A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

A theoretical Deduction from the Hubble law based on a Modified Newtonian Dynamics with field of Yukawa inverse

NASA Astrophysics Data System (ADS)

Falcon, N.

2017-07-01

At cosmic scales the dynamics of the Universe are almost exclusively prescribed by the force of gravity; however the assumption of the law of gravitation, depending on the inverse of the distance, leads to the known problems of the rotation curves of galaxies and missing mass (dark matter). The problem of the coupling of gravity to changes in scale and deviations from the law of the inverse square is an old problem (Laplace, 1805; Seeliger 1898), which has motivated alternatives to Newtonian dynamics compatible with observations. The present paper postulates a modified Newtonian dynamics by adding an inverse Yukawa potential: U(r)≡U0(M)(r-r0)e-α/r is the the potential per unit mass (in N/kg) as a function of the barionic mass that causes the field, r0 is of the order of 50h-1 Mpc and alpha is a coupling constant of the order of 2.5 h-1 Mpc. This potential is zero within the solar system, slightly attractive at interstellar distances, very attractive in galactic range and repulsive at cosmic scales. Its origin is the barionic matter, it allows to include the Milgrow MoND theory to explain the rotation curves, it is compatible with the experiments Eovos type, and allows to deduce the law of Hubble to cosmic scales, in the form H0=100h km/s Mpc≍U0(M)/c, where U0(M)≍ 4pi×6.67 10-11m/s2, is obtained from the Laplace's equation, assuming that the gravitational force is the law of the inverse of the square plus a non-linear term type Yukawa inverse. It is concluded that the modification of the law of gravity with nonlinear terms, allows to model the dynamics of the Universe on a large scale and include non-locality without dark matter. (See Falcon et al. 2014, International Journal of Astronomy and Astrophysics, 4, 551-559).

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

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.

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The primary objective of this research is to develop an efficient and robust trajectory optimization tool for the optimal ascent problem of the National Aerospace Plane (NASP). This report is organized in the following order to summarize the complete work: Section two states the formulation and models of the trajectory optimization problem. An inverse dynamics approach to the problem is introduced in Section three. Optimal trajectories corresponding to various conditions and performance parameters are presented in Section four. A midcourse nonlinear feedback controller is developed in Section five. Section six demonstrates the performance of the inverse dynamics approach and midcourse controller during disturbances. Section seven discusses rocket assisted ascent which may be beneficial when orbital altitude is high. Finally, Section eight recommends areas of future research.

Improved real-time dynamics from imaginary frequency lattice simulations

NASA Astrophysics Data System (ADS)

Pawlowski, Jan M.; Rothkopf, Alexander

2018-03-01

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time information in the form of spectral functions by setting up a simulation prescription in imaginary frequencies. By carefully distinguishing between initial conditions and quantum dynamics one obtains access to correlation functions also outside the conventional Matsubara frequencies. In particular the range between ω0 and ω1 = 2πT, which is most relevant for the inverse problem may be more highly resolved. In combination with the fact that in imaginary frequencies the kernel of the inverse problem is not an exponential but only a rational function we observe significant improvements in the reconstruction of spectral functions, demonstrated in a simple 0+1 dimensional scalar field theory toy model.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Feedback control by online learning an inverse model.

PubMed

Waegeman, Tim; Wyffels, Francis; Schrauwen, Francis

2012-10-01

A model, predictor, or error estimator is often used by a feedback controller to control a plant. Creating such a model is difficult when the plant exhibits nonlinear behavior. In this paper, a novel online learning control framework is proposed that does not require explicit knowledge about the plant. This framework uses two learning modules, one for creating an inverse model, and the other for actually controlling the plant. Except for their inputs, they are identical. The inverse model learns by the exploration performed by the not yet fully trained controller, while the actual controller is based on the currently learned model. The proposed framework allows fast online learning of an accurate controller. The controller can be applied on a broad range of tasks with different dynamic characteristics. We validate this claim by applying our control framework on several control tasks: 1) the heating tank problem (slow nonlinear dynamics); 2) flight pitch control (slow linear dynamics); and 3) the balancing problem of a double inverted pendulum (fast linear and nonlinear dynamics). The results of these experiments show that fast learning and accurate control can be achieved. Furthermore, a comparison is made with some classical control approaches, and observations concerning convergence and stability are made.

