NASA Astrophysics Data System (ADS)
Chang, Wei-Der; Yan, Jun-Juh
2006-10-01
In this paper, we propose a novel genetic algorithm (GA) with a multi-crossover fashion to estimate the associated coefficients for a class of nonlinear discrete-time multivariable dynamical systems. Unlike the traditional crossover method of using two chromosomes, the proposed method uses three chromosomes to achieve a crossover. According to the adjusting direction by crossing three chromosomes, more excellent offspring can be produced. To solve the identification problem of multivariable nonlinear discrete-time systems, each of estimated system coefficients represents a gene, and a collection of genes is referred to as a chromosome in the view of GA. The chromosomes in the population are then evolved using the proposed multi-crossover method. An illustrative example of multivariable nonlinear systems is given to demonstrate the effectiveness, as compared with the traditional crossover method, of the proposed method.
A Signal Transmission Technique for Stability Analysis of Multivariable Non-Linear Control Systems
NASA Technical Reports Server (NTRS)
Jackson, Mark; Zimpfer, Doug; Adams, Neil; Lindsey, K. L. (Technical Monitor)
2000-01-01
Among the difficulties associated with multivariable, non-linear control systems is the problem of assessing closed-loop stability. Of particular interest is the class of non-linear systems controlled with on/off actuators, such as spacecraft thrusters or electrical relays. With such systems, standard describing function techniques are typically too conservative, and time-domain simulation analysis is prohibitively extensive, This paper presents an open-loop analysis technique for this class of non-linear systems. The technique is centered around an innovative use of multivariable signal transmission theory to quantify the plant response to worst case control commands. The technique has been applied to assess stability of thruster controlled flexible space structures. Examples are provided for Space Shuttle attitude control with attached flexible payloads.
Identification of discontinuous nonlinear systems via a multivariate Padé approach
NASA Astrophysics Data System (ADS)
Keshavarzzadeh, V.; Masri, S. F.
2016-02-01
We present a nonlinear system identification technique based on multi-dimensional rational polynomials. A multi-dimensional Padé-Legendre approximation is developed to circumvent challenges in dealing with sharp shocks. The purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems, particularly systems with a non-smooth response surface. This identification approach utilizes the generalized form of a Padé-Legendre approximation for studying multivariable functions. In the studied problems, the nonlinearity is a function of state variables (displacement and velocity), which requires multi-dimensional formulation. Furthermore, a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface. This study presents different types of nonlinearities including smooth, irregular, and hysteretic functions, in order to demonstrate the performance of the approach under different conditions. In order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation, a nonlinear system with a sharp discontinuous restoring force surface is considered. The performance of both approaches is investigated for different degrees of "sharpness". In addition, the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system (computed on the basis of the identified model) from data sets corresponding to different excitations than those used for identification purposes. It is shown that the proposed approach provides a robust identification technique for a broad class of highly-nonlinear systems, and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties.
Constructing networks from a dynamical system perspective for multivariate nonlinear time series
NASA Astrophysics Data System (ADS)
Nakamura, Tomomichi; Tanizawa, Toshihiro; Small, Michael
2016-03-01
We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.
NASA Technical Reports Server (NTRS)
Aires, Filipe; Rossow, William B.; Hansen, James E. (Technical Monitor)
2001-01-01
A new approach is presented for the analysis of feedback processes in a nonlinear dynamical system by observing its variations. The new methodology consists of statistical estimates of the sensitivities between all pairs of variables in the system based on a neural network modeling of the dynamical system. The model can then be used to estimate the instantaneous, multivariate and nonlinear sensitivities, which are shown to be essential for the analysis of the feedbacks processes involved in the dynamical system. The method is described and tested on synthetic data from the low-order Lorenz circulation model where the correct sensitivities can be evaluated analytically.
NASA Technical Reports Server (NTRS)
Sidar, M.
1976-01-01
The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.
He, Shouling
2002-10-01
In this paper multilayer neural networks (MNNs) are used to control the balancing of a class of inverted pendulums. Unlike normal inverted pendulums, the pendulum discussed here has two degrees of rotational freedom and the base-point moves randomly in three-dimensional space. The goal is to apply control torques to keep the pendulum in a prescribed position in spite of the random movement at the base-point. Since the inclusion of the base-point motion leads to a non-autonomous dynamic system with time-varying parametric excitation, the design of the control system is a challenging task. A feedback control algorithm is proposed that utilizes a set of neural networks to compensate for the effect of the system's nonlinearities. The weight parameters of neural networks updated on-line, according to a learning algorithm that guarantees the Lyapunov stability of the control system. Furthermore, since the base-point movement is considered unmeasurable, a neural inverse model is employed to estimate it from only measured state variables. The estimate is then utilized within the main control algorithm to produce compensating control signals. The examination of the proposed control system, through simulations, demonstrates the promise of the methodology and exhibits positive aspects, which cannot be achieved by the previously developed techniques on the same problem. These aspects include fast, yet well-maintained damped responses with reasonable control torques and no requirement for knowledge of the model or the model parameters. The work presented here can benefit practical problems such as the study of stable locomotion of human upper body and bipedal robots. PMID:12424811
Multivariate Padé Approximations For Solving Nonlinear Diffusion Equations
NASA Astrophysics Data System (ADS)
Turut, V.
2015-11-01
In this paper, multivariate Padé approximation is applied to power series solutions of nonlinear diffusion equations. As it is seen from tables, multivariate Padé approximation (MPA) gives reliable solutions and numerical results.
Multi-application controls: Robust nonlinear multivariable aerospace controls applications
NASA Technical Reports Server (NTRS)
Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob
1994-01-01
This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented
Multivariable nonlinear identification of smart buildings
NASA Astrophysics Data System (ADS)
Kim, Yeesock; Kim, Young Hoon; Lee, Seongsoo
2015-10-01
This paper presents a new multi-input-multi-output (MIMO) fuzzy model for nonlinear system identification (SI) of smart structures under a variety of random forces. The fuzzy SI model is developed through the integration of wavelet transform (WT), multiple MIMO linear autoregressive exogenous (ARX) input models, Takagi-Sugeno (TS) fuzzy model, weighted linear least squares, and data clustering algorithms: MIMO WARX-TS fuzzy model. To demonstrate the effectiveness of the MIMO WARX-TS fuzzy model, a three-story building equipped with a magnetorheological (MR) damper under a variety of random signals is investigated. To train the proposed model, an artificial earthquake and control forces are used as input signals while displacement and acceleration responses are used as outputs. To validate the trained model, four real recorded earthquake signals are used. It is shown from the simulation that the proposed MIMO WARX-TS fuzzy identification algorithm is effective in estimating nonlinear behavior of a building-MR damper system under a variety of seismic excitations.
Different approaches to multivariate calibration of nonlinear sensor data.
Dieterle, Frank; Busche, Stefan; Gauglitz, Günter
2004-10-01
In this study, different approaches to the multivariate calibration of the vapors of two refrigerants are reported. As the relationships between the time-resolved sensor signals and the concentrations of the analytes are nonlinear, the widely used partial least-squares regression (PLS) fails. Therefore, different methods are used, which are known to be able to deal with nonlinearities present in data. First, the Box-Cox transformation, which transforms the dependent variables nonlinearly, was applied. The second approach, the implicit nonlinear PLS regression, tries to account for nonlinearities by introducing squared terms of the independent variables to the original independent variables. The third approach, quadratic PLS (QPLS), uses a nonlinear quadratic inner relationship for the model instead of a linear relationship such as PLS. Tree algorithms are also used, which split a nonlinear problem into smaller subproblems, which are modeled using linear methods or discrete values. Finally, neural networks are applied, which are able to model any relationship. Different special implementations, like genetic algorithms with neural networks and growing neural networks, are also used to prevent an overfitting. Among the fast and simpler algorithms, QPLS shows good results. Different implementations of neural networks show excellent results. Among the different implementations, the most sophisticated and computing-intensive algorithms (growing neural networks) show the best results. Thus, the optimal method for the data set presented is a compromise between quality of calibration and complexity of the algorithm. PMID:15156303
System identification for multivariable control
NASA Astrophysics Data System (ADS)
Vanzee, G. A.
1981-05-01
System identification methods and modern control theory are applied to industrial processes. These processes must often be controlled in order to meet certain requirements with respect to the product quality, safety, energy consumption, and environmental load. Modern control system design methods which take the occurring interaction phenomena and stochastic disturbances into account are used. An accurate dynamic mathematical model of the process, by theoretical modelling and/or by system identification is obtained. The computational aspects of two important types of identifications methods, i.e., stochastic realization and prediction error based parameter estimation are studied. The studied computational aspects are the robustness, the accuracy, and the computational costs of the methods. Theoretical analyses and applications to a multivariable pilot scale process, operating under closed loop conditions are investigated.
Guaranteed robustness properties of multivariable nonlinear stochastic optimal regulators
NASA Technical Reports Server (NTRS)
Tsitsiklis, J. N.; Athans, M.
1984-01-01
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators
NASA Technical Reports Server (NTRS)
Tsitsiklis, J. N.; Athans, M.
1983-01-01
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
NASA Technical Reports Server (NTRS)
Callier, F. M.; Desoer, C. A.
1973-01-01
A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.
NASA Technical Reports Server (NTRS)
Leininger, G. G.
1981-01-01
Using nonlinear digital simulation as a representative model of the dynamic operation of the QCSEE turbofan engine, a feedback control system is designed by variable frequency design techniques. Transfer functions are generated for each of five power level settings covering the range of operation from approach power to full throttle (62.5% to 100% full power). These transfer functions are then used by an interactive control system design synthesis program to provide a closed loop feedback control using the multivariable Nyquist array and extensions to multivariable Bode diagrams and Nichols charts.
Multivariable control systems with saturating actuators antireset windup strategies
NASA Technical Reports Server (NTRS)
Kapasouris, P.; Athans, M.
1985-01-01
Preliminary, promising, results for introducing antireset windup (ARW) properties in multivariable feedback control systems with multiple saturating actuator nonlinearities and integrating actions are presented. The ARW method introduces simple nonlinear feedback around the integrators. The multiloop circle criterion is used to derive sufficient conditions for closed-loop stability that employ frequency-domain singular value tests. The improvement in transient response due to the ARW feedback is demonstrated using a 2-input 2-outpurt control system based upon F-404 jet engine dynamics.
NASA Astrophysics Data System (ADS)
Kannan, Rohit; Tangirala, Arun K.
2014-06-01
Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.
Output feedback for linear multivariable systems with parameter uncertainty.
NASA Technical Reports Server (NTRS)
Basuthakur, S.; Knapp, C. H.
1973-01-01
A minimax design method is applied to the problem of obtaining an acceptable output feedback matrix for linear multivariable systems with parameter uncertainty. The result is a set of nonlinear matrix equations (similar to those obtained by Levine and Athans (1970)), which must be solved for the feedback matrix. An example illustrates the technique and the fact that better results are achieved for large parameter variation than with a purely nominal design.
Multivariate optimization of production systems
Carroll, J.A.; Horne, R.N. )
1992-07-01
This paper reports that mathematically, optimization involves finding the extreme values of a function. Given a function of several variables, Z = {integral}({rvec x}{sub 1}, {rvec x}{sub 2},{rvec x}{sub 3},{yields}x{sub n}), an optimization scheme will find the combination of these variables that produces an extreme value in the function, whether it is a minimum or a maximum value. Many examples of optimization exist. For instance, if a function gives and investor's expected return on the basis of different investments, numerical optimization of the function will determine the mix of investments that will yield the maximum expected return. This is the basis of modern portfolio theory. If a function gives the difference between a set of data and a model of the data, numerical optimization of the function will produce the best fit of the model to the data. This is the basis for nonlinear parameter estimation. Similar examples can be given for network analysis, queuing theory, decision analysis, etc.
Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.
Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing
2011-12-01
For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method. PMID:22106143
Estimating the decomposition of predictive information in multivariate systems.
Faes, Luca; Kugiumtzis, Dimitris; Nollo, Giandomenico; Jurysta, Fabrice; Marinazzo, Daniele
2015-03-01
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep. PMID:25871169
Estimating the decomposition of predictive information in multivariate systems
NASA Astrophysics Data System (ADS)
Faes, Luca; Kugiumtzis, Dimitris; Nollo, Giandomenico; Jurysta, Fabrice; Marinazzo, Daniele
2015-03-01
In the study of complex systems from observed multivariate time series, insight into the evolution of one system may be under investigation, which can be explained by the information storage of the system and the information transfer from other interacting systems. We present a framework for the model-free estimation of information storage and information transfer computed as the terms composing the predictive information about the target of a multivariate dynamical process. The approach tackles the curse of dimensionality employing a nonuniform embedding scheme that selects progressively, among the past components of the multivariate process, only those that contribute most, in terms of conditional mutual information, to the present target process. Moreover, it computes all information-theoretic quantities using a nearest-neighbor technique designed to compensate the bias due to the different dimensionality of individual entropy terms. The resulting estimators of prediction entropy, storage entropy, transfer entropy, and partial transfer entropy are tested on simulations of coupled linear stochastic and nonlinear deterministic dynamic processes, demonstrating the superiority of the proposed approach over the traditional estimators based on uniform embedding. The framework is then applied to multivariate physiologic time series, resulting in physiologically well-interpretable information decompositions of cardiovascular and cardiorespiratory interactions during head-up tilt and of joint brain-heart dynamics during sleep.
Intermittent control of unstable multivariate systems.
Loram, I; Gawthrop, P; Gollee, H
2015-08-01
A sensorimotor architecture inspired from biological, vertebrate control should (i) explain the interface between high dimensional sensory analysis, low dimensional goals and high dimensional motor mechanisms and (ii) provide both stability and flexibility. Our interest concerns whether single-input-single-output intermittent control (SISO_IC) generalized to multivariable intermittent control (MIC) can meet these requirements.We base MIC on the continuous-time observer-predictorstate-feedback architecture. MIC uses event detection. A system matched hold (SMH), using the underlying continuoustime optimal control design, generates multivariate open-loop control signals between samples of the predicted state. Combined, this serial process provides a single-channel of control with optimised sensor fusion and motor synergies. Quadratic programming provides constrained, optimised equilibrium control design to handle unphysical configurations, redundancy and provides minimum, necessary reduction of open loop instability through optimised joint impedance. In this multivariate form, dimensionality is linked to goals rather than neuromuscular or sensory degrees of freedom. The biological and engineering rationale for intermittent rather than continuous multivariate control, is that the generalised hold sustains open loop predictive control while the open loop interval provides time within the feedback loop for online centralised, state dependent optimisation and selection. PMID:26736539
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
NASA Astrophysics Data System (ADS)
Leeds, W. B.; Wikle, C. K.
2012-12-01
Spatio-temporal statistical models, and in particular Bayesian hierarchical models (BHMs), have become increasingly popular as means of representing natural processes such as climate and weather that evolve over space and time. Hierarchical models make it possible to specify separate, conditional probability distributions that account for uncertainty in the observations, the underlying process, and parameters in situations when specifying these sources of uncertainty in a joint probability distribution may be difficult. As a result, BHMs are a natural setting for climatologists, meteorologists, and other environmental scientists to incorporate scientific information (e.g., PDEs, IDEs, etc.) a priori into a rigorous statistical framework that accounts for error in measurements, uncertainty in the understanding of the true underlying process, and uncertainty in the parameters that describe the process. While much work has been done in the development of statistical models for linear dynamic spatio-temporal processes, statistical modeling for nonlinear (and particularly, multivariate nonlinear) spatio-temporal dynamical processes is still a relatively open area of inquiry. As a result, general statistical models for environmental scientists to model complicated nonlinear processes is limited. We address this limitation in the methodology by introducing a multivariate "general quadratic nonlinear" framework for modeling multivariate, nonlinear spatio-temporal random processes inside of a BHM in a way that is especially applicable for problems in the ocean and atmospheric sciences. We show that in addition to the fact that this model addresses the previously mentioned sources of uncertainty for a wide spectrum of multivariate, nonlinear spatio-temporal processes, it is also a natural framework for data assimilation, allowing for the fusing of observations with computer models, computer model emulators, computer model output, or "mechanistically motivated" statistical
Compensator improvement for multivariable control systems
NASA Technical Reports Server (NTRS)
Mitchell, J. R.; Mcdaniel, W. L., Jr.; Gresham, L. L.
1977-01-01
A theory and the associated numerical technique are developed for an iterative design improvement of the compensation for linear, time-invariant control systems with multiple inputs and multiple outputs. A strict constraint algorithm is used in obtaining a solution of the specified constraints of the control design. The result of the research effort is the multiple input, multiple output Compensator Improvement Program (CIP). The objective of the Compensator Improvement Program is to modify in an iterative manner the free parameters of the dynamic compensation matrix so that the system satisfies frequency domain specifications. In this exposition, the underlying principles of the multivariable CIP algorithm are presented and the practical utility of the program is illustrated with space vehicle related examples.
Multivariate, non-linear trend analysis of heterogeneous water quality monitoring data
NASA Astrophysics Data System (ADS)
Lischeid, Gunnar; Kalettka, Thomas; Steidl, Jörg; Merz, Christoph; Lehr, Christian
2014-05-01
Comprehensive water quality monitoring is considered a necessary prerequisite for sound water resources management and a valuable source for science. In practice, however, use of large monitoring data sets is often limited due to heterogeneous data sources, spatially and temporally variable monitoring schemes, non-equidistant sampling, large natural variability, and, last but not least, by the sheer size of the data sets that makes identification of unexpected peculiarities a tedious task. As a consequence, any initiation of gradual long-term system shifts can hardly be detected, especially as long as it is restricted to a small fraction of sampling sites. In addition, trends might be limited to a rather small subset of sampling sites or to certain periods of time and might thus escape attention. Usually, numerous solutes are monitored in parallel, but trend analyses are performed for each solute separately. However, in water quality samples trends are hardly restricted to single solutes, but affect various solutes synchronously in a characteristic way. Thus performing joint multivariate trend analyses would not only save effort and time, but would yield more robust assessments of system shifts. We present a non-linear multivariate data visualization approach that allows a rapid assessment of non-linear, possibly local trends and unexpected behaviour in large water quality monitoring data sets. It consists of a combination of Self-Organizing Maps and Sammon's Mapping (SOM-SM). The approach was applied to a data set of 2900 water samples, each comprising 13 solutes, compiled from various monitoring programs in the Federal State of Brandenburg (Germany). In total, 128 stream water, groundwater and small pond sites had been sampled between 1994 and 2012 at different and irregular time intervals. The SOM-SM product is a graph where every sample is represented by a symbol. Location of the symbols in the graph is optimized such that the distance between any two symbols
Tortajada-Genaro, L A; Campíns-Falcó, P
2007-05-15
Multivariate standardisation is proposed for the successful chemiluminescence determination of chromium based on luminol-hydrogen peroxide reaction. In an extended concentration range, non-linear calibration model is needed. The studied instrumental situations were different detection cells, instruments, assemblies, time and their possible combinations. Chemiluminescence kinetic registers have been transferred using piecewise direct standardisation (PDS) method. The optimisation of transfer parameters has been carried out based on the prediction residual error criteria. Non-linear principal component regression (NL-PCR) and non-linear partial least square regression (NL-PLS) were chosen for modelling the relationship signal-concentration of transferred registers. Good accuracy and precision were obtained for water samples. The concentrations of chromium were statistically in agreement with reference method values and with recovery studies. Therefore, it is possible to transfer chemiluminescence curves without loosing ability of prediction, even the presence of a non-linear behaviour. PMID:19071716
Apparatus and system for multivariate spectral analysis
Keenan, Michael R.; Kotula, Paul G.
2003-06-24
An apparatus and system for determining the properties of a sample from measured spectral data collected from the sample by performing a method of multivariate spectral analysis. The method can include: generating a two-dimensional matrix A containing measured spectral data; providing a weighted spectral data matrix D by performing a weighting operation on matrix A; factoring D into the product of two matrices, C and S.sup.T, by performing a constrained alternating least-squares analysis of D=CS.sup.T, where C is a concentration intensity matrix and S is a spectral shapes matrix; unweighting C and S by applying the inverse of the weighting used previously; and determining the properties of the sample by inspecting C and S. This method can be used by a spectrum analyzer to process X-ray spectral data generated by a spectral analysis system that can include a Scanning Electron Microscope (SEM) with an Energy Dispersive Detector and Pulse Height Analyzer.
Uniform approach to linear and nonlinear interrelation patterns in multivariate time series
NASA Astrophysics Data System (ADS)
Rummel, Christian; Abela, Eugenio; Müller, Markus; Hauf, Martinus; Scheidegger, Olivier; Wiest, Roland; Schindler, Kaspar
2011-06-01
Currently, a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series. Whereas the former are by definition insensitive to nonlinear effects, the latter detect both nonlinear and linear interrelation. In the present contribution we employ a uniform surrogate-based approach, which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation. The bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation. To demonstrate applicability of the approach to multivariate real-world time series we investigate resting state functional magnetic resonance imaging (rsfMRI) data of two healthy subjects as well as intracranial electroencephalograms (iEEG) of two epilepsy patients with focal onset seizures. The main findings are that for our rsfMRI data interrelations can be described by linear cross-correlation. Rejection of the null hypothesis of linear iEEG interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures.
Dr. Katja Lindenberg
2005-11-20
During the one-year period 2004-2005 our work continued to focus on nonlinear noisy systems, with special attention to spatially extended systems. There is a history of many decades of research in the sciences and engineering on the behavior of noninear noisy systems, but only in the past ten years or so has a theoretical understanding of spatially extended systems begun to emerge. This has been the outcome of a symbiosis of numerical simulations not possible until recently, laboratory experiments, and new analytic methods.
Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review
Montzka, Carsten; Pauwels, Valentijn R. N.; Franssen, Harrie-Jan Hendricks; Han, Xujun; Vereecken, Harry
2012-01-01
More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a
NASA Astrophysics Data System (ADS)
Irving, A. D.; Dewson, T.
1997-02-01
A new method is described for extracting mixed linear-nonlinear coupled differential equations from multivariate discrete time series data. It is assumed in the present work that the solution of the coupled ordinary differential equations can be represented as a multivariate Volterra functional expansion. A tractable hierarchy of moment equations is generated by operating on a suitably truncated Volterra functional expansion. The hierarchy facilitates the calculation of the coefficients of the coupled differential equations. In order to demonstrate the method's ability to accurately estimate the coefficients of the governing differential equations, it is applied to data derived from the numerical solution of the Lorenz equations with additive noise. The method is then used to construct a dynamic global mid- and high-magnetic latitude ionospheric model where nonlinear phenomena such as period doubling and quenching occur. It is shown that the estimated inhomogeneous coupled second-order differential equation model for the ionospheric foF2 peak plasma density can accurately forecast the future behaviour of a set of ionosonde stations which encompass the earth. Finally, the method is used to forecast the future behaviour of a portfolio of Japanese common stock prices. The hierarchy method can be used to characterise the observed behaviour of a wide class of coupled linear and mixed linear-nonlinear phenomena.
NASA Astrophysics Data System (ADS)
Sarhadi, Ali; Burn, Donald H.; Johnson, Fiona; Mehrotra, Raj; Sharma, Ashish
2016-05-01
Accurate projection of global warming on the probabilistic behavior of hydro-climate variables is one of the main challenges in climate change impact assessment studies. Due to the complexity of climate-associated processes, different sources of uncertainty influence the projected behavior of hydro-climate variables in regression-based statistical downscaling procedures. The current study presents a comprehensive methodology to improve the predictive power of the procedure to provide improved projections. It does this by minimizing the uncertainty sources arising from the high-dimensionality of atmospheric predictors, the complex and nonlinear relationships between hydro-climate predictands and atmospheric predictors, as well as the biases that exist in climate model simulations. To address the impact of the high dimensional feature spaces, a supervised nonlinear dimensionality reduction algorithm is presented that is able to capture the nonlinear variability among projectors through extracting a sequence of principal components that have maximal dependency with the target hydro-climate variables. Two soft-computing nonlinear machine-learning methods, Support Vector Regression (SVR) and Relevance Vector Machine (RVM), are engaged to capture the nonlinear relationships between predictand and atmospheric predictors. To correct the spatial and temporal biases over multiple time scales in the GCM predictands, the Multivariate Recursive Nesting Bias Correction (MRNBC) approach is used. The results demonstrate that this combined approach significantly improves the downscaling procedure in terms of precipitation projection.
NASA Astrophysics Data System (ADS)
Kourehli, S. S.
2015-07-01
Damage detection and estimation in structures using incomplete modal data is presented. In the proposed approach, damage location and severity is determined by solving an optimization problem using the constrained nonlinear multivariable function of Matlab (so- called fmincon) to perform constrained minimization. The feasibility of the presented method is validated with a three-story plane frame as numerical example containing one or several damages with different value of damage severity. The obtained results indicated that proposed method is effective and robust in detection and estimation of damage.
NASA Technical Reports Server (NTRS)
Turner, L. R.
1960-01-01
The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.
Ecological prediction with nonlinear multivariate time-frequency functional data models
Yang, Wen-Hsi; Wikle, Christopher K.; Holan, Scott H.; Wildhaber, Mark L.
2013-01-01
Time-frequency analysis has become a fundamental component of many scientific inquiries. Due to improvements in technology, the amount of high-frequency signals that are collected for ecological and other scientific processes is increasing at a dramatic rate. In order to facilitate the use of these data in ecological prediction, we introduce a class of nonlinear multivariate time-frequency functional models that can identify important features of each signal as well as the interaction of signals corresponding to the response variable of interest. Our methodology is of independent interest and utilizes stochastic search variable selection to improve model selection and performs model averaging to enhance prediction. We illustrate the effectiveness of our approach through simulation and by application to predicting spawning success of shovelnose sturgeon in the Lower Missouri River.
NASA Technical Reports Server (NTRS)
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
NASA Astrophysics Data System (ADS)
Okou, Francis A.; Akhrif, Ouassima; Dessaint, Louis A.; Bouchard, Derrick
2013-05-01
This papter introduces a decentralized multivariable robust adaptive voltage and frequency regulator to ensure the stability of large-scale interconnnected generators. Interconnection parameters (i.e. load, line and transormer parameters) are assumed to be unknown. The proposed design approach requires the reformulation of conventiaonal power system models into a multivariable model with generator terminal voltages as state variables, and excitation and turbine valve inputs as control signals. This model, while suitable for the application of modern control methods, introduces problems with regards to current design techniques for large-scale systems. Interconnection terms, which are treated as perturbations, do not meet the common matching condition assumption. A new adaptive method for a certain class of large-scale systems is therefore introduces that does not require the matching condition. The proposed controller consists of nonlinear inputs that cancel some nonlinearities of the model. Auxiliary controls with linear and nonlinear components are used to stabilize the system. They compensate unknown parametes of the model by updating both the nonlinear component gains and excitation parameters. The adaptation algorithms involve the sigma-modification approach for auxiliary control gains, and the projection approach for excitation parameters to prevent estimation drift. The computation of the matrix-gain of the controller linear component requires the resolution of an algebraic Riccati equation and helps to solve the perturbation-mismatching problem. A realistic power system is used to assess the proposed controller performance. The results show that both stability and transient performance are considerably improved following a severe contingency.
Steady-state decoupling and design of linear multivariable systems
NASA Technical Reports Server (NTRS)
Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations.
Power system stability improvement with multivariable self-tuning control
Fan, J.Y.; Ortmeyer, T.H.; Mukundan, R. )
1990-02-01
A multivariable self-tuning adaptive control scheme is presented. This scheme is of a decentralized nature and is implemented locally for individual generating units. A discrete multivariable auto-regressive-moving-average model is developed to represent a generating unit. The recursive-least-squares (RLS) estimation algorithm with variable-forgetting factor and the generalized-minimum-variance control technique are utilized to synthesize the local controllers. A dynamic goal-point-generating model is introduced to provide varying goal point for the local controller which leads the subsystem output to its equilibrium gradually. Extensive simulations are performed on the IEEE 10-machine test system. The results show that the proposed multivariable adaptive control scheme is effective in damping the severe oscillations after large disturbances as well as improving the system dynamics under small oscillations and is better than the conventional PSS method. The controller demonstrates robustness and is compatible with the existing conventional controllers in multimachine systems.
Fixed order dynamic compensation for multivariable linear systems
NASA Technical Reports Server (NTRS)
Kramer, F. S.; Calise, A. J.
1986-01-01
This paper considers the design of fixed order dynamic compensators for multivariable time invariant linear systems, minimizing a linear quadratic performance cost functional. Attention is given to robustness issues in terms of multivariable frequency domain specifications. An output feedback formulation is adopted by suitably augmenting the system description to include the compensator states. Either a controller or observer canonical form is imposed on the compensator description to reduce the number of free parameters to its minimal number. The internal structure of the compensator is prespecified by assigning a set of ascending feedback invariant indices, thus forming a Brunovsky structure for the nominal compensator.
NASA Astrophysics Data System (ADS)
Deng, Linhua
2015-07-01
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
Design of multivariable feedback control systems via spectral assignment
NASA Technical Reports Server (NTRS)
Mielke, R. R.; Tung, L. J.; Marefat, M.
1983-01-01
The applicability of spectral assignment techniques to the design of multivariable feedback control systems was investigated. A fractional representation design procedure for unstable plants is presented and illustrated with an example. A computer aided design software package implementing eigenvalue/eigenvector design procedures is described. A design example which illustrates the use of the program is explained.
Nonlinear dynamical systems analyzer
NASA Astrophysics Data System (ADS)
Coffey, Adrian S.; Johnson, Martin; Jones, Robin
1994-10-01
Computationally intensive algorithms are an ever more common requirement of modern signal processing. Following the work of Gentleman and Kung, McWhirter, Shepherd and Proudler suggested that certain matrix-orientated algorithms can be mapped onto systolic array architectures for adaptive linear signal processing. This has been extended by Broomhead et al. to the calculation of nonlinear predictive models and applied by Jones et al. to target identification and recognition. We shall show that predictive models are extremely sharp discriminators. Our chosen problem, if implemented as a systolic array, would require 3403 processors which would result in high through-put rate at excessive cost. We are developing an efficient sub-optimally implemented systolic array; one processor servicing more than one systolic node. We describe a prototype Heuristic Processor which computes a multi- dimensional, nonlinear, predictive model. It consists of a Radial Basis Function Network and a least squares optimizer using QR decomposition. The optimized solution of a set of simultaneous equations in 81 unknowns is calculated in 150 (mu) S. The QR section emulates a triangular systolic array by the novel use of an array of 40 mature silicon DSP chips costing under DOL100 each. The DSP chips operate in synchronism at a 50 MHz clock rate passing data to each other through multi-port memories on a dead-letter box principle; there are no memory access conflicts and only two-port and three-port memories are required. The processor provides 1-GFlop of computing power per cubic-foot of electronics for a component cost of approximately DOL15,000.
Canonical forms for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.; Meyer, G.
1983-01-01
Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David Albert; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the Causality Recovery Methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
A method for designing robust multivariable feedback systems
NASA Technical Reports Server (NTRS)
Milich, David A.; Athans, Michael; Valavani, Lena; Stein, Gunter
1988-01-01
A new methodology is developed for the synthesis of linear, time-invariant (LTI) controllers for multivariable LTI systems. The aim is to achieve stability and performance robustness of the feedback system in the presence of multiple unstructured uncertainty blocks; i.e., to satisfy a frequency-domain inequality in terms of the structured singular value. The design technique is referred to as the causality recovery methodology (CRM). Starting with an initial (nominally) stabilizing compensator, the CRM produces a closed-loop system whose performance-robustness is at least as good as, and hopefully superior to, that of the original design. The robustness improvement is obtained by solving an infinite-dimensional, convex optimization program. A finite-dimensional implementation of the CRM was developed, and it was applied to a multivariate design example.
Nonlinear input-output systems
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Bilgel, Murat; Prince, Jerry L; Wong, Dean F; Resnick, Susan M; Jedynak, Bruno M
2016-07-01
It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. These are especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain at the level of voxels, whose volumes are on the order of mm(3). These voxelwise measurements provide a rich collection of disease indicators. Longitudinal neuroimaging studies enable the analysis of changes in these voxelwise measures. However, commonly used longitudinal analysis approaches, such as linear mixed effects models, do not account for the fact that individuals enter a study at various disease stages and progress at different rates, and generally consider each voxelwise measure independently. We propose a multivariate nonlinear mixed effects model for estimating the trajectories of voxelwise neuroimaging biomarkers from longitudinal data that accounts for such differences across individuals. The method involves the prediction of a progression score for each visit based on a collective analysis of voxelwise biomarker data within an expectation-maximization framework that efficiently handles large amounts of measurements and variable number of visits per individual, and accounts for spatial correlations among voxels. This score allows individuals with similar progressions to be aligned and analyzed together, which enables the construction of a trajectory of brain changes as a function of an underlying progression or disease stage. We apply our method to studying cortical β-amyloid deposition, a hallmark of preclinical Alzheimer's disease, as measured using positron emission tomography. Results on 104 individuals with a total of 300 visits suggest that precuneus is the earliest cortical region to
Steady state decoupling and design of linear multivariable systems
NASA Technical Reports Server (NTRS)
Huang, J. Y.; Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of linear multivariable systems is developed. The criterion consists of n(n-1) inequalities with the type numbers of the compensator transfer functions as the unknowns. These unknowns can be chosen to satisfy the inequalities and hence achieve a steady state decoupling scheme. It turns out that pure integrators in the loops play an important role. An extended root locus design method is then developed to take care of the stability and transient response. The overall procedure is applied to the compensation design for STOL C-8A aircraft in the approach mode.
NASA Technical Reports Server (NTRS)
Bosworth, John T.; Burken, John J.
1997-01-01
Safety and productivity of the initial flight test phase of a new vehicle have been enhanced by developing the ability to measure the stability margins of the combined control system and vehicle in flight. One shortcoming of performing this analysis is the long duration of the excitation signal required to provide results over a wide frequency range. For flight regimes such as high angle of attack or hypersonic flight, the ability to maintain flight condition for this time duration is difficult. Significantly reducing the required duration of the excitation input is possible by tailoring the input to excite only the frequency range where the lowest stability margin is expected. For a multiple-input/multiple-output system, the inputs can be simultaneously applied to the control effectors by creating each excitation input with a unique set of frequency components. Chirp-Z transformation algorithms can be used to match the analysis of the results to the specific frequencies used in the excitation input. This report discusses the application of a tailored excitation input to a high-fidelity X-31A linear model and nonlinear simulation. Depending on the frequency range, the results indicate the potential to significantly reduce the time required for stability measurement.
Multivariable control of the Space Shuttle Remote Manipulator System
NASA Technical Reports Server (NTRS)
Adams, Neil J.; Appleby, Brent D.; Prakash, OM, II
1991-01-01
Linear controllers are designed to regulate the end effector of the Space Shuttle Remote Manipulator System (SRMS) operating in position hold mode. Design techniques used include H2 and H-infinity optimization. The nonlinear SRMS is linearized by modeling the effects of the significant nonlinearities as uncertain parameters. Each regulator design is evaluated for robust stability using both the small gain theorem with an H-infinity norm and the less conservative mu-analysis test. Regulator designs offer significant improvement over the current system for the nominal plant. Unfortunately, the SRMS model suffers from lightly damped poles with real parametric uncertainty. Under such conditions, the mu-analysis test, which allows for complex perturbations, cannot guarantee robust stability.
