flow capacities related to each major engine module. Through Kalman-filter-based estimation techniques, the level of engine performance degradation can be estimated, given that there are at least as many sensors as health parameters to be estimated. However, in an aircraft engine, the number of sensors available is typically less than the number of health parameters, presenting an under-determined estimation problem. A common approach to address this shortcoming is to estimate a subset of the health parameters, referred to as model tuning parameters. The problem/objective is to optimally select the model tuning parameters to minimize Kalman-filterbased estimation error. A tuner selection technique has been developed that specifically addresses the under-determined estimation problem, where there are more unknown parameters than available sensor measurements. A systematic approach is applied to produce a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. Tuning parameter selection is performed using a multi-variable iterative search routine that seeks to minimize the theoretical mean-squared estimation error of the Kalman filter. This approach can significantly reduce the error in onboard aircraft engine parameter estimation applications such as model-based diagnostic, controls, and life usage calculations. The advantage of the innovation is the significant reduction in estimation errors that it can provide relative to the conventional approach of selecting a subset of health parameters to serve as the model tuning parameter vector. Because this technique needs only to be performed during the system design process, it places no additional computation burden on the onboard Kalman filter implementation. The technique has been developed for aircraft engine onboard estimation applications, as this application typically presents an under-determined estimation problem. However, this generic technique could be applied to other industries using gas turbine engine technology.

A Biomathematical Model of Pneumococcal Lung Infection and Antibiotic Treatment in Mice.

PubMed

Schirm, Sibylle; Ahnert, Peter; Wienhold, Sandra; Mueller-Redetzky, Holger; Nouailles-Kursar, Geraldine; Loeffler, Markus; Witzenrath, Martin; Scholz, Markus

2016-01-01

Pneumonia is considered to be one of the leading causes of death worldwide. The outcome depends on both, proper antibiotic treatment and the effectivity of the immune response of the host. However, due to the complexity of the immunologic cascade initiated during infection, the latter cannot be predicted easily. We construct a biomathematical model of the murine immune response during infection with pneumococcus aiming at predicting the outcome of antibiotic treatment. The model consists of a number of non-linear ordinary differential equations describing dynamics of pneumococcal population, the inflammatory cytokine IL-6, neutrophils and macrophages fighting the infection and destruction of alveolar tissue due to pneumococcus. Equations were derived by translating known biological mechanisms and assuming certain response kinetics. Antibiotic therapy is modelled by a transient depletion of bacteria. Unknown model parameters were determined by fitting the predictions of the model to data sets derived from mice experiments of pneumococcal lung infection with and without antibiotic treatment. Time series of pneumococcal population, debris, neutrophils, activated epithelial cells, macrophages, monocytes and IL-6 serum concentrations were available for this purpose. The antibiotics Ampicillin and Moxifloxacin were considered. Parameter fittings resulted in a good agreement of model and data for all experimental scenarios. Identifiability of parameters is also estimated. The model can be used to predict the performance of alternative schedules of antibiotic treatment. We conclude that we established a biomathematical model of pneumococcal lung infection in mice allowing predictions regarding the outcome of different schedules of antibiotic treatment. We aim at translating the model to the human situation in the near future.