Solving Inverse Kinematics of Robot Manipulators by Means of Meta-Heuristic Optimisation

NASA Astrophysics Data System (ADS)

Wichapong, Kritsada; Bureerat, Sujin; Pholdee, Nantiwat

2018-05-01

This paper presents the use of meta-heuristic algorithms (MHs) for solving inverse kinematics of robot manipulators based on using forward kinematic. Design variables are joint angular displacements used to move a robot end-effector to the target in the Cartesian space while the design problem is posed to minimize error between target points and the positions of the robot end-effector. The problem is said to be a dynamic problem as the target points always changed by a robot user. Several well established MHs are used to solve the problem and the results obtained from using different meta-heuristics are compared based on the end-effector error and searching speed of the algorithms. From the study, the best performer will be obtained for setting as the baseline for future development of MH-based inverse kinematic solving.

Spatial operator approach to flexible multibody system dynamics and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.

1991-01-01

The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.

Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chen, C. L.

1989-01-01

Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed.

Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach

NASA Astrophysics Data System (ADS)

di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

2016-01-01

We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.

Real-Time Wing-Vortex and Pressure Distribution Estimation on Wings Via Displacements and Strains in Unsteady and Transitional Flight Conditions

DTIC Science & Technology

2016-09-07

approach in co simulation with fluid-dynamics solvers is used. An original variational formulation is developed for the inverse problem of...by the inverse solution meshing. The same approach is used to map the structural and fluid interface kinematics and loads during the fluid structure...co-simulation. The inverse analysis is verified by reconstructing the deformed solution obtained with a corresponding direct formulation, based on

The Lanchester square-law model extended to a (2,2) conflict

NASA Astrophysics Data System (ADS)

Colegrave, R. K.; Hyde, J. M.

1993-01-01

A natural extension of the Lanchester (1,1) square-law model is the (M,N) linear model in which M forces oppose N forces with constant attrition rates. The (2,2) model is treated from both direct and inverse viewpoints. The inverse problem means that the model is to be fitted to a minimum number of observed force levels, i.e. the attrition rates are to be found from the initial force levels together with the levels observed at two subsequent times. An approach based on Hamiltonian dynamics has enabled the authors to derive a procedure for solving the inverse problem, which is readily computerized. Conflicts in which participants unexpectedly rally or weaken must be excluded.

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model.

NASA Astrophysics Data System (ADS)

Wan, S.; He, W.

2016-12-01

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

Duality and symmetry lost in solid mechanics

NASA Astrophysics Data System (ADS)

Bui, Huy Duong

2008-01-01

Some conservation laws in Solids and Fracture Mechanics present a lack of symmetry between kinematic and dynamic variables. It is shown that Duality is the right tool to re-establish the symmetry between equations and variables and to provide conservation laws of the pure divergence type which provide true path independent integrals. The loss of symmetry of some energetic expressions is exploited to derive a new method for solving some inverse problems. In particular, the earthquake inverse problem is solved analytically. To cite this article: H.D. Bui, C. R. Mecanique 336 (2008).

Query-based learning for aerospace applications.

PubMed

Saad, E W; Choi, J J; Vian, J L; Wunsch, D C Ii

2003-01-01

Models of real-world applications often include a large number of parameters with a wide dynamic range, which contributes to the difficulties of neural network training. Creating the training data set for such applications becomes costly, if not impossible. In order to overcome the challenge, one can employ an active learning technique known as query-based learning (QBL) to add performance-critical data to the training set during the learning phase, thereby efficiently improving the overall learning/generalization. The performance-critical data can be obtained using an inverse mapping called network inversion (discrete network inversion and continuous network inversion) followed by oracle query. This paper investigates the use of both inversion techniques for QBL learning, and introduces an original heuristic to select the inversion target values for continuous network inversion method. Efficiency and generalization was further enhanced by employing node decoupled extended Kalman filter (NDEKF) training and a causality index (CI) as a means to reduce the input search dimensionality. The benefits of the overall QBL approach are experimentally demonstrated in two aerospace applications: a classification problem with large input space and a control distribution problem.

Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Scheid, R. E., Jr.

1987-01-01

This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander

2011-01-01

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems

NASA Astrophysics Data System (ADS)

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

A matrix-based approach to solving the inverse Frobenius-Perron problem using sequences of density functions of stochastically perturbed dynamical systems.

PubMed

Nie, Xiaokai; Coca, Daniel

2018-01-01

The paper introduces a matrix-based approach to estimate the unique one-dimensional discrete-time dynamical system that generated a given sequence of probability density functions whilst subjected to an additive stochastic perturbation with known density.

Computation of forces from deformed visco-elastic biological tissues

NASA Astrophysics Data System (ADS)

Muñoz, José J.; Amat, David; Conte, Vito

2018-04-01

We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.

Mantle Circulation Models with variational data assimilation: Inferring past mantle flow and structure from plate motion histories and seismic tomography

NASA Astrophysics Data System (ADS)

Bunge, H.; Hagelberg, C.; Travis, B.

2002-12-01

EarthScope will deliver data on structure and dynamics of continental North America and the underlying mantle on an unprecedented scale. Indeed, the scope of EarthScope makes its mission comparable to the large remote sensing efforts that are transforming the oceanographic and atmospheric sciences today. Arguably the main impact of new solid Earth observing systems is to transform our use of geodynamic models increasingly from conditions that are data poor to an environment that is data rich. Oceanographers and meteorologists already have made substantial progress in adapting to this environment, by developing new approaches of interpreting oceanographic and atmospheric data objectively through data assimilation methods in their models. However, a similarly rigorous theoretical framework for merging EarthScope derived solid Earth data with geodynamic models has yet to be devised. Here we explore the feasibility of data assimilation in mantle convection studies in an attempt to fit global geodynamic model calculations explicitly to tomographic and tectonic constraints. This is an inverse problem not quite unlike the inverse problem of finding optimal seismic velocity structures faced by seismologists. We derive the generalized inverse of mantle convection from a variational approach and present the adjoint equations of mantle flow. The substantial computational burden associated with solutions to the generalized inverse problem of mantle convection is made feasible using a highly efficient finite element approach based on the 3-D spherical fully parallelized mantle dynamics code TERRA, implemented on a cost-effective topical PC-cluster (geowulf) dedicated specifically to large-scale geophysical simulations. This dedicated geophysical modeling computer allows us to investigate global inverse convection problems having a spatial discretization of less than 50 km throughout the mantle. We present a synthetic high-resolution modeling experiment to demonstrate that mid-Cretaceous mantle structure can be inferred accurately from our inverse approach assuming present-day mantle structure is well-known, even if an initial first guess assumption about the mid-Cretaceous mantle involved only a simple 1-D radial temperature profile. We suggest that geodynamic inverse modeling should make it possible to infer a number of flow parameters from observational constraints of the mantle.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-03-01

Recently, the notion of non-standard Lagrangians was discussed widely in literature in an attempt to explore the inverse variational problem of nonlinear differential equations. Different forms of non-standard Lagrangians were introduced in literature and have revealed nice mathematical and physical properties. One interesting form related to the inverse variational problem is the logarithmic Lagrangian, which has a number of motivating features related to the Liénard-type and Emden nonlinear differential equations. Such types of Lagrangians lead to nonlinear dynamics based on non-standard Hamiltonians. In this communication, we show that some new dynamical properties are obtained in stellar dynamics if standard Lagrangians are replaced by Logarithmic Lagrangians and their corresponding non-standard Hamiltonians. One interesting consequence concerns the emergence of an extra pressure term, which is related to the gravitational field suggesting that gravitation may act as a pressure in a strong gravitational field. The case of the stellar halo of the Milky Way is considered.

Dynamic loading and stress life analysis of permanent space station modules

NASA Astrophysics Data System (ADS)

Anisimov, A. V.; Krokhin, I. A.; Likhoded, A. I.; Malinin, A. A.; Panichkin, N. G.; Sidorov, V. V.; Titov, V. A.