Modeling of Nonlinear Systems using Genetic Algorithm
NASA Astrophysics Data System (ADS)
Hayashi, Kayoko; Yamamoto, Toru; Kawada, Kazuo
In this paper, a newly modeling system by using Genetic Algorithm (GA) is proposed. The GA is an evolutionary computational method that simulates the mechanisms of heredity or evolution of living things, and it is utilized in optimization and in searching for optimized solutions. Most process systems have nonlinearities, so it is necessary to anticipate exactly such systems. However, it is difficult to make a suitable model for nonlinear systems, because most nonlinear systems have a complex structure. Therefore the newly proposed method of modeling for nonlinear systems uses GA. Then, according to the newly proposed scheme, the optimal structure and parameters of the nonlinear model are automatically generated.
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
Multivariate optimization of production systems: The time dimension
Ravindran, N.; Horne, R.N.
1993-04-01
Traditional analysis of oil and gas production systems treats individual nodes one at a time. This only calculates a feasible solution which is not necessarily optimal. Multivariate optimization is able to determine the most profitable configuration, including all variables simultaneously. The optimization can also find the optimal recovery over a period of time, rather than just at a single instant as in traditional methods. This report describes the development of multivariate optimization for situations in which the decision variables may change as a function of time. For example, instead of estimating a tubing size which is optimal over the life of the project, this approach determines a series of optimal tubing sizes which may change from year to year. Examples show that under an optimal strategy, tubing size can be changed only infrequently while still increasing profitability of a project. The methods used in this work considered the special requirements of objectives which are not smooth functions of their decision variables. The physical problems considered included artificial lift production systems.
Multivariable control system installed at ARCO west Texas gas plant
Chou, K. ); Clay, R.M. ); Gamez, J.P. ); Berkowitz, P.N.; Papadopoulos, M.N. )
1992-11-16
This paper reports that a PC-based, multivariable process control (MVC) system was installed last year at an ARCO Oil and Gas Co. gas plant in West Texas. This gas-processing application was developed under sponsorship of the Gas Research Institute. The system was installed, tuned, and on-line within 2 weeks and fully verified in closed loop service by operations in 8 weeks. Four more gas processing installations are currently under way. The general and main objective of the MVC control system is to achieve continuous optimum operation of a process unit through on-line prediction and control of setpoints for the key process variables in the unit. specifically, the objective is to achieve this operation, especially under constantly changing conditions, with reliable solutions requiring minimal operator intervention, customization, or update effort upon each plant change. MVC was developed by continental Controls Inc. (CCI), Houston.
Theoretical constraints in the design of multivariable control systems
NASA Technical Reports Server (NTRS)
Rynaski, E. G.; Mook, D. J.
1993-01-01
The theoretical constraints inherent in the design of multivariable control systems were defined and investigated. These constraints are manifested by the system transmission zeros that limit or bound the areas in which closed loop poles and individual transfer function zeros may be placed. These constraints were investigated primarily in the context of system decoupling or non-interaction. It was proven that decoupling requires the placement of closed loop poles at the system transmission zeros. Therefore, the system transmission zeros must be minimum phase to guarantee a stable decoupled system. Once decoupling has been accomplished, the remaining part of the system exhibits transmission zeros at infinity, so nearly complete design freedom is possible in terms of placing both poles and zeros of individual closed loop transfer functions. A general, dynamic inversion model following system architecture was developed that encompasses both the implicit and explicit configuration. Robustness properties are developed along with other attributes of this type of system. Finally, a direct design is developed for the longitudinal-vertical degrees of freedom of aircraft motion to show how a direct lift flap can be used to improve the pitch-heave maneuvering coordination for enhanced flying qualities.
Investigation of a Nonlinear Control System
NASA Technical Reports Server (NTRS)
Flugge-Lotz, I; Taylor, C F; Lindberg, H E
1958-01-01
A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.
On stability theory. [of nonlinear feedback control systems
NASA Technical Reports Server (NTRS)
Safonov, M. G.; Athans, M.
1979-01-01
It is found that under mild assumptions, feedback system stability can be concluded if one can 'topologically separate' the infinite-dimensional function space containing the system's dynamical input-output relations into two regions, one region containing the dynamical input-output relation of the 'feedforward' element of the system and the other region containing the dynamical output-input relation of the 'feedback' element. Nonlinear system stability criteria of both the input-output type and the state-space (Liapunov) type are interpreted in this context. The abstract generality and conceptual simplicity afforded by the topological separation perspective clarifies some of the basic issues underlying stability theory and serves to suggest improvements in existing stability criteria. A generalization of Zames' (1966) conic-relation stability criterion is proved, laying the foundation for improved multivariable generalizations of the frequency-domain circle stability criterion for nonlinear systems.
Describing functions for nonlinear optical systems.
Ghosh, A K
1997-10-10
The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested. PMID:18264243
NASA Astrophysics Data System (ADS)
Hussain, Mirza Zahid; Li, Fuguo; Wang, Jing; Yuan, Zhanwei; Li, Pan; Wu, Tao
2015-07-01
The present study comprises the determination of constitutive relationship for thermo-mechanical processing of INCONEL 718 through double multivariate nonlinear regression, a newly developed approach which not only considers the effect of strain, strain rate, and temperature on flow stress but also explains the interaction effect of these thermo-mechanical parameters on flow behavior of the alloy. Hot isothermal compression experiments were performed on Gleeble-3500 thermo-mechanical testing machine in the temperature range of 1153 to 1333 K within the strain rate range of 0.001 to 10 s-1. The deformation behavior of INCONEL 718 is analyzed and summarized by establishing the high temperature deformation constitutive equation. The calculated correlation coefficient ( R) and average absolute relative error ( AARE) underline the precision of proposed constitutive model.
Harinath, Eranda; Mann, George K I
2008-06-01
This paper describes a design and two-level tuning method for fuzzy proportional-integral derivative (FPID) controllers for a multivariable process where the fuzzy inference uses the inference of standard additive model. The proposed method can be used for any n x n multi-input-multi-output process and guarantees closed-loop stability. In the two-level tuning scheme, the tuning follows two steps: low-level tuning followed by high-level tuning. The low-level tuning adjusts apparent linear gains, whereas the high-level tuning changes the nonlinearity in the normalized fuzzy output. In this paper, two types of FPID configurations are considered, and their performances are evaluated by using a real-time multizone temperature control problem having a 3 x 3 process system. PMID:18558531
A canonical form for nonlinear systems
NASA Technical Reports Server (NTRS)
Su, R.; Hunt, L. R.
1986-01-01
The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.
Multivariable Techniques for High-Speed Research Flight Control Systems
NASA Technical Reports Server (NTRS)
Newman, Brett A.
1999-01-01
This report describes the activities and findings conducted under contract with NASA Langley Research Center. Subject matter is the investigation of suitable multivariable flight control design methodologies and solutions for large, flexible high-speed vehicles. Specifically, methodologies are to address the inner control loops used for stabilization and augmentation of a highly coupled airframe system possibly involving rigid-body motion, structural vibrations, unsteady aerodynamics, and actuator dynamics. Design and analysis techniques considered in this body of work are both conventional-based and contemporary-based, and the vehicle of interest is the High-Speed Civil Transport (HSCT). Major findings include: (1) control architectures based on aft tail only are not well suited for highly flexible, high-speed vehicles, (2) theoretical underpinnings of the Wykes structural mode control logic is based on several assumptions concerning vehicle dynamic characteristics, and if not satisfied, the control logic can break down leading to mode destabilization, (3) two-loop control architectures that utilize small forward vanes with the aft tail provide highly attractive and feasible solutions to the longitudinal axis control challenges, and (4) closed-loop simulation sizing analyses indicate the baseline vane model utilized in this report is most likely oversized for normal loading conditions.
Steinhaeuser, Karsten J K; Ganguly, Auroop R; Chawla, Nitesh
2011-01-01
A systematic characterization of multivariate dependence at multiple spatio-temporal scales is critical to understanding climate system dynamics and improving predictive ability from models and data. However, dependence structures in climate are complex due to nonlinear dynamical generating processes, long-range spatial and long-memory temporal relationships, as well as low-frequency variability. Here we utilize complex networks to explore dependence in climate data. Specifically, networks constructed from reanalysis-based atmospheric variables over oceans and partitioned with community detection methods demonstrate the potential to capture regional and global dependence structures within and among climate variables. Proximity-based dependence as well as long-range spatial relationships are examined along with their evolution over time, yielding new insights on ocean meteorology. The tools are implicitly validated by confirming conceptual understanding about aggregate correlations and teleconnections. Our results also suggest a close similarity of observed dependence patterns in relative humidity and horizontal wind speed over oceans. In addition, updraft velocity, which relates to convective activity over the oceans, exhibits short spatiotemporal decorrelation scales but long-range dependence over time. The multivariate and multi-scale dependence patterns broadly persist over multiple time windows. Our findings motivate further investigations of dependence structures among observations, reanalysis and model-simulated data to enhance process understanding, assess model reliability and improve regional climate predictions.
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Berry phase in nonlinear systems
Liu, J.; Fu, L. B.
2010-05-15
The Berry phase acquired by an eigenstate that experienced a nonlinear adiabatic evolution is investigated thoroughly. The circuit integral of the Berry connection of the instantaneous eigenstate cannot account for the adiabatic geometric phase, while the Bogoliubov excitations around the eigenstates are found to be accumulated during the nonlinear adiabatic evolution and contribute a finite phase of geometric nature. A two-mode model is used to illustrate our theory. Our theory is applicable to Bose-Einstein condensate, nonlinear light propagation, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics.
ERIC Educational Resources Information Center
Hsieh, Fushing; Ferrer, Emilio; Chen, Shuchun; Mauss, Iris B.; John, Oliver; Gross, James J.
2011-01-01
We present an approach for evaluating coherence in multivariate systems that considers all the variables simultaneously. We operationalize the multivariate system as a network and define coherence as the efficiency with which a signal is transmitted throughout the network. We illustrate this approach with time series data from 15…
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.; Tung, L. J.
1981-01-01
Applied research in the area of spectral assignment in multivariable systems is reported. A frequency domain technique for determining the set of all stabilizing controllers for a single feedback loop multivariable system is described. It is shown that decoupling and tracking are achievable using this procedure. The technique is illustrated with a simple example.
Nonlinear model for building-soil systems
McCallen, D.B.; Romstad, K.M.
1994-05-01
A finite-element based, numerical analysis methodology has been developed for the nonlinear analysis of building-soil systems. The methodology utilizes a reduced-order, nonlinear continuum model to represent the building, and the soil is represented with a simple nonlinear two-dimensional plane strain finite element. The foundation of the building is idealized as a rigid block and the interface between the soil and the foundation is modeled with an interface contract element. The objectives of the current paper are to provide the theoretical development of the system model, with particular emphasis on the modeling of the foundation-soil contact, and to demonstrate the special-purpose finite-element program that has been developed for nonlinear analysis of the building-soil system. Examples are included that compare the results obtained with the special-purpose program with the results of a general-purpose nonlinear finite-element program.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
A System of Multivariable Krawtchouk Polynomials and a Probabilistic Application
NASA Astrophysics Data System (ADS)
Grünbaum, F. Alberto; Rahman, Mizan
2011-12-01
The one variable Krawtchouk polynomials, a special case of the 2F1 function did appear in the spectral representation of the transition kernel for a Markov chain studied a long time ago by M. Hoare and M. Rahman. A multivariable extension of this Markov chain was considered in a later paper by these authors where a certain two variable extension of the F1 Appel function shows up in the spectral analysis of the corresponding transition kernel. Independently of any probabilistic consideration a certain multivariable version of the Gelfand-Aomoto hypergeometric function was considered in papers by H. Mizukawa and H. Tanaka. These authors and others such as P. Iliev and P. Tertwilliger treat the two-dimensional version of the Hoare-Rahman work from a Lie-theoretic point of view. P. Iliev then treats the general n-dimensional case. All of these authors proved several properties of these functions. Here we show that these functions play a crucial role in the spectral analysis of the transition kernel that comes from pushing the work of Hoare-Rahman to the multivariable case. The methods employed here to prove this as well as several properties of these functions are completely different to those used by the authors mentioned above.
Arnautovic, D.; Medanic, J.
1987-12-01
A methodology for the design of decentralized multivariable excitation and controllers in multimachine power systems is developed using projective controls. The existing methodology, is extended to permit the coordinated design of AVR and PSS controllers in power systems.
NASA Technical Reports Server (NTRS)
Young, G.
1982-01-01
A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.
Markovian master equation for nonlinear systems
NASA Astrophysics Data System (ADS)
de los Santos-Sánchez, O.; Récamier, J.; Jáuregui, R.
2015-06-01
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular case of a Morse-like oscillator interacting with a thermal field is illustrated, and the decay of quantum coherence in such a system is analyzed in terms of the evolution on phase space of its nonlinear coherent states via the Wigner function.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M.
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
The effect of system nonlinearities on system noise statistics
NASA Technical Reports Server (NTRS)
Robinson, L. H., Jr.
1971-01-01
The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.
Nonlinear dynamical system approaches towards neural prosthesis
Torikai, Hiroyuki; Hashimoto, Sho
2011-04-19
An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
Damage detection in initially nonlinear systems
Bornn, Luke; Farrar, Charles; Park, Gyuhae
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
Discrete time learning control in nonlinear systems
NASA Technical Reports Server (NTRS)
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Impulsive synchronization of networked nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Jiang, Haibo; Bi, Qinsheng
2010-06-01
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.
State Identification in Nonlinear Systems
Holloway, James Paul
2005-02-06
A state estimation method based on finding a system state that causes a model to match a set of system measurements is regularized by requiring that sudden changes in system state be avoided. The required optimization is accomplished by a pattern search algorithm. The method does not require derivative information or linearization of the model. Is has been applied to a 10 dimensional model of a fast reactor system.
NASA Astrophysics Data System (ADS)
Athans, M.; Lee, W. H.; Lehtomaki, N. A.; Levy, B. C.; Ng, P. T. P.
1982-05-01
The robustness of the stability of multivariable linear time-invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available and new robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point of a single-input, single-output (SISO) Nyquist diagram. Using the return difference transfer matrix a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness of linear-quadratic-Gaussian control systems are analyzed via this robustness theory and multiloop stability margins are presented; in particular, a new type of margin, a cross-feed margin, is introduced. Other frequency domain analysis and design techniques are also briefly discussed and their relation to the present robustness analysis is examined. In addition a linear-quadratic based design procedure that quarantees a prescribed degree of stability is developed, with special emphasis upon its robustness properties.
Decoupling in linear time-varying multivariable systems
NASA Technical Reports Server (NTRS)
Sankaran, V.
1973-01-01
The necessary and sufficient conditions for the decoupling of an m-input, m-output, linear time varying dynamical system by state variable feedback is described. The class of feedback matrices which decouple the system are illustrated. Systems which do not satisfy these results are described and systems with disturbances are considered. Some examples are illustrated to clarify the results.
Quadratic boundedness of uncertain nonlinear dynamic systems
NASA Astrophysics Data System (ADS)
Brockman, Mark Lawrence
Physical systems are often perturbed by unknown external disturbances or contain important system parameters which are difficult to model exactly. However, engineers are expected to design systems which perform well even in the presence of uncertainties. For example, an airplane designer can never know the precise direction or magnitude of wind gusts, or the exact mass distribution inside the aircraft, but passengers expect to arrive on time after a smooth ride. This thesis will first present the concept of quadratic boundedness of an uncertain nonlinear dynamic system, and then develop analysis techniques and control design methods for systems containing unknown disturbances and parameters. For a class of nonlinear systems, conditions for quadratic boundedness are given, and the relationship between quadratic boundedness and quadratic stability is explored. An important consequence of quadratic boundedness is the ability to calculate an upper bound on the system gain of an uncertain nonlinear system. For nominally linear systems, necessary and sufficient conditions for quadratic boundedness are given. The innovative use of linear matrix inequalities in an iterative algorithm provides a means to analyze the quadratic boundedness properties of systems containing parameter uncertainties. The analysis results establish a framework for the development of design methods which integrate performance specifications into the control design process for all the types of systems considered. Numerous examples illustrate the major results of the thesis.
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances. PMID:26174586
Simple method of designing centralized PI controllers for multivariable systems based on SSGM.
Dhanya Ram, V; Chidambaram, M
2015-05-01
A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35-41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix. PMID:25530257
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
NASA Technical Reports Server (NTRS)
Ryan, Laurie E.; Stengel, Robert F.
1990-01-01
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Squeezing spectra for nonlinear optical systems
NASA Technical Reports Server (NTRS)
Collett, M. J.; Walls, D. F.
1985-01-01
The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems. PMID:25833428
NASA Technical Reports Server (NTRS)
Hague, D. S.; Vanderberg, J. D.; Woodbury, N. W.
1974-01-01
A method for rapidly examining the probable applicability of weight estimating formulae to a specific aerospace vehicle design is presented. The Multivariate Analysis Retrieval and Storage System (MARS) is comprised of three computer programs which sequentially operate on the weight and geometry characteristics of past aerospace vehicles designs. Weight and geometric characteristics are stored in a set of data bases which are fully computerized. Additional data bases are readily added to the MARS system and/or the existing data bases may be easily expanded to include additional vehicles or vehicle characteristics.
Computer-Aided Decisions in Human Services: Expert Systems and Multivariate Models.
ERIC Educational Resources Information Center
Sicoly, Fiore
1989-01-01
This comparison of two approaches to the development of computerized supports for decision making--expert systems and multivariate models--focuses on computerized systems that assist professionals with tasks related to diagnosis or classification in human services. Validation of both expert systems and statistical models is emphasized. (39…
NASA Astrophysics Data System (ADS)
Zhang, Xiaoyu; Li, Qingbo; Zhang, Guangjun
2013-11-01
In this paper, a modified single-index signal regression (mSISR) method is proposed to construct a nonlinear and practical model with high-accuracy. The mSISR method defines the optimal penalty tuning parameter in P-spline signal regression (PSR) as initial tuning parameter and chooses the number of cycles based on minimizing root mean squared error of cross-validation (RMSECV). mSISR is superior to single-index signal regression (SISR) in terms of accuracy, computation time and convergency. And it can provide the character of the non-linearity between spectra and responses in a more precise manner than SISR. Two spectra data sets from basic research experiments, including plant chlorophyll nondestructive measurement and human blood glucose noninvasive measurement, are employed to illustrate the advantages of mSISR. The results indicate that the mSISR method (i) obtains the smooth and helpful regression coefficient vector, (ii) explicitly exhibits the type and amount of the non-linearity, (iii) can take advantage of nonlinear features of the signals to improve prediction performance and (iv) has distinct adaptability for the complex spectra model by comparing with other calibration methods. It is validated that mSISR is a promising nonlinear modeling strategy for multivariate calibration.
NASA Astrophysics Data System (ADS)
Li, Heng; Ren, Changzhi; Song, Libin; Wu, Jun
2014-07-01
The direct drive tracking system of Telescope is one multivariable, nonlinear and strong coupling complex mechanical control system which is disturbed by some nonlinear disturbance such torque ripple, wind disturbance during the tracking process. the traditional PID control cannot fundamentally solved the contradiction between static and dynamic performance, tracking data and disturbance .This paper explores a kind of CMAC with nonlinear PID parallel composite control method for dual redundant telescope tracing servo system. The simulation result proves that combined algorithm based on CMAC and PID realizes the servo system without overshoot and accelerates the response of the system. What's more, CMAC feedforward control improves anti-disturbance ability and the control precision of the servo system.
Indirect learning control for nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Ryu, Yeong Soon; Longman, Richard W.
1993-01-01
In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.
Hypoglycemia Early Alarm Systems Based On Multivariable Models
Turksoy, Kamuran; Bayrak, Elif S; Quinn, Lauretta; Littlejohn, Elizabeth; Rollins, Derrick; Cinar, Ali
2013-01-01
Hypoglycemia is a major challenge of artificial pancreas systems and a source of concern for potential users and parents of young children with Type 1 diabetes (T1D). Early alarms to warn the potential of hypoglycemia are essential and should provide enough time to take action to avoid hypoglycemia. Many alarm systems proposed in the literature are based on interpretation of recent trends in glucose values. In the present study, subject-specific recursive linear time series models are introduced as a better alternative to capture glucose variations and predict future blood glucose concentrations. These models are then used in hypoglycemia early alarm systems that notify patients to take action to prevent hypoglycemia before it happens. The models developed and the hypoglycemia alarm system are tested retrospectively using T1D subject data. A Savitzky-Golay filter and a Kalman filter are used to reduce noise in patient data. The hypoglycemia alarm algorithm is developed by using predictions of future glucose concentrations from recursive models. The modeling algorithm enables the dynamic adaptation of models to inter-/intra-subject variation and glycemic disturbances and provides satisfactory glucose concentration prediction with relatively small error. The alarm systems demonstrate good performance in prediction of hypoglycemia and ultimately in prevention of its occurrence. PMID:24187436
NASA Technical Reports Server (NTRS)
Lefkowitz, C. P.; Tekawy, J. A.; Pujara, P. K.; Safonov, M. G.
1989-01-01
AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft.
Spectral decomposition of nonlinear systems with memory
NASA Astrophysics Data System (ADS)
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J.
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
Practical robustness measures in multivariable control system analysis. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Lehtomaki, N. A.
1981-01-01
The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed.
A summary of spectral synthesis procedures for multivariable systems
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.; Maynard, R. A.
1979-01-01
A new approach to the eigensystem assignment problem is presented. The approach utilizes a null-space formulation of the eigenvalue/eigenvector assignment problem to simultaneously realize arbitrary eigenvalue specifications, approximate desired modal behavior, and achieve low eigensystem sensitivity with respect to plant parameter variations. The methods are applied to the design of regulator and integral plus proportional servo control systems.
NASA Technical Reports Server (NTRS)
Stevens, P. K.
1981-01-01
This paper presents a generalization of the Nyquist stability criterion to include general multivariable linear stationary systems subject to linear static and dynamic feedback. At the same time, a unifying proof is given for all known versions of the Nyquist criterion for finite dimensional systems.
NASA Technical Reports Server (NTRS)
Sanchez Pena, Ricardo S.; Sideris, Athanasios
1988-01-01
A computer program implementing an algorithm for computing the multivariable stability margin to check the robust stability of feedback systems with real parametric uncertainty is proposed. The authors present in some detail important aspects of the program. An example is presented using lateral directional control system.
Finite-time consensus of time-varying nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Liu, Qingrong; Liang, Zhishan
2016-08-01
This paper investigates the problem of leader-follower finite-time consensus for a class of time-varying nonlinear multi-agent systems. The dynamics of each agent is assumed to be represented by a strict feedback nonlinear system, where nonlinearities satisfy Lipschitz growth conditions with time-varying gains. The main design procedure is outlined as follows. First, it is shown that the leader-follower consensus problem is equivalent to a conventional control problem of multi-variable high-dimension systems. Second, by introducing a state transformation, the control problem is converted into the construction problem of two dynamic equations. Third, based on the Lyapunov stability theorem, the global finite-time stability of the closed-loop control system is proved, and the finite-time consensus of the concerned multi-agent systems is thus guaranteed. An example is given to verify the effectiveness of the proposed consensus protocol algorithm.
FREQ: A computational package for multivariable system loop-shaping procedures
NASA Technical Reports Server (NTRS)
Giesy, Daniel P.; Armstrong, Ernest S.
1989-01-01
Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.; Christenson, D.; Gordon, M.; Kistler, R.; Lampert, S.; Marshall, R.; Mclaughlin, R.
1974-01-01
The MIDAS System is a third-generation, fast, multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS Program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughout. The hardware and software generated in Phase I of the over-all program are described. The system contains a mini-computer to control the various high-speed processing elements in the data path and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating 2 x 105 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation. Diagnostic programs used to test MIDAS' operations are presented.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.
1974-01-01
The MIDAS System is described as a third-generation fast multispectral recognition system able to keep pace with the large quantity and high rates of data acquisition from present and projected sensors. A principal objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turnaround time and significant gains in throughput. The hardware and software are described. The system contains a mini-computer to control the various high-speed processing elements in the data path, and a classifier which implements an all-digital prototype multivariate-Gaussian maximum likelihood decision algorithm operating at 200,000 pixels/sec. Sufficient hardware was developed to perform signature extraction from computer-compatible tapes, compute classifier coefficients, control the classifier operation, and diagnose operation.
Structural analysis and design of multivariable control systems: An algebraic approach
NASA Technical Reports Server (NTRS)
Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen
1988-01-01
The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.
Nonlinear dynamic macromodeling techniques for audio systems
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
Detection of decoupled input/output pairs in multivariable systems.
Potts, Alain Segundo; Massaro, Leandro Cuenca; Garcia, Claudio
2015-03-01
A method is proposed to detect if there is no coupling between an input and an output in systems operating in open-loop, that is, without a supervisory controller. The proposed technique is applicable to multiple input multiple output (MIMO) systems, whose intent is to detect no-model input/output (IO) combinations in a transfer matrix. Traditional approaches for selecting IO pairs are usually performed after the plant model is identified. The presented approach is applied during the pre-identification stage and is based on IO cross-correlation, signal filtering and fuzzy logic analysis. A case study involving the identification of a 7×6 simulated Fluid Catalytic Cracking (FCC) is discussed, as well as an influence analysis of detecting no-model IO pairs in the identification process and in the performance index of a Model Predictive Controller (MPC) applied to a 2×2 simulated distillation column. Finally, the method is tested with a real dataset obtained from an FCC unit of a petrol refinery. PMID:25433943
Model reduction of systems with localized nonlinearities.
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Rasouli, Zolaikha; Ghavami, Raouf
2016-08-01
Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61-20.99 [LOD=0.12], 0.67-23.19 [LOD=0.13] and 0.73-25.12 [LOD=0.15] μgmL(-1) for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples. PMID:27176001
NASA Astrophysics Data System (ADS)
Rasouli, Zolaikha; Ghavami, Raouf
2016-08-01
Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61-20.99 [LOD = 0.12], 0.67-23.19 [LOD = 0.13] and 0.73-25.12 [LOD = 0.15] μg mL- 1 for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples.
NASA Astrophysics Data System (ADS)
Pai, P. Frank
2011-10-01
Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.
Nonlinear Network Dynamics on Earthquake Fault Systems
Rundle, Paul B.; Rundle, John B.; Tiampo, Kristy F.; Sa Martins, Jorge S.; McGinnis, Seth; Klein, W.
2001-10-01
Earthquake faults occur in interacting networks having emergent space-time modes of behavior not displayed by isolated faults. Using simulations of the major faults in southern California, we find that the physics depends on the elastic interactions among the faults defined by network topology, as well as on the nonlinear physics of stress dissipation arising from friction on the faults. Our results have broad applications to other leaky threshold systems such as integrate-and-fire neural networks.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Explaining Student Success and Failure in a Distance Teaching System: A Multi-variate Approach.
ERIC Educational Resources Information Center
Woodley, Alan
A multivariate model to explain student success and failure at the Open University of the United Kingdom is outlined. The model is based on the results of an evaluation study that explored the suitability of this teaching system for young people under 21 years old. Twenty-three characteristics were designated as social and psychological problems,…
On the applicability of eigenvalue/eigenvector assignment in multivariable systems
NASA Technical Reports Server (NTRS)
Liberty, S. R.; Mielke, R. R.
1979-01-01
The technique of multivariable control-system design via assignment of the closed loop state matrix eigensystem is described. Features of this developing methodology include exact eigenvalue assignment, eigenvector assignment that approximates in a least squares sense a priori modal specifications, and an interactive design trade-off between the latter and desired eigensystem sensitivity with respect to plant parameters.
Lall, Upmanu; Devineni, Naresh; Kaheil, Yasir
2016-01-01
Multivariate simulations of a set of random variables are often needed for risk analysis. Given a historical data set, the goal is to develop simulations that reproduce the dependence structure in that data set so that the risk of potentially correlated factors can be evaluated. A nonparametric, copula-based simulation approach is developed and exemplified. It can be applied to multiple variables or to spatial fields with arbitrary dependence structures and marginal densities. The nonparametric simulator uses logspline density estimation in the univariate setting, together with a sampling strategy to reproduce dependence across variables or spatial instances, through a nonparametric numerical approximation of the underlying copula function. The multivariate data vectors are assumed to be independent and identically distributed. A synthetic example is provided to illustrate the method, followed by an application to the risk of livestock losses in Mongolia. PMID:26177987
Arbitrary eigenvalue assignments for linear time-varying multivariable control systems
NASA Technical Reports Server (NTRS)
Nguyen, Charles C.
1987-01-01
The problem of eigenvalue assignments for a class of linear time-varying multivariable systems is considered. Using matrix operators and canonical transformations, it is shown that a time-varying system that is 'lexicography-fixedly controllable' can be made via state feedback to be equivalent to a time-invariant system whose eigenvalues are arbitrarily assignable. A simple algorithm for the design of the state feedback is provided.
Linear pattern dynamics in nonlinear threshold systems
Rundle, John B.; Klein, W.; Tiampo, Kristy; Gross, Susanna
2000-03-01
Complex nonlinear threshold systems frequently show space-time behavior that is difficult to interpret. We describe a technique based upon a Karhunen-Loeve expansion that allows dynamical patterns to be understood as eigenstates of suitably constructed correlation operators. The evolution of space-time patterns can then be viewed in terms of a ''pattern dynamics'' that can be obtained directly from observable data. As an example, we apply our methods to a particular threshold system to forecast the evolution of patterns of observed activity. Finally, we perform statistical tests to measure the quality of the forecasts. (c) 2000 The American Physical Society.
Nonlinear Tides in Close Binary Systems
NASA Astrophysics Data System (ADS)
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-06-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the
NONLINEAR TIDES IN CLOSE BINARY SYSTEMS
Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh
2012-06-01
We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' {approx}> 10-100 M{sub Circled-Plus} at orbital periods P Almost-Equal-To 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P {approx}< 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N Almost-Equal-To 10{sup 3}[P/10 days] for a solar-type star) and drives them as a single coherent unit with
Nonlinear control for dual quaternion systems
NASA Astrophysics Data System (ADS)
Price, William D.
The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is
Optimal and multivariable control of a turbogenerator
NASA Astrophysics Data System (ADS)
Lahoud, M. A.; Harley, R. G.; Secker, A.
The use of modern control methods to design multivariable controllers which improve the performance of a turbogenerator was investigated. The turbogenerator nonlinear mathematical model from which a linearized model is deduced is presented. The inverse Nyquist Array method and the theory of optimal control are both applied to the linearized model to generate two alternative control schemes. The schemes are implemented on the nonlinear simulation model to assess their dynamic performance. Results from modern multivariable control schemes are compared with the classical automatic voltage regulator and speed governor system.
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Particle systems and nonlinear Landau damping
Villani, Cédric
2014-03-15
Some works dealing with the long-time behavior of interacting particle systems are reviewed and put into perspective, with focus on the classical Kolmogorov–Arnold–Moser theory and recent results of Landau damping in the nonlinear perturbative regime, obtained in collaboration with Clément Mouhot. Analogies are discussed, as well as new qualitative insights in the theory. Finally, the connection with a more recent work on the inviscid Landau damping near the Couette shear flow, by Bedrossian and Masmoudi, is briefly discussed.
Design of suboptimal regulators for nonlinear systems
NASA Technical Reports Server (NTRS)
Balaram, J.; Saridis, G. N.
1985-01-01
An optimal feedback control law is preferred for the regulation of a deterministic nonlinear system. In this paper, a practical, iterative design method leading to a sequence of suboptimal control laws with successively improved performance is presented. The design method requires the determination of an upper bound to the performance of each successive control law. This is obtained by solving a partial differential inequality by means of a linear programming technique. Robustness properties and the application of the design method to the control of a robot manipulator arm are also presented.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations. PMID:25104646
Gain-scheduling multivariable LPV control of an irrigation canal system.
Bolea, Yolanda; Puig, Vicenç
2016-07-01
The purpose of this paper is to present a multivariable linear parameter varying (LPV) controller with a gain scheduling Smith Predictor (SP) scheme applicable to open-flow canal systems. This LPV controller based on SP is designed taking into account the uncertainty in the estimation of delay and the variation of plant parameters according to the operating point. This new methodology can be applied to a class of delay systems that can be represented by a set of models that can be factorized into a rational multivariable model in series with left/right diagonal (multiple) delays, such as, the case of irrigation canals. A multiple pool canal system is used to test and validate the proposed control approach. PMID:27184416
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. PMID:25277626
Boosted X Waves in Nonlinear Optical Systems
Arevalo, Edward
2010-01-15
X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.
Impulse position control algorithms for nonlinear systems
NASA Astrophysics Data System (ADS)
Sesekin, A. N.; Nepp, A. N.
2015-11-01
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Impulse position control algorithms for nonlinear systems
Sesekin, A. N.; Nepp, A. N.
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1990-01-01
Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.
Nonlinear Mixing in Optical Multicarrier Systems
NASA Astrophysics Data System (ADS)
Hameed, Mahmood Abdul
Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.
Optimal uniform-damping ratio controller for sequential design of multivariable systems
NASA Technical Reports Server (NTRS)
Shieh, Leang G.; Liu, Zhen; Sunkel, John W.
1991-01-01
An optimal uniform-damping ratio controller is developed for the sequential design of a multivariable control system so that the designed closed-loop poles of the respective multivariable system and reduced-order observer are exactly placed on the negative real axis and/or the boundaries of desired sectors with constant-damping ratios. The functions in the quadratic performance index to be minimized are chosen as a combination of the weighted outputs, reduced states and inputs. Also, the optimal uniform-damping ratio controller is a combination of optimal output-feedback and optimal reduced-order state-feedback controllers. A numerical example is given to demonstrate the design procedure.
Passive dynamic controllers for nonlinear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1991-01-01
A methodology for model-independant controller design for controlling large angular motion of multi-body dynamic systems is outlined. The controlled system may consist of rigid and flexible components that undergo large rigid body motion and small elastic deformations. Control forces/torques are applied to drive the system and at the same time suppress the vibration due to flexibility of the components. The proposed controller consists of passive second-order systems which may be designed with little knowledge of the system parameter, even if the controlled system is nonlinear. Under rather general assumptions, the passive design assures that the closed loop system has guaranteed stability properties. Unlike positive real controller design, stabilization can be accomplished without direct velocity feedback. In addition, the second-order passive design allows dynamic feedback controllers with considerable freedom to tune for desired system response, and to avoid actuator saturation. After developing the basic mathematical formulation of the design methodology, simulation results are presented to illustrate the proposed approach to a flexible six-degree-of-freedom manipulator.
A multivariate analysis approach for the Imaging Atmospheric Cerenkov Telescopes System H.E.S.S
Dubois, F.; Lamanna, G.
2008-12-24
We present a multivariate classification approach applied to the analysis of data from the H.E.S.S. Very High Energy (VHE){gamma}-ray IACT stereoscopic system. This approach combines three complementary analysis methods already successfully applied in the H.E.S.S. data analysis. The proposed approach, with the combined effective estimator X{sub eff}, is conceived to improve the signal-to-background ratio and therefore particularly relevant to the morphological studies of faint extended sources.
Nonlinear dynamic analysis of flexible multibody systems
NASA Technical Reports Server (NTRS)
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
Direct adaptive control for nonlinear uncertain dynamical systems
NASA Astrophysics Data System (ADS)
Hayakawa, Tomohisa
In light of the complex and highly uncertain nature of dynamical systems requiring controls, it is not surprising that reliable system models for many high performance engineering and life science applications are unavailable. In the face of such high levels of system uncertainty, robust controllers may unnecessarily sacrifice system performance whereas adaptive controllers are clearly appropriate since they can tolerate far greater system uncertainty levels to improve system performance. In this dissertation, we develop a Lyapunov-based direct adaptive and neural adaptive control framework that addresses parametric uncertainty, unstructured uncertainty, disturbance rejection, amplitude and rate saturation constraints, and digital implementation issues. Specifically, we consider the following research topics; direct adaptive control for nonlinear uncertain systems with exogenous disturbances; robust adaptive control for nonlinear uncertain systems; adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints; adaptive reduced-order dynamic compensation for nonlinear uncertain systems; direct adaptive control for nonlinear matrix second-order dynamical systems with state-dependent uncertainty; adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia; direct adaptive control of nonnegative and compartmental dynamical systems with time delay; adaptive control for nonlinear nonnegative and compartmental dynamical systems with applications to clinical pharmacology; neural network adaptive control for nonlinear nonnegative dynamical systems; passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems; neural network adaptive dynamic output feedback control for nonlinear nonnegative systems using tapped delay memory units; Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances
Application of nonlinear time series models to driven systems
Hunter, N.F. Jr.
1990-01-01
In our laboratory we have been engaged in an effort to model nonlinear systems using time series methods. Our objectives have been, first, to understand how the time series response of a nonlinear system unfolds as a function of the underlying state variables, second, to model the evolution of the state variables, and finally, to predict nonlinear system responses. We hope to address the relationship between model parameters and system parameters in the near future. Control of nonlinear systems based on experimentally derived parameters is also a planned topic of future research. 28 refs., 15 figs., 2 tabs.
NASA Technical Reports Server (NTRS)
Kriegler, F. J.; Gordon, M. F.; Mclaughlin, R. H.; Marshall, R. E.
1975-01-01
The MIDAS (Multivariate Interactive Digital Analysis System) processor is a high-speed processor designed to process multispectral scanner data (from Landsat, EOS, aircraft, etc.) quickly and cost-effectively to meet the requirements of users of remote sensor data, especially from very large areas. MIDAS consists of a fast multipipeline preprocessor and classifier, an interactive color display and color printer, and a medium scale computer system for analysis and control. The system is designed to process data having as many as 16 spectral bands per picture element at rates of 200,000 picture elements per second into as many as 17 classes using a maximum likelihood decision rule.
A Visualization System for Space-Time and Multivariate Patterns (VIS-STAMP)
Guo, Diansheng; Chen, Jin; MacEachren, Alan M.; Liao, Ke
2011-01-01
The research reported here integrates computational, visual, and cartographic methods to develop a geovisual analytic approach for exploring and understanding spatio-temporal and multivariate patterns. The developed methodology and tools can help analysts investigate complex patterns across multivariate, spatial, and temporal dimensions via clustering, sorting, and visualization. Specifically, the approach involves a self-organizing map, a parallel coordinate plot, several forms of reorderable matrices (including several ordering methods), a geographic small multiple display, and a 2-dimensional cartographic color design method. The coupling among these methods leverages their independent strengths and facilitates a visual exploration of patterns that are difficult to discover otherwise. The visualization system we developed supports overview of complex patterns and, through a variety of interactions, enables users to focus on specific patterns and examine detailed views. We demonstrate the system with an application to the IEEE InfoVis 2005 Contest data set, which contains time-varying, geographically referenced, and multivariate data for technology companies in the US. PMID:17073369
Exploring lipids with nonlinear optical microscopy in multiple biological systems
NASA Astrophysics Data System (ADS)
Alfonso-Garcia, Alba
Lipids are crucial biomolecules for the well being of humans. Altered lipid metabolism may give rise to a variety of diseases that affect organs from the cardiovascular to the central nervous system. A deeper understanding of lipid metabolic processes would spur medical research towards developing precise diagnostic tools, treatment methods, and preventive strategies for reducing the impact of lipid diseases. Lipid visualization remains a complex task because of the perturbative effect exerted by traditional biochemical assays and most fluorescence markers. Coherent Raman scattering (CRS) microscopy enables interrogation of biological samples with minimum disturbance, and is particularly well suited for label-free visualization of lipids, providing chemical specificity without compromising on spatial resolution. Hyperspectral imaging yields large datasets that benefit from tailored multivariate analysis. In this thesis, CRS microscopy was combined with Raman spectroscopy and other label-free nonlinear optical techniques to analyze lipid metabolism in multiple biological systems. We used nonlinear Raman techniques to characterize Meibum secretions in the progression of dry eye disease, where the lipid and protein contributions change in ratio and phase segregation. We employed similar tools to examine lipid droplets in mice livers aboard a spaceflight mission, which lose their retinol content contributing to the onset of nonalcoholic fatty-liver disease. We also focused on atherosclerosis, a disease that revolves around lipid-rich plaques in arterial walls. We examined the lipid content of macrophages, whose variable phenotype gives rise to contrasting healing and inflammatory activities. We also proposed new label-free markers, based on lifetime imaging, for macrophage phenotype, and to detect products of lipid oxidation. Cholesterol was also detected in hepatitis C virus infected cells, and in specific strains of age-related macular degeneration diseased cells by
On state representations of nonlinear implicit systems
NASA Astrophysics Data System (ADS)
Pereira da Silva, Paulo Sergio; Batista, Simone
2010-03-01
This work considers a semi-implicit system Δ, that is, a pair (S, y), where S is an explicit system described by a state representation ? , where x(t) ∈ ℝ n and u(t) ∈ ℝ m , which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) ∈ ℝ l . An input candidate is a set of functions v = (v 1, …, v s ), which may depend on time t, on x, and on u and its derivatives up to a finite order. The problem of finding a (local) proper state representation ż = g(t, z, v) with input v for the implicit system Δ is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Δ. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Lévine, Martin, and Rouchon (1999) ('A Lie-Bäcklund Approach to Equivalence and Flatness of Nonlinear Systems', IEEE Transactions on Automatic Control, 44(5), (922-937)).
Bifurcations and Patterns in Nonlinear Dissipative Systems
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Dagne, Getachew; Huang, Yangxin
2016-01-01
Censored data are characteristics of many bioassays in HIV/AIDS studies where assays may not be sensitive enough to determine gradations in viral load determination among those below a detectable threshold. Not accounting for such left-censoring appropriately can lead to biased parameter estimates in most data analysis. To properly adjust for left-censoring, this paper presents an extension of the Tobit model for fitting nonlinear dynamic mixed-effects models with skew distributions. Such extensions allow one to specify the conditional distributions for viral load response to account for left-censoring, skewness and heaviness in the tails of the distributions of the response variable. A Bayesian modeling approach via Markov Chain Monte Carlo (MCMC) algorithm is used to estimate model parameters. The proposed methods are illustrated using real data from an HIV/AIDS study. PMID:22992288
Dagne, Getachew; Huang, Yangxin
2012-01-01
Censored data are characteristics of many bioassays in HIV/AIDS studies where assays may not be sensitive enough to determine gradations in viral load determination among those below a detectable threshold. Not accounting for such left-censoring appropriately can lead to biased parameter estimates in most data analysis. To properly adjust for left-censoring, this paper presents an extension of the Tobit model for fitting nonlinear dynamic mixed-effects models with skew distributions. Such extensions allow one to specify the conditional distributions for viral load response to account for left-censoring, skewness and heaviness in the tails of the distributions of the response variable. A Bayesian modeling approach via Markov Chain Monte Carlo (MCMC) algorithm is used to estimate model parameters. The proposed methods are illustrated using real data from an HIV/AIDS study. PMID:22992288
Nonlinear resonant phenomena in multilevel quantum systems
NASA Astrophysics Data System (ADS)
Hicke, Christian
We study nonlinear resonant phenomena in two-level and multilevel quantum systems. Our results are of importance for applications in the areas of quantum control, quantum computation, and quantum measurement. We present a method to perform fault-tolerant single-qubit gate operations using Landau-Zener tunneling. In a single Landau-Zoner pulse, the qubit transition frequency is varied in time so that it passes through the frequency of a radiation field. We show that a simple three-pulse sequence allows eliminating errors in the gate up to the third order in errors in the qubit energies or the radiation frequency. We study the nonlinear transverse response of a spin S > 1/2 with easy-axis anisotropy. The coherent transverse response displays sharp dips or peaks when the modulation frequency is adiabatically swept through multiphoton resonance. The effect is a consequence of a certain conformal property of the spin dynamics in a magnetic field for the anisotropy energy ∝ S2z . The occurrence of the dips or peaks is determined by the spin state. Their shape strongly depends on the modulation amplitude. Higher-order anisotropy breaks the symmetry, leading to sharp steps in the transverse response as function of frequency. The results bear on the dynamics of molecular magnets in a static magnetic field. We show that a modulated large-spin system has special symmetry. In the presence of dissipation it leads to characteristic nonlinear effects. They include abrupt switching between transverse magnetization branches with varying modulating field without hysteresis and a specific pattern of switching in the presence of multistability and hysteresis. Along with steady forced vibrations the transverse spin components can display transient vibrations at a combination of the Larmor frequency and a slower frequency determined by the anisotropy energy. The analysis is based on a microscopic theory that takes into account relaxation mechanisms important for single
Sivasamy, Aneetha Avalappampatty; Sundan, Bose
2015-01-01
The ever expanding communication requirements in today's world demand extensive and efficient network systems with equally efficient and reliable security features integrated for safe, confident, and secured communication and data transfer. Providing effective security protocols for any network environment, therefore, assumes paramount importance. Attempts are made continuously for designing more efficient and dynamic network intrusion detection models. In this work, an approach based on Hotelling's T(2) method, a multivariate statistical analysis technique, has been employed for intrusion detection, especially in network environments. Components such as preprocessing, multivariate statistical analysis, and attack detection have been incorporated in developing the multivariate Hotelling's T(2) statistical model and necessary profiles have been generated based on the T-square distance metrics. With a threshold range obtained using the central limit theorem, observed traffic profiles have been classified either as normal or attack types. Performance of the model, as evaluated through validation and testing using KDD Cup'99 dataset, has shown very high detection rates for all classes with low false alarm rates. Accuracy of the model presented in this work, in comparison with the existing models, has been found to be much better. PMID:26357668
Avalappampatty Sivasamy, Aneetha; Sundan, Bose
2015-01-01
The ever expanding communication requirements in today's world demand extensive and efficient network systems with equally efficient and reliable security features integrated for safe, confident, and secured communication and data transfer. Providing effective security protocols for any network environment, therefore, assumes paramount importance. Attempts are made continuously for designing more efficient and dynamic network intrusion detection models. In this work, an approach based on Hotelling's T2 method, a multivariate statistical analysis technique, has been employed for intrusion detection, especially in network environments. Components such as preprocessing, multivariate statistical analysis, and attack detection have been incorporated in developing the multivariate Hotelling's T2 statistical model and necessary profiles have been generated based on the T-square distance metrics. With a threshold range obtained using the central limit theorem, observed traffic profiles have been classified either as normal or attack types. Performance of the model, as evaluated through validation and testing using KDD Cup'99 dataset, has shown very high detection rates for all classes with low false alarm rates. Accuracy of the model presented in this work, in comparison with the existing models, has been found to be much better. PMID:26357668
A PID de-tuned method for multivariable systems, applied for HVAC plant
NASA Astrophysics Data System (ADS)
Ghazali, A. B.
2015-09-01
A simple yet effective de-tuning of PID parameters for multivariable applications has been described. Although the method is felt to have wider application it is simulated in a 3-input/ 2-output building energy management system (BEMS) with known plant dynamics. The controller performances such as the sum output squared error and total energy consumption when the system is at steady state conditions are studied. This tuning methodology can also be extended to reduce the number of PID controllers as well as the control inputs for specified output references that are necessary for effective results, i.e. with good regulation performances being maintained.
Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings
Kadtke, J.B.; Bulsara, A.
1997-12-01
These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Experimental nonlinear laser systems: Bigger data for better science?
NASA Astrophysics Data System (ADS)
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-01
Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems - one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.
Nonlinear energy transfer in classical and quantum systems.
Manevitch, Leonid; Kovaleva, Agnessa
2013-02-01
In this paper we investigate the effect of slowly-varying parameters on the energy transfer in a weakly coupled system. For definiteness, we consider a system of two nonlinear oscillators, in which the directly excited first oscillator with constant parameter is attached to the oscillator with slowly time-varying frequency. It is proved that the equations of the slow passage through resonance in this system are identical to the equations of nonlinear Landau-Zener (LZ) tunneling. Three types of dynamical behavior are distinguished, namely, quasilinear, moderately nonlinear, and strongly nonlinear ones. Quasilinear systems exhibit a gradual energy transfer from the excited to the attached oscillator, while moderately nonlinear systems are characterized by an abrupt transition from the energy localization on the excited oscillator to the localization on the attached oscillator. In strongly nonlinear systems, the transition from the energy localization to strong energy exchange between the oscillators is revealed. Explicit approximate solutions describing the transient processes in moderately and strongly nonlinear systems are suggested. Correctness of the constructed approximations is confirmed by numerical results. The results presented in this paper, in addition to providing an analytical framework for understanding the transient dynamics, suggest an approximate procedure for solving the nonlinear LZ problem with arbitrary initial conditions over a finite time-interval. PMID:23496588
A Method for Exploiting Redundancy to Accommodate Actuator Limits in Multivariable Systems
NASA Technical Reports Server (NTRS)
Litt, Jonathan; Roulette, Greg
1995-01-01
This paper introduces a new method for accommodating actuator saturation in a multivariable system with actuator redundancy. Actuator saturation can cause significant deterioration in control system performance because unmet demand may result in sluggish transients and oscillations in response to setpoint changes. To help compensate for this problem, a technique has been developed which takes advantage of redundancy in multivariable systems to redistribute the unmet control demand over the remaining useful effectors. This method is not a redesign procedure, rather it modifies commands to the unlimited effectors to compensate for those which are limited, thereby exploiting the built-in redundancy. The original commands are modified by the increments due to unmet demand, but when a saturated effector comes off its limit, the incremental commands disappear and the original unmodified controller remains intact. This scheme provides a smooth transition between saturated and unsaturated modes as it divides up the unmet requirement over any available actuators. This way, if there is sufficiently redundant control authority, performance can be maintained.
A mathematical theory of learning control for linear discrete multivariable systems
NASA Technical Reports Server (NTRS)
Phan, Minh; Longman, Richard W.
1988-01-01
When tracking control systems are used in repetitive operations such as robots in various manufacturing processes, the controller will make the same errors repeatedly. Here consideration is given to learning controllers that look at the tracking errors in each repetition of the process and adjust the control to decrease these errors in the next repetition. A general formalism is developed for learning control of discrete-time (time-varying or time-invariant) linear multivariable systems. Methods of specifying a desired trajectory (such that the trajectory can actually be performed by the discrete system) are discussed, and learning controllers are developed. Stability criteria are obtained which are relatively easy to use to insure convergence of the learning process, and proper gain settings are discussed in light of measurement noise and system uncertainties.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
State analysis of nonlinear systems using local canonical variate analysis
Hunter, N.F.
1997-01-01
There are many instances in which time series measurements are used to derive an empirical model of a dynamical system. State space reconstruction from time series measurement has applications in many scientific and engineering disciplines including structural engineering, biology, chemistry, climatology, control theory, and physics. Prediction of future time series values from empirical models was attempted as early as 1927 by Yule, who applied linear prediction methods to the sunspot values. More recently, efforts in this area have centered on two related aspects of time series analysis, namely prediction and modeling. In prediction future time series values are estimated from past values, in modeling, fundamental characteristics of the state model underlying the measurements are estimated, such as dimension and eigenvalues. In either approach a measured time series, [{bold y}(t{sub i})], i= 1,... N is assumed to derive from the action of a smooth dynamical system, s(t+{bold {tau}})=a(s(t)), where the bold notation indicates the (potentially ) multivariate nature of the time series. The time series is assumed to derive from the state evolution via a measurement function c. {bold y}(t)=c(s(t)) In general the states s(t), the state evolution function a and the measurement function c are In unknown, and must be inferred from the time series measurements. We approach this problem from the standpoint of time series analysis. We review the principles of state space reconstruction. The specific model formulation used in the local canonical variate analysis algorithm and a detailed description of the state space reconstruction algorithm are included. The application of the algorithm to a single-degree-of- freedom Duffing-like Oscillator and the difficulties involved in reconstruction of an unmeasured degree of freedom in a four degree of freedom nonlinear oscillator are presented. The advantages and current limitations of state space reconstruction are summarized.
Tools for Nonlinear Control Systems Design
NASA Technical Reports Server (NTRS)
Sastry, S. S.
1997-01-01
This is a brief statement of the research progress made on Grant NAG2-243 titled "Tools for Nonlinear Control Systems Design", which ran from 1983 till December 1996. The initial set of PIs on the grant were C. A. Desoer, E. L. Polak and myself (for 1983). From 1984 till 1991 Desoer and I were the Pls and finally I was the sole PI from 1991 till the end of 1996. The project has been an unusually longstanding and extremely fruitful partnership, with many technical exchanges, visits, workshops and new avenues of investigation begun on this grant. There were student visits, long term.visitors on the grant and many interesting joint projects. In this final report I will only give a cursory description of the technical work done on the grant, since there was a tradition of annual progress reports and a proposal for the succeeding year. These progress reports cum proposals are attached as Appendix A to this report. Appendix B consists of papers by me and my students as co-authors sorted chronologically. When there are multiple related versions of a paper, such as a conference version and journal version they are listed together. Appendix C consists of papers by Desoer and his students as well as 'solo' publications by other researchers supported on this grant similarly chronologically sorted.
Sakhanenko, Nikita A.; Skupin, Alexander; Ignac, Tomasz
2014-01-01
Abstract Context dependence is central to the description of complexity. Keying on the pairwise definition of “set complexity,” we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multivariable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multivariable dependency, “differential interaction information.” This quantity for two variables reduces to the pairwise “set complexity” previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the “differential interaction information” are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for the study of complexity. The properties of “differential interaction information” also suggest new approaches to data analysis. Given a data set of system measurements, differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multivariable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system. PMID:24377753
NASA Astrophysics Data System (ADS)
Alfonso, Lester; Zamora, Jose; Cruz, Pedro
2015-04-01
The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.
NASA Astrophysics Data System (ADS)
Usui, Norihisa; Ishizaki, Shiro; Fujii, Yosuke; Tsujino, Hiroyuki; Yasuda, Tamaki; Kamachi, Masafumi
The Meteorological Research Institute multivariate ocean variational estimation (MOVE) System has been developed as the next-generation ocean data assimilation system in Japan Meteorological Agency. A multivariate three-dimensional variational (3DVAR) analysis scheme with vertical coupled temperature salinity empirical orthogonal function modes is adopted. The MOVE system has two varieties, the global (MOVE-G) and North Pacific (MOVE-NP) systems. The equatorial Pacific and western North Pacific are analyzed with assimilation experiments using MOVE-G and -NP, respectively. In each system, the salinity and velocity fields are well reproduced, even in cases without salinity data. Changes in surface and subsurface zonal currents during the 1997/98 El Niño event are captured well, and their transports are reasonably consistent with in situ observations. For example, the eastward transport in the upper layer around the equator has 70 Sv in spring 1997 and weakens in spring 1998. With MOVE-NP, the Kuroshio transport has 25 Sv in the East China Sea, and 40 Sv crossing the ASUKA (Affiliated Surveys of the Kuroshio off Cape Ashizuri) line south of Japan. The variations in the Kuroshio transports crossing the ASUKA line agree well with observations. The Ryukyu Current System has a transport ranging from 6 Sv east of Taiwan to 17 Sv east of Amami. The Oyashio transport crossing the OICE (Oyashio Intensive observation line off Cape Erimo) line south of Hokkaido has 14 Sv southwestward (near shore) and 11 Sv northeastward (offshore). In the Kuroshio Oyashio transition area east of Japan, the eastward transport has 41 Sv (32 36°N) and 12 Sv (36 39°N) crossing the 145°E line.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Nonlinear normal modes in electrodynamic systems: A nonperturbative approach
NASA Astrophysics Data System (ADS)
Kudrin, A. V.; Kudrina, O. A.; Petrov, E. Yu.
2016-06-01
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
Nonlinear Optics in Novel Polymer Systems.
NASA Astrophysics Data System (ADS)
Li, Lian
Polymeric nonlinear optical (NLO) materials have recently attracted considerable attention and been the subject of intensive investigations. Polymeric NLO materials possessing large second and third order NLO properties, ultrafast response times, high optical damage threshold, transparency over a broad wavelength range, and capability to be easily processed into good optical quality thin films, offer significant advantages over the traditional inorganic materials for applications in fabricating integrated optical devices, such as waveguide electro-optic (EO) modulators and optical frequency doublers, and optical signal processing devices. This dissertation presents the experimental investigations on novel NLO polymers synthesized in the Laboratory of Electronic and Photonic Materials at University of Massachusetts Lowell. Progress made for the past few years on polymeric NLO materials is reviewed, especially with regard to the second order NLO properties of the polymeric materials. Two novel stable second order NLO polymer systems, an interpenetrating polymer network (IPN) formed via thermal crosslinking and a sol-gel process, and a photocrosslinkable conducting polymer, upon poling and crosslinking, exhibited large and stable second order NLO properties measured for these polymers by using the second harmonic generation (SHG) technique. For the IPN system, the SHG measurements as a function of time at several elevated temperatures indicate the superb stability of the second order NLO properties. For the conducting NLO polymer, the NLO property of the poled and photocrosslinked polymer film is stable at room temperature. The wavelength shifting of a Q-switched Nd:YAG laser by stimulated Raman scattering is also described. Measurements were made on the third order NLO properties of a dye doped photocrosslinkable guest-host polymer system at different dye concentrations with a modified Michelson interferometer. By functionalizing the dye to make it more compatible to
Energy harvesting in the nonlinear electromagnetic system
NASA Astrophysics Data System (ADS)
Kucab, K.; Górski, G.; Mizia, J.
2015-11-01
We examine the electrical response of electromagnetic device working both in the linear and nonlinear domain. The harvester is consisted of small magnet moving in isolating tube surrounded by the coil attached to the electrical circuit. In the nonlinear case the magnet vibrates in between two fixed magnets attached to the both ends of the tube. Additionally we use two springs which limit the movement of the small magnet. The linear case is when the moving magnet is attached to the repelling springs, and the static magnets have been replaced by the non-magnetic material. The potentials and forces were calculated using both the analytical expressions and the finite elements method. We compare the results for energy harvesting obtained in these two cases. The generated output power in the linear case reaches the peak value 80 mW near the resonance frequency ω0 for maximum base acceleration considered by us, whereas in the non-linear case the corresponding outpot power has the peak value 95 mW and additionally relatively high values in the excitation frequencies range up to ω = 1.2ω0. The numerical results also show that the power efficiency in the nonlinear case exceeds the corresponding efficiency in the linear case at relatively high values of base accelerations greater than 5 g. The results show the increase of harvested energy in the broad band of excitation frequencies in the nonlinear case.
Multivariate model of female black bear habitat use for a Geographic Information System
Clark, Joseph D.; Dunn, James E.; Smith, Kimberly G.
1993-01-01
Simple univariate statistical techniques may not adequately assess the multidimensional nature of habitats used by wildlife. Thus, we developed a multivariate method to model habitat-use potential using a set of female black bear (Ursus americanus) radio locations and habitat data consisting of forest cover type, elevation, slope, aspect, distance to roads, distance to streams, and forest cover type diversity score in the Ozark Mountains of Arkansas. The model is based on the Mahalanobis distance statistic coupled with Geographic Information System (GIS) technology. That statistic is a measure of dissimilarity and represents a standardized squared distance between a set of sample variates and an ideal based on the mean of variates associated with animal observations. Calculations were made with the GIS to produce a map containing Mahalanobis distance values within each cell on a 60- × 60-m grid. The model identified areas of high habitat use potential that could not otherwise be identified by independent perusal of any single map layer. This technique avoids many pitfalls that commonly affect typical multivariate analyses of habitat use and is a useful tool for habitat manipulation or mitigation to favor terrestrial vertebrates that use habitats on a landscape scale.
Nonlinear dynamics in tunable graphene nanoelectromechanical systems
NASA Astrophysics Data System (ADS)
Guan, Fen; Kumaravadivel, Piranavan; Averin, Dmitri; Du, Xu
2015-03-01
We report the fabrication and characterization of graphene nanoelectromechanical resonators (GNEMR) on flexible substrates. The intrinsic stain in graphene is tuned by bending the substrate, during which a transition from hardening to softening resonance behavior and a minimum resonance frequency are observed. To explain these observations, a resonator model taking into account the intrinsic strain and electrostatic force is developed. Including higher-order nonlinear terms, a minimum frequency is obtained analytically from the model and matches with experimental data. Results from numerical simulation demonstrate also the transition in the nonlinear behavior. Additionally, the model-based fittings determine the intrinsic strain and mass of graphene samples accurately. Our devices allow thorough exploration of the nonlinear dynamics in GNEMR and may help further study of the intrinsic electrical properties of the materials under strain.
NASA Technical Reports Server (NTRS)
Waszak, Martin R.
1992-01-01
The application of a sector-based stability theory approach to the formulation of useful uncertainty descriptions for linear, time-invariant, multivariable systems is explored. A review of basic sector properties and sector-based approach are presented first. The sector-based approach is then applied to several general forms of parameter uncertainty to investigate its advantages and limitations. The results indicate that the sector uncertainty bound can be used effectively to evaluate the impact of parameter uncertainties on the frequency response of the design model. Inherent conservatism is a potential limitation of the sector-based approach, especially for highly dependent uncertain parameters. In addition, the representation of the system dynamics can affect the amount of conservatism reflected in the sector bound. Careful application of the model can help to reduce this conservatism, however, and the solution approach has some degrees of freedom that may be further exploited to reduce the conservatism.
NASA Technical Reports Server (NTRS)
Beattie, E. C.
1980-01-01
An inlet/engine/nozzle integrated control mode for the propulsion system of an advanced supersonic commercial aircraft was studied. Results show that integration of these control functions can result in both operational and performance benefits for the propulsion system. For example, this integrated control mode may make it possible to minimize the use of inlet bypass doors for shock position control. This may be of benefit to the aircraft as a result of minimizing: (1) bypass bleed drag effects; (2) perturbations to the aircraft resulting from the side thrust effect of the bypass bleeds; and (3) potential unstarts of the inlet. A conceptual integrated control mode was developed which makes use of many cross coupling paths between inlet and engine control variables and inlet and engine sensed variables. A multivariable control design technique based upon linear quadratic regulator theory was applied to designing the feedback gains for this control to allow a simulation evaluation of the benefits of the integrated control mode.
NASA Astrophysics Data System (ADS)
Ravindranath, A.; Devineni, N.
2015-12-01
While India has a long history of prediction of the All India Monsoon, work on spatially specific attributes of the monsoon, as well as monsoon break periods has only recently emerged. However, from a risk management context, prognostic information of a single variable such as total precipitation or average temperature will be of less utility especially for specific operational purposes. An integrated regional climate-weather forecast system covering precipitation, temperature and humidity etc. over the year will benefit the farmers in the context of a specific decision time table for irrigation scheduling as well as for pre-season crop choices. Hence, contrary to the existing forecasting methods that develop multi time scale information of a single variable at a time, in this paper, we introduce an integrated regional multivariate climate-weather forecasting system that directly relates to agricultural decision making and risk mitigation. These multi-scale risk attributes include mutually dependent, spatially disaggregated statistics such as total rainfall, average temperature, growing degree days, relative humidity, total number of rainfall days/dry spell length, and cumulative water deficits that inform the potential irrigation water requirements for crops. Given that these attributes exhibit mutual dependence across space and time, we propose to explore common ocean-atmospheric conditions from the observations and the state of the art Global Circulation Models (GCMs) that can be utilized as the predictor variables for the forecasting system. Hierarchical Bayesian methods are be used to develop the integrated forecast system. The developed multivariate forecasts will be adapted and disseminated as decision tools for the farmers under the extension projects in Punjab region of India.
NASA Astrophysics Data System (ADS)
Devineni, N.; Lall, U.; Perveen, S.
2012-12-01
While India has a long history of prediction of the All India Monsoon, work on spatially specific attributes of the monsoon, as well as monsoon break periods has only recently emerged. However, from a risk management context, prognostic information of a single variable such as total precipitation or average temperature will be of less utility especially for specific operational purposes. An integrated regional climate-weather forecast system covering precipitation, temperature and humidity etc. over the year will benefit the farmers in the context of a specific decision time table for irrigation scheduling as well as for pre-season crop choices. Hence, contrary to the existing forecasting methods that develop multi time scale information of a single variable at a time, in this paper, we introduce an integrated regional multivariate climate-weather forecasting system that directly relates to agricultural decision making and risk mitigation. These multi-scale risk attributes include mutually dependent, spatially disaggregated statistics such as total rainfall, average temperature, growing degree days, relative humidity, total number of rainfall days/dry spell length, and cumulative water deficits that inform the potential irrigation water requirements for crops etc. Given that these attributes exhibit mutual dependence across space and time, we propose to explore common ocean-atmospheric conditions from the observations and the state of the art Global Circulation Models (GCMs) that can be utilized as the predictor variables for the forecasting system. Non parametric bootstrap resampling methods and Hierarchical Bayesian methods that can easily handle the high dimensionality of such problems will be used to develop the integrated forecast system. The developed multivariate forecasts will be adapted and disseminated as decision tools for the farmers under the Columbia Water Center's pilot project in Punjab region of India.
Analysis and design of robust decentralized controllers for nonlinear systems
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1990-01-01
A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Multivariate Multi-data Assimilation System in Regional Model with High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Chanut, J.; Giraud St Albin, S.; Drillet, Y.
2010-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12°). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12°). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12°) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12°).
Multivariate Multi-Data Assimilation System in Regional Model With High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Chanut, J.; Greiner, E.; Giraud St Albin, S.; Drillet, Y.
2008-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12).
Multivariate Multi-data Assimilation System in Regional Model with High Resolution
NASA Astrophysics Data System (ADS)
Benkiran, M.; Bourdalle-Badie, R.; Drillet, Y.; Greiner, E.; Chanut, J.
2009-12-01
Mercator Ocean has developed a regional North East Shelf forecasting system over the North East Atlantic, taking advantage of the recent developments in NEMO (1/12°). This regional forecasting system uses boundary conditions from the operational real-time Mercator Ocean North Atlantic high resolution system (1/12°). The assimilation component of the Mercator Ocean system, is based on a reduced-order Kalman filter (the SEEK or Singular Extended Evolutive Kalman filter). The error statistics are represented in a sub-space spanned by a small number of dominant 3D error directions. The data assimilation system allows to constrain the model in a multivariate way with Sea Surface Temperature (RTG-SST), together with all available satellite Sea Level Anomalies, and with in situ observations from the CORIOLIS database, including ARGO floats temperature and salinity measurements.At last, we used PALM coupler which provides a general structure for a modular implementation of a data assimilation system, and makes easier the changes in the analysis algorithm. We will confront the results obtained with the regional forecast system (1/12°) with IAU (Incremental Analysis Updates) to the ones obtained with Mercator Ocean North Atlantic high resolution system (1/12°).
Computational studies of nonlinear dispersive plasma systems
NASA Astrophysics Data System (ADS)
Qian, Xin
Plasma systems with dispersive waves are ubiquitous. Dispersive waves have the property that their wave velocity depends on the wave number of the wave. These waves show up in weakly as well as strongly coupled plasmas, and play a significant role in the underlying plasma dynamics. Dispersive waves bring new challenges to the computer simulation of nonlinear phenomena. The goal of this thesis is to discuss two computational studies of plasma phenomena, one drawn from strongly coupled complex or dusty plasmas, and the other from weakly coupled hydrogen plasmas. In the realm of dusty plasmas, we focus on the problem of three-dimensional (3D) Mach cones which we study by means of Molecular Dynamics (MD) simulations, assuming that the dust particles interact via a Yukawa potential. While laboratory and MD simulations have explored thoroughly the properties of Mach cones in 2D, elucidating the important role of dispersive waves in the formation of multiple cones, the simulations presented in this thesis represent the first 3D MD studies of Mach cones in strongly coupled dusty plasmas. These results have qualitative similarities with experimental observations on 3D Mach cones from the PK-3 plus project, which studies complex plasmas under microgravity conditions aboard the International Space station. In the realm of weakly coupled plasmas, we present results on the application of non-oscillatory central schemes to Hall MHD reconnection problems, in which the presence of dispersive whistler waves presents a formidable challenge for numerical algorithms that rely on explicit time-stepping schemes. In particular, we focus on the semi-discrete central formulation of Kurganov and Tadmor (2000), which has the advantage that it allow for larger time steps, and with significantly smaller numerical viscosity, than fully discrete schemes. We implement the Hall MHD equations through the CentPACK software package that implements the Kurganov-Tadmor formulation for a wide range of
An experimental study of nonlinear dynamic system identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D, Joseph
1991-01-01
A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions.
Multivariable output feedback robust adaptive tracking control design for a class of delayed systems
NASA Astrophysics Data System (ADS)
Mirkin, Boris; Gutman, Per-Olof
2015-02-01
In this paper, we develop a model reference adaptive control scheme for a class of multi-input multi-output nonlinearly perturbed dynamic systems with unknown time-varying state delays which is also robust with respect to an external disturbance with unknown bounds. The output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov-Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.
Self-characterization of linear and nonlinear adaptive optics systems.
Hampton, Peter J; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan
2008-01-10
We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM. PMID:18188192
Applications of nonlinear systems theory to control design
NASA Technical Reports Server (NTRS)
Hunt, L. R.; Villarreal, Ramiro
1988-01-01
For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.
On-line robust nonlinear state estimators for nonlinear bioprocess systems
NASA Astrophysics Data System (ADS)
Iratni, A.; Katebi, R.; Mostefai, M.
2012-04-01
This paper presents the design of a new robust nonlinear estimator for estimation of states of nonlinear systems. Two approaches are considered based on the state-dependent Riccati equation formulation and the technique of H-infinity control design. The proposed method differs from other well-known state estimators, because not only nonlinear dynamics but also the robustness is taken into account. The proposed method is implemented and tested on a biological wastewater system. The simulation study compares the Extended Kalman Estimator ( EKE), the State-Dependent Riccati Estimator ( SDRE), and the Extended H-infinity Estimator ( EHE) with a new proposed State Dependent H-infinity Estimator ( SDHE). The results are compared for different weather conditions, i.e. dry, rain and storm, showing a superior performance of the proposed method.
Nonlinear dynamic phenomena in the space shuttle thermal protection system
NASA Technical Reports Server (NTRS)
Housner, J. M.; Edighoffer, H. H.; Park, K. C.
1981-01-01
The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system. PMID:24808035
Analysis techniques for multivariate root loci. [a tool in linear control systems
NASA Technical Reports Server (NTRS)
Thompson, P. M.; Stein, G.; Laub, A. J.
1980-01-01
Analysis and techniques are developed for the multivariable root locus and the multivariable optimal root locus. The generalized eigenvalue problem is used to compute angles and sensitivities for both types of loci, and an algorithm is presented that determines the asymptotic properties of the optimal root locus.