2016-11-01

Some methodological approaches to solving several key problems of dynamic loading and structural strength analysis of Permanent Space Station (PSS)modules developed on the basis of the working experience of Soviet and Russian PSS and the International Space station (ISS) are presented. The solutions of the direct and semi-inverse problems of PSS structure dynamics are mathematically stated. Special attention is paid to the use of the results of ground structural strength tests of space station modules and the data on the actual flight actions on the station and its dynamic responses in the orbital operation regime. The procedure of determining the dynamics and operation life parameters of elements of the PSS modules is described.

Inverse problems and computational cell metabolic models: a statistical approach

NASA Astrophysics Data System (ADS)

Calvetti, D.; Somersalo, E.

2008-07-01

In this article, we give an overview of the Bayesian modelling of metabolic systems at the cellular and subcellular level. The models are based on detailed description of key biochemical reactions occurring in tissue, which may in turn be compartmentalized into cytosol and mitochondria, and of transports between the compartments. The classical deterministic approach which models metabolic systems as dynamical systems with Michaelis-Menten kinetics, is replaced by a stochastic extension where the model parameters are interpreted as random variables with an appropriate probability density. The inverse problem of cell metabolism in this setting consists of estimating the density of the model parameters. After discussing some possible approaches to solving the problem, we address the issue of how to assess the reliability of the predictions of a stochastic model by proposing an output analysis in terms of model uncertainties. Visualization modalities for organizing the large amount of information provided by the Bayesian dynamic sensitivity analysis are also illustrated.

Preview-Based Stable-Inversion for Output Tracking

NASA Technical Reports Server (NTRS)

Zou, Qing-Ze; Devasia, Santosh

1999-01-01

Stable Inversion techniques can be used to achieve high-accuracy output tracking. However, for nonminimum phase systems, the inverse is non-causal - hence the inverse has to be pre-computed using a pre-specified desired-output trajectory. This requirement for pre-specification of the desired output restricts the use of inversion-based approaches to trajectory planning problems (for nonminimum phase systems). In the present article, it is shown that preview information of the desired output can be used to achieve online inversion-based output tracking of linear systems. The amount of preview-time needed is quantified in terms of the tracking error and the internal dynamics of the system (zeros of the system). The methodology is applied to the online output tracking of a flexible structure and experimental results are presented.

Simulation of Constrained Musculoskeletal Systems in Task Space.

PubMed

Stanev, Dimitar; Moustakas, Konstantinos

2018-02-01

This paper proposes an operational task space formalization of constrained musculoskeletal systems, motivated by its promising results in the field of robotics. The change of representation requires different algorithms for solving the inverse and forward dynamics simulation in the task space domain. We propose an extension to the direct marker control and an adaptation of the computed muscle control algorithms for solving the inverse kinematics and muscle redundancy problems, respectively. Experimental evaluation demonstrates that this framework is not only successful in dealing with the inverse dynamics problem, but also provides an intuitive way of studying and designing simulations, facilitating assessment prior to any experimental data collection. The incorporation of constraints in the derivation unveils an important extension of this framework toward addressing systems that use absolute coordinates and topologies that contain closed kinematic chains. Task space projection reveals a more intuitive encoding of the motion planning problem, allows for better correspondence between observed and estimated variables, provides the means to effectively study the role of kinematic redundancy, and most importantly, offers an abstract point of view and control, which can be advantageous toward further integration with high level models of the precommand level. Task-based approaches could be adopted in the design of simulation related to the study of constrained musculoskeletal systems.

COMBINED DELAY AND GRAPH EMBEDDING OF EPILEPTIC DISCHARGES IN EEG REVEALS COMPLEX AND RECURRENT NONLINEAR DYNAMICS.

PubMed

Erem, B; Hyde, D E; Peters, J M; Duffy, F H; Brooks, D H; Warfield, S K

2015-04-01

The dynamical structure of the brain's electrical signals contains valuable information about its physiology. Here we combine techniques for nonlinear dynamical analysis and manifold identification to reveal complex and recurrent dynamics in interictal epileptiform discharges (IEDs). Our results suggest that recurrent IEDs exhibit some consistent dynamics, which may only last briefly, and so individual IED dynamics may need to be considered in order to understand their genesis. This could potentially serve to constrain the dynamics of the inverse source localization problem.

jInv: A Modular and Scalable Framework for Electromagnetic Inverse Problems

NASA Astrophysics Data System (ADS)

Belliveau, P. T.; Haber, E.