Wallace, Jack; Champagne, Pascale; Monnier, Anne-Charlotte
2015-01-01
A pilot-scale hybrid-passive treatment system operated at the Merrick Landfill in North Bay, Ontario, Canada, treats municipal landfill leachate and provides for subsequent natural attenuation. Collected leachate is directed to a hybrid-passive treatment system, followed by controlled release to a natural attenuation zone before entering the nearby Little Sturgeon River. The study presents a comprehensive evaluation of the performance of the system using multivariate statistical techniques to determine the interactions between parameters, major pollutants in the leachate, and the biological and chemical processes occurring in the system. Five parameters (ammonia, alkalinity, chemical oxygen demand (COD), "heavy" metals of interest, with atomic weights above calcium, and iron) were set as criteria for the evaluation of system performance based on their toxicity to aquatic ecosystems and importance in treatment with respect to discharge regulations. System data for a full range of water quality parameters over a 21-month period were analyzed using principal components analysis (PCA), as well as principal components (PC) and partial least squares (PLS) regressions. PCA indicated a high degree of association for most parameters with the first PC, which explained a high percentage (>40%) of the variation in the data, suggesting strong statistical relationships among most of the parameters in the system. Regression analyses identified 8 parameters (set as independent variables) that were most frequently retained for modeling the five criteria parameters (set as dependent variables), on a statistically significant level: conductivity, dissolved oxygen (DO), nitrite (NO2(-)), organic nitrogen (N), oxidation reduction potential (ORP), pH, sulfate and total volatile solids (TVS). The criteria parameters and the significant explanatory parameters were most important in modeling the dynamics of the passive treatment system during the study period. Such techniques and
Impact of nonlinear and polarization effects in coherent systems.
Xie, Chongjin
2011-12-12
Coherent detection with digital signal processing (DSP) significantly changes the ways impairments are managed in optical communication systems. In this paper, we review the recent advances in understanding the impact of fiber nonlinearities, polarization-mode dispersion (PMD), and polarization-dependent loss (PDL) in coherent optical communication systems. We first discuss nonlinear transmission performance of three coherent optical communication systems, homogeneous polarization-division-multiplexed (PDM) quadrature-phase-shift-keying (QPSK), hybrid PDM-QPSK and on/off keying (OOK), and PDM 16-ary quadrature-amplitude modulation (QAM) systems. We show that while the dominant nonlinear effects in coherent optical communication systems without optical dispersion compensators (ODCs) are intra-channel nonlinearities, the dominant nonlinear effects in dispersion-managed (DM) systems with inline dispersion compensation fiber (DCF) are different when different modulation formats are used. In DM coherent optical communication systems using modulation formats of constant amplitude, the dominant nonlinear effect is nonlinear polarization scattering induced by cross-polarization modulation (XPolM), whereas when modulation formats of non-constant amplitude are used, the impact of inter-channel cross-phase modulation (XPM) is much larger than XPolM. We then describe the effects of PMD and PDL in coherent systems. We show that although in principle PMD can be completely compensated in a coherent optical receiver, a real coherent receiver has limited tolerance to PMD due to hardware limitations. Two PDL models used to evaluate PDL impairments are discussed. We find that a simple lumped model significantly over-estimates PDL impairments and show that a distributed model has to be used in order to accurately evaluate PDL impairments. Finally, we apply system outage considerations to coherent systems, taking into account the statistics of polarization effects in fiber. PMID
Nonlinear signal processing using neural networks: Prediction and system modelling
Lapedes, A.; Farber, R.
1987-06-01
The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.
NASA Technical Reports Server (NTRS)
Valavani, Lena
1995-01-01
The main motivation for the work under the present grant was to use nonlinear feedback linearization methods to further enhance performance capabilities of the aircraft, and robustify its response throughout its operating envelope. The idea was to use these methods in lieu of standard Taylor series linearization, in order to obtain a well behaved linearized plant, in its entire operational regime. Thus, feedback linearization was going to constitute an 'inner loop', which would then define a 'design plant model' to be compensated for robustness and guaranteed performance in an 'outer loop' application of modern linear control methods. The motivation for this was twofold; first, earlier work had shown that by appropriately conditioning the plant through conventional, simple feedback in an 'inner loop', the resulting overall compensated plant design enjoyed considerable enhancement of performance robustness in the presence of parametric uncertainty. Second, the nonlinear techniques did not have any proven robustness properties in the presence of unstructured uncertainty; a definition of robustness (and performance) is very difficult to achieve outside the frequency domain; to date, none is available for the purposes of control system design. Thus, by proper design of the outer loop, such properties could still be 'injected' in the overall system.
Quantum-criticality-induced strong Kerr nonlinearities in optomechanical systems
Lü, Xin-You; Zhang, Wei-Min; Ashhab, Sahel; Wu, Ying; Nori, Franco
2013-01-01
We investigate a hybrid electro-optomechanical system that allows us to realize controllable strong Kerr nonlinearities even in the weak-coupling regime. We show that when the controllable electromechanical subsystem is close to its quantum critical point, strong photon-photon interactions can be generated by adjusting the intensity (or frequency) of the microwave driving field. Nonlinear optical phenomena, such as the appearance of the photon blockade and the generation of nonclassical states (e.g., Schrödinger cat states), are demonstrated in the weak-coupling regime, making the observation of strong Kerr nonlinearities feasible with currently available optomechanical technology. PMID:24126279
Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method.
Energy Science and Technology Software Center (ESTSC)
1981-08-31
Version 00 REGN solves nonlinear systems of numerical equations in difficult cases: high nonlinearity, poor initial approximations, a large number of unknowns, ill condition or degeneracy of a problem.
Development of a nonlinear optical measurement-4 coherent imaging system
NASA Astrophysics Data System (ADS)
Chen, Xiaojun; Song, Yinglin; Gu, Jihua; Yang, Junyi; Shui, Min; Hou, Dengke; Zhu, Zongjie
2009-07-01
After the nonlinear optical phenomena were discovered, people began to research the techniques to detect the optical nonlinearities of materials. In this paper, a new optical nonlinear measurement technique-4f coherent imaging system is recommended. The system has many advantages: single shot real-time measurement, simple experimental apparatus, high sensitivity, being able to detect the magnitude and sign of both nonlinear absorption and refraction at the same time, low requirement of beam spatial distribution, and so on. This paper introduces the theory of the 4f system and makes a detailed review and expounds development and application of the 4f coherent image system. The nerve of the experiment is improving the phase diaphragm. The shape of the diaphragm from the double-slits to the small rectangular object, and transition to a circular aperture, finally forming a circular phase diaphragm, which is a circular aperture in the center add a phase object. Following these diaphragm changes, the sensitivity of the system is greatly improved. The latest developments of the system are series-wound double 4f coherent imaging technique and the time-resolved pump-probe system based on NIT-PO. The time-resolved pump-probe system based on NIT-PO can be used to measure the dynamic characteristics of excited states nonlinear absorption and refraction.
Applications of nonlinear system identification to structural health monitoring.
Farrar, C. R.; Sohn, H.; Robertson, A. N.
2004-01-01
The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.
Damage detection in nonlinear systems using multiple system augmentations and matrix updating
NASA Astrophysics Data System (ADS)
D'Souza, Kiran; Epureanu, Bogdan I.
2006-03-01
Recently, a damage detection method for nonlinear systems using model updating has been developed by the authors. The method uses an augmented linear model of the system, which is determined from the functional form of the nonlinearities and a nonlinear discrete model of the system. The modal properties of the augmented system after the onset of damage are extracted from the system using a modal analysis technique that uses known but not prescribed forcing. Minimum Rank Perturbation Theory was generalized so that damage location and extent could be determined using the augmented modal properties. The method was demonstrated previously for cubic springs and Coulomb friction nonlinearities. In this work, the methodology is extended to handle large systems where only the first few of the augmented eigenvectors are known. The methodology capitalizes on the ability to create multiple augmentations for a single nonlinear system. Cubic spring nonlinearities are explored within a nonlinear 3-bay truss structure for various damage scenarios simulated numerically.
Non-linear system identification in flow-induced vibration
Spanos, P.D.; Zeldin, B.A.; Lu, R.
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Simulation program of nonlinearities applied to telecommunication systems
NASA Technical Reports Server (NTRS)
Thomas, C.
1979-01-01
In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.
Aeroelasticity of Nonlinear Tail / Rudder Systems with Freeplay
NASA Astrophysics Data System (ADS)
Rishel, Evan
This thesis details the development of a linear/nonlinear three degree of freedom aeroelastic system designed and manufactured at the University of Washington (UW). Describing function analysis was carried out in the frequency domain. Time domain simulations were carried out to account for all types of motion. Nonlinear aeroelastic behavior may lead to limit cycles which can be captured in the frequency domain using describing function approximation and numerically using Runga-Kutta integration. Linear and nonlinear aeroelastic tests were conducted in the UW 3x3 low-speed wind tunnel to determine the linear flutter speed and frequency of the system as well as its nonlinear behavior when freeplay is introduced. The test data is presented along with the results of the MATLAB-based simulations. The correlation between test and numerical results is very high.
Diagnosis of nonlinear systems using time series analysis
Hunter, N.F. Jr.
1991-01-01
Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.
3-D Mesh Generation Nonlinear Systems
Energy Science and Technology Software Center (ESTSC)
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surfacemore » equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.« less
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time. PMID:26986334
Chaotic and hyperchaotic attractors of a complex nonlinear system
NASA Astrophysics Data System (ADS)
Mahmoud, Gamal M.; Al-Kashif, M. A.; Farghaly, A. A.
2008-02-01
In this paper, we introduce a complex nonlinear hyperchaotic system which is a five-dimensional system of nonlinear autonomous differential equations. This system exhibits both chaotic and hyperchaotic behavior and its dynamics is very rich. Based on the Lyapunov exponents, the parameter values at which this system has chaotic, hyperchaotic attractors, periodic and quasi-periodic solutions and solutions that approach fixed points are calculated. The stability analysis of these fixed points is carried out. The fractional Lyapunov dimension of both chaotic and hyperchaotic attractors is calculated. Some figures are presented to show our results. Hyperchaos synchronization is studied analytically as well as numerically, and excellent agreement is found.
Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.
Zhang, Yanjun; Tao, Gang; Chen, Mou
2016-09-01
This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method. PMID:26285223
Experimental nonlinear laser systems: Bigger data for better science?
Kane, D. M.; Toomey, J. P.; McMahon, C.; Noblet, Y.; Argyris, A.; Syvridis, D.
2014-10-06
Bigger data is supporting knowledge discovery in nonlinear laser systems as will be demonstrated with examples from three semiconductor laser based systems – one with optical feedback, a photonic integrated circuit (PIC) chaotic laser and a frequency shifted feedback laser system.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-10-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Geometric nonlinear formulation for thermal-rigid-flexible coupling system
NASA Astrophysics Data System (ADS)
Fan, Wei; Liu, Jin-Yang
2013-09-01
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal effect. Different from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly, based on nonlinear strain-displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach, and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.
Wallace, Jack; Champagne, Pascale; Monnier, Anne-Charlotte
2015-01-15
Highlights: • Performance of a hybrid passive landfill leachate treatment system was evaluated. • 33 Water chemistry parameters were sampled for 21 months and statistically analyzed. • Parameters were strongly linked and explained most (>40%) of the variation in data. • Alkalinity, ammonia, COD, heavy metals, and iron were criteria for performance. • Eight other parameters were key in modeling system dynamics and criteria. - Abstract: A pilot-scale hybrid-passive treatment system operated at the Merrick Landfill in North Bay, Ontario, Canada, treats municipal landfill leachate and provides for subsequent natural attenuation. Collected leachate is directed to a hybrid-passive treatment system, followed by controlled release to a natural attenuation zone before entering the nearby Little Sturgeon River. The study presents a comprehensive evaluation of the performance of the system using multivariate statistical techniques to determine the interactions between parameters, major pollutants in the leachate, and the biological and chemical processes occurring in the system. Five parameters (ammonia, alkalinity, chemical oxygen demand (COD), “heavy” metals of interest, with atomic weights above calcium, and iron) were set as criteria for the evaluation of system performance based on their toxicity to aquatic ecosystems and importance in treatment with respect to discharge regulations. System data for a full range of water quality parameters over a 21-month period were analyzed using principal components analysis (PCA), as well as principal components (PC) and partial least squares (PLS) regressions. PCA indicated a high degree of association for most parameters with the first PC, which explained a high percentage (>40%) of the variation in the data, suggesting strong statistical relationships among most of the parameters in the system. Regression analyses identified 8 parameters (set as independent variables) that were most frequently retained for modeling
A nonlinear complementarity approach for the national energy modeling system
Gabriel, S.A.; Kydes, A.S.
1995-03-08
The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP.
Robust Nonlinear Feedback Control of Aircraft Propulsion Systems
NASA Technical Reports Server (NTRS)
Garrard, William L.; Balas, Gary J.; Litt, Jonathan (Technical Monitor)
2001-01-01
This is the final report on the research performed under NASA Glen grant NASA/NAG-3-1975 concerning feedback control of the Pratt & Whitney (PW) STF 952, a twin spool, mixed flow, after burning turbofan engine. The research focussed on the design of linear and gain-scheduled, multivariable inner-loop controllers for the PW turbofan engine using H-infinity and linear, parameter-varying (LPV) control techniques. The nonlinear turbofan engine simulation was provided by PW within the NASA Rocket Engine Transient Simulator (ROCETS) simulation software environment. ROCETS was used to generate linearized models of the turbofan engine for control design and analysis as well as the simulation environment to evaluate the performance and robustness of the controllers. Comparison between the H-infinity, and LPV controllers are made with the baseline multivariable controller and developed by Pratt & Whitney engineers included in the ROCETS simulation. Simulation results indicate that H-infinity and LPV techniques effectively achieve desired response characteristics with minimal cross coupling between commanded values and are very robust to unmodeled dynamics and sensor noise.
Baez-Cazull, S. E.; McGuire, J.T.; Cozzarelli, I.M.; Voytek, M.A.
2008-01-01
Determining the processes governing aqueous biogeochemistry in a wetland hydrologically linked to an underlying contaminated aquifer is challenging due to the complex exchange between the systems and their distinct responses to changes in precipitation, recharge, and biological activities. To evaluate temporal and spatial processes in the wetland-aquifer system, water samples were collected using cm-scale multichambered passive diffusion samplers (peepers) to span the wetland-aquifer interface over a period of 3 yr. Samples were analyzed for major cations and anions, methane, and a suite of organic acids resulting in a large dataset of over 8000 points, which was evaluated using multivariate statistics. Principal component analysis (PCA) was chosen with the purpose of exploring the sources of variation in the dataset to expose related variables and provide insight into the biogeochemical processes that control the water chemistry of the system. Factor scores computed from PCA were mapped by date and depth. Patterns observed suggest that (i) fermentation is the process controlling the greatest variability in the dataset and it peaks in May; (ii) iron and sulfate reduction were the dominant terminal electron-accepting processes in the system and were associated with fermentation but had more complex seasonal variability than fermentation; (iii) methanogenesis was also important and associated with bacterial utilization of minerals as a source of electron acceptors (e.g., barite BaSO4); and (iv) seasonal hydrological patterns (wet and dry periods) control the availability of electron acceptors through the reoxidation of reduced iron-sulfur species enhancing iron and sulfate reduction. Copyright ?? 2008 by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America. All rights reserved.
A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis
Liu, Zitao; Hauskrecht, Milos
2015-01-01
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS’s hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs’ spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets. PMID:25905027
Huang, Shuangbing; Liu, Changrong; Wang, Yanxin; Zhan, Hongbin
2014-01-01
The effects of various geochemical processes on arsenic enrichment in a high-arsenic aquifer at Jianghan Plain in Central China were investigated using multivariate models developed from combined adaptive neuro-fuzzy inference system (ANFIS) and multiple linear regression (MLR). The results indicated that the optimum variable group for the AFNIS model consisted of bicarbonate, ammonium, phosphorus, iron, manganese, fluorescence index, pH, and siderite saturation. These data suggest that reductive dissolution of iron/manganese oxides, phosphate-competitive adsorption, pH-dependent desorption, and siderite precipitation could integrally affect arsenic concentration. Analysis of the MLR models indicated that reductive dissolution of iron(III) was primarily responsible for arsenic mobilization in groundwaters with low arsenic concentration. By contrast, for groundwaters with high arsenic concentration (i.e., > 170 μg/L), reductive dissolution of iron oxides approached a dynamic equilibrium. The desorption effects from phosphate-competitive adsorption and the increase in pH exhibited arsenic enrichment superior to that caused by iron(III) reductive dissolution as the groundwater chemistry evolved. The inhibition effect of siderite precipitation on arsenic mobilization was expected to exist in groundwater that was highly saturated with siderite. The results suggest an evolutionary dominance of specific geochemical process over other factors controlling arsenic concentration, which presented a heterogeneous distribution in aquifers. Supplemental materials are available for this article. Go to the publisher's online edition of the Journal of Environmental Science and Health, Part A, to view the supplemental file. PMID:24345245
Multivariate Strategies in Functional Magnetic Resonance Imaging
ERIC Educational Resources Information Center
Hansen, Lars Kai
2007-01-01
We discuss aspects of multivariate fMRI modeling, including the statistical evaluation of multivariate models and means for dimensional reduction. In a case study we analyze linear and non-linear dimensional reduction tools in the context of a "mind reading" predictive multivariate fMRI model.
NASA Astrophysics Data System (ADS)
Smolders, K.; Volckaert, M.; Swevers, J.
2008-11-01
This paper presents a nonlinear model-based iterative learning control procedure to achieve accurate tracking control for nonlinear lumped mechanical continuous-time systems. The model structure used in this iterative learning control procedure is new and combines a linear state space model and a nonlinear feature space transformation. An intuitive two-step iterative algorithm to identify the model parameters is presented. It alternates between the estimation of the linear and the nonlinear model part. It is assumed that besides the input and output signals also the full state vector of the system is available for identification. A measurement and signal processing procedure to estimate these signals for lumped mechanical systems is presented. The iterative learning control procedure relies on the calculation of the input that generates a given model output, so-called offline model inversion. A new offline nonlinear model inversion method for continuous-time, nonlinear time-invariant, state space models based on Newton's method is presented and applied to the new model structure. This model inversion method is not restricted to minimum phase models. It requires only calculation of the first order derivatives of the state space model and is applicable to multivariable models. For periodic reference signals the method yields a compact implementation in the frequency domain. Moreover it is shown that a bandwidth can be specified up to which learning is allowed when using this inversion method in the iterative learning control procedure. Experimental results for a nonlinear single-input-single-output system corresponding to a quarter car on a hydraulic test rig are presented. It is shown that the new nonlinear approach outperforms the linear iterative learning control approach which is currently used in the automotive industry on durability test rigs.
Energy transfer in systems with random forcing and nonlinear dissipation
NASA Astrophysics Data System (ADS)
Pignol, Ricardo Jorge
The purpose of this thesis is to study energy transfer in nonlinear systems. In the first part, I focus on a model of two nonlinearly coupled (complex) oscillators subject to stochastic forcing and nonlinear dissipation. This model arises from isolating an individual resonant quartet in a general dispersive system, and reducing it further by exploiting some of the system's symmetries. It turns out that the reduced model exhibits a rich and complex behavior encountered in far larger systems, with two qualitatively distinct regimes arising as one varies the system's single non-dimensional parameter: one that can be characterized as a perturbation of thermal equilibrium, and another highly constrained state, with phase and amplitude locking , and singular invariant measures. The relative simplicity of the reduced model allows a thorough numerical and theoretical treatment (including a closed expression for the system's invariant measures) that furnishes valuable insight on the energy transfer process in systems with much higher dimensionality. In the second part, the damped oscillator is replaced by an individual mode of the inviscid Burgers equation. Here, the dissipation occurs through shocks. Despite the complexity resulting from the inclusion of a nonlinear partial differential equation, I show that much of this system's behavior can be inferred precisely from a reduction to one of the cases studied in the first part.
Numerical studies of identification in nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.
1989-01-01
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
Applications of equivalent linearization approaches to nonlinear piping systems
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
Dynamic analysis of nonlinear rotor-housing systems
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1988-01-01
Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.
Nonlinear control structures based on embedded neural system models.
Lightbody, G; Irwin, G W
1997-01-01
This paper investigates in detail the possible application of neural networks to the modeling and adaptive control of nonlinear systems. Nonlinear neural-network-based plant modeling is first discussed, based on the approximation capabilities of the multilayer perceptron. A structure is then proposed to utilize feedforward networks within a direct model reference adaptive control strategy. The difficulties involved in training this network, embedded within the closed-loop are discussed and a novel neural-network-based sensitivity modeling approach proposed to allow for the backpropagation of errors through the plant to the neural controller. Finally, a novel nonlinear internal model control (IMC) strategy is suggested, that utilizes a nonlinear neural model of the plant to generate parameter estimates over the nonlinear operating region for an adaptive linear internal model, without the problems associated with recursive parameter identification algorithms. Unlike other neural IMC approaches the linear control law can then be readily designed. A continuous stirred tank reactor was chosen as a realistic nonlinear case study for the techniques discussed in the paper. PMID:18255659
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
NASA Astrophysics Data System (ADS)
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-01
Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.
Nonlinear system guidance in the presence of transmission zero dynamics
NASA Technical Reports Server (NTRS)
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
Accelerator-Feasible N-Body Nonlinear Integrable System
Danilov, V.; Nagaitsev, S.
2014-12-23
Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This paper presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.
Multivariate analysis of groundwater quality and modeling impact of ground heat pump system
NASA Astrophysics Data System (ADS)
Thuyet, D. Q.; Saito, H.; Muto, H.; Saito, T.; Hamamoto, S.; Komatsu, T.
2013-12-01
The ground source heat pump system (GSHP) has recently become a popular building heating or cooling method, especially in North America, Western Europe, and Asia, due to advantages in reducing energy consumption and greenhouse gas emission. Because of the stability of the ground temperature, GSHP can effectively exchange the excess or demand heat of the building to the ground during the building air conditioning in the different seasons. The extensive use of GSHP can potentially disturb subsurface soil temperature and thus the groundwater quality. Therefore the assessment of subsurface thermal and environmental impacts from the GSHP operations is necessary to ensure sustainable use of GSHP system as well as the safe use of groundwater resources. This study aims to monitor groundwater quality during GSHP operation and to develop a numerical model to assess changes in subsurface soil temperature and in groundwater quality as affected by GSHP operation. A GSHP system was installed in Fuchu city, Tokyo, and consists of two closed double U-tubes (50-m length) buried vertically in the ground with a distance of 7.3 m from each U-tube located outside a building. An anti-freezing solution was circulated inside the U-tube for exchanging the heat between the building and the ground. The temperature at every 5-m depth and the groundwater quality including concentrations of 16 trace elements, pH, EC, Eh and DO in the shallow aquifer (32-m depth) and the deep aquifer (44-m depth) were monitored monthly since 2012, in an observation well installed 3 m from the center of the two U-tubes.Temporal variations of each element were evaluated using multivariate analysis and geostatistics. A three-dimensional heat exchange model was developed in COMSOL Multiphysics4.3b to simulate the heat exchange processes in subsurface soils. Results showed the difference in groundwater quality between the shallow and deep aquifers to be significant for some element concentrations and DO, but
Perturbation analysis of a clearance-type nonlinear system
NASA Astrophysics Data System (ADS)
Zhu, Farong; Parker, Robert G.
2006-05-01
This study applies the method of multiple scales to obtain periodic solutions of a two-pulley belt system with clearance-type nonlinearity. The purpose is to explain the published numerical results and clarify how design parameters affect the system dynamics. The validity of the perturbation method for such strong nonlinearity is evaluated. The closed-form frequency-response relation is determined at the first order, and an implicit expression is obtained for the second-order approximation. The preload applied to the accessory determines the softening level of the nonlinearity. Larger preload leads to less disengagement and less softening. For a considerable range of practical parameter values, the analytical solutions well approximate the numerical results from harmonic balance.
A simple approach to nonlinear estimation of physical systems
Christakos, G.
1988-01-01
Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1991-01-01
Work continues on frequency analysis for transfer function identification, both with respect to the continued development of the underlying algorithms and in the identification study of two physical systems. Some new results of a theoretical nature were recently obtained that lend further insight into the frequency domain interpretation of the research. Progress in each of those areas is summarized. Although not related to the system identification problem, some new results were obtained on the feedback stabilization of linear time lag systems.
The coupled nonlinear dynamics of a lift system
NASA Astrophysics Data System (ADS)
Crespo, Rafael Sánchez; Kaczmarczyk, Stefan; Picton, Phil; Su, Huijuan
2014-12-01
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
The coupled nonlinear dynamics of a lift system
Crespo, Rafael Sánchez E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Picton, Phil E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk; Su, Huijuan E-mail: stefan.kaczmarczyk@northampton.ac.uk E-mail: huijuan.su@northampton.ac.uk
2014-12-10
Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Non-linear dynamic analysis of geared systems, part 2
NASA Technical Reports Server (NTRS)
Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet
1990-01-01
A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.
Multivariate dynamical systems models for estimating causal interactions in fMRI
Ryali, Srikanth; Supekar, Kaustubh; Chen, Tianwen; Menon, Vinod
2010-01-01
Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of casual interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data
Simple nonlinear systems and navigating catastrophes
NASA Astrophysics Data System (ADS)
Harré, Michael S.; Atkinson, Simon R.; Hossain, Liaquat
2013-06-01
Tipping points are a common occurrence in complex adaptive systems. In such systems feedback dynamics strongly influence equilibrium points and they are one of the principal concerns of research in this area. Tipping points occur as small changes in system parameters result in disproportionately large changes in the global properties of the system. In order to show how tipping points might be managed we use the Maximum Entropy (MaxEnt) method developed by Jaynes to find the fixed points of an economic system in two different ways. In the first, economic agents optimise their choices based solely on their personal benefits. In the second they optimise the total benefits of the system, taking into account the effects of all agent's actions. The effect is to move the game from a recently introduced dual localised Lagrangian problem to that of a single global Lagrangian. This leads to two distinctly different but related solutions where localised optimisation provides more flexibility than global optimisation. This added flexibility allows an economic system to be managed by adjusting the relationship between macro parameters, in this sense such manipulations provide for the possibility of "steering" an economy around potential disasters.
Terminal Sliding Modes In Nonlinear Control Systems
NASA Technical Reports Server (NTRS)
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
Multivariate time series modeling of short-term system scale irrigation demand
NASA Astrophysics Data System (ADS)
Perera, Kushan C.; Western, Andrew W.; George, Biju; Nawarathna, Bandara
2015-12-01
Travel time limits the ability of irrigation system operators to react to short-term irrigation demand fluctuations that result from variations in weather, including very hot periods and rainfall events, as well as the various other pressures and opportunities that farmers face. Short-term system-wide irrigation demand forecasts can assist in system operation. Here we developed a multivariate time series (ARMAX) model to forecast irrigation demands with respect to aggregated service points flows (IDCGi, ASP) and off take regulator flows (IDCGi, OTR) based across 5 command areas, which included area covered under four irrigation channels and the study area. These command area specific ARMAX models forecast 1-5 days ahead daily IDCGi, ASP and IDCGi, OTR using the real time flow data recorded at the service points and the uppermost regulators and observed meteorological data collected from automatic weather stations. The model efficiency and the predictive performance were quantified using the root mean squared error (RMSE), Nash-Sutcliffe model efficiency coefficient (NSE), anomaly correlation coefficient (ACC) and mean square skill score (MSSS). During the evaluation period, NSE for IDCGi, ASP and IDCGi, OTR across 5 command areas were ranged 0.98-0.78. These models were capable of generating skillful forecasts (MSSS ⩾ 0.5 and ACC ⩾ 0.6) of IDCGi, ASP and IDCGi, OTR for all 5 lead days and IDCGi, ASP and IDCGi, OTR forecasts were better than using the long term monthly mean irrigation demand. Overall these predictive performance from the ARMAX time series models were higher than almost all the previous studies we are aware. Further, IDCGi, ASP and IDCGi, OTR forecasts have improved the operators' ability to react for near future irrigation demand fluctuations as the developed ARMAX time series models were self-adaptive to reflect the short-term changes in the irrigation demand with respect to various pressures and opportunities that farmers' face, such as
Passive dynamic controllers for non-linear mechanical systems
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Wu, Shih-Chin; Phan, Minh; Longman, Richard W.
1992-01-01
The objective is to develop active model-independent controllers for slewing and vibration control of nonlinear multibody flexible systems, including flexible robots. The topics are presented in viewgraph form and include: passive stabilization; work-energy rate principle; Liapunov theory; displacement feedback; dynamic controller; displacement and acceleration feedback; velocity feedback; displacement feedback; physical interaction; a 6-DOF robot; and simulation results.
Application of dynamical systems theory to nonlinear aircraft dynamics
NASA Technical Reports Server (NTRS)
Culick, Fred E. C.; Jahnke, Craig C.
1988-01-01
Dynamical systems theory has been used to study nonlinear aircraft dynamics. A six degree of freedom model that neglects gravity has been analyzed. The aerodynamic model, supplied by NASA, is for a generic swept wing fighter and includes nonlinearities as functions of the angle of attack. A continuation method was used to calculate the steady states of the aircraft, and bifurcations of these steady states, as functions of the control deflections. Bifurcations were used to predict jump phenomena and the onset of periodic motion for roll coupling instabilities and high angle of attack maneuvers. The predictions were verified with numerical simulations.
Arithmetic coding as a non-linear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.; Bhat, Kishor G.
2009-04-01
In order to perform source coding (data compression), we treat messages emitted by independent and identically distributed sources as imprecise measurements (symbolic sequence) of a chaotic, ergodic, Lebesgue measure preserving, non-linear dynamical system known as Generalized Luröth Series (GLS). GLS achieves Shannon's entropy bound and turns out to be a generalization of arithmetic coding, a popular source coding algorithm, used in international compression standards such as JPEG2000 and H.264. We further generalize GLS to piecewise non-linear maps (Skewed-nGLS). We motivate the use of Skewed-nGLS as a framework for joint source coding and encryption.
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Nonlinear dynamics of fluid-structure systems. Annual technical report
Moon, F.C.; Muntean, G.
1994-01-01
We are investigating the nonlinear dynamics of a row of cylindrical tubes excited by the cross flow of fluid. Both experimental and analytical/numerical studies have been conducted. The goal of this research is to look for low dimensional dynamic models in flow- induced vibrations using modern methods of dynamical systems and chaos theory. The experimental study uses a 25 cm {times} 25 cm wind tunnel with flow velocity in the range of 15 m/sec. The use of a wind tunnel to explore dynamic phenomenon compliments the work of Chen at Argonne National Laboratory who also is conducting experiments with a water tunnel. The principal nonlinearities studies are impact constraints due to gaps in the cylinder supports and nonlinear fluid forces.
Nonlinearity as a resource for nonclassicality in anharmonic systems
NASA Astrophysics Data System (ADS)
Albarelli, Francesco; Ferraro, Alessandro; Paternostro, Mauro; Paris, Matteo G. A.
2016-03-01
Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macroscopic quantum coherence. Considering various exactly solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the entropic nonlinearity of the considered potentials and their ground-state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing, which is not captured by the negativity of the Wigner function, we focus on the Glauber-Sudarshan P function and address the nonclassicality-nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.
Synchronised output regulation of nonlinear multi-agent systems
NASA Astrophysics Data System (ADS)
Xiang, Ji; Li, Yanjun; Wei, Wei
2015-01-01
This paper considers a synchronised output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents have their outputs synchronised but also ultimately evolve on a manifold determined by a predefined exosystem. Each agent constructs its local copy of the predefined exosystem and exchanges the state information of the local exosystem to realise the synchronisation of local exosystem. A controller based on the nonlinear output regulation theory is then presented to force the agent's output track the output of local exosystem. It is shown that the SOR is solvable under the assumptions same as that for nonlinear output regulation of a single agent, if the switching graph satisfies the bounded interconnectivity times condition. Both state feedback and output feedback are addressed. A numerical simulation is made to show the efficacy of the analytic results.
Hamiltonian formalism of weakly nonlinear hydrodynamic systems
Pavlov, M.V.
1988-05-01
A study is made of systems of quasilinear equations that are diagonalizable and Hamiltonian and have the condition /delta//sub i/v/sub i/ /triple bond/ 0, where u/sub t//sup i/ /equal/ v/sup i/(u)u/sub x//sup i/, i = 1, ..., N. The conservation laws of such systems are found, together with the metric and Poisson bracket. For definite examples it is shown how solutions are found. The conditions for the existence of solutions and continuity of commuting flows are found.
On discrete control of nonlinear systems with applications to robotics
NASA Technical Reports Server (NTRS)
Eslami, Mansour
1989-01-01
Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.
Response of MDOF strongly nonlinear systems to fractional Gaussian noises.
Deng, Mao-Lin; Zhu, Wei-Qiu
2016-08-01
In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems. PMID:27586630
A nonlinear model for gas chromatograph systems
NASA Technical Reports Server (NTRS)
Feinberg, M. P.
1975-01-01
Fundamental engineering design techniques and concepts were studied for the optimization of a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned, Martian roving vehicle. Previously developed mathematical models of the gas chromatograph are found to be inadequate for predicting peak heights and spreading for some experimental conditions and chemical systems. A modification to the existing equilibrium adsorption model is required; the Langmuir isotherm replaces the linear isotherm. The numerical technique of Crank-Nicolson was studied for use with the linear isotherm to determine the utility of the method. Modifications are made to the method eliminate unnecessary calculations which result in an overall reduction of the computation time of about 42 percent. The Langmuir isotherm is considered which takes into account the composition-dependent effects on the thermodynamic parameter, mRo.
NASA Astrophysics Data System (ADS)
Aerts, Johan R. M.; de Greef, Daniël; Peacock, John; Dirckx, Joris J. J.
2011-08-01
Recently, a new signal analysis method was developed to detect small non-linear distortions in weakly non-linear systems using specially designed broadband excitation signals, i.e. odd random phase multisines. The method allows the detection and quantification of the system response, noise level and both odd and even degree nonlinear distortions over an extensive frequency range from one single short-term measurement. Here, this method is implemented in an opto-acoustical set-up to detect small non-linearities in the response of vibrating structures. Because of the highly linear response achievable with heterodyne vibrometry, it is possible to detect non-linearities in the system under test with extremely high sensitivity. Non-linear behaviour is very common in biomechanical systems, but their dynamics and thus response might change over time. This leads to measurement artifacts that cause an overestimation of the noise level. A correction algorithm can be applied to remove the effect of these time variations, so that heterodyne vibrometry also allows the detection and quantification of non-linearities in unstable biomechanical systems. In this paper the technique is demonstrated with a measurement of the non-linear distortions in the vibration of the gerbil middle ear, where the use of a non-contact optical detection method is essential to not disturb the tiny vibrating structures.
Parameter identification for nonlinear aerodynamic systems
NASA Technical Reports Server (NTRS)
Pearson, Allan E.
1993-01-01
This final technical report covers a three and one-half year period preceding February 28, 1993 during which support was provided under NASA Grant NAG-1-1065. Following a general description of the system identification problem and a brief survey of methods to attack it, the basic ideas behind the approach taken in this research effort are presented. The results obtained are described with reference to the published work, including the five semiannual progress reports previously submitted and two interim technical reports.
Downing, D.J.; Fedorov, V.; Lawkins, W.F.; Morris, M.D.; Ostrouchov, G.
1996-05-01
Large data series with more than several million multivariate observations, representing tens of megabytes or even gigabytes of data, are difficult or impossible to analyze with traditional software. The shear amount of data quickly overwhelms both the available computing resources and the ability of the investigator to confidently identify meaningful patterns and trends which may be present. The purpose of this research is to give meaningful definition to `large data set analysis` and to describe and illustrate a technique for identifying unusual events in large data series. The technique presented here is based on the theory of nonlinear dynamical systems.
Dissipative control for a class of nonlinear descriptor systems
NASA Astrophysics Data System (ADS)
Zhou, Juan; Zhang, Qingling; Li, Jinghao; Men, Bo; Ren, Junchao
2016-04-01
This paper is concerned with the dissipative control problem for a class of nonlinear descriptor systems. Based on Lyapunov stability theory, sufficient conditions are derived, which guarantee that the underlying systems are strictly dissipative. Then, the design method for a state feedback controller is provided. All the conditions can be expressed via linear matrix inequalities. Finally, a numerical example is presented to demonstrate the validity of the proposed methods.
Liu, Zhi; Lai, Guanyu; Zhang, Yun; Chen, Chun Lung Philip
2015-08-01
This paper addresses the problem of adaptive neural output-feedback control for a class of special nonlinear systems with the hysteretic output mechanism and the unmeasured states. A modified Bouc-Wen model is first employed to capture the output hysteresis phenomenon in the design procedure. For its fusion with the neural networks and the Nussbaum-type function, two key lemmas are established using some extended properties of this model. To avoid the bad system performance caused by the output nonlinearity, a barrier Lyapunov function technique is introduced to guarantee the prescribed constraint of the tracking error. In addition, a robust filtering method is designed to cancel the restriction that all the system states require to be measured. Based on the Lyapunov synthesis, a new neural adaptive controller is constructed to guarantee the prescribed convergence of the tracking error and the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system. Simulations are implemented to evaluate the performance of the proposed neural control algorithm in this paper. PMID:25915964
Nonlinear Network Dynamics on Earthquake Fault Systems
NASA Astrophysics Data System (ADS)
Rundle, P. B.; Rundle, J. B.; Tiampo, K. F.
2001-12-01
Understanding the physics of earthquakes is essential if large events are ever to be forecast. Real faults occur in topologically complex networks that exhibit cooperative, emergent space-time behavior that includes precursory quiescence or activation, and clustering of events. The purpose of this work is to investigate the sensitivity of emergent behavior of fault networks to changes in the physics on the scale of single faults or smaller. In order to investigate the effect of changes at small scales on the behavior of the network, we need to construct models of earthquake fault systems that contain the essential physics. A network topology is therefore defined in an elastic medium, the stress Green's functions (i.e. the stress transfer coefficients) are computed, frictional properties are defined and the system is driven via the slip deficit as defined below. The long-range elastic interactions produce mean-field dynamics in the simulations. We focus in this work on the major strike-slip faults in Southern California that produce the most frequent and largest magnitude events. To determine the topology and properties of the network, we used the tabulation of fault properties published in the literature. We have found that the statistical distribution of large earthquakes on a model of a topologically complex, strongly correlated real fault network is highly sensitive to the precise nature of the stress dissipation properties of the friction laws associated with individual faults. These emergent, self-organizing space-time modes of behavior are properties of the network as a whole, rather than of the individual fault segments of which the network is comprised (ref: PBR et al., Physical Review Letters, in press, 2001).
Predicting catastrophes in nonlinear dynamical systems by compressive sensing
Wang, Wen-Xu; Yang, Rui; Lai, Ying-Cheng; Kovanis, Vassilios; Grebogi, Celso
2013-01-01
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea and potential challenges are discussed. PMID:21568562
Tensor methods for large sparse systems of nonlinear equations
Bouaricha, A.; Schnabel, R.B.
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Nonlinear stability of discrete shocks for systems of conservation laws
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo; Xin, Zhouping
1993-09-01
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m×m systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the L p-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws. If the Riemann solution corresponding to the given far-field states is a superposition of m single shocks from each characteristic family, we show that the corresponding multiple discrete shocks are nonlinearly stable in L p (P ≧ 2). These results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.
NASA Astrophysics Data System (ADS)
Salman, A.; Shufan, E.; Lapidot, I.; Tsror, L.; Zeiri, L.; Sahu, R. K.; Moreh, R.; Mordechai, S.; Huleihel, M.
2015-12-01
Fourier Transform Infrared (FTIR) and Raman spectroscopies have emerged as powerful tools for chemical analysis. This is due to their ability to provide detailed information about the spatial distribution of chemical composition at the molecular level. A biological sample, i.e. bacteria or fungi, has a typical spectrum. This spectral fingerprint, characterizes the sample and can therefore be used for differentiating between biology samples which belong to different groups, i.e., several different isolates of a given fungi. When the spectral differences between the groups are minute, multivariate analysis should be used to provide a good differentiation. We hereby review several results which demonstrate the differentiation success obtained by combining spectroscopy measurements and multivariate analysis.
PVODE and KINSOL: parallel software for differential and nonlinear systems
Hindmarsh, A.C.; Taylor, A.G.
1998-02-01
In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary differential equation systems, based on robustmathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for systems of nonlinear algebraic equations. KINSOL was first developed as a sequential solver, on a design that permitted extending it to a parallel version with fairly minimal additions. Both PVODE and KINSOL are being used within a parallel version of the tokamak edge plasma model UEDGE. KINSOL is also being applied in the ParFlow groundwater flow model to solve a nonlinear pressure equation.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
Williams, Rube B.
2004-02-04
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
Digital self-triggered robust control of nonlinear systems
NASA Astrophysics Data System (ADS)
Di Benedetto, M. D.; Di Gennaro, S.; D'Innocenzo, A.
2013-09-01
In this paper, we develop novel results on self-triggered control of nonlinear systems, subject to perturbations, and sensing/computation/actuation delays. First, considering an unperturbed nonlinear system with bounded delays, we provide conditions that guarantee the existence of a self-triggered control strategy stabilizing the closed-loop system. Then, considering parameter uncertainties, disturbances and bounded delays, we provide conditions guaranteeing the existence of a self-triggered strategy that keeps the state arbitrarily close to the equilibrium point. In both cases, we provide a methodology for the computation of the next execution time. We show on an example the relevant benefits obtained with this approach in terms of energy consumption with respect to control algorithms based on a constant sampling with a sensible reduction of the average sampling time.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems
NASA Astrophysics Data System (ADS)
Williams, Rube B.
2004-02-01
Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.
NASA Technical Reports Server (NTRS)
Christenson, D.; Gordon, M.; Kistler, R.; Kriegler, F.; Lampert, S.; Marshall, R.; Mclaughlin, R.
1977-01-01
A third-generation, fast, low cost, multispectral recognition system (MIDAS) able to keep pace with the large quantity and high rates of data acquisition from large regions with present and projected sensots is described. The program can process a complete ERTS frame in forty seconds and provide a color map of sixteen constituent categories in a few minutes. A principle objective of the MIDAS program is to provide a system well interfaced with the human operator and thus to obtain large overall reductions in turn-around time and significant gains in throughput. The hardware and software generated in the overall program is described. The system contains a midi-computer to control the various high speed processing elements in the data path, a preprocessor to condition data, and a classifier which implements an all digital prototype multivariate Gaussian maximum likelihood or a Bayesian decision algorithm. Sufficient software was developed to perform signature extraction, control the preprocessor, compute classifier coefficients, control the classifier operation, operate the color display and printer, and diagnose operation.
Digital simulation and modeling of nonlinear stochastic systems
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.
Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng
2015-01-12
A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced. PMID:25835706
Observer-based controller for nonlinear analytical systems
NASA Astrophysics Data System (ADS)
Elloumi, S.; Belhouane, M. M.; Benhadj Braiek, N.
2016-06-01
In this paper, we propose to design a polynomial observer-based control for nonlinear systems and to determine sufficient linear matrix inequality (LMI) global stabilisation conditions of the polynomial controlled system augmented by its observer. The design of the observer-based control leverages some notations from the Kronecker product and the power of matrices properties for the state space description of polynomial systems. The stability study of the polynomial controlled system augmented by its observer is based on the Lyapunov stability direct method. Intensive simulations are performed to illustrate the validity and the effectiveness of the polynomial approach used to design the control.
On the orthogonalised reverse path method for nonlinear system identification
NASA Astrophysics Data System (ADS)
Muhamad, P.; Sims, N. D.; Worden, K.
2012-09-01
The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.
Numerical analysis of nonlinear properties of rail fastening systems
NASA Astrophysics Data System (ADS)
Liu, Y.; Luo, Y.; Yin, H. P.
2014-10-01
Higher demand on vibration isolation of track structure in nowadays leads to a trend of lower stiffness of rail fastening system accompanied with larger deformation of its rubber component. Nonlinear properties of rubber material under large deformation thus should be taken into account. Uniaxial tension, uniaxial compression and planar tension experiments of a rubber material were carried out to defined mathematical material models by using Abaqus. Accuracy of the material model and model coefficients were supported by good agreement between measured and simulated results. A shear type and a bonded compressed type of rail fastening system are designed and produced with the same rubber material. Quasi-static experiment of these two rail fastening systems were performed and simulated as well. Predictions of the preload dependent nonlinear properties of the two different rail fastening systems by Abaqus were found to be in good agreement with experiments. Nonlinearities of the two specimens, due both to the intrinsic rubber material properties and the geometric characteristics, were well analyzed and explained. This is believed to contribute to product designing and geometrical optimization with rubber component under general or local large deformation.
NASA Astrophysics Data System (ADS)
Lamarque, C.-H.; Ture Savadkoohi, A.; Naudan, M.
2013-09-01
The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.
NASA Astrophysics Data System (ADS)
Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen
2016-04-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].
Adaptive control of nonlinear systems using multistage dynamic neural networks
NASA Astrophysics Data System (ADS)
Gupta, Madan M.; Rao, Dandina H.
1992-11-01
In this paper we present a new architecture of neuron, called the dynamic neural unit (DNU). The topology of the proposed neuronal model embodies delay elements, feedforward and feedback signals weighted by the synaptic weights and a time-varying nonlinear activation function, and is thus different from the conventionally and assumed architecture of neurons. The learning algorithm for the proposed neuronal structure and the corresponding implementation scheme are presented. A multi-stage dynamic neural network is developed using the DNU as the basic processing element. The performance evaluation of the dynamic neural network is presented for nonlinear dynamic systems under various situations. The capabilities of the proposed neural network model not only account for the learning and control actions emulating some of the biological control functions, but also provide a promising parallel-distributed intelligent control scheme for large-scale complex dynamic systems.
The relative degree enhancement problem for MIMO nonlinear systems
Schoenwald, D.A.; Oezguener, Ue.
1995-07-01
The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for a completely decentralized feedback linearization result for at least one input-output channel.
Adaptive control of Hammerstein-Wiener nonlinear systems
NASA Astrophysics Data System (ADS)
Zhang, Bi; Hong, Hyokchan; Mao, Zhizhong
2016-07-01
The Hammerstein-Wiener model is a block-oriented model, having a linear dynamic block sandwiched by two static nonlinear blocks. This note develops an adaptive controller for a special form of Hammerstein-Wiener nonlinear systems which are parameterized by the key-term separation principle. The adaptive control law and recursive parameter estimation are updated by the use of internal variable estimations. By modeling the errors due to the estimation of internal variables, we establish convergence and stability properties. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under sufficient condition. From a qualitative analysis of the sufficient condition, we introduce an adaptive weighted factor to improve the performance of the adaptive controller. Numerical examples are given to confirm the results in this paper.
Dark state in a nonlinear optomechanical system with quadratic coupling
NASA Astrophysics Data System (ADS)
Huang, Yue-Xin; Zhou, Xiang-Fa; Guo, Guang-Can; Zhang, Yong-Sheng
We consider a hybrid system consisting of a cavity optomechanical device with nonlinear quadratic radiation pressure coupled to an atomic ensemble. By considering the collective excitation, we show that this system supports nontrivial, nonlinear dark states. The coupling strength can be tuned via the lasers that ensure the population transfer adiabatically between the mechanical modes and the collective atomic excitations in a controlled way. In addition, we show how to detect the dark-state resonance by calculating the single-photon spectrum of the output fields and the transmission of the probe beam based on two-phonon optomechanically induced transparency. Possible application and extension of the dark states are also discussed. Supported by the National Fundamental Research Program of China (Grants No. 2011CB921200 and No. 2011CBA00200), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB01030200), and NSFC (Grants No. 61275122 and 11474266).
NASA Astrophysics Data System (ADS)
Donges, Jonathan F.; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V.; Marwan, Norbert; Dijkstra, Henk A.; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
Donges, Jonathan F; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. PMID:26627561
Global nonexistence for nonlinear Kirchhoff systems with memory term
NASA Astrophysics Data System (ADS)
Liu, Gongwei; Hou, Changshun; Guo, Xiulan
2014-10-01
The initial boundary value problem for nonlinear wave equations of Kirchhoff systems with memory type in a bounded domain is considered. By modifying the method introduced in a work by Autuori et al. (Arch Rational Mech Anal 196:489-516, 2010), we establish the nonexistence result of global solutions with the initial energy controlled above by a critical value, that is, when the initial data belong to a specific region in the phase plane. This improves earlier results in the literatures.
On the Davey-Stewartson system with competing nonlinearities
NASA Astrophysics Data System (ADS)
Zhu, Shihui
2016-03-01
This paper is concerned with the blow-up solutions for the Davey-Stewartson system with competing nonlinearities, which results in the loss of scaling invariance. The best constant of a new gG-N type inequality is given to find the sharp threshold mass of blow-up and global existence. Moreover, under the sharp threshold mass, the dynamical behavior of blow-up solutions is investigated, including L2-concentration, L2 weak limits, and limiting profile.
An iterative method for systems of nonlinear hyperbolic equations
NASA Technical Reports Server (NTRS)
Scroggs, Jeffrey S.
1989-01-01
An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented.
NASA Technical Reports Server (NTRS)
Gettman, Chang-Ching LO
1993-01-01
This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.
The leaf ionome as a multivariable system to detect a plant's physiological status
Baxter, Ivan R.; Vitek, Olga; Lahner, Brett; Muthukumar, Balasubramaniam; Borghi, Monica; Morrissey, Joe; Guerinot, Mary Lou; Salt, David E.
2008-01-01
The contention that quantitative profiles of biomolecules contain information about the physiological state of the organism has motivated a variety of high-throughput molecular profiling experiments. However, unbiased discovery and validation of biomolecular signatures from these experiments remains a challenge. Here we show that the Arabidopsis thaliana (Arabidopsis) leaf ionome, or elemental composition, contains such signatures, and we establish statistical models that connect these multivariable signatures to defined physiological responses, such as iron (Fe) and phosphorus (P) homeostasis. Iron is essential for plant growth and development, but potentially toxic at elevated levels. Because of this, shoot Fe concentrations are tightly regulated and show little variation over a range of Fe concentrations in the environment, making them a poor probe of a plant's Fe status. By evaluating the shoot ionome in plants grown under different Fe nutritional conditions, we have established a multivariable ionomic signature for the Fe response status of Arabidopsis. This signature has been validated against known Fe-response proteins and allows the high-throughput detection of the Fe status of plants with a false negative/positive rate of 18%/16%. A “metascreen” of previously collected ionomic data from 880 Arabidopsis mutants and natural accessions for this Fe response signature successfully identified the known Fe mutants frd1 and frd3. A similar approach has also been taken to identify and use a shoot ionomic signature associated with P homeostasis. This study establishes that multivariable ionomic signatures of physiological states associated with mineral nutrient homeostasis do exist in Arabidopsis and are in principle robust enough to detect specific physiological responses to environmental or genetic perturbations. PMID:18697928
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
NASA Technical Reports Server (NTRS)
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Bandlimited computerized improvements in characterization of nonlinear systems with memory
NASA Astrophysics Data System (ADS)
Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.
2016-05-01
The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.
Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems
NASA Astrophysics Data System (ADS)
Mikhlin, Yu V.; Perepelkin, N. V.; Klimenko, A. A.; Harutyunyan, E.
2012-08-01
Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.
Decentralized robust nonlinear model predictive controller for unmanned aerial systems
NASA Astrophysics Data System (ADS)
Garcia Garreton, Gonzalo A.
The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1. A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2. A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3. An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4. A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible.
Del Giudice, G; Padulano, R; Siciliano, D
2016-01-01
The lack of geometrical and hydraulic information about sewer networks often excludes the adoption of in-deep modeling tools to obtain prioritization strategies for funds management. The present paper describes a novel statistical procedure for defining the prioritization scheme for preventive maintenance strategies based on a small sample of failure data collected by the Sewer Office of the Municipality of Naples (IT). Novelty issues involve, among others, considering sewer parameters as continuous statistical variables and accounting for their interdependences. After a statistical analysis of maintenance interventions, the most important available factors affecting the process are selected and their mutual correlations identified. Then, after a Box-Cox transformation of the original variables, a methodology is provided for the evaluation of a vulnerability map of the sewer network by adopting a joint multivariate normal distribution with different parameter sets. The goodness-of-fit is eventually tested for each distribution by means of a multivariate plotting position. The developed methodology is expected to assist municipal engineers in identifying critical sewers, prioritizing sewer inspections in order to fulfill rehabilitation requirements. PMID:26901717
Neural networks for feedback feedforward nonlinear control systems.
Parisini, T; Zoppoli, R
1994-01-01
This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method. PMID:18267810
Reduced bases for nonlinear structural dynamic systems: A comparative study
NASA Astrophysics Data System (ADS)
Lülf, Fritz Adrian; Tran, Duc-Minh; Ohayon, Roger
2013-07-01
The presented work provides an overview of some commonly used approaches for generating reduced bases for discrete nonlinear dynamic systems. It investigates the performance and the robustness of these bases if they are applied in a reduction-by-projection procedure on different test cases. The bases are created from the Linear Normal Modes, the Ritz-vectors, the Proper and the Smooth Orthogonal Decomposition method, the A Priori Reduction, the Centroidal Voronoi Tessellation and the Local Equivalent Linear Stiffness Method. Second-Order Terms and an Enhanced Proper Orthogonal Decomposition formulation are included as variants. The test cases are small dimensional, locally or entirely nonlinear system subjected to a harmonic or an impulse force excitation. The double objective of this numerical study is, first, to determine which bases are most adequate for a given combination of nonlinearity and excitation and, second, to which extend the bases exhibit an inherent robustness if the parameterisation of the excitation is changed. A specific multicriteria decision analysis score is developed to assess the bases' performance. As a major result, a strong dependence of the performance of the bases on the type of excitation is established and thus some bases become more adequate for a certain situation than others. Also a lack of robustness for all considered bases can be observed. This situation improves in most cases if the basis is generated with the most critical values of the parameter.
Telescopic systems with dynamic nonlinear optical correction for distortions
Vasil'ev, Michail V; Venediktov, Vladimir Yu; Leshchev, Alexey A
2001-01-31
The review of basic achievements in the field of non-linear adaptive optics is presented. In particular, schematics and properties of adaptive optical telescopes considered in which the image distortions introduced by defects of the primary mirror and other optical elements are compensated by nonlinear optical methods. The conventional methods of laser optics, such as phase conjugation and dynamic holography, make it possible both to solve the problems of classical (imaging) optics related to the building of telescopes for imaging remote objects with high resolution, which are based on large, light-weight or sectional mirrors, and create the systems that produce laser beams with the high-quality wave front. The basic designs of such telescopes are considered and the possibilities of corrections for distortions in them are analysed and confirmed by experiments. (review)
Autonomous navigation system using a fuzzy adaptive nonlinear H∞ filter.
Outamazirt, Fariz; Li, Fu; Yan, Lin; Nemra, Abdelkrim
2014-01-01
Although nonlinear H∞ (NH∞) filters offer good performance without requiring assumptions concerning the characteristics of process and/or measurement noises, they still require additional tuning parameters that remain fixed and that need to be determined through trial and error. To address issues associated with NH∞ filters, a new SINS/GPS sensor fusion scheme known as the Fuzzy Adaptive Nonlinear H∞ (FANH∞) filter is proposed for the Unmanned Aerial Vehicle (UAV) localization problem. Based on a real-time Fuzzy Inference System (FIS), the FANH∞ filter continually adjusts the higher order of the Taylor development thorough adaptive bounds and adaptive disturbance attenuation , which significantly increases the UAV localization performance. The results obtained using the FANH∞ navigation filter are compared to the NH∞ navigation filter results and are validated using a 3D UAV flight scenario. The comparison proves the efficiency and robustness of the UAV localization process using the FANH∞ filter. PMID:25244587
Swarming behaviors in multi-agent systems with nonlinear dynamics
Yu, Wenwu; Chen, Guanrong; Cao, Ming; Lü, Jinhu; Zhang, Hai-Tao
2013-12-15
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Nonlinear dynamics of global atmospheric and earth system processes
NASA Technical Reports Server (NTRS)
Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu
1995-01-01
During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.
Discrete-time ? filtering for nonlinear polynomial systems
NASA Astrophysics Data System (ADS)
Basin, M. V.; Hernandez-Gonzalez, M.
2016-07-01
This paper presents a suboptimal ? filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like ? filter.
Global adaptive control for uncertain nonaffine nonlinear hysteretic systems.
Liu, Yong-Hua; Huang, Liangpei; Xiao, Dongming; Guo, Yong
2015-09-01
In this paper, the global output tracking is investigated for a class of uncertain nonlinear hysteretic systems with nonaffine structures. By combining the solution properties of the hysteresis model with the novel backstepping approach, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The proposed control scheme is further modified to tackle the bounded disturbances by adaptively estimating their bounds. It is rigorously proven that the designed adaptive controllers can guarantee global stability of the closed-loop system. Two numerical examples are provided to show the effectiveness of the proposed control schemes. PMID:26169122
Temporal and spatial structures of nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Purwins, Hans-Georg; Klempt, Günter; Berkemeier, Jürgen
The present article contains the description of simple experiments mounted for a demonstration of temporal and spatial structures of dissipative nonlinear dynamical systems. The systematic approach possible to systems with few degrees of freedom is described on an elementary level showing experiments on a rotating nonlinear oscillator. The temporal structure elements are those contained in the stationary, periodic, quasi-periodic, and chaotic motion. Structures of systems with many degrees of freedom are demonstrated by showing experiments on real spatially extended electronic circuits and gas discharge systems both described by reaction diffusion equations. Such systems have a complexity and richness of structures far beyond what can be described systematically by current techniques. However, for special cases a quantitative understanding is possible. Also filaments of rather well defined size and shape observed in our experiments can be considered as simple elements building up a variety of spatial patterns. We also show that noise is decisive in many cases for the formation and the nonreproducibility of stationary structures. Finally, we stress some features common to reaction diffusion systems and living beings.
Optimal spatiotemporal reduced order modeling for nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
LaBryer, Allen
Proposed in this dissertation is a novel reduced order modeling (ROM) framework called optimal spatiotemporal reduced order modeling (OPSTROM) for nonlinear dynamical systems. The OPSTROM approach is a data-driven methodology for the synthesis of multiscale reduced order models (ROMs) which can be used to enhance the efficiency and reliability of under-resolved simulations for nonlinear dynamical systems. In the context of nonlinear continuum dynamics, the OPSTROM approach relies on the concept of embedding subgrid-scale models into the governing equations in order to account for the effects due to unresolved spatial and temporal scales. Traditional ROMs neglect these effects, whereas most other multiscale ROMs account for these effects in ways that are inconsistent with the underlying spatiotemporal statistical structure of the nonlinear dynamical system. The OPSTROM framework presented in this dissertation begins with a general system of partial differential equations, which are modified for an under-resolved simulation in space and time with an arbitrary discretization scheme. Basic filtering concepts are used to demonstrate the manner in which residual terms, representing subgrid-scale dynamics, arise with a coarse computational grid. Models for these residual terms are then developed by accounting for the underlying spatiotemporal statistical structure in a consistent manner. These subgrid-scale models are designed to provide closure by accounting for the dynamic interactions between spatiotemporal macroscales and microscales which are otherwise neglected in a ROM. For a given resolution, the predictions obtained with the modified system of equations are optimal (in a mean-square sense) as the subgrid-scale models are based upon principles of mean-square error minimization, conditional expectations and stochastic estimation. Methods are suggested for efficient model construction, appraisal, error measure, and implementation with a couple of well-known time
Nonlinear stochastic system identification of skin using volterra kernels.
Chen, Yi; Hunter, Ian W
2013-04-01
Volterra kernel stochastic system identification is a technique that can be used to capture and model nonlinear dynamics in biological systems, including the nonlinear properties of skin during indentation. A high bandwidth and high stroke Lorentz force linear actuator system was developed and used to test the mechanical properties of bulk skin and underlying tissue in vivo using a non-white input force and measuring an output position. These short tests (5 s) were conducted in an indentation configuration normal to the skin surface and in an extension configuration tangent to the skin surface. Volterra kernel solution methods were used including a fast least squares procedure and an orthogonalization solution method. The practical modifications, such as frequency domain filtering, necessary for working with low-pass filtered inputs are also described. A simple linear stochastic system identification technique had a variance accounted for (VAF) of less than 75%. Representations using the first and second Volterra kernels had a much higher VAF (90-97%) as well as a lower Akaike information criteria (AICc) indicating that the Volterra kernel models were more efficient. The experimental second Volterra kernel matches well with results from a dynamic-parameter nonlinearity model with fixed mass as a function of depth as well as stiffness and damping that increase with depth into the skin. A study with 16 subjects showed that the kernel peak values have mean coefficients of variation (CV) that ranged from 3 to 8% and showed that the kernel principal components were correlated with location on the body, subject mass, body mass index (BMI), and gender. These fast and robust methods for Volterra kernel stochastic system identification can be applied to the characterization of biological tissues, diagnosis of skin diseases, and determination of consumer product efficacy. PMID:23264003
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
1994-01-01
The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1993-01-01
The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate
Stability of dithered non-linear systems with backlash or hysteresis
NASA Technical Reports Server (NTRS)
Desoer, C. A.; Shahruz, S. M.
1986-01-01
A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.
Turing pattern formation in the Brusselator system with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Gambino, G.; Lombardo, M. C.; Sammartino, M.; Sciacca, V.
2013-10-01
In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.
Stochastic resonance in a nonlinear mechanical vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Chen, Li-Qun; Brennan, Michael J.; Yang, Tiejun; Ding, Hu; Liu, Zhigang
2016-05-01
This paper concerns the effect that a stochastic resonance can have on a vibration isolation system. Rather than reducing the transmitted force, it is shown that it is possible to significantly mask the component of the force transmitted though the isolator, when the system is excited harmonically. This can be achieved by adding a very low intensity of random noise to the harmonic excitation force. The nonlinear mechanical vibration isolation system used in the study consists of a vertical linear spring in parallel with two horizontal springs, which are configured so that the potential energy of the system has a double-well. Prior to the analytical and numerical study, an experiment to demonstrate stochastic resonance in a mechanical system is described.
Quantised consensus of multi-agent systems with nonlinear dynamics
NASA Astrophysics Data System (ADS)
Zhu, Yunru; Zheng, Yuanshi; Wang, Long
2015-08-01
This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.
A Nonlinear Propulsion System Simulation Technique for Piloted Simulators
NASA Technical Reports Server (NTRS)
Mihaloew, J. R.
1981-01-01
In the past, propulsion system simulations used in flight simulators have been extremely simple. This resulted in a loss of simulation realism since significant engine and aircraft interactions were neglected and important internal engine parameters were not computed. More detailed propulsion system simulators are needed to permit evaluations of modern aircraft propulsion systems in a simulated flight environment. A real time digital simulation technique has been developed which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators. A parameter correlation technique is used with real and pseudo dynamics in a stable integration convergence loop. The technique has been applied to a multivariable propulsion system for use in a piloted NASA flight simulator program. Cycle time is 2.0 ms on a Univac 1110 computer and 5.7 ms on the simulator computer, a Xerox Sigma 8. The model is stable and accurate with time steps up to 50 ms. The program evaluated the simulation technique and the propulsion system digital control. The simulation technique and model used in that program are described and results from the simulation are presented.
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
General purpose nonlinear system solver based on Newton-Krylov method.
Energy Science and Technology Software Center (ESTSC)
2013-12-01
KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].
NASA Astrophysics Data System (ADS)
Gupta, Samit Kumar; Sarma, Amarendra K.
2016-07-01
In this work, we have studied the peregrine rogue wave dynamics, with a solitons on finite background (SFB) ansatz, in the recently proposed (Ablowitz and Musslimani, (2013) [31]) continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity. We have found that the continuous nonlinear Schrödinger system with PT-symmetric nonlinearity also admits Peregrine soliton solution. Motivated by the fact that Peregrine solitons are regarded as prototypical solutions of rogue waves, we have studied Peregrine rogue wave dynamics in the c-PTNLSE model. Upon numerical computation, we observe the appearance of low-intense Kuznetsov-Ma (KM) soliton trains in the absence of transverse shift (unbroken PT-symmetry) and well-localized high-intense Peregrine rogue waves in the presence of transverse shift (broken PT-symmetry) in a definite parametric regime.
On the transmissibilities of nonlinear vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Brennan, Michael J.; Chen, Li-Qun
2016-08-01
Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.
FINDS: A fault inferring nonlinear detection system. User's guide
NASA Technical Reports Server (NTRS)
Lancraft, R. E.; Caglayan, A. K.
1983-01-01
The computer program FINDS is written in FORTRAN-77, and is intended for operation on a VAX 11-780 or 11-750 super minicomputer, using the VMS operating system. The program detects, isolates, and compensates for failures in navigation aid instruments and onboard flight control and navigation sensors of a Terminal Configured Vehicle aircraft in a Microwave Landing System environment. In addition, FINDS provides sensor fault tolerant estimates for the aircraft states which are then used by an automatic guidance and control system to land the aircraft along a prescribed path. FINDS monitors for failures by evaluating all sensor outputs simultaneously using the nonlinear analytic relationships between the various sensor outputs arising from the aircraft point mass equations of motion. Hence, FINDS is an integrated sensor failure detection and isolation system.
A universal approach to the study of nonlinear systems
NASA Astrophysics Data System (ADS)
Hwa, Rudolph C.
2004-07-01
A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.
NASA Technical Reports Server (NTRS)
Crutcher, H. L.; Falls, L. W.
1976-01-01
Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.
Limits of localized control in extended nonlinear systems
NASA Astrophysics Data System (ADS)
Handel, Andreas
We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under
Nonlinear dynamics of a simplified engine-propeller system
NASA Astrophysics Data System (ADS)
Yu, S. D.; Warwick, S. A.; Zhang, X.
2009-07-01
This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge-Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness. PMID:26277007
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Practical application of equivalent linearization approaches to nonlinear piping systems
Park, Y.J.; Hofmayer, C.H.
1995-05-01
The use of mechanical energy absorbers as an alternative to conventional hydraulic and mechanical snubbers for piping supports has attracted a wide interest among researchers and practitioners in the nuclear industry. The basic design concept of energy absorbers (EA) is to dissipate the vibration energy of piping systems through nonlinear hysteretic actions of EA!s under design seismic loads. Therefore, some type of nonlinear analysis needs to be performed in the seismic design of piping systems with EA supports. The equivalent linearization approach (ELA) can be a practical analysis tool for this purpose, particularly when the response approach (RSA) is also incorporated in the analysis formulations. In this paper, the following ELA/RSA methods are presented and compared to each other regarding their practice and numerical accuracy: Response approach using the square root of sum of squares (SRSS) approximation (denoted RS in this paper). Classical ELA based on modal combinations and linear random vibration theory (denoted CELA in this paper). Stochastic ELA based on direct solution of response covariance matrix (denoted SELA in this paper). New algorithms to convert response spectra to the equivalent power spectral density (PSD) functions are presented for both the above CELA and SELA methods. The numerical accuracy of the three EL are studied through a parametric error analysis. Finally, the practicality of the presented analysis is demonstrated in two application examples for piping systems with EA supports.
NASA Technical Reports Server (NTRS)
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A formulation is presented for identification of linear multivariable from a single set of input-output data. The identification method is formulated with the mathematical framework of learning identifications, by extension of the repetition domain concept to include shifting time intervals. This method contrasts with existing learning approaches that require data from multiple experiments. In this method, the system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded real eigenvalue assignment procedure. Through this relationship, the Markov parameters of the observer are identified. The Markov parameters of the actual system are recovered from those of the observer, and then used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and numerical examples presented to illustrate.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
Memristive non-linear system and hidden attractor
NASA Astrophysics Data System (ADS)
Saha, P.; Saha, D. C.; Ray, A.; Chowdhury, A. R.
2015-07-01
Effects of memristor on non-linear dynamical systems exhibiting chaos are analysed both form the view point of theory and experiment. It is observed that the memristive system has always fewer number of fixed points than the original one. Sometimes there is no fixed point in the memristive system. But its chaotic properties are retained. As such we have a situation known as hidden attractor because if it is a stable fixed point then the attractor does not evolve from its basin of attraction(obtained from its stable fixed point) or if there is no fixed point, the question of basin of attraction from fixed point does not arise at all [1, 2]. Our analysis gives a detailed accounts of properties related to its chaotic behavior. Important observations are also obtained with the help of electronic circuits to support the numerical simulations.
THz impulse radar for biomedical sensing: nonlinear system behavior
NASA Astrophysics Data System (ADS)
Brown, E. R.; Sung, Shijun; Grundfest, W. S.; Taylor, Z. D.
2014-03-01
The THz impulse radar is an "RF-inspired" sensor system that has performed remarkably well since its initial development nearly six years ago. It was developed for ex vivo skin-burn imaging, and has since shown great promise in the sensitive detection of hydration levels in soft tissues of several types, such as in vivo corneal and burn samples. An intriguing aspect of the impulse radar is its hybrid architecture which combines the high-peak-power of photoconductive switches with the high-responsivity and -bandwidth (RF and video) of Schottky-diode rectifiers. The result is a very sensitive sensor system in which the post-detection signal-to-noise ratio depends super-linearly on average signal power up to a point where the diode is "turned on" in the forward direction, and then behaves quasi-linearly beyond that point. This paper reports the first nonlinear systems analysis done on the impulse radar using MATLAB.
Fuzzy fractional order sliding mode controller for nonlinear systems
NASA Astrophysics Data System (ADS)
Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.
2010-04-01
In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.
Dynamics of large constrained nonlinear systems -- A taxonomy theory
Venkatasubramanian, V.; Schaettler, H.; Zaborszky, J.
1995-11-01
This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe operating region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation. An overview of the recent results which prove that the two-level structure exists even in nonsmooth models that incorporate the effects of system hard limits is also included. Specifically hard limits induce a number of new bifurcations. This natural taxonomy of the system dynamics stands as the backbone for developing practical and rigorous computational techniques in detecting diverse instability mechanisms.
Transient dynamics and nonlinear stability of spatially extended systems.