2016-12-01

Inversion is a key tool in the interpretation of geophysical electromagnetic (EM) data. Three-dimensional (3D) EM inversion is very computationally expensive and practical software for inverting large 3D EM surveys must be able to take advantage of high performance computing (HPC) resources. It has traditionally been difficult to achieve those goals in a high level dynamic programming environment that allows rapid development and testing of new algorithms, which is important in a research setting. With those goals in mind, we have developed jInv, a framework for PDE constrained parameter estimation problems. jInv provides optimization and regularization routines, a framework for user defined forward problems, and interfaces to several direct and iterative solvers for sparse linear systems. The forward modeling framework provides finite volume discretizations of differential operators on rectangular tensor product meshes and tetrahedral unstructured meshes that can be used to easily construct forward modeling and sensitivity routines for forward problems described by partial differential equations. jInv is written in the emerging programming language Julia. Julia is a dynamic language targeted at the computational science community with a focus on high performance and native support for parallel programming. We have developed frequency and time-domain EM forward modeling and sensitivity routines for jInv. We will illustrate its capabilities and performance with two synthetic time-domain EM inversion examples. First, in airborne surveys, which use many sources, we achieve distributed memory parallelism by decoupling the forward and inverse meshes and performing forward modeling for each source on small, locally refined meshes. Secondly, we invert grounded source time-domain data from a gradient array style induced polarization survey using a novel time-stepping technique that allows us to compute data from different time-steps in parallel. These examples both show that it is possible to invert large scale 3D time-domain EM datasets within a modular, extensible framework written in a high-level, easy to use programming language.

Secular dynamics of an exterior test particle: the inverse Kozai and other eccentricity-inclination resonances

NASA Astrophysics Data System (ADS)

Vinson, Benjamin R.; Chiang, Eugene

2018-03-01

The behaviour of an interior test particle in the secular three-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periastron librates about ±90° and large oscillations in eccentricity and inclination are possible. Less explored is the inverse problem: the dynamics of an exterior test particle and an interior perturber. We survey numerically the inverse secular problem, expanding the potential to hexadecapolar order and correcting an error in the published expansion. Four secular resonances are uncovered that persist in full N-body treatments (in what follows, ϖ and Ω are the longitudes of periapse and of ascending node, ω is the argument of periapse, and subscripts 1 and 2 refer to the inner perturber and the outer test particle): (i) an orbit-flipping quadrupole resonance requiring a non-zero perturber eccentricity e1, in which Ω2 - ϖ1 librates about ±90°; (ii) a hexadecapolar resonance (the `inverse Kozai' resonance) for perturbers that are circular or nearly so and inclined by I ≃ 63°/117°, in which ω2 librates about ±90° and which can vary the particle eccentricity by Δe2 ≃ 0.2 and lead to orbit crossing; (iii) an octopole `apse-aligned' resonance at I ≃ 46°/107° wherein ϖ2 - ϖ1 librates about 0° and Δe2 grows with e1; and (iv) an octopole resonance at I ≃ 73°/134° wherein ϖ2 + ϖ1 - 2Ω2 librates about 0° and Δe2 can be as large as 0.3 for small but non-zero e1. Qualitatively, the more eccentric the perturber, the more the particle's eccentricity and inclination vary; also, more polar orbits are more chaotic. Our solutions to the inverse problem have potential application to the Kuiper belt and debris discs, circumbinary planets, and hierarchical stellar systems.

Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm.