Handel, Andreas; Grigoriev, Roman O
2006-09-01
As studies of various systems have shown, the sole focus on the eigenvalues in a linear stability analysis can be misleading, especially when the dynamics of disturbances is characterized by strong transient growth. The aim of this paper is to extend the generalized stability analysis, in the context of spatially extended systems, by examining the role of the nonlinear terms in the destabilization process. The critical noise level leading to destabilization is often found to scale as a power of the magnitude of transient amplification. In what follows we show that the power law exponent sensitively depends on the type of nonlinear terms and their potential for generating self-sustaining noise amplification cycles (bootstrapping). We find, however, that the exponents are not universal and also depend on the more subtle details of the transient dynamics. We also show that the basin of attraction of a spatially uniform state is bounded by the stable manifold(s) of nearby saddle(s) which play a major role in the transition. PMID:17025738
NASA Astrophysics Data System (ADS)
Zhang, Qian; Wang, Qunjing; Li, Guoli
2016-05-01
This article deals with the identification of nonlinear model and Nonlinear Predictive Functional Controller (NPFC) design based on the Hammerstein structure for the turntable servo system. As a mechanism with multi-mass rotational system, nonlinearities significantly influence the system operation, especially when the turntable is in the states of zero-crossing distortion or rapid acceleration/deceleration, etc. The field data from identification experiments are processed by Comprehensive Learning Particle Swarm Optimization (CLPSO). As a result, Hammerstein model can be derived to describe the input-output relationship globally, considering all the linear and nonlinear factors of the turntable system. Cross validation results demonstrate good correspondence between the real equipment and the identified model. In the second part of this manuscript, a nonlinear control strategy based on the genetic algorithm and predictive control is developed. The global nonlinear predictive controller is carried out by two steps: (i) build the linear predictive functional controller with state space equations for the linear subsystem of Hammerstein model, and (ii) optimize the global control variable by minimizing the cost function through genetic algorithm. On the basis of distinguish model for turntable and the effectiveness of NPFC, the good performance of tracking ability is achieved in the simulation results.
Adaptive RSOV filter using the FELMS algorithm for nonlinear active noise control systems
NASA Astrophysics Data System (ADS)
Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou; Li, Tianrui
2013-01-01
This paper presents a recursive second-order Volterra (RSOV) filter to solve the problems of signal saturation and other nonlinear distortions that occur in nonlinear active noise control systems (NANC) used for actual applications. Since this nonlinear filter based on an infinite impulse response (IIR) filter structure can model higher than second-order and third-order nonlinearities for systems where the nonlinearities are harmonically related, the RSOV filter is more effective in NANC systems with either a linear secondary path (LSP) or a nonlinear secondary path (NSP). Simulation results clearly show that the RSOV adaptive filter using the multichannel structure filtered-error least mean square (FELMS) algorithm can further greatly reduce the computational burdens and is more suitable to eliminate nonlinear distortions in NANC systems than a SOV filter, a bilinear filter and a third-order Volterra (TOV) filter.
A Nonlinear Elastic Beam System with Inelastic Contact Constraints
Russell, D.L. White, L.W.
2002-12-19
In this paper we study freely propagating inertial, i.e., unforced, waves, in an elastic beam constrained so that all motion takes place above and on a flat, rigid support surface, subject to a gravitational force and a compressive longitudinal load. Contact between the beam and the support surface is assumed to be completely inelastic. A nonlinear beam model is used, incorporating a quartic extension of the familiar quadratic potential energy functional for the standard Euler-Bernoulli model. After briefly reviewing the rationale for the model and some of its properties, as developed in earlier articles, we present existence and uniqueness results for the constrained system obtained with the use of a 'penalty function' approach involving the addition of a 'uni-directional friction' dissipative term, active only when the constraint is violated, to the unconstrained system.
One-Time Pad as a nonlinear dynamical system
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin
2012-11-01
The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding - a scheme for joint compression and encryption.
A globalization procedure for solving nonlinear systems of equations
NASA Astrophysics Data System (ADS)
Shi, Yixun
1996-09-01
A new globalization procedure for solving a nonlinear system of equationsF(x)D0 is proposed based on the idea of combining Newton step and the steepest descent step WITHIN each iteration. Starting with an arbitrary initial point, the procedure converges either to a solution of the system or to a local minimizer off(x)D1/2F(x)TF(x). Each iteration is chosen to be as close to a Newton step as possible and could be the Newton step itself. Asymptotically the Newton step will be taken in each iteration and thus the convergence is quadratic. Numerical experiments yield positive results. Further generalizations of this procedure are also discussed in this paper.
Inverse problem of nonlinear dynamical systems: a constructive approach
Gonzalez-Gascon, F.; Moreno-Insertis, F.; Rodriguez-Camino, E.
1980-08-01
A quite simple and practical method is developed for the construction of two dimensional nonlinear dynamical systems (plane vector fields) possessing an arbitrary number of given limit cycles. The method is applied to the construction of n-dimensional dynamical systems (R/sup n/ vector fields) possessing at least one limit cycle and, under certain circumstances, more than one, or even a numerable infinity. Interesting open problems arise when n is greater than two, or where more than one limit cycle appears. Our constructive algorithm for this type of inverse problem is also applied to the construction of second order differential equations (Newtonian differential equations) possessing a finite or infinite number of invariant speeds. This last problem is relevant for certain aspects of the special theory of relativity.
NASA Astrophysics Data System (ADS)
Nevolin, V. I.
2003-04-01
We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker-Planck-Kolmogorov (FPK) equations in the form of series of functions over Hermite-Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.
Multivariate moment closure techniques for stochastic kinetic models
Lakatos, Eszter Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-07
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models
NASA Astrophysics Data System (ADS)
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.
Multivariate moment closure techniques for stochastic kinetic models.
Lakatos, Eszter; Ale, Angelique; Kirk, Paul D W; Stumpf, Michael P H
2015-09-01
Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs. PMID:26342359
Nonlinear observer designs for fuel cell power systems
NASA Astrophysics Data System (ADS)
Gorgun, Haluk
A fuel cell is an electrochemical device that combines hydrogen and oxygen, with the aid of electro-catalysts, to produce electricity. A fuel cell consists of a negatively charged anode, a positively charged cathode and an electrolyte, which transports protons or ions. A low temperature fuel cell has an electrical potential of about 0.7 Volt when generating a current density of 300--500 mA/cm2. Practical fuel cell power systems will require a combination of several cells in series (a stack) to satisfy the voltage requirements of specific applications. Fuel cells are suitable for a potentially wide variety of applications, from stationary power generation in the range of hundreds of megawatts to portable electronics in the range of a couple of watts. Efficient operation of a fuel cell system requires advanced feedback control designs. Reliable measurements from the system are necessary to implement such designs. However, most of the commercially available sensors do not operate properly in the reformate and humidified gas streams in fuel cell systems. Sensors working varying degrees of success are too big and costly, and sensors that are potentially low cost are not reliable or do not have the required life time [28]. Observer designs would eliminate sensor needs for measurements, and make feedback control implementable. Since the fuel cell system dynamics are highly nonlinear, observer design is not an easy task. In this study we aim to develop nonlinear observer design methods applicable to fuel cell systems. In part I of the thesis we design an observer to estimate the hydrogen partial pressure in the anode channel. We treat inlet partial pressure as an unknown slowly varying parameter and develop an adaptive observer that employs a nonlinear voltage injection term. However in this design Fuel Processing System (FPS) dynamics are not modelled, and their effect on the anode dynamics are treated as plant uncertainty. In part II of the thesis we study the FPS
Kumar, Shiva; Liu, Ling
2007-03-01
An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI. PMID:19532453
An approximation theory for the identification of nonlinear distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1990-01-01
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 appproximation 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.
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.
Predictability of extremes in non-linear hierarchically organized systems
NASA Astrophysics Data System (ADS)
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Appropriate time scales for nonlinear analyses of deterministic jump systems
NASA Astrophysics Data System (ADS)
Suzuki, Tomoya
2011-06-01
In the real world, there are many phenomena that are derived from deterministic systems but which fluctuate with nonuniform time intervals. This paper discusses the appropriate time scales that can be applied to such systems to analyze their properties. The financial markets are an example of such systems wherein price movements fluctuate with nonuniform time intervals. However, it is common to apply uniform time scales such as 1-min data and 1-h data to study price movements. This paper examines the validity of such time scales by using surrogate data tests to ascertain whether the deterministic properties of the original system can be identified from uniform sampled data. The results show that uniform time samplings are often inappropriate for nonlinear analyses. However, for other systems such as neural spikes and Internet traffic packets, which produce similar outputs, uniform time samplings are quite effective in extracting the system properties. Nevertheless, uniform samplings often generate overlapping data, which can cause false rejections of surrogate data tests.
Optimum Damping in a Non-Linear Base Isolation System
NASA Astrophysics Data System (ADS)
Jangid, R. S.
1996-02-01
Optimum isolation damping for minimum acceleration of a base-isolated structure subjected to earthquake ground excitation is investigated. The stochastic model of the El-Centro1940 earthquake, which preserves the non-stationary evolution of amplitude and frequency content of ground motion, is used as an earthquake excitation. The base isolated structure consists of a linear flexible shear type multi-storey building supported on a base isolation system. The resilient-friction base isolator (R-FBI) is considered as an isolation system. The non-stationary stochastic response of the system is obtained by the time dependent equivalent linearization technique as the force-deformation of the R-FBI system is non-linear. The optimum damping of the R-FBI system is obtained under important parametric variations; i.e., the coefficient of friction of the R-FBI system, the period and damping of the superstructure; the effective period of base isolation. The criterion selected for optimality is the minimization of the top floor root mean square (r.m.s.) acceleration. It is shown that the above parameters have significant effects on optimum isolation damping.
Dispersion and nonlinear effects in OFDM-RoF system
NASA Astrophysics Data System (ADS)
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
NASA Astrophysics Data System (ADS)
Yang, Jun; Li, Shihua; Chen, Wen-Hua
2012-08-01
For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples.
Turksoy, Kamuran; Samadi, Sediqeh; Feng, Jianyuan; Littlejohn, Elizabeth; Quinn, Laurie; Cinar, Ali
2016-01-01
A novel meal-detection algorithm is developed based on continuous glucose measurements. Bergman's minimal model is modified and used in an unscented Kalman filter for state estimations. The estimated rate of appearance of glucose is used for meal detection. Data from nine subjects are used to assess the performance of the algorithm. The results indicate that the proposed algorithm works successfully with high accuracy. The average change in glucose levels between the meals and the detection points is 16(±9.42) [mg/dl] for 61 successfully detected meals and snacks. The algorithm is developed as a new module of an integrated multivariable adaptive artificial pancreas control system. Meal detection with the proposed method is used to administer insulin boluses and prevent most of postprandial hyperglycemia without any manual meal announcements. A novel meal bolus calculation method is proposed and tested with the UVA/Padova simulator. The results indicate significant reduction in hyperglycemia. PMID:26087510
Noise in Nonlinear Dynamical Systems 3 Volume Paperback Set
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2011-11-01
Volume 1: List of contributors; Preface; Introduction to volume one; 1. Noise-activated escape from metastable states: an historical view Rolf Landauer; 2. Some Markov methods in the theory of stochastic processes in non-linear dynamical systems R. L. Stratonovich; 3. Langevin equations with coloured noise J. M. Sancho and M. San Miguel; 4. First passage time problems for non-Markovian processes Katja Lindenberg, Bruce J. West and Jaume Masoliver; 5. The projection approach to the Fokker-Planck equation: applications to phenomenological stochastic equations with coloured noises Paolo Grigolini; 6. Methods for solving Fokker-Planck equations with applications to bistable and periodic potentials H. Risken and H. D. Vollmer; 7. Macroscopic potentials, bifurcations and noise in dissipative systems Robert Graham; 8. Transition phenomena in multidimensional systems - models of evolution W. Ebeling and L. Schimansky-Geier; 9. Coloured noise in continuous dynamical systems: a functional calculus approach Peter Hanggi; Appendix. On the statistical treatment of dynamical systems L. Pontryagin, A. Andronov and A. Vitt; Index. Volume 2: List of contributors; Preface; Introduction to volume two; 1. Stochastic processes in quantum mechanical settings Ronald F. Fox; 2. Self-diffusion in non-Markovian condensed-matter systems Toyonori Munakata; 3. Escape from the underdamped potential well M. Buttiker; 4. Effect of noise on discrete dynamical systems with multiple attractors Edgar Knobloch and Jeffrey B. Weiss; 5. Discrete dynamics perturbed by weak noise Peter Talkner and Peter Hanggi; 6. Bifurcation behaviour under modulated control parameters M. Lucke; 7. Period doubling bifurcations: what good are they? Kurt Wiesenfeld; 8. Noise-induced transitions Werner Horsthemke and Rene Lefever; 9. Mechanisms for noise-induced transitions in chemical systems Raymond Kapral and Edward Celarier; 10. State selection dynamics in symmetry-breaking transitions Dilip K. Kondepudi; 11. Noise in a
Nonlinear dynamics of global atmospheric and Earth-system processes
NASA Technical Reports Server (NTRS)
Saltzman, Barry; Ebisuzaki, Wesley; Maasch, Kirk A.; Oglesby, Robert; Pandolfo, Lionel
1990-01-01
Researchers are continuing their studies of the nonlinear dynamics of global weather systems. Sensitivity analyses of large-scale dynamical models of the atmosphere (i.e., general circulation models i.e., GCM's) were performed to establish the role of satellite-signatures of soil moisture, sea surface temperature, snow cover, and sea ice as crucial boundary conditions determining global weather variability. To complete their study of the bimodality of the planetary wave states, they are using the dynamical systems approach to construct a low-order theoretical explanation of this phenomenon. This work should have important implications for extended range forecasting of low-frequency oscillations, elucidating the mechanisms for the transitions between the two wave modes. Researchers are using the methods of jump analysis and attractor dimension analysis to examine the long-term satellite records of significant variables (e.g., long wave radiation, and cloud amount), to explore the nature of mode transitions in the atmosphere, and to determine the minimum number of equations needed to describe the main weather variations with a low-order dynamical system. Where feasible they will continue to explore the applicability of the methods of complex dynamical systems analysis to the study of the global earth-system from an integrative viewpoint involving the roles of geochemical cycling and the interactive behavior of the atmosphere, hydrosphere, and biosphere.
Third-order nonlinear optical response of energy transfer systems
NASA Astrophysics Data System (ADS)
Yang, Mino; Fleming, Graham R.
1999-07-01
The third-order nonlinear optical response of energy transfer systems is theoretically investigated. A system composed of two chromophores having the same electronic transition energies is considered. The dynamics of energy transfer between the two chromophores is assumed to occur via a hopping (incoherent) mechanism. We introduce new types of pathways incorporating the hopping processes occurring while the system is in population states and reconstruct a third-order response function which is computationally viable. The nuclear propagators in the electronic population states are written as convolution integrals between those of the nonreactive two-state system weighted by some factors for the energy transfer. The response function is given by multitime correlation functions and these are analyzed by the cumulant expansion method. Based on this approach, the three-pulse photon echo peak shift for several models of energy transfer systems is discussed. It is shown that the rephasing capability of the induced signal is reduced by the memory loss due to resonant energy transfer. A previous model which incorporates resonant energy transfers in an intuitive way is reviewed and modified to supplement the loss of dynamic correlation of nuclear motion within the framework of the theory. The response function obtained by our new approach gives a more accurate description than the existing theory and a comparative discussion is given. The effect of inhomogeneity in rate constants on the third-order signal is discussed and the temperature dependence of the echo signal is examined.
Equations for Nonlinear MHD Convection in Shearless Magnetic Systems
Pastukhov, V.P.
2005-07-15
A closed set of reduced dynamic equations is derived that describe nonlinear low-frequency flute MHD convection and resulting nondiffusive transport processes in weakly dissipative plasmas with closed or open magnetic field lines. The equations obtained make it possible to self-consistently simulate transport processes and the establishment of the self-consistent plasma temperature and density profiles for a large class of axisymmetric nonparaxial shearless magnetic devices: levitated dipole configurations, mirror systems, compact tori, etc. Reduced equations that are suitable for modeling the long-term evolution of the plasma on time scales comparable to the plasma lifetime are derived by the method of the adiabatic separation of fast and slow motions.
Method and system for non-linear motion estimation
NASA Technical Reports Server (NTRS)
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
NASA Technical Reports Server (NTRS)
Baheti, R. S.
1982-01-01
The magnetic suspension and balance system for an airplane model in a large wind tunnel is considered. In this system, superconducting coils generate magnetic forces and torques on the magnetized soft iron core of the airplane model. The control system is a position servo where the airplane model, with six degrees of feedom, follows the reference static or dynamic input commands. The controller design, based on the characteristic loci method, minimizes the effects of aerodynamic and inertial cross-couplings, and provides the specified dynamic response.
Guidance of Nonlinear Nonminimum-Phase Dynamic Systems
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1996-01-01
The research work has advanced the inversion-based guidance theory for: systems with non-hyperbolic internal dynamics; systems with parameter jumps; and systems where a redesign of the output trajectory is desired. A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics was developed. This approach integrated stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics was used (a) to remove non-hyperbolicity which is an obstruction to applying stable inversion techniques and (b) to reduce large preactuation times needed to apply stable inversion for near non-hyperbolic cases. The method was applied to an example helicopter hover control problem with near non-hyperbolic internal dynamics for illustrating the trade-off between exact tracking and reduction of preactuation time. Future work will extend these results to guidance of nonlinear non-hyperbolic systems. The exact output tracking problem for systems with parameter jumps was considered. Necessary and sufficient conditions were derived for the elimination of switching-introduced output transient. While previous works had studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches), such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is also applicable to nonminimum-phase systems and leads to bounded but possibly non-causal solutions. In addition, for the case when the reference trajectories are generated by an exosystem, we developed an exact-tracking controller which could be written in a feedback form. As in standard regulator theory, we also obtained a linear map from the states of the exosystem to the desired system state, which was defined via a matrix differential equation.
NASA Technical Reports Server (NTRS)
Anderson, B. D. O.; Brockett, R. W.; Byrnes, C. I.; Ghosh, B. K.; Stevens, P. K.
1983-01-01
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined.
The SWAN/NPSOL code system for multivariable multiconstraint shield optimization
Watkins, E.F.; Greenspan, E.
1995-12-31
SWAN is a useful code for optimization of source-driven systems, i.e., systems for which the neutron and photon distribution is the solution of the inhomogeneous transport equation. Over the years, SWAN has been applied to the optimization of a variety of nuclear systems, such as minimizing the thickness of fusion reactor blankets and shields, the weight of space reactor shields, the cost for an ICF target chamber shield, and the background radiation for explosive detection systems and maximizing the beam quality for boron neutron capture therapy applications. However, SWAN`s optimization module can handle up to a single constraint and was inefficient in handling problems with many variables. The purpose of this work is to upgrade SWAN`s optimization capability.
Modeling and detecting localized nonlinearity in continuum systems with a multistage transform.
Bryant, Paul H; Nichols, J M
2010-02-01
A general method is presented for modeling spatially extended systems that may contain a localized source of nonlinearity. It has direct applications to structural health monitoring (SHM) where physical damage may cause such nonlinearity and also communications channels which may exhibit localized nonlinearity due to bad electrical contacts or component nonlinearity. The method uses a multistage nonlinear transform in order to model the system dynamics. We discuss the application to SHM and provide a preliminary test of the method with experimental data from a randomly shaken beam with loose bolts. We discuss the application to telecommunications, provide an experimental observation of symmetric nonlinearity in a "bad" electrical contact, and provide a preliminary test of using this method to remove nonlinear echo (and thereby improve data rate) on a telephone line used for data transmission. PMID:20365640
Mondal, Sanjoy; Mahanta, Chitralekha
2013-05-01
In this paper, a chattering free adaptive sliding mode controller (SMC) is proposed for stabilizing a class of multi-input multi-output (MIMO) systems affected by both matched and mismatched types of uncertainties. The proposed controller uses a proportional plus integral sliding surface whose gain is adaptively tuned to prevent overestimation. A vertical take-off and landing (VTOL) aircraft system is simulated to demonstrate the effectiveness of the proposed control scheme. PMID:23357555
NASA Astrophysics Data System (ADS)
Bona, J. L.; Chen, M.; Saut, J.-C.
2004-05-01
In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.
Macrosimulation of nonlinear dynamic systems for wave-shaping applications
NASA Astrophysics Data System (ADS)
Ogrodzki, Jan; Bieńkowski, Piotr
2014-11-01
Macromodeling is a technique widely used in circuits simulation. Macromodels usually describe complex, repetitive parts of large systems. They are often created on the base of original circuits by their simplification, e.g. macromodels of operational amplifiers. Another group of macromodels makes use of the circuit response approximation. This approach is called behavioral macromodeling. Low numerical complexity of behavioral macromodels is especially useful in CAD systems where circuit simulation must be run many times. In this paper the behavioral macromodeling technique has been applied to the whole circuit not to its part. This technique may be understood as shaping of the circuit output response and so belongs to a class of wave-shaping methods. We have used it to nonlinear, dynamic circuits with periodic signals of finite spectra, as e.g. in audio systems. The macromodels shape their frequency and spectral characteristics with a sufficient simplicity to omit unwanted distortions and with a sufficient efficiency to run the simulator in real time. Elaboration of this wave-shaping simulator is based on dynamic circuits identification, Fourier approximation of signals and harmonic balance technique. The obtained macromodel can be run as a software substitute for a hardware audio system.
Nonlinear Dynamics of Extended Hydrologic Systems over long time scales
NASA Astrophysics Data System (ADS)
Lall, Upmanu
2014-05-01
We often view our knowledge of hydrology and hence of nature as intransient, at least over the time scales over which we study processes we wish to predict and understand. Over the last few decades, this assumption has come under question, largely because of the vocal expression of a changing climate, but also the recurrent demonstration of significant land use change, both of which significantly affect the boundary conditions for terrestrial hydrology that is our forte. Most recently, the concepts of hydromorphology and social hydrology have entered the discussion, and the notion that climate and hydrology influence human action, which in turn shapes hydrology, is being recognized. Finally, as a field, we seem to be coming to the conclusion that the hydrologic system is an open system, whose boundaries evolve in time, and that the hydrologic system, at many scales, has a profound effect on the systems that drive it -- whether they be the ecological and climatic systems, or the social system. What a mess! Complexity! Unpredictability! At a certain level of abstraction, one can consider the evolution of these coupled systems with nonlinear feedbacks and ask what types of questions are relevant in terms of such a coupled evolution? What are their implications at the planetary scale? What are their implications for a subsistence farmer in an arid landscape who may under external influence achieve a new transient hydro-ecological equilibrium? What are the implications for the economy and power of nations? In this talk, I will try to raise some of these questions and also provide some examples with very simple dynamical systems that suggest ways of thinking about some practical issues of feedback across climate, hydrology and human behavior.
NASA Technical Reports Server (NTRS)
Fitzjerrell, D. G.
1974-01-01
A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.
Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems
Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...
A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems
ERIC Educational Resources Information Center
Stavrou, D.; Duit, R.; Komorek, M.
2008-01-01
A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…
R-parametrization and its role in classification of linear multivariable feedback systems
NASA Technical Reports Server (NTRS)
Chen, Robert T. N.
1988-01-01
A classification of all the compensators that stabilize a given general plant in a linear, time-invariant multi-input, multi-output feedback system is developed. This classification, along with the associated necessary and sufficient conditions for stability of the feedback system, is achieved through the introduction of a new parameterization, referred to as R-Parameterization, which is a dual of the familiar Q-Parameterization. The classification is made to the stability conditions of the compensators and the plant by themselves; and necessary and sufficient conditions are based on the stability of Q and R themselves.
A distributed system for visualizing and analyzing multivariate and multidisciplinary data
NASA Technical Reports Server (NTRS)
Jacobson, Allan S.; Allen, Mark; Bailey, Michael; Blom, Ronald; Blume, Leo; Elson, Lee
1993-01-01
THe Linked Windows Interactive Data System (LinkWinds) is being developed with NASA support. The objective of this proposal is to adapt and apply that system in a complex network environment containing elements to be found by scientists working multidisciplinary teams on very large scale and distributed data sets. The proposed three year program will develop specific visualization and analysis tools, to be exercised locally and remotely in the LinkWinds environment, to demonstrate visual data analysis, interdisciplinary data analysis and cooperative and interactive televisualization and analysis of data by geographically separated science teams. These demonstrators will involve at least two science disciplines with the aim of producing publishable results.
The Impact of Fiber Nonlinearities on Digital Optical Communication Systems
NASA Astrophysics Data System (ADS)
Chiang, Ting-Kuang
Wavelength-division multiplexing (WDM) enables high throughput fiber-optic networks by sending several optical channels through a single fiber. Even though the bandwidth of optical fibers is over 25 THz, fiber nonlinearities can limit the capacity of WDM communication systems. Cross -phase modulation (XPM) is one of the nonlinear effects that affect WDM systems. This thesis provides an in-depth understanding of the properties of XPM-induced phase shift and suggests techniques to suppress XPM in long-distance WDM optical networks. In this thesis, XPM is theoretically and experimentally investigated in fiber links with optical amplifiers and dispersion compensators. The theoretical analysis suggests that the XPM effect can be modeled as a phase modulator with inputs from the intensity of co-propagating waves. The frequency response of the phase modulator depends on fiber dispersion, wavelength separation, and fiber length. In non-dispersive fibers, XPM is frequency-independent; in dispersive fibers, the response is approximately inversely proportional to modulation frequency, fiber dispersion, and wavelength separation. In N-segment amplified links with no dispersion compensators, the XPM frequency response is increased N -fold, but only in very narrow frequency bands. In most other frequency bands, the increase is limited and almost independent of N. However, in N-segment amplified links with dispersion compensators, the frequency response of XPM is increased N-fold at all frequencies if the dispersion is compensated for within each fiber segment. The XPM-induced sensitivity penalty in multichannel continuous-phase frequency-shift-keying optical communication systems is investigated by theoretical analysis, computer simulations, and experimental measurements. It is shown that high-frequency components in the XPM-induced phase shift play a more important role in determining the sensitivity penalty than the low-frequency components. The XPM-induced sensitivity penalty
ERIC Educational Resources Information Center
Mather, Richard
2015-01-01
This paper explores the application of canonical gradient analysis to evaluate and visualize student performance and acceptance of a learning system platform. The subject of evaluation is a first year BSc module for computer programming. This uses "Ceebot," an animated and immersive game-like development environment. Multivariate…
AESOP: A computer-aided design program for linear multivariable control systems
NASA Technical Reports Server (NTRS)
Lehtinen, B.; Geyser, L. C.
1982-01-01
An interactive computer program (AESOP) which solves quadratic optimal control and is discussed. The program can also be used to perform system analysis calculations such as transient and frequency responses, controllability, observability, etc., in support of the control and filter design computations.
Indicators are commonly used for evaluating relative sustainability for competing products and processes. When a set of indicators is chosen for a particular system of study, it is important to ensure that they are variable independently of each other. Often the number of indicat...
Linear versus nonlinear response of a forced wave turbulence system.
Cadot, Olivier; Touzé, Cyril; Boudaoud, Arezki
2010-10-01
A vibrating plate is set into a chaotic state of wave turbulence by a forcing having periodic and random components. Both components are weighted in order to explore continuously intermediate forcing from the periodic to the random one, but keeping constant its rms value. The transverse velocity of the plate is measured at the application point of the force. It is found that whatever the detail of the forcing is, the velocity spectra exhibit a universal cascade for frequencies larger than the forcing frequency range. In contrast, the velocity spectra strongly depend on the nature of the forcing within the range of forcing frequencies. The coherence function is used to extract the contribution of the velocity fluctuations that display a linear relationship with the forcing. The nonlinear contribution to the velocity fluctuations is found to be almost constant, about 55% of the total velocity fluctuations whatever the nature of the forcing from random to periodic. On the other hand, the nonlinear contribution to the fluctuations of the injected power depends on the nature of the forcing; it is significantly larger for the periodic forcing (60%) and decreases continuously as the randomness is increased, reaching a value of 40% for the pure random forcing. For all the cases of intermediate forcing from random to periodic, a simple model of the velocity response recovers in a fairly good agreement the probability density function of the injected power. The consequence of the existence of a linear-response component is discussed in the context of the fluctuation-dissipation theorem validation in experiments of out-of-equilibrium systems. PMID:21230369
Nonlinear Network Modes in Cyclic Systems with Applications to Connected Vehicles
NASA Astrophysics Data System (ADS)
Avedisov, Sergei S.; Orosz, Gábor
2015-08-01
In this paper, we propose a novel technique to decompose networked systems with cyclic structure into nonlinear modes and apply these ideas to a system of connected vehicles. We perform linear and nonlinear transformations that exploit the network structure and lead to nonlinear modal equations that are decoupled. Each mode can be obtained by solving a small set of algebraic equations without deriving the coefficients for any other mode. By focusing on the mode that is loosing stability, bifurcation analysis can be carried out. The techniques developed are applied to evaluate the impact of connected cruise control on the nonlinear dynamics of a connected vehicle system.
A new method of modelling and numerical simulation of nonlinear dynamical systems
Colosi, T.; Codreanu, S.
1996-06-01
This work presents the most significant aspects of an original method of modelling and numerical simulation of nonlinear (linear) dynamical systems (1) it assures the local-iterative linearization (LIL) of nonlinear (linear) differential equations and transforms them, in the close proximity of a pivot moment, into algebraic equations. The use of this method is illustrated in the study of a particular nonlinear dynamical systems. The conclusions highlight the advantages of the proposed procedure. {copyright} {ital 1996 American Institute of Physics.}
ERIC Educational Resources Information Center
LAND, KENNETH C.
THIS REPORT PRESENTS A DISCUSSION OF 2 TECHNIQUES WHICH CAN BE USED TO REPRESENT AND INTERPRET MULTIVARIATE STATISTICAL SYSTEMS WHEN IT IS FELT THAT THERE ARE CAUSAL RELATIONS BETWEEN SOME OF THE VARIABLES. THE BASIC TECHNIQUE IS PATH ANALYSIS AND THE OTHER IS ITS EXTENSION THROUGH THE USE OF RECURSIVE SYSTEMS OF EQUATIONS. THE ANALYSIS IS…
Design of a multivariable flutter control/gust load alleviation system
NASA Technical Reports Server (NTRS)
Liebst, B. S.; Garrard, W. L.; Farm, J. A.
1986-01-01
This paper discusses the use of eigenspace techniques for the design of an active flutter control/gust load alleviation system for a hypothetical research drone. One leading edge and two trailing edge aerodynamic surfaces are available for control. Full state control laws are designed for two combinations of control surfaces by selecting feedback gains which place closed loop eigenvalues and shape closed loop eigenvectors so as to stabilize wing flutter and reduce gust loads at the wing root while yielding acceptable robustness and satisfying constraints on rms control surface activity. These controllers are realized by state estimators designed using an eigenvalue placement/eigenvector shaping technique which results in recovery of the loop transfer characteristics of the full state feedback systems. The resulting feedback compensators are shown to perform almost as well as the full state designs. They also exhibit acceptable performance in situations in which the failure of an actuator is simulated.
Multivariable closed loop control analysis and synthesis for complex flight systems
NASA Technical Reports Server (NTRS)
Schmidt, D. K.
1981-01-01
A flight control system analysis and synthesis method is presented that is intended to be especially suitable for application to vehicles exhibiting complex dynamic characteristics. For such vehicles quantitative handling qualities specifications are not usually available. Howver, handling qualities objectives are specifically introduced in this method via the hypothesis of correlation between pilot ratings and the objective function of an optimal control model of the human pilot. Further, since augmentation and pilot operate in parallel, simultaneous determination of the augmentation and pilot model gains is required. Desirable augmented dynamics are obtained for a variety of complex systems and the method is experimentally verified in the case of simple pilot damper gain selection for optimum pitch tracking performance.
Multi-variable mathematical models for the air-cathode microbial fuel cell system
Ou, Shiqi; Kashima, Hiroyuki; Aaron, Douglas S.; Regan, John M.; Mench, Matthew M.
2016-03-10
This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explainmore » elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect we considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). We found simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.« less
Multi-variable mathematical models for the air-cathode microbial fuel cell system
NASA Astrophysics Data System (ADS)
Ou, Shiqi; Kashima, Hiroyuki; Aaron, Douglas S.; Regan, John M.; Mench, Matthew M.
2016-05-01
This research adopted the version control system into the model construction for the single chamber air-cathode microbial fuel cell (MFC) system, to understand the interrelation of biological, chemical, and electrochemical reactions. The anodic steady state model was used to consider the chemical species diffusion and electric migration influence to the MFC performance. In the cathodic steady state model, the mass transport and reactions in a multi-layer, abiotic cathode and multi-bacteria cathode biofilm were simulated. Transport of hydroxide was assumed for cathodic pH change. This assumption is an alternative to the typical notion of proton consumption during oxygen reduction to explain elevated cathode pH. The cathodic steady state model provided the power density and polarization curve performance results that can be compared to an experimental MFC system. Another aspect considered was the relative contributions of platinum catalyst and microbes on the cathode to the oxygen reduction reaction (ORR). Simulation results showed that the biocatalyst in a cathode that includes a Pt/C catalyst likely plays a minor role in ORR, contributing up to 8% of the total power calculated by the models.
Robust Control Design for Uncertain Nonlinear Dynamic Systems
NASA Technical Reports Server (NTRS)
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
Nonlinear dynamics of global atmospheric and Earth system processes
NASA Technical Reports Server (NTRS)
Saltzman, Barry
1993-01-01
During the past eight years, we have been engaged in a NASA-supported program of research aimed at establishing the connection between satellite signatures of the earth's environmental state and the nonlinear dynamics of the global weather and climate system. Thirty-five publications and four theses have resulted from this work, which included contributions in five main areas of study: (1) cloud and latent heat processes in finite-amplitude baroclinic waves; (2) application of satellite radiation data in global weather analysis; (3) studies of planetary waves and low-frequency weather variability; (4) GCM studies of the atmospheric response to variable boundary conditions measurable from satellites; and (5) dynamics of long-term earth system changes. Significant accomplishments from the three main lines of investigation pursued during the past year are presented and include the following: (1) planetary atmospheric waves and low frequency variability; (2) GCM studies of the atmospheric response to changed boundary conditions; and (3) dynamics of long-term changes in the global earth system.
Adaptation with disturbance attenuation in nonlinear control systems
Basar, T.
1997-12-31
We present an optimization-based adaptive controller design for nonlinear systems exhibiting parametric as well as functional uncertainty. The approach involves the formulation of an appropriate cost functional that places positive weight on deviations from the achievement of desired objectives (such as tracking of a reference trajectory while the system exhibits good transient performance) and negative weight on the energy of the uncertainty. This cost functional also translates into a disturbance attenuation inequality which quantifies the effect of the presence of uncertainty on the desired objective, which in turn yields an interpretation for the optimizing control as one that optimally attenuates the disturbance, viewed as the collection of unknown parameters and unknown signals entering the system dynamics. In addition to this disturbance attenuation property, the controllers obtained also feature adaptation in the sense that they help with identification of the unknown parameters, even though this has not been set as the primary goal of the design. In spite of this adaptation/identification role, the controllers obtained are not of certainty-equivalent type, which means that the identification and the control phases of the design are not decoupled.