PubMed

Sarode, Ketan Dinkar; Kumar, V Ravi; Kulkarni, B D

2016-05-01

An efficient inverse problem approach for parameter estimation, state and structure identification from dynamic data by embedding training functions in a genetic algorithm methodology (ETFGA) is proposed for nonlinear dynamical biosystems using S-system canonical models. Use of multiple shooting and decomposition approach as training functions has been shown for handling of noisy datasets and computational efficiency in studying the inverse problem. The advantages of the methodology are brought out systematically by studying it for three biochemical model systems of interest. By studying a small-scale gene regulatory system described by a S-system model, the first example demonstrates the use of ETFGA for the multifold aims of the inverse problem. The estimation of a large number of parameters with simultaneous state and network identification is shown by training a generalized S-system canonical model with noisy datasets. The results of this study bring out the superior performance of ETFGA on comparison with other metaheuristic approaches. The second example studies the regulation of cAMP oscillations in Dictyostelium cells now assuming limited availability of noisy data. Here, flexibility of the approach to incorporate partial system information in the identification process is shown and its effect on accuracy and predictive ability of the estimated model are studied. The third example studies the phenomenological toy model of the regulation of circadian oscillations in Drosophila that follows rate laws different from S-system power-law. For the limited noisy data, using a priori information about properties of the system, we could estimate an alternate S-system model that showed robust oscillatory behavior with predictive abilities. Copyright © 2016 Elsevier Inc. All rights reserved.

Stability analysis of an implicitly defined labor market model

NASA Astrophysics Data System (ADS)

Mendes, Diana A.; Mendes, Vivaldo M.

2008-06-01

Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1-10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.

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.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

NASA Technical Reports Server (NTRS)

Ustinov, Eugene A.; Sunseri, Richard F.

2005-01-01

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

Self-organizing radial basis function networks for adaptive flight control and aircraft engine state estimation

NASA Astrophysics Data System (ADS)

Shankar, Praveen

The performance of nonlinear control algorithms such as feedback linearization and dynamic inversion is heavily dependent on the fidelity of the dynamic model being inverted. Incomplete or incorrect knowledge of the dynamics results in reduced performance and may lead to instability. Augmenting the baseline controller with approximators which utilize a parametrization structure that is adapted online reduces the effect of this error between the design model and actual dynamics. However, currently existing parameterizations employ a fixed set of basis functions that do not guarantee arbitrary tracking error performance. To address this problem, we develop a self-organizing parametrization structure that is proven to be stable and can guarantee arbitrary tracking error performance. The training algorithm to grow the network and adapt the parameters is derived from Lyapunov theory. In addition to growing the network of basis functions, a pruning strategy is incorporated to keep the size of the network as small as possible. This algorithm is implemented on a high performance flight vehicle such as F-15 military aircraft. The baseline dynamic inversion controller is augmented with a Self-Organizing Radial Basis Function Network (SORBFN) to minimize the effect of the inversion error which may occur due to imperfect modeling, approximate inversion or sudden changes in aircraft dynamics. The dynamic inversion controller is simulated for different situations including control surface failures, modeling errors and external disturbances with and without the adaptive network. A performance measure of maximum tracking error is specified for both the controllers a priori. Excellent tracking error minimization to a pre-specified level using the adaptive approximation based controller was achieved while the baseline dynamic inversion controller failed to meet this performance specification. The performance of the SORBFN based controller is also compared to a fixed RBF network based adaptive controller. While the fixed RBF network based controller which is tuned to compensate for control surface failures fails to achieve the same performance under modeling uncertainty and disturbances, the SORBFN is able to achieve good tracking convergence under all error conditions.

Integrated Approach to the Dynamics and Control of Maneuvering Flexible Aircraft

NASA Technical Reports Server (NTRS)

Waszak, Martin R. (Technical Monitor); Meirovitch, Leonard; Tuzcu, Ilhan

2003-01-01

This work uses a fundamental approach to the problem of simulating the flight of flexible aircraft. To this end, it integrates into a single formulation the pertinent disciplines, namely, analytical dynamics, structural dynamics, aerodynamics, and controls. It considers both the rigid body motions of the aircraft, three translations (forward motion, sideslip and plunge) and three rotations (roll, pitch and yaw), and the elastic deformations of every point of the aircraft, as well as the aerodynamic, propulsion, gravity and control forces. The equations of motion are expressed in a form ideally suited for computer processing. A perturbation approach yields a flight dynamics problem for the motions of a quasi-rigid aircraft and an 'extended aeroelasticity' problem for the elastic deformations and perturbations in the rigid body motions, with the solution of the first problem entering as an input into the second problem. The control forces for the flight dynamics problem are obtained by an 'inverse' process and the feedback controls for the extended aeroservoelasticity problem are determined by the LQG theory. A numerical example presents time simulations of rigid body perturbations and elastic deformations about 1) a steady level flight and 2) a level steady turn maneuver.

Dynamic electrical impedance imaging with the interacting multiple model scheme.

PubMed

Kim, Kyung Youn; Kim, Bong Seok; Kim, Min Chan; Kim, Sin; Isaacson, David; Newell, Jonathan C

2005-04-01

In this paper, an effective dynamical EIT imaging scheme is presented for on-line monitoring of the abruptly changing resistivity distribution inside the object, based on the interacting multiple model (IMM) algorithm. The inverse problem is treated as a stochastic nonlinear state estimation problem with the time-varying resistivity (state) being estimated on-line with the aid of the IMM algorithm. In the design of the IMM algorithm multiple models with different process noise covariance are incorporated to reduce the modeling uncertainty. Simulations and phantom experiments are provided to illustrate the proposed algorithm.

Thermal and Dynamic Properties of Volcanic Lava Inferred from Measurements on its Surface

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.; Korotkii, A.; Kovtunov, D.; Tsepelev, I.; Melnik, O. E.

2015-12-01

Modern remote sensing technologies allow for detecting the absolute temperature at the surface of volcanic lava, and the heat flow could be then inferred from the Stefan-Boltzmann law. Is it possible to use these surface thermal data to constrain the thermal and dynamic conditions inside the lava? We propose a quantitative approach to reconstruct temperature and velocity in the steady-state volcanic lava flow from thermal observations at its surface. This problem is reduced to a combination of the direct and inverse problems of mass- and heat transport. Namely, using known conditions at the lava surface we determine the missing condition at the bottom of lava (the inverse problem) and then search for the physical properties of lava - temperature and flow velocity - inside the lava (the direct problem). Assuming that the lava rheology and the thermal conductivity are temperature-dependent, we determine the flow characteristics in the model domain using an adjoint method. We show that in the case of smooth input data (observations) the lava temperature and the flow velocity can be reconstructed with a high accuracy. The noise imposed on the smooth input data results in a less accurate solution, but still acceptable below some noise level.

The boundary element method applied to 3D magneto-electro-elastic dynamic problems

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Markov, I. P.; Kuznetsov, Iu A.

2017-11-01

Due to the coupling properties, the magneto-electro-elastic materials possess a wide number of applications. They exhibit general anisotropic behaviour. Three-dimensional transient analyses of magneto-electro-elastic solids can hardly be found in the literature. 3D direct boundary element formulation based on the weakly-singular boundary integral equations in Laplace domain is presented in this work for solving dynamic linear magneto-electro-elastic problems. Integral expressions of the three-dimensional fundamental solutions are employed. Spatial discretization is based on a collocation method with mixed boundary elements. Convolution quadrature method is used as a numerical inverse Laplace transform scheme to obtain time domain solutions. Numerical examples are provided to illustrate the capability of the proposed approach to treat highly dynamic problems.

Inferring Fault Frictional and Reservoir Hydraulic Properties From Injection-Induced Seismicity

NASA Astrophysics Data System (ADS)

Jagalur-Mohan, Jayanth; Jha, Birendra; Wang, Zheng; Juanes, Ruben; Marzouk, Youssef

2018-02-01

Characterizing the rheological properties of faults and the evolution of fault friction during seismic slip are fundamental problems in geology and seismology. Recent increases in the frequency of induced earthquakes have intensified the need for robust methods to estimate fault properties. Here we present a novel approach for estimation of aquifer and fault properties, which combines coupled multiphysics simulation of injection-induced seismicity with adaptive surrogate-based Bayesian inversion. In a synthetic 2-D model, we use aquifer pressure, ground displacements, and fault slip measurements during fluid injection to estimate the dynamic fault friction, the critical slip distance, and the aquifer permeability. Our forward model allows us to observe nonmonotonic evolutions of shear traction and slip on the fault resulting from the interplay of several physical mechanisms, including injection-induced aquifer expansion, stress transfer along the fault, and slip-induced stress relaxation. This interplay provides the basis for a successful joint inversion of induced seismicity, yielding well-informed Bayesian posterior distributions of dynamic friction and critical slip. We uncover an inverse relationship between dynamic friction and critical slip distance, which is in agreement with the small dynamic friction and large critical slip reported during seismicity on mature faults.

Model Order Reduction for the fast solution of 3D Stokes problems and its application in geophysical inversion

NASA Astrophysics Data System (ADS)

Ortega Gelabert, Olga; Zlotnik, Sergio; Afonso, Juan Carlos; Díez, Pedro

2017-04-01

The determination of the present-day physical state of the thermal and compositional structure of the Earth's lithosphere and sub-lithospheric mantle is one of the main goals in modern lithospheric research. All this data is essential to build Earth's evolution models and to reproduce many geophysical observables (e.g. elevation, gravity anomalies, travel time data, heat flow, etc) together with understanding the relationship between them. Determining the lithospheric state involves the solution of high-resolution inverse problems and, consequently, the solution of many direct models is required. The main objective of this work is to contribute to the existing inversion techniques in terms of improving the estimation of the elevation (topography) by including a dynamic component arising from sub-lithospheric mantle flow. In order to do so, we implement an efficient Reduced Order Method (ROM) built upon classic Finite Elements. ROM allows to reduce significantly the computational cost of solving a family of problems, for example all the direct models that are required in the solution of the inverse problem. The strategy of the method consists in creating a (reduced) basis of solutions, so that when a new problem has to be solved, its solution is sought within the basis instead of attempting to solve the problem itself. In order to check the Reduced Basis approach, we implemented the method in a 3D domain reproducing a portion of Earth that covers up to 400 km depth. Within the domain the Stokes equation is solved with realistic viscosities and densities. The different realizations (the family of problems) is created by varying viscosities and densities in a similar way as it would happen in an inversion problem. The Reduced Basis method is shown to be an extremely efficiently solver for the Stokes equation in this context.

Kinematics and dynamics of a six-degree-of-freedom robot manipulator with closed kinematic chain mechanism

NASA Technical Reports Server (NTRS)

Nguyen, Charles C.; Pooran, Farhad J.

1989-01-01

This paper deals with a class of robot manipulators built based on the kinematic chain mechanism (CKCM). This class of CKCM manipulators consists of a fixed and a moving platform coupled together via a number of in-parallel actuators. A closed-form solution is derived for the inverse kinematic problem of a six-degre-of-freedom CKCM manipulator designed to study robotic applications in space. Iterative Newton-Raphson method is employed to solve the forward kinematic problem. Dynamics of the above manipulator is derived using the Lagrangian approach. Computer simulation of the dynamical equations shows that the actuating forces are strongly dependent on the mass and centroid of the robot links.

Gender recognition from vocal source

NASA Astrophysics Data System (ADS)

Sorokin, V. N.; Makarov, I. S.

2008-07-01

Efficiency of automatic recognition of male and female voices based on solving the inverse problem for glottis area dynamics and for waveform of the glottal airflow volume velocity pulse is studied. The inverse problem is regularized through the use of analytical models of the voice excitation pulse and of the dynamics of the glottis area, as well as the model of one-dimensional glottal airflow. Parameters of these models and spectral parameters of the volume velocity pulse are considered. The following parameters are found to be most promising: the instant of maximum glottis area, the maximum derivative of the area, the slope of the spectrum of the glottal airflow volume velocity pulse, the amplitude ratios of harmonics of this spectrum, and the pitch. On the plane of the first two main components in the space of these parameters, an almost twofold decrease in the classification error relative to that for the pitch alone is attained. The male voice recognition probability is found to be 94.7%, and the female voice recognition probability is 95.9%.

A Discrete Events Delay Differential System Model for Transmission of Vancomycin-Resistant Enterococcus (VRE) in Hospitals

DTIC Science & Technology

2010-09-19

estimated directly form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after...hospital infections , is used to motivate possibilities of modeling nosocomial infec- tion dynamics. This is done in the context of hospital monitoring and...model development. Key Words: Delay equations, discrete events, nosocomial infection dynamics, surveil- lance data, inverse problems, parameter

Specific Features in Measuring Particle Size Distributions in Highly Disperse