Nonlinear damage identification of breathing cracks in Truss system
NASA Astrophysics Data System (ADS)
Zhao, Jie; DeSmidt, Hans
2014-03-01
The breathing cracks in truss system are detected by Frequency Response Function (FRF) based damage identification method. This method utilizes damage-induced changes of frequency response functions to estimate the severity and location of structural damage. This approach enables the possibility of arbitrary interrogation frequency and multiple inputs/outputs which greatly enrich the dataset for damage identification. The dynamical model of truss system is built using the finite element method and the crack model is based on fracture mechanics. Since the crack is driven by tensional and compressive forces of truss member, only one damage parameter is needed to represent the stiffness reduction of each truss member. Assuming that the crack constantly breathes with the exciting frequency, the linear damage detection algorithm is developed in frequency/time domain using Least Square and Newton Raphson methods. Then, the dynamic response of the truss system with breathing cracks is simulated in the time domain and meanwhile the crack breathing status for each member is determined by the feedback from real-time displacements of member's nodes. Harmonic Fourier Coefficients (HFCs) of dynamical response are computed by processing the data through convolution and moving average filters. Finally, the results show the effectiveness of linear damage detection algorithm in identifying the nonlinear breathing cracks using different combinations of HFCs and sensors.
Multi-agent motion planning for nonlinear Gaussian systems
NASA Astrophysics Data System (ADS)
Postlethwaite, Ian; Kothari, Mangal
2013-11-01
In this paper, a multi-agent motion planner is developed for nonlinear Gaussian systems using a combination of probabilistic approaches and a rapidly exploring random tree (RRT) algorithm. A closed-loop model consisting of a controller and estimation loops is used to predict future distributions to manage the level of uncertainty in the path planner. The closed-loop model assumes the existence of a feedback control law that drives the actual system towards a nominal system. This ensures the uncertainty in the evolution does not grow significantly and the tracking errors are bounded. To trade conservatism with the risk of infeasibility and failure, we use probabilistic constraints to limit the probability of constraint violation. The probability of leaving the configuration space is included by using a chance constraint approach and the probability of closeness between two agents is imposed using an overlapping coefficient approach. We augment these approaches with the RRT algorithm to develop a robust path planner. Conflict among agents is resolved using a priority-based technique. Numerical results are presented to demonstrate the effectiveness of the planner.
Multivariate analysis and visualization of soil quality data for no-till systems.
Villamil, M B; Miguez, F E; Bollero, G A
2008-01-01
To evidence the multidimensionality of the soil quality concept, we propose the use of data visualization as a tool for exploratory data analyses, model building, and diagnostics. Our objective was to establish the best edaphic indicators for assessing soil quality in four no-till systems with regard to functioning as a medium for crop production and nutrient cycling across two Illinois locations. The compared situations were no-till corn-soybean rotations including either winter fallowing (C/S) or cover crops of rye (Secale cereale; C-R/S-R), hairy vetch (Vicia villosa; C-R/S-V), or their mixture (C-R/S-VR). The dataset included the variables bulk density (BD), penetration resistance (PR), water aggregate stability (WAS), soil reaction (pH), and the contents of soil organic matter (SOM), total nitrogen (TN), soil nitrates (NO(3)-N), and available phosphorus (P). Interactive data visualization along with canonical discriminant analysis (CDA) allowed us to show that WAS, BD, and the contents of P, TN, and SOM have the greatest potential as soil quality indicators in no-till systems in Illinois. It was more difficult to discriminate among WCC rotations than to separate these from C/S, considerably inflating the error rate associated with CDA. We predict that observations of no-till C/S will be classified correctly 51% of the time, while observations of no-till WCC rotations will be classified correctly 74% of the time. High error rates in CDA underscore the complexity of no-till systems and the need in this area for more long-term studies with larger datasets to increase accuracy to acceptable levels. PMID:18948459
Bomb/no bomb: From multivariate analysis to artificial neural systems
NASA Astrophysics Data System (ADS)
Shea, Patrick; Liu, Felix; Yedidia, Barak
1992-05-01
Systems for the detection of explosives hidden in checked airline baggage have been under development at the Science Applications International Corporation (SAIC) for the FAA since 1985. In May of 1987, the first prototype was fielded for testing at San Francisco International Airport. In 1989, the first production unit was field at JFK Airport in New York. Since than, over 550,000 bags have been screened by SAIC units around the world. The system uses thermal neutron activation (TNA) to detect the presence of explosives. In this technique a suitcase on a conveyor belt moves past a source and an array of detectors. Neutrons from the source easily penetrate the luggage, and are absorbed by all of the materials present. Different elements will emit different energy gamma rays after absorbing these neutrons (much like fluorescence). These gamma rays are of a high enough energy that they easily penetrate the luggage, and are detected by a detector array which surrounds the cavity enclosing the suitcase and conveyor belt. The detectors record the number of gamma rays observed at each energy. The number of gamma rays of a characteristic energy which are observed depends on the amount of the element present, its location, the number of neutrons present, and the probability that the element will capture a thermal neutron and emit the gamma ray. Since this probability is a known constant for any particular element, and the number of neutrons present and the number of characteristic gamma rays are measured, the amount of each element and its location can, in theory, be determined from the array of signals. Commercial and military explosives, such as are used by terrorists, have several characteristics which distinguish them from most objects in luggage. On of these characteristics is a high density of nitrogen. A description of the decision algorithms is presented, and the artificial neural system (ANS) is discussed. On-line experience and decision surfaces are also covered.
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems
DOE R&D Accomplishments Database
McMillan, E. M.
1967-09-05
A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
Projection methods for solving nonlinear systems of equations
Brown, P.N. ); Saad, Y. . Ames Research Center)
1990-04-01
This paper describes several nonlinear projection methods based on Krylov subspaces and analyzes their convergence. The prototype of these methods is a technique that generalizes the conjugate direction method by minimizing the norm of the function F over some subspace. The emphasis of this paper is on nonlinear least squares problems which can also be handled by this general approach.
Overview of nonlinear dynamical systems and complexity theory
Herbert, D.E.
1996-06-01
A brief overview is presented of the principal elements of {open_quote}{open_quote}nonlinear dynamics{close_quote}{close_quote}: catastrophes, fractals, chaos, solitary waves, and coherent and dissipative structures. The text is followed by a set of 10 portraits of the strange and violent world of nonlinear dynamics. {copyright} {ital 1996 American Institute of Physics.}
Nonlinear phase field model for electrodeposition in electrochemical systems
Liang, Linyun; Chen, Long-Qing
2014-12-29
A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.
Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems
NASA Astrophysics Data System (ADS)
Gomes, Susana; Pradas, Marc; Kalliadasis, Serafim; Papageorgiou, Demetrios; Pavliotis, Grigorios
2015-11-01
We present a novel generic methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. The methodology is exemplified with the generalized Kuramoto-Sivashinsky equation, the simplest possible prototype that retains that fundamental elements of any nonlinear process involving wave evolution. The equation is applicable on a wide variety of systems including falling liquid films and plasma waves with dispersion due to finite banana width. We show that applying the appropriate choice of time-dependent feedback controls via blowing and suction, we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, travelling waves and spatiotemporal chaos, but also use the controls obtained to stabilize the solutions to more general long wave models. We acknowledge financial support from Imperial College through a Roth PhD studentship, Engineering and Physical Sciences Research Council of the UK through Grants No. EP/H034587, EP/J009636, EP/K041134, EP/L020564 and EP/L024926 and European Research Council via Advanced Grant No. 247031.
Thermostatistics of small nonlinear systems: Poissonian athermal bath
NASA Astrophysics Data System (ADS)
Morgado, Welles A. M.; Queirós, Sílvio M. Duarte
2016-01-01
We extend an earlier study [W. A. M. Morgado and S. M. Duarte Queirós, Phys. Rev. E 90, 022110 (2014), 10.1103/PhysRevE.90.022110] to the case of a small system subject to nonlinear interaction and in contact with an athermal shot-noise reservoir. We first focus on steady state properties, namely, on the impact of the singular measure of the reservoir in the steady state energy. We introduce the concept of temperatures of higher order, which aim to represent the effect produced by the cumulants of the noise of order larger than 2 in the form of sources of energy of higher order and new response functions such as high-order specific heats that zero out when the system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the heat and energy fluxes and determine asymptotic expressions for its large deviation functions. Finally, by analyzing the probabilistics of the injected power, we verify that the exponential form of its fluctuation relation is only asymptotically valid, whereas in the thermal case it is valid for the injected power at all times.
Limit cycle analysis of active disturbance rejection control system with two nonlinearities.
Wu, Dan; Chen, Ken
2014-07-01
Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function. PMID:24795034
Tesfalidet, Solomon; Geladi, Paul; Shimizu, Kenichi; Lindholm-Sethson, Britta
2016-03-31
Methotrexate (MTX), a common pharmaceutical drug in cancer therapy and treatment of rheumatic diseases, is known to cause severe adverse side effects at high dose. As the side effect may be life threatening, there is an urgent need for a continuous, bed-side monitoring of the nominal MTX serum level in a patient while the chemical is being administered. This article describes a detection of MTX using a flow system that consists two modified gold electrodes. Interaction of MTX with the antibodies fixed on the electrode surface is detected by electrochemical impedance spectroscopy and evaluated using singular value decomposition (SVD). The key finding of this work is that the change in the electrode capacitance is found to be quantitative with respect to the concentration of MTX. Moreover a calibration curve constructed using the principal component regression method has a linear range of six orders of magnitude and a detection limit of 1.65 × 10(-10) M. PMID:26965322
Identification of limit cycles in multi-nonlinearity, multiple path systems
NASA Technical Reports Server (NTRS)
Mitchell, J. R.; Barron, O. L.
1979-01-01
A method of analysis which identifies limit cycles in autonomous systems with multiple nonlinearities and multiple forward paths is presented. The FORTRAN code for implementing the Harmonic Balance Algorithm is reported. The FORTRAN code is used to identify limit cycles in multiple path and nonlinearity systems while retaining the effects of several harmonic components.
On the estimation of the attainability set of nonlinear control systems
Ekimov, A.V.; Balykina, Yu.E.; Svirkin, M.V.
2015-03-10
Analysis of the attainability set and construction of its estimates greatly facilitates the solution of a variety of problems in mathematical control theory. In the paper, the problem of boundedness of the integral funnel of nonlinear controlled system is considered. Some estimates of the attainability sets for a nonlinear controlled system are presented. Theorems on the boundedness of considered integral funnels are proved.
NASA Technical Reports Server (NTRS)
Behbehani, K.
1980-01-01
A new sensor/actuator failure analysis technique for turbofan jet engines was developed. Three phases of failure analysis, namely detection, isolation, and accommodation are considered. Failure detection and isolation techniques are developed by utilizing the concept of Generalized Likelihood Ratio (GLR) tests. These techniques are applicable to both time varying and time invariant systems. Three GLR detectors are developed for: (1) hard-over sensor failure; (2) hard-over actuator failure; and (3) brief disturbances in the actuators. The probability distribution of the GLR detectors and the detectability of sensor/actuator failures are established. Failure type is determined by the maximum of the GLR detectors. Failure accommodation is accomplished by extending the Multivariable Nyquest Array (MNA) control design techniques to nonsquare system designs. The performance and effectiveness of the failure analysis technique are studied by applying the technique to a turbofan jet engine, namely the Quiet Clean Short Haul Experimental Engine (QCSEE). Single and multiple sensor/actuator failures in the QCSEE are simulated and analyzed and the effects of model degradation are studied.
Identification of nonlinear dynamic systems using functional link artificial neural networks.
Patra, J C; Pal, R N; Chatterji, B N; Panda, G
1999-01-01
We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of functional expansion in a FLANN, this network performs as good as and in some cases even better than the MLP structure for the problem of nonlinear system identification. PMID:18252296
Develop Advanced Nonlinear Signal Analysis Topographical Mapping System
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1997-01-01
During the development of the SSME, a hierarchy of advanced signal analysis techniques for mechanical signature analysis has been developed by NASA and AI Signal Research Inc. (ASRI) to improve the safety and reliability for Space Shuttle operations. These techniques can process and identify intelligent information hidden in a measured signal which is often unidentifiable using conventional signal analysis methods. Currently, due to the highly interactive processing requirements and the volume of dynamic data involved, detailed diagnostic analysis is being performed manually which requires immense man-hours with extensive human interface. To overcome this manual process, NASA implemented this program to develop an Advanced nonlinear signal Analysis Topographical Mapping System (ATMS) to provide automatic/unsupervised engine diagnostic capabilities. The ATMS will utilize a rule-based Clips expert system to supervise a hierarchy of diagnostic signature analysis techniques in the Advanced Signal Analysis Library (ASAL). ASAL will perform automatic signal processing, archiving, and anomaly detection/identification tasks in order to provide an intelligent and fully automated engine diagnostic capability. The ATMS has been successfully developed under this contract. In summary, the program objectives to design, develop, test and conduct performance evaluation for an automated engine diagnostic system have been successfully achieved. Software implementation of the entire ATMS system on MSFC's OISPS computer has been completed. The significance of the ATMS developed under this program is attributed to the fully automated coherence analysis capability for anomaly detection and identification which can greatly enhance the power and reliability of engine diagnostic evaluation. The results have demonstrated that ATMS can significantly save time and man-hours in performing engine test/flight data analysis and performance evaluation of large volumes of dynamic test data.
Multiscale Analysis of Nonlinear Systems Using Computational Topology
Schatz, Michael F.; Mischaikow, Konstantin; Kalies, William; Wanner, Thomas
2010-08-31
Computational Homology in Fluids: M. Schatz, K. Mischaikow. This effort focused on characterizing both the structure and dynamics of complex spatio-temporal flows that arise in thermal convection. Microstructure Characterization: T. Wanner, K. Mischaikow. We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. Probabilistic Homology Validation: W. Kalies, T. Wanner, K. Mischaikow. Our above mentioned work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. Computational Homology and Dynamics: W. Kalies, T. Wanner, K. Mischaikow. Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. Stress Networks in Polycrystals: T. Wanner. Together with E. Fuller (NIST) and D. Saylor (FDA) we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. Microstructure-Controlled Drug Release: K. Mischaikow, T. Wanner. This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. Microstructure of Fuel Cells: W. Kalies, K. Mischaikow. In collaboration with P. Voorhees (Northwestern Univ.) and M. Gameiro (Rutgers) we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid
Advanced data assimilation in strongly nonlinear dynamical systems
NASA Technical Reports Server (NTRS)
Miller, Robert N.; Ghil, Michael; Gauthiez, Francois
1994-01-01
Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
NASA Technical Reports Server (NTRS)
Murthy, V. R.; Shultz, Louis A.
1994-01-01
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Nonlinear System Identification for Aeroelastic Systems with Application to Experimental Data
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.
2008-01-01
Representation and identification of a nonlinear aeroelastic pitch-plunge system as a model of the Nonlinear AutoRegressive, Moving Average eXogenous (NARMAX) class is considered. A nonlinear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (1) the outputs of the NARMAX model closely match those generated using continuous-time methods, and (2) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
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. PMID:24012389
Toward a nonlinear ensemble filter for high-dimensional systems
NASA Astrophysics Data System (ADS)
Bengtsson, Thomas; Snyder, Chris; Nychka, Doug
2003-12-01
Many geophysical problems are characterized by high-dimensional, nonlinear systems and pose difficult challenges for real-time data assimilation (updating) and forecasting. The present work builds on the ensemble Kalman filter (EnsKF), with the goal of producing ensemble filtering techniques applicable to non-Gaussian densities and high-dimensional systems. Three filtering algorithms, based on representing the prior density as a Gaussian mixture, are presented. The first, referred to as a mixture ensemble Kalman filter (XEnsF), models local covariance structures adaptively using nearest neighbors. The XEnsF is effective in a three-dimensional system, but the required ensemble grows rapidly with the dimension and, even in a 40-dimensional system, we find the XEnsF to be unstable and inferior to the EnsKF for all computationally feasible ensemble sizes. A second algorithm, the local-local ensemble filter (LLEnsF), combines localizations in physical as well as phase space, allowing the update step in high-dimensional systems to be decomposed into a sequence of lower-dimensional updates tractable by the XEnsF. Given the same prior forecasts in a 40-dimensional system, the LLEnsF update produces more accurate state estimates than the EnsKF if the forecast distributions are sufficiently non-Gaussian. Cycling the LLEnsF for long times, however, produces results inferior to the EnsKF because the LLEnsF ignores spatial continuity or smoothness between local state estimates. To address this weakness of the LLEnsF, we consider ways of enforcing spatial smoothness by conditioning the local updates on the prior estimates outside the localization in physical space. These considerations yield a third algorithm, which is a hybrid of the LLEnsF and the EnsKF. The hybrid uses information from the EnsKF to ensure spatial continuity of local updates and outperforms the EnsKF by 5.7% in RMS error in the 40-dimensional system.
Perturbation Methods and Closure Approximations in Nonlinear Systems.
NASA Astrophysics Data System (ADS)
Dubin, Daniel Herschel Eli
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, we consider the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. For small Larmor radius the equations are similar to those of Lee. Several new effects appear which are absent from conventional theories. We show that the wave kinetic equation of Galeev and Sagdeev neglects several important gyrokinetic effects. In the second section, statistical closure theories are applied to simple dynamical systems. We use the logistic map as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the Direct Interaction Approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodicity constraint on a Langevin form of the D.I.A. a new stable closure is developed. The relation between the predictability theory of Kraichnan and the theory of Liapunov exponents is considered. Realizability constraints on the moments of a distribution are formulated using Kuhn-Tucker multipliers. Results are related to the work of Sandri and Kraichnan, but the variational technique employed allows for a more elegant and general approach. The realizability criteria are
Nonlinearity management in fiber transmission systems with hybrid amplification
NASA Astrophysics Data System (ADS)
Ania-Castañón, J. D.; Nasieva, I. O.; Kurukitkoson, N.; Turitsyn, S. K.; Borsier, C.; Pincemin, E.
2004-04-01
Nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-Erbium doped fiber amplification is studied both analytically and numerically. Different transmission/compensating fiber pairs are considered, with particular focus on the SMF/DCF case.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis. PMID:27347461
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum
DOE R&D Accomplishments Database
McMillan, Edwin M.
1968-03-29
Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
NASA Technical Reports Server (NTRS)
Hays, J. R.
1969-01-01
Lumped parametric system models are simplified and computationally advantageous in the frequency domain of linear systems. Nonlinear least squares computer program finds the least square best estimate for any number of parameters in an arbitrarily complicated model.
A method for zooming of nonlinear models of biochemical systems
2011-01-01
Background Models of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model. Results In this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved. Conclusions We introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to
A nonlinear lumped model for ultrasound systems using CMUT arrays.
Satir, Sarp; Degertekin, F Levent
2015-10-01
We present a nonlinear lumped model that predicts the electrical input-output behavior of an ultrasonic system using CMUTs with arbitrary array/membrane/electrode geometry in different transmit-receive configurations and drive signals. The receive-only operation, where the electrical output signal of the CMUT array in response to incident pressure field is calculated, is included by modifying the boundary elementbased vibroacoustic formulation for a CMUT array in rigid baffle. Along with the accurate large signal transmit model, this formulation covers pitch-catch and pulse-echo operation when transmit and receive signals can be separated in time. In cases when this separation is not valid, such as CMUTs used in continuous wave transmit-receive mode, pulse-echo mode with a nearby hard or soft wall or in a bounded space such as in a microfluidic channel, an efficient formulation based on the method of images is used. Some of these particular applications and the overall modeling approach have been validated through comparison with finite element analysis on specific examples including CMUTs with multiple electrodes. To further demonstrate the capability of the model for imaging applications, the two-way response of a partial dual-ring intravascular ultrasound array is simulated using a parallel computing cluster, where the output currents of individual array elements are calculated for given input pulse and compared with experimental results. With its versatility, the presented model can be a useful tool for rapid iterative CMUT-based system design and simulation for a broad range of ultrasonic applications. PMID:26470049
Lin, Tai-Chia; Belić, Milivoj R.; Petrović, Milan S.; Chen, Goong
2014-01-15
Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip
2016-01-01
In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example. PMID:26353383
Andrianov, I.V.; Danishevsky, V.V.
1994-12-31
Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions.
Modeling a multivariable reactor and on-line model predictive control.
Yu, D W; Yu, D L
2005-10-01
A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown. PMID:16294779
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space-stnuctures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore for the second case the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems including flexible space-structures with articulated flexible appendages.
NASA Technical Reports Server (NTRS)
Kelkar, Atul G.; Joshi, Suresh M.
1994-01-01
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
MacDonald, Shannon E; Schopflocher, Donald P; Vaudry, Wendy
2014-01-01
Children who begin but do not fully complete the recommended series of childhood vaccines by 2 y of age are a much larger group than those who receive no vaccines. While parents who refuse all vaccines typically express concern about vaccine safety, it is critical to determine what influences parents of ‘partially’ immunized children. This case-control study examined whether parental concern about vaccine safety was responsible for partial immunization, and whether other personal or system-level factors played an important role. A random sample of parents of partially and completely immunized 2 y old children were selected from a Canadian regional immunization registry and completed a postal survey assessing various personal and system-level factors. Unadjusted odds ratios (OR) and adjusted ORs (aOR) were calculated with logistic regression. While vaccine safety concern was associated with partial immunization (OR 7.338, 95% CI 4.138– 13.012), other variables were more strongly associated and reduced the strength of the relationship between concern and partial immunization in multivariable analysis (aOR 2.829, 95% CI 1.151 – 6.957). Other important factors included perceived disease susceptibility and severity (aOR 4.629, 95% CI 2.017 – 10.625), residential mobility (aOR 3.908, 95% CI 2.075 – 7.358), daycare use (aOR 0.310, 95% CI 0.144 - 0.671), number of needles administered at each visit (aOR 7.734, 95% CI 2.598 – 23.025) and access to a regular physician (aOR 0.219, 95% CI 0.057 – 0.846). While concern about vaccine safety may be addressed through educational strategies, this study suggests that additional program and policy-level strategies may positively impact immunization uptake. PMID:25483477
Okazaki, Shuntaro; Hirotani, Masako; Koike, Takahiko; Bosch-Bayard, Jorge; Takahashi, Haruka K.; Hashiguchi, Maho; Sadato, Norihiro
2015-01-01
People’s behaviors synchronize. It is difficult, however, to determine whether synchronized behaviors occur in a mutual direction—two individuals influencing one another—or in one direction—one individual leading the other, and what the underlying mechanism for synchronization is. To answer these questions, we hypothesized a non-leader-follower postural sway synchronization, caused by a reciprocal visuo-postural feedback system operating on pairs of individuals, and tested that hypothesis both experimentally and via simulation. In the behavioral experiment, 22 participant pairs stood face to face either 20 or 70 cm away from each other wearing glasses with or without vision blocking lenses. The existence and direction of visual information exchanged between pairs of participants were systematically manipulated. The time series data for the postural sway of these pairs were recorded and analyzed with cross correlation and causality. Results of cross correlation showed that postural sway of paired participants was synchronized, with a shorter time lag when participant pairs could see one another’s head motion than when one of the participants was blindfolded. In addition, there was less of a time lag in the observed synchronization when the distance between participant pairs was smaller. As for the causality analysis, noise contribution ratio (NCR), the measure of influence using a multivariate autoregressive model, was also computed to identify the degree to which one’s postural sway is explained by that of the other’s and how visual information (sighted vs. blindfolded) interacts with paired participants’ postural sway. It was found that for synchronization to take place, it is crucial that paired participants be sighted and exert equal influence on one another by simultaneously exchanging visual information. Furthermore, a simulation for the proposed system with a wider range of visual input showed a pattern of results similar to the behavioral
Parametric and nonparametric nonlinear system identification of lung tissue strip mechanics.
Yuan, H; Westwick, D T; Ingenito, E P; Lutchen, K R; Suki, B
1999-01-01
Lung parenchyma is a soft biological material composed of many interacting elements such as the interstitial cells, extracellular collagen-elastin fiber network, and proteoglycan ground substance. The mechanical behavior of this delicate structure is complex showing several mild but distinct types of nonlinearities and a fractal-like long memory stress relaxation characterized by a power-law function. To characterize tissue nonlinearity in the presence of such long memory, we investigated the robustness and predictive ability of several nonlinear system identification techniques on stress-strain data obtained from lung tissue strips with various input wave forms. We found that in general, for a mildly nonlinear system with long memory, a nonparametric nonlinear system identification in the frequency domain is preferred over time-domain techniques. More importantly, if a suitable parametric nonlinear model is available that captures the long memory of the system with only a few parameters, high predictive ability with substantially increased robustness can be achieved. The results provide evidence that the first-order kernel of the stress-strain relationship is consistent with a fractal-type long memory stress relaxation and the nonlinearity can be described as a Wiener-type nonlinear structure for displacements mimicking tidal breathing. PMID:10468239
A nonlinear screen as an element for sound absorption and frequency conversion systems
NASA Astrophysics Data System (ADS)
Rudenko, O. V.
2016-01-01
The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications are described.
On Schrödinger systems with cubic dissipative nonlinearities of derivative type
NASA Astrophysics Data System (ADS)
Li, Chunhua; Sunagawa, Hideaki
2016-05-01
Consider the initial value problem for systems of cubic derivative nonlinear Schrödinger equations in one space dimension with the masses satisfying a suitable resonance relation. We give structural conditions on the nonlinearity under which the small data solution gains an additional logarithmic decay as t\\to +∞ compared with the corresponding free evolution.
Is DNA a nonlinear dynamical system where solitary conformational waves are possible?
Yakushevich, L V
2001-09-01
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA's nonlinear properties. PMID:11568475
Garbow, B.S.; Hillstrom, K.E.; More, J.J.
1980-07-01
MINPACK-1 is a package of Fortran subprograms for the numerical solution of systems of nonlinear equations and nonlinear least-squares problems. This report describes how to implement the package from the tape on which it is transmitted. 3 tables.
The peak response distributions of structure-DVA systems with nonlinear damping
NASA Astrophysics Data System (ADS)
Love, J. S.; Tait, M. J.
2015-07-01
Dynamic vibration absorbers (DVAs) with nonlinear damping are often modelled using a power-law equivalent viscous damping relationship. There is currently not a method available to predict the peak response of this type of nonlinear DVA without resorting to computationally expensive nonlinear simulations. Since the peak response of the DVA is required during the design process, it is advantageous to have a simplified method to estimate the peak response. In this study, statistical linearization is employed to represent the nonlinear damping as amplitude-dependent viscous damping and predict the rms response of the structure-DVA system. Subsequently, statistical nonlinearization is used to describe the probability density function of the DVA response amplitude. A probability density function is developed, which enables the peak response expected during an interval of time (e.g. 1-h) to be estimated from the rms response of the structure-DVA system. Higher power-law damping exponents are shown to result in smaller peak factors. Results of nonlinear simulations reveal that the model can estimate the peak structural and DVA responses with acceptable accuracy. A plot is developed to show the peak factors for nonlinear DVAs as a function of the number of system cycles for several power-law damping exponents. This plot can be used to estimate the peak response of a nonlinear DVA as a function of its rms response.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller. PMID:24021543
Discrete-time neural inverse optimal control for nonlinear systems via passivation.
Ornelas-Tellez, Fernando; Sanchez, Edgar N; Loukianov, Alexander G
2012-08-01
This paper presents a discrete-time inverse optimal neural controller, which is constituted by combination of two techniques: 1) inverse optimal control to avoid solving the Hamilton-Jacobi-Bellman equation associated with nonlinear system optimal control and 2) on-line neural identification, using a recurrent neural network trained with an extended Kalman filter, in order to build a model of the assumed unknown nonlinear system. The inverse optimal controller is based on passivity theory. The applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot. PMID:24807528
Yang, Zaiyue; Yang, Qinmin; Sun, Youxian
2015-08-01
This brief considers the asymptotic tracking problem for a class of high-order nonaffine nonlinear dynamical systems with nonsmooth actuator nonlinearities. A novel transformation approach is proposed, which is able to systematically transfer the original nonaffine nonlinear system into an equivalent affine one. Then, to deal with the unknown dynamics and unknown control coefficient contained in the affine system, online approximator and Nussbaum gain techniques are utilized in the controller design. It is proven rigorously that asymptotic convergence of the tracking error and ultimate uniform boundedness of all the other signals can be guaranteed by the proposed control method. The control feasibility is further verified by numerical simulations. PMID:25265633
Transitions to broad cells in a nonlinear thermal convection system
NASA Astrophysics Data System (ADS)
Fiedler, Brian H.
This paper explores the properties of a two-dimensional, Boussinesq convection model with an ad hoc term in the buoyancy tendency equation that represents a positive external feedback process acting on the buoyancy fluctuations. Linear stability analyses and nonlinear integrations are presented for the case of constant heat flux boundary conditions. Although the large wavenumber modes grow the fastest from a state of rest, the nonlinear solutions progressively evolve to cells of small wavenumber. Applications to mesoscale cellular convection in the atmosphere are discussed.
NASA Astrophysics Data System (ADS)
Venkatapathi, Murugesan; Rajwa, Bartek; Ragheb, Kathy; Banada, Padmapriya P.; Lary, Todd; Robinson, J. Paul; Hirleman, E. Daniel
2008-02-01
We describe a model-based instrument design combined with a statistical classification approach for the development and realization of high speed cell classification systems based on light scatter. In our work, angular light scatter from cells of four bacterial species of interest, Bacillus subtilis, Escherichia coli, Listeria innocua, and Enterococcus faecalis, was modeled using the discrete dipole approximation. We then optimized a scattering detector array design subject to some hardware constraints, configured the instrument, and gathered experimental data from the relevant bacterial cells. Using these models and experiments, it is shown that optimization using a nominal bacteria model (i.e., using a representative size and refractive index) is insufficient for classification of most bacteria in realistic applications. Hence the computational predictions were constituted in the form of scattering-data-vector distributions that accounted for expected variability in the physical properties between individual bacteria within the four species. After the detectors were optimized using the numerical results, they were used to measure scatter from both the known control samples and unknown bacterial cells. A multivariate statistical method based on a support vector machine (SVM) was used to classify the bacteria species based on light scatter signatures. In our final instrument, we realized correct classification of B. subtilis in the presence of E. coli,L. innocua, and E. faecalis using SVM at 99.1%, 99.6%, and 98.5%, respectively, in the optimal detector array configuration. For comparison, the corresponding values for another set of angles were only 69.9%, 71.7%, and 70.2% using SVM, and more importantly, this improved performance is consistent with classification predictions.
Correlation techniques to determine model form in robust nonlinear system realization/identification
NASA Technical Reports Server (NTRS)
Stry, Greselda I.; Mook, D. Joseph
1991-01-01
The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.
Analysis of start-up transient for a powertrain system with a nonlinear clutch damper
NASA Astrophysics Data System (ADS)
Li, Laihang; Singh, Rajendra
2015-10-01
The transient vibration phenomenon in a vehicle powertrain system during the start-up (or shut-down) process is studied with a focus on the nonlinear characteristics of a multi-staged clutch damper. First, a four-degree-of-freedom torsional model with multiple discontinuous nonlinearities under flywheel motion input is developed, and the powertrain transient event is validated with a vehicle start-up experiment. Second, the role of the nonlinear torsional path on the transient event is investigated in the time and time-frequency domains; interactions between the clutch damper and the transmission transients are estimated by using two metrics. Third, the harmonic balance method is applied to examine the nonlinear characteristics of clutch damper during a slowly varying non-stationary process in a simplified and validated single-degree-of-freedom powertrain system model. Finally, analytical formulas are successfully developed and verified to approximate the nonlinear amplification level for a rapidly varying process.
Noise-induced transitions and resonant effects in nonlinear systems
NASA Astrophysics Data System (ADS)
Zaikin, Alexei
2003-02-01
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences. Unsere alltägliche Erfahrung ist mit verschiedenen akustischen Einfluessen wie Lärm, aber auch Musik verbunden. Jeder weiss, wie Lärm stören kann und Kommunikation behindert oder gar unterbindet. Ähnliche optische Effekte sind bekannt: starkes Schneetreiben oder Regengüsse verschlechtern die Sicht und lassen uns Umrisse nur noch schemenhaft erkennen. Jedoch koennen ähnliche Stimuli auch sehr positive Auswirkungen haben: Autofahrer fahren bei leiser Musik konzentrierter -- die Behauptung von Schulkindern, nur bei dröhnenden Bässen die Mathehausaufgaben richtig rechnen zu können, ist allerdings nicht wissenschaftlich
Teaching and Learning the Interplay Between Chance and Determinism in Nonlinear Systems
NASA Astrophysics Data System (ADS)
Stavrou, Dimitrios; Duit, Reinders
2014-02-01
That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear systems in school science instruction. An analysis of the relevant scientific literature and an explorative learning process study with 30 11th-grade students are included. Three experiments displaying the behaviour of nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment demonstrating the behaviour of linear systems were discussed using a teaching experiment design. The findings show that although the majority of students initially considered chance and determinism as contradictory conceptions, they finally developed sound explanations concerning the interplay of chance and determinism in the investigated nonlinear systems.
Formation of nonlinear holographic images in powerful laser systems.
Bel'kov, Sergey A; Garanin, Sergey G; Epatko, Igor V; Serov, Rene V; Voronich, Ivan N
2012-08-20
The formation of nonlinear holographic images behind a multislab amplifier is studied. The analytical expressions describing magnitudes and locations of intensity maxima depending on the corresponding image number are derived. Comparison with numerical calculations results is given. On the basis of numerical modeling, analysis of gain saturation, slab thickness, and slab aberrations influence is carried out. PMID:22907023
Robust Model-Based Sensor Fault Monitoring System for Nonlinear Systems in Sensor Networks
Wang, Dejun; Song, Shiyao
2014-01-01
A new model-based sensor fault diagnosis (FD) scheme, using an equivalent model, is developed for a kind of Multiple Inputs Multiple Outputs (MIMO) nonlinear system which fulfills the Lipschitz condition. The equivalent model, which is a bank of one-dimensional linear state equations with the bounded model uncertainty, can take the place of a plant's exact nonlinear model in the case of sensor FD. This scheme shows a new perspective whereby, by using the equivalent model, it doesn't have to study the nonlinear internal structure character or get the exact model. The influence of the model uncertainty on the residuals is explained in this paper. A method, called pretreatment, is utilized to minimize the model uncertainty. The eigenstructure assignment method with assistant state is employed to solve the problem of perfect decoupling against the model uncertainty, disturbance, system faults, the relevant actuator faults, or even the case of no input from the relevant actuator. The realization of the proposed scheme is given by an algorithm according to a single sensor FD, and verified by a simulation example. Depending on the above, a sensor fault monitoring system is established by the sensor network and diagnosis logic, then the effectiveness is testified by a simulation. PMID:25320904
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1993-01-01
A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.
Multivariate respiratory motion prediction
NASA Astrophysics Data System (ADS)
Dürichen, R.; Wissel, T.; Ernst, F.; Schlaefer, A.; Schweikard, A.
2014-10-01
In extracranial robotic radiotherapy, tumour motion is compensated by tracking external and internal surrogates. To compensate system specific time delays, time series prediction of the external optical surrogates is used. We investigate whether the prediction accuracy can be increased by expanding the current clinical setup by an accelerometer, a strain belt and a flow sensor. Four previously published prediction algorithms are adapted to multivariate inputs—normalized least mean squares (nLMS), wavelet-based least mean squares (wLMS), support vector regression (SVR) and relevance vector machines (RVM)—and evaluated for three different prediction horizons. The measurement involves 18 subjects and consists of two phases, focusing on long term trends (M1) and breathing artefacts (M2). To select the most relevant and least redundant sensors, a sequential forward selection (SFS) method is proposed. Using a multivariate setting, the results show that the clinically used nLMS algorithm is susceptible to large outliers. In the case of irregular breathing (M2), the mean root mean square error (RMSE) of a univariate nLMS algorithm is 0.66 mm and can be decreased to 0.46 mm by a multivariate RVM model (best algorithm on average). To investigate the full potential of this approach, the optimal sensor combination was also estimated on the complete test set. The results indicate that a further decrease in RMSE is possible for RVM (to 0.42 mm). This motivates further research about sensor selection methods. Besides the optical surrogates, the sensors most frequently selected by the algorithms are the accelerometer and the strain belt. These sensors could be easily integrated in the current clinical setup and would allow a more precise motion compensation.
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow; Michael Schatz; William Kalies; Thomas Wanner
2010-05-24
- We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow, Rutgers University /Georgia Institute of Technology, Michael Schatz, Georgia Institute of Technology, William Kalies, Florida Atlantic University, Thomas Wanner,George Mason University
2010-05-19
- We extended our previous work on studying the time evolution of patterns associated with phase separation in conserved concentration fields. (6) Probabilistic Homology Validation - work on microstructure characterization is based on numerically studying the homology of certain sublevel sets of a function, whose evolution is described by deterministic or stochastic evolution equations. (7) Computational Homology and Dynamics - Topological methods can be used to rigorously describe the dynamics of nonlinear systems. We are approaching this problem from several perspectives and through a variety of systems. (8) Stress Networks in Polycrystals - we have characterized stress networks in polycrystals. This part of the project is aimed at developing homological metrics which can aid in distinguishing not only microstructures, but also derived mechanical response fields. (9) Microstructure-Controlled Drug Release - This part of the project is concerned with the development of topological metrics in the context of controlled drug delivery systems, such as drug-eluting stents. We are particularly interested in developing metrics which can be used to link the processing stage to the resulting microstructure, and ultimately to the achieved system response in terms of drug release profiles. (10) Microstructure of Fuel Cells - we have been using our computational homology software to analyze the topological structure of the void, metal and ceramic components of a Solid Oxide Fuel Cell.
Finite-time H∞ filtering for non-linear stochastic systems
NASA Astrophysics Data System (ADS)
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Optimal feedback control of strongly non-linear systems excited by bounded noise
NASA Astrophysics Data System (ADS)
Zhu, W. Q.; Huang, Z. L.; Ko, J. M.; Ni, Y. Q.
2004-07-01
A strategy for non-linear stochastic optimal control of strongly non-linear systems subject to external and/or parametric excitations of bounded noise is proposed. A stochastic averaging procedure for strongly non-linear systems under external and/or parametric excitations of bounded noise is first developed. Then, the dynamical programming equation for non-linear stochastic optimal control of the system is derived from the averaged Itô equations by using the stochastic dynamical programming principle and solved to yield the optimal control law. The Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations is solved to give the response of optimally controlled system. The application and effectiveness of the proposed control strategy are illustrated with the control of cable vibration in cable-stayed bridges and the feedback stabilization of the cable under parametric excitation of bounded noise.
Analysis of some large-scale nonlinear stochastic dynamic systems with subspace-EPC method
NASA Astrophysics Data System (ADS)
Er, GuoKang; Iu, VaiPan
2011-09-01
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method. PMID:25420238
Russev, S H
1989-04-15
Systematic errors due to nonlinearity and polarization-dependent sensitivity in the detection system of rotating analyzer ellipsometers are described. Post Fourier analysis procedures for detection and correction of these effects are presented. PMID:20548687
Vacuum Rabi splitting effect in nanomechanical QED system with nonlinear resonator
NASA Astrophysics Data System (ADS)
Zhao, MingYue; Gao, YiBo
2016-08-01
Considering the intrinsic nonlinearity in a nanomechanical resonator coupled to a charge qubit, vacuum Rabi splitting effect is studied in a nanomechanical QED (qubit-resonator) system. A driven nonlinear Jaynes-Cummings model describes the dynamics of this qubit-resonator system. Using quantum regression theorem and master equation approach, we have calculated the two-time correlation spectrum analytically. In the weak driving limit, these analytical results clarify the influence of the driving strength and nonlinearity parameter on the correlation spectrum. Also, numerical calculations confirm these analytical results.
Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay
NASA Astrophysics Data System (ADS)
Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai
2016-08-01
In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.
Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
NASA Astrophysics Data System (ADS)
Colli, Pierluigi; Fukao, Takeshi
2016-05-01
An asymptotic limit of a class of Cahn-Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose-Fife type, fast diffusion equation and so on. Namely, by setting the suitable potential of the Cahn-Hilliard systems, all these problems can be obtained as limits of the Cahn-Hilliard related problems. Convergence results and error estimates are proved.
NASA Astrophysics Data System (ADS)
Aghababa, Mohammad Pourmahmood
2012-03-01
The aim of this note is to point out some comments to the article [Delavari H, Ghaderi R, Ranjbar A, Momani S. Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963-978].
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement. PMID:25532936
NASA Astrophysics Data System (ADS)
Collin, E.; Bunkov, Yu. M.; Godfrin, H.
2010-12-01
We report on low-temperature measurements performed on microelectromechanical systems driven deeply into the nonlinear regime. The materials are kept in their elastic domain while the observed nonlinearity is purely of geometrical origin. Two techniques are used, harmonic drive and free decay. For each case, we present an analytic theory fitting the data. The harmonic drive is fit with a modified Lorentzian line shape obtained from an extended version of Landau and Lifshitz’s nonlinear theory. The evolution in the time domain is fit with an amplitude-dependent frequency decaying function derived from the Lindstedt-Poincaré theory of nonlinear differential equations. The technique is perfectly generic and can be straightforwardly adapted to any mechanical device made of ideally elastic constituents, and which can be reduced to a single degree of freedom, for an experimental definition of its nonlinear dynamics equation.
Landau-Zener tunneling in a nonlinear three-level system
Wang Guanfang; Ye Difa; Fu Libin; Liu Jie; Chen Xuzong
2006-09-15
We present a comprehensive analysis of the Landau-Zener tunneling of a nonlinear three-level system in a linearly sweeping external field. We find the presence of nonzero tunneling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of the linear case. In particular, the tunneling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunneling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunneling probability when the nonlinear 'internal field' resonate with the external field. We also discuss the asymmetry of the tunneling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.
Time domain simulation of nonlinear response of a coupled TLP system in random seas
Kim, C.H.; Kim, M.H.; Liu, Y.H.; Zhao, C.T.
1994-12-31
This paper presents a result of an analysis of the nonlinear interaction and response of the coupled ISSC-TLP System to the random seas in the time domain. The environmental load also includes the effect of the concurrent steady winds and currents. The first- and second-order wave-exciting forces are calculated using a robust higher-order boundary element method (HOBEM), while the nonlinear tendon dynamic analysis is performed using the three-dimensional hybrid element method with the upgated Lagrangian formulation. The Morison equation is employed for the wave and current load on slender structures. The analysis is focused on the nonlinear responses due to the nonlinear environmental load and nonlinear interaction between the platform and tendons that includes the offset, setdown, large coupled surge-heave motion in the low frequency and resonant heave/pitch responses with the springing loads in the high frequency.
The effect of problem perturbations on nonlinear dynamical systems and their reduced order models
Serban, R; Homescu, C; Petzold, L
2005-03-03
Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'
Approximated Stable Inversion for Nonlinear Systems with Nonhyperbolic Internal Dynamics. Revised
NASA Technical Reports Server (NTRS)
Devasia, Santosh
1999-01-01
A technique to achieve output tracking for nonminimum phase nonlinear systems with non- hyperbolic internal dynamics is presented. The present paper integrates stable inversion techniques (that achieve exact-tracking) with approximation techniques (that modify the internal dynamics) to circumvent the nonhyperbolicity of the internal dynamics - this nonhyperbolicity is an obstruction to applying presently available stable inversion techniques. The theory is developed for nonlinear systems and the method is applied to a two-cart with inverted-pendulum example.
Non-Linear System Identification for Aeroelastic Systems with Application to Experimental Data
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.
2008-01-01
Representation and identification of a non-linear aeroelastic pitch-plunge system as a model of the NARMAX class is considered. A non-linear difference equation describing this aircraft model is derived theoretically and shown to be of the NARMAX form. Identification methods for NARMAX models are applied to aeroelastic dynamics and its properties demonstrated via continuous-time simulations of experimental conditions. Simulation results show that (i) the outputs of the NARMAX model match closely those generated using continuous-time methods and (ii) NARMAX identification methods applied to aeroelastic dynamics provide accurate discrete-time parameter estimates. Application of NARMAX identification to experimental pitch-plunge dynamics data gives a high percent fit for cross-validated data.
Vlad, Marcel O.; Szedlacsek, Stefan E.; Pourmand, Nader; Cavalli-Sforza, L. Luca; Oefner, Peter; Ross, John
2005-01-01
We study different physical, chemical, or biological processes involving replication, transformation, and disappearance processes, as well as transport processes, and assume that the time and space dependence of the species densities are known. We derive two types of Fisher equations. The first type relates the average value of the time derivative of the relative time-specific rates of growth of the different species to the variance of the relative, time-specific rates of growth. A second type relates the average value of the gradient or the divergence of the relative, space-specific rates of growth to the space correlation matrix of the relative, space-specific rates of growth. These Fisher equations are exact results, which are independent of the detailed kinetics of the process: they are valid whether the evolution equations are linear or nonlinear, local or nonlocal in space and/or time and can be applied for the study of a large class of physical, chemical, and biological systems described in terms of time- and/or space-dependent density fields. We examine the implications of our generalized Fisher relations in population genetics, biochemistry, and chemical kinetics (reaction–diffusion systems). We show that there is a connection between the enhanced (hydrodynamic) transport of mutations induced by population growth and space-specific rate vectors: the velocity of enhanced transport is proportional to the product of the diffusion coefficient of the species and the space rate vector; this relation is similar to a fluctuation–dissipation relation in statistical mechanics. PMID:15994224
Salvati, Luca; Mavrakis, Anastasios; Colantoni, Andrea; Mancino, Giuseppe; Ferrara, Agostino
2015-07-15
Degradation of soils and sensitivity of land to desertification are intensified in last decades in the Mediterranean region producing heterogeneous spatial patterns determined by the interplay of factors such as climate, land-use changes, and human pressure. The present study hypothesizes that rising levels of soil degradation and land sensitivity to desertification are reflected into increasingly complex (and non-linear) relationships between environmental and socioeconomic variables. To verify this hypothesis, the Complex Adaptive Systems (CAS) framework was used to explore the spatiotemporal dynamics of eleven indicators derived from a standard assessment of soil degradation and land sensitivity to desertification in Italy. Indicators were made available on a detailed spatial scale (773 agricultural districts) for various years (1960, 1990, 2000 and 2010) and analyzed through a multi-dimensional exploratory data analysis. Our results indicate that the number of significant pair-wise correlations observed between indicators increased with the level of soil and land degradation, although with marked differences between northern and southern Italy. 'Fast' and 'slow' factors underlying soil and land degradation, and 'rapidly-evolving' or 'locked' agricultural districts were identified according to the rapidity of change estimated for each of the indicators studied. In southern Italy, 'rapidly-evolving' districts show a high level of soil degradation and land sensitivity to desertification during the whole period of investigation. On the contrary, those districts in northern Italy are those experiencing a moderate soil degradation and land sensitivity to desertification with the highest increase in the level of sensitivity over time. The study framework contributes to the assessment of complex local systems' dynamics in affluent but divided countries. Results may inform thematic strategies for the mitigation of land and soil degradation in the framework of action
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2015-10-01
This paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances. Unlike most previous approaches on saturated systems, which assumed affine nonlinear systems, in this paper, tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation. To deal with the saturation constraint, an auxiliary system is constructed and a modified tracking error is defined. Then, by employing implicit function theorem, mean value theorem, and modified tracking error, updating rules are derived based on the well-known back-propagation (BP) algorithm, which has been proven to be the most relevant updating rule to control problems. However, most of the previous approaches on BP algorithm suffer from lack of stability analysis. By injecting a damping term to the standard BP algorithm, uniformly ultimately boundedness of all the signals of the closed-loop system is ensured via Lyapunov's direct method. Furthermore, the presented approach employs nonlinear in parameter neural networks. Hence, the proposed scheme is applicable to systems with higher degrees of nonlinearity. Using a high-gain observer to reconstruct the states of the system, an output feedback controller is also presented. Finally, the simulation results performed on a Duffing-Holmes chaotic system, a generalized pendulum-type system, and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes. PMID:25532213
Estimation on nonlinear damping in second order distributed parameter systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1989-01-01
An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.
IDENTIFICATION OF NONLINEARITIES IN AN 8-DOF SYSTEM THROUGH SPECTRAL FEEDBACK
B. ARCAND; J. WAIT
2000-08-01
The accurate detection and characterization of nonlinearities associated with damage in structural systems is an area of vibration analysis that is being widely researched. In this paper, nonlinear behavior is considered a potential indicator of damage. Most conventional damage detection methods, such as those based on resonant frequencies and mode shapes, do not accurately identify the location and extent of nonlinearities present in a given structural system. As an extension of previous work at LANL, an effort is made to validate a damage detection method proposed by Adams. This method states that the frequency response function (FRF) matrix obtained from a low-level vibration test approximates the underlying linear FRF matrix of the system. The nonlinear systems' responses to high level excitation are combined with the linear FRF in a classic feedback loop to obtain the contributions of nonlinear internal forces. The temporal and spatial characteristics of the nonlinearities present in a structural system are identified. An 8-DOF system is used as a test case to validate the aforementioned method. Results of the tests and important issues concerning the method are presented.
NASA Technical Reports Server (NTRS)
Hague, D. S.; Woodbury, N. W.
1975-01-01
The Mars system is a tool for rapid prediction of aircraft or engine characteristics based on correlation-regression analysis of past designs stored in the data bases. An example of output obtained from the MARS system, which involves derivation of an expression for gross weight of subsonic transport aircraft in terms of nine independent variables is given. The need is illustrated for careful selection of correlation variables and for continual review of the resulting estimation equations. For Vol. 1, see N76-10089.
Ryali, Srikanth; Ian Shih, Yen-Yu; Chen, Tianwen; Kochalka, John; Albaugh, Daniel; Fang, Zhongnan; Supekar, Kaustubh; Lee, Jin Hyung; Menon, Vinod
2016-01-01
State-space multivariate dynamical systems (MDS) (Ryali et al., 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods is poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in fMRI. More
Ryali, Srikanth; Shih, Yen-Yu Ian; Chen, Tianwen; Kochalka, John; Albaugh, Daniel; Fang, Zhongnan; Supekar, Kaustubh; Lee, Jin Hyung; Menon, Vinod
2016-05-15
State-space multivariate dynamical systems (MDS) (Ryali et al. 2011) and other causal estimation models are being increasingly used to identify directed functional interactions between brain regions. However, the validity and accuracy of such methods are poorly understood. Performance evaluation based on computer simulations of small artificial causal networks can address this problem to some extent, but they often involve simplifying assumptions that reduce biological validity of the resulting data. Here, we use a novel approach taking advantage of recently developed optogenetic fMRI (ofMRI) techniques to selectively stimulate brain regions while simultaneously recording high-resolution whole-brain fMRI data. ofMRI allows for a more direct investigation of causal influences from the stimulated site to brain regions activated downstream and is therefore ideal for evaluating causal estimation methods in vivo. We used ofMRI to investigate whether MDS models for fMRI can accurately estimate causal functional interactions between brain regions. Two cohorts of ofMRI data were acquired, one at Stanford University and the University of California Los Angeles (Cohort 1) and the other at the University of North Carolina Chapel Hill (Cohort 2). In each cohort, optical stimulation was delivered to the right primary motor cortex (M1). General linear model analysis revealed prominent downstream thalamic activation in Cohort 1, and caudate-putamen (CPu) activation in Cohort 2. MDS accurately estimated causal interactions from M1 to thalamus and from M1 to CPu in Cohort 1 and Cohort 2, respectively. As predicted, no causal influences were found in the reverse direction. Additional control analyses demonstrated the specificity of causal interactions between stimulated and target sites. Our findings suggest that MDS state-space models can accurately and reliably estimate causal interactions in ofMRI data and further validate their use for estimating causal interactions in f
NASA Astrophysics Data System (ADS)
Fujii, Kensaku; Aoki, Ryo; Muneyasu, Mitsuji
This paper proposes an adaptive algorithm for identifying unknown systems containing nonlinear amplitude characteristics. Usually, the nonlinearity is so small as to be negligible. However, in low cost systems, such as acoustic echo canceller using a small loudspeaker, the nonlinearity deteriorates the performance of the identification. Several methods preventing the deterioration, polynomial or Volterra series approximations, have been hence proposed and studied. However, the conventional methods require high processing cost. In this paper, we propose a method approximating the nonlinear characteristics with a piecewise linear curve and show using computer simulations that the performance can be extremely improved. The proposed method can also reduce the processing cost to only about twice that of the linear adaptive filter system.
NASA Astrophysics Data System (ADS)
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT
NASA Technical Reports Server (NTRS)
Trumper, David L.
1991-01-01
In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.
Al-Khateeb, Mohammad A Z; McCarthy, Mary; Sánchez, Christian; Ellis, Andrew
2016-04-15
In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dB_{SNR}/dB_{Power} suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error. PMID:27082361
Yang, Yuan; Solis-Escalante, Teodoro; Yao, Jun; Daffertshofer, Andreas; Schouten, Alfred C; van der Helm, Frans C T
2016-02-01
Interaction between distant neuronal populations is essential for communication within the nervous system and can occur as a highly nonlinear process. To better understand the functional role of neural interactions, it is important to quantify the nonlinear connectivity in the nervous system. We introduce a general approach to measure nonlinear connectivity through phase coupling: the multi-spectral phase coherence (MSPC). Using simulated data, we compare MSPC with existing phase coupling measures, namely n : m synchronization index and bi-phase locking value. MSPC provides a system description, including (i) the order of the nonlinearity, (ii) the direction of interaction, (iii) the time delay in the system, and both (iv) harmonic and (v) intermodulation coupling beyond the second order; which are only partly revealed by other methods. We apply MSPC to analyze data from a motor control experiment, where subjects performed isotonic wrist flexions while receiving movement perturbations. MSPC between the perturbation, EEG and EMG was calculated. Our results reveal directional nonlinear connectivity in the afferent and efferent pathways, as well as the time delay (43 ± 8 ms) between the perturbation and the brain response. In conclusion, MSPC is a novel approach capable to assess high-order nonlinear interaction and timing in the nervous system. PMID:26404514
NASA Astrophysics Data System (ADS)
Hamel, Sarah; Boulkroune, Abdesselem
2016-08-01
In this paper, a modified generalized function projective synchronization scheme for a class of master-slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.
Nonlinear analysis of rotor-bearing systems using component mode synthesis
NASA Technical Reports Server (NTRS)
Nelson, H. D.; Meacham, W. L.; Fleming, D. P.; Kascak, A. F.
1982-01-01
The method of component mode synthesis is developed to determine the forced response of nonlinear, multishaft, rotor-bearing systems. The formulation allows for simulation of system response due to blade loss, distributed unbalance, base shock, maneuver loads, and specified fixed frame forces. The motion of each rotating component of the system is described by superposing constraint modes associated with boundary coordinates and constrained precessional modes associated with internal coordinates. The precessional modes are truncated for each component and the reduced component equations are assembled with the nonlinear supports and interconnections to form a set of nonlinear system equations of reduced order. These equations are then numerically integrated to obtain the system response. A computer program, which is presently restricted to single shaft systems, has been written and results are presented for transient system response associated with blade loss dynamics with squeeze film dampers, and with interference rubs.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-01-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity.
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
2016-01-01
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Bui, Lam Anh; Mitchell, Arnan
2013-04-01
A novel remoted instantaneous frequency measurement system using all optical mixing is demonstrated. This system copies an input intensity modulated optical carrier using four wave mixing, delays this copy and then mixes it with the original signal, to produce an output idler tone. The intensity of this output can be used to determine the RF frequency of the input signal. This system is inherently broadband and can be easily scaled beyond 40 GHz while maintaining a DC output which greatly simplifies receiving electronics. The remoted configuration isolates the sensitive and expensive receiver hardware from the signal sources and importantly allows the system to be added to existing microwave photonic implementations without modification of the transmission module. PMID:23571944
Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Killingsworth, W. R., Jr.
1972-01-01
The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.
Iterative methods for large scale nonlinear and linear systems. Final report, 1994--1996
Walker, H.F.
1997-09-01
The major goal of this research has been to develop improved numerical methods for the solution of large-scale systems of linear and nonlinear equations, such as occur almost ubiquitously in the computational modeling of physical phenomena. The numerical methods of central interest have been Krylov subspace methods for linear systems, which have enjoyed great success in many large-scale applications, and newton-Krylov methods for nonlinear problems, which use Krylov subspace methods to solve approximately the linear systems that characterize Newton steps. Krylov subspace methods have undergone a remarkable development over the last decade or so and are now very widely used for the iterative solution of large-scale linear systems, particularly those that arise in the discretization of partial differential equations (PDEs) that occur in computational modeling. Newton-Krylov methods have enjoyed parallel success and are currently used in many nonlinear applications of great scientific and industrial importance. In addition to their effectiveness on important problems, Newton-Krylov methods also offer a nonlinear framework within which to transfer to the nonlinear setting any advances in Krylov subspace methods or preconditioning techniques, or new algorithms that exploit advanced machine architectures. This research has resulted in a number of improved Krylov and Newton-Krylov algorithms together with applications of these to important linear and nonlinear problems.
H∞ consensus and synchronization of nonlinear systems based on a novel fuzzy model.
Zhao, Yan; Li, Bing; Qin, Jiahu; Gao, Huijun; Karimi, Hamid Reza
2013-12-01
This paper investigates the H∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H(∞) performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H(∞) controller is designed so that two nonlinear systems reach synchronization with a prescribed H(∞) performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results. PMID:23757525
Solving nonlinear evolution equation system using two different methods
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.
2015-12-01
This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.
Nonlinear dynamics of a stack/cable system
Cai, Y.; Chen, S.S.
1995-07-01
In this study, we developed a coupled model of wind-induced vibration of a stack, based on an unsteady-flow theory and nonlinear dynamics of the stack`s heavy elastic suspended cables. Numerical analysis was performed to identify excitation mechanisms. The stack was found to be excited by vortex shedding. Once lock-in resonance occurred, the cables were excited by the transverse motion of the stack. Large-amplitude oscillations of the cables were due to parametric resonance. Appropriate techniques have been proposed to alleviate the vibration problem.
NASA Astrophysics Data System (ADS)
Mokaddem, S.; Khaber, F.
2008-06-01
This work presents a development of adaptive type-1 and type-2 fuzzy controls for uncertain nonlinear systems. Using the adaptive type-1 fuzzy control, the dynamic of the nonlinear systems is approximated with type-1 fuzzy systems whose parameters are adjusted by appropriate law adaptation. For adaptive type-2 fuzzy control, the dynamic of the nonlinear systems is approximated with interval type-2 fuzzy systems. The use of this type-2 control requires an additional operation witch is the type reduction, in comparing with typ-1 control. The closed-loop system stability is guaranteed by the Lyaponov synthesis. To show the performance of the developed controls, a comparative study is realized through the application of these controls so that an inverted pendulum tracks a given trajectory in presence of disturbances.
Rogue waves for a system of coupled derivative nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Chan, H. N.; Malomed, B. A.; Chow, K. W.; Ding, E.
2016-01-01
Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics, plasmas, etc., exhibits RWs only in the regime of modulation instability (MI) of the background. For a system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect is demonstrated here for a system of coupled derivative NLSEs (DNLSEs) where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs depend on the mismatch in group velocities between the components, and the parameters for cubic nonlinearity and self-steepening. RWs considered in this paper differ from those of the NLSEs in terms of the amplification ratio and criteria of existence. Applications to optics and plasma physics are discussed.
NASA Technical Reports Server (NTRS)
Oakley, David R.; Knight, Norman F., Jr.
1994-01-01
A parallel adaptive dynamic relaxation (ADR) algorithm has been developed for nonlinear structural analysis. This algorithm has minimal memory requirements, is easily parallelizable and scalable to many processors, and is generally very reliable and efficient for highly nonlinear problems. Performance evaluations on single-processor computers have shown that the ADR algorithm is reliable and highly vectorizable, and that it is competitive with direct solution methods for the highly nonlinear problems considered. The present algorithm is implemented on the 512-processor Intel Touchstone DELTA system at Caltech, and it is designed to minimize the extent and frequency of interprocessor communication. The algorithm has been used to solve for the nonlinear static response of two and three dimensional hyperelastic systems involving contact. Impressive relative speedups have been achieved and demonstrate the high scalability of the ADR algorithm. For the class of problems addressed, the ADR algorithm represents a very promising approach for parallel-vector processing.
Flutter analysis of an airplane with multiple structural nonlinearities in the control system
NASA Technical Reports Server (NTRS)
Breitbach, E. J.
1980-01-01
Experience has shown that the flutter prediction process for airplanes can be greatly affected by strong concentrated nonlinearities which may be localized in the linking elements of the control mechanism, in the pivot joints of variable-sweep-wing systems, and in the connecting points between wing and pylon-mounted external stores. The principle of equivalent linearization offers an efficent possibility for solving the related nonlinear flutter equations in the frequency domain as a complement to the well-known time domain procedures. Taking as an example an airplane with nonlinear control characteristics, it is demonstrated how the equivalent linearization approach can be extended to rather complicated systems with multiple sets of strongly interacting, concentrated nonlinearities.
Hybrid Takagi-Sugeno Fuzzy FED PID Control of Nonlinear Systems
NASA Astrophysics Data System (ADS)
Hamed, Basil; El Khateb, Ahmad
2008-06-01
The new method of proportional-integral-derivative (PID) controller is proposed in this paper for a hybrid fuzzy PID controller for nonlinear system. The important feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy fed PID controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller contains one part. This single part of the rules uses the Takagi-Sugeno method for solving the nonlinear problem. The simulation results of a nonlinear system show that the performance of a fed PID Hybrid Takagi-Sugeno fuzzy controller is better than that of the conventional fuzzy PID controller or Hybrid Mamdani fuzzy FED PID controller.
Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan
2016-01-01
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control. PMID:26919740
Weak concentration and wave operator for a 3D coupled nonlinear Schrödinger system
NASA Astrophysics Data System (ADS)
Pastor, Ademir
2015-02-01
Reported in this paper are results concerning the Cauchy problem and the dynamics for a cubic nonlinear Schrödinger system arising in nonlinear optics. A sharp criterion is given concerned with the dichotomy global existence versus finite time blow-up. When a radial solution blows up in finite time, we prove the concentration in the critical Lebesgue space. Sufficient condition for the scattering and the construction of the wave operator in the energy space is also provided.
Nonlinear control design for stressed power systems using normal forms of vector fields
NASA Astrophysics Data System (ADS)
Jang, Gilsoo
Large stressed interconnected power systems exhibit complicated dynamic behavior when subjected to disturbances. This nonlinear complex behavior is not well analyzed with present tools, and a complete theoretical analysis of this is not feasible in large systems. In stressed power systems, due to the presence of increased nonlinearity and the existence of nonlinear modal interactions, there exist some limitation to the use of conventional linear control design techniques. Therefore there is a need to understand the nature of nonlinear modal interactions and their influences on control performance for optimal controller setting. This work deals with control design in power systems using the method of normal forms. The objective of this work is to understand the effect of the nonlinear modal interaction on control performance and to develop a procedure to design controls incorporating the nonlinear information. For power systems equipped with fast exciters, the exciter gains have crucial influence on the system dynamic behavior. In order to be able to tune the exciter gains for optimal system performance, one has to understand, how the system response changes with different gain settings. In linear analysis, this consists of determining the eigenvalues for various gains, and computing the sensitivity of the eigenvalues under gain variations. If one takes into account the influence of the second order normal forms on the system response, then the corresponding interaction coefficients and their sensitivity with respect to gain variations has to be studied as well. This is the topic of the study presented here. The concept of nonlinear participation factors, and sensitivity of the normal forms coefficient, together with linear participation factors and eigenvalue sensitivity are used to vary control settings. The control settings are varied to obtain improved stability and to reduce the nonlinearity in the system. The proposed procedure was applied to the 50-generator
Nonlinear stability research on the hydraulic system of double-side rolling shear.
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation. PMID:26520981
Nonlinear stability research on the hydraulic system of double-side rolling shear
NASA Astrophysics Data System (ADS)
Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu
2015-10-01
This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.
Simulation-based optimal Bayesian experimental design for nonlinear systems
Huan, Xun; Marzouk, Youssef M.
2013-01-01
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters. Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics.
Eliminating Nonlinear Acoustical Effects From Thermoacoustic Refrigeration Systems
NASA Astrophysics Data System (ADS)
Garrett, Steven L.; Smith, Robert W. M.; Poese, Matthew E.
2006-05-01
Nonlinear acoustical effects dissipate energy that degrades thermoacoustic refrigerator performance. The largest of these effects occur in acoustic resonators and include shock formation; turbulence and boundary layer disruption; and entry/exit (minor) losses induced by changes in resonator cross-sectional area. Effects such as these also make the creation of accurate performance models more complicated. Suppression of shock formation by intentional introduction of resonator anharmonicity has been common practice for the past two decades. Recent attempts to increase cooling power density by increasing pressure amplitudes has required reduction of turbulence and minor loss by using an new acousto-mechanical resonator topology. The hybrid resonator still stores potential energy in the compressibility of the gaseous working fluid, but stores kinetic energy in the moving (solid) mass of the motor and piston. This talk will first present nonlinear acoustical loss measurements obtained in a "conventional" double-Helmholtz resonator geometry (TRITON) that dissipated four kilowatts of acoustic power. We will then describe the performance of the new "bellows bounce" resonator configuration and "vibromechanical multiplier" used in the first successful implementation of this approach that created an ice cream freezer produced at Penn State for Ben & Jerry's.
Fox, John D.; Mastorides, Themis; Rivetta, Claudio Hector; Van Winkle, Daniel; /SLAC
2007-07-06
Several high-current accelerators use feedback techniques in the accelerating RF systems to control the impedances seen by the circulating beam. These Direct and Comb Loop architectures put the high power klystron and LLRF signal processing components inside feedback loops, and the ultimate behavior of the systems depends on the individual sub-component properties. Imperfections and non-idealities in the signal processing leads to reduced effectiveness in the impedance control loops. In the PEP-II LLRF systems non-linear effects have been shown to reduce the achievable beam currents, increase low-mode longitudinal growth rates and reduce the margins and stability of the LLRF control loops. We present measurements of the driver amplifiers used in the PEP-II systems, and present measurement techniques needed to quantify the small-signal gain, linearity, transient response and image frequency generation of these amplifiers.
Green, P. L.; Worden, K.
2015-01-01
In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories. PMID:26303916
Stability analysis of a general family of nonlinear positive discrete time-delay systems
NASA Astrophysics Data System (ADS)
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
NASA Astrophysics Data System (ADS)
Aerts, J. R. M.; Dirckx, J. J. J.; Pintelon, R.
2008-06-01
Recently, a measurement set-up was presented to detect small nonlinear distortions in the vibration of acoustically driven mechanical systems. A speaker generates a specially designed multisine excitation signal that drives the vibration of a test object. The generated sound pressure is measured with a probe microphone in front of the test object, and an heterodyne vibrometer measures the corresponding vibration. Due to the high degree of linearity of the heterodyne technique, very small nonlinear distortions can be detected. In this paper the set-up is used to verify whether small nonlinear distortions are present in the vibration of the middle ear system, which is classically considered to be a completely linear system. In vitro measurements on the right ear of an adult male gerbil proved that nonlinear distortions are present in the vibration of the tympanic membrane. Similar results were seen in measurements on the left ear. The influence of post-mortem changes on the nonlinear behaviour of the middle ear was verified in a number of successive measurements. These indicated that the nonlinear behaviour of the middle ear decreases in time.
Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system
NASA Technical Reports Server (NTRS)
Leifer, Joel; Gross, Michael
1987-01-01
The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure.
Observed-Based Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems With Dead-Zone.
Tong, Shaocheng; Sui, Shuai; Li, Yongming
2015-12-01
In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach. PMID:25594991
A genuine nonlinear approach for controller design of a boiler-turbine system.
Yang, Shizhong; Qian, Chunjiang; Du, Haibo
2012-05-01
This paper proposes a genuine nonlinear approach for controller design of a drum-type boiler-turbine system. Based on a second order nonlinear model, a finite-time convergent controller is first designed to drive the states to their setpoints in a finite time. In the case when the state variables are unmeasurable, the system will be regulated using a constant controller or an output feedback controller. An adaptive controller is also designed to stabilize the system since the model parameters may vary under different operating points. The novelty of the proposed controller design approach lies in fully utilizing the system nonlinearities instead of linearizing or canceling them. In addition, the newly developed techniques for finite-time convergent controller are used to guarantee fast convergence of the system. Simulations are conducted under different cases and the results are presented to illustrate the performance of the proposed controllers. PMID:22222312
Bouaricha, A.; Schnabel, R.B.
1996-12-31
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
NASA Astrophysics Data System (ADS)
Maboodi, M.; Khaki-Sedigh, A.; Camacho, E. F.
2015-08-01
In this paper, control performance assessment for a class of nonlinear systems modelled by autoregressive second-order Volterra series with a general linear additive disturbance is presented. The proposed approach employs the nonlinear generalised minimum variance (NGMV) controller concept. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The polynomial operator form is used throughout this paper for the description of the system input-output model. The closed form formulation of NGMV controller for autoregressive second-order Volterra series is presented in a polynomial form then a control assessment criterion based on the NGMV control is given. Simulation results and comparison studies are used to show the effectiveness of the proposed approach for a class of nonlinear systems.
How nonlinear systems inform meaning and early education.
Fromberg, Doris Pronin
2010-01-01
This paper contends that educators need to prepare young learners to function with the predictable unpredictability of life in this century by participating in the kind of education that is transformational and adaptive to the ways in which children acquire meaning. When teachers implement a dynamic-themes theory of early education they can help children younger than nine years of age to integrate meaning. The isomorphic relationships apparent within each of several theories--script theory, Theory of Mind as metacognition, and chaos and complexity theory--together can provide evidence for the nature of meaning and its relationship to the nonlinear early education of children. The transformational-generative characteristics of these theories, that include constructed learning, inform dynamic early educational practice. Play, as one condition for meaningful early learning, also has particular significance in early education by affording an environment for assessing learning. PMID:20021777
Nonlinear standing Alfven wave current system at Io - Theory
NASA Astrophysics Data System (ADS)
Neubauer, F. M.
1980-03-01
A nonlinear analytical model is presented of the Alfven current tubes continuing the currents through Io generated by the unipolar inductor effect due to Io's motion relative to the magnetospheric plasma. It was shown that: (1) the portion of the currents needing Io is aligned with the Alfven characteristics at a specific angle to the magnetic field for the special case of perpendicular flow; (2) the Alfven tubes act like an external conductance; (3) the Alfven tubes may be reflected from the torus boundary or the Jovian atmosphere; and (4) from the point of view of the electrodynamic interaction, Io is unique among the Jovian satellites because of its ionosphere arising from ionized volcanic gases and a high external Alfvenic conductance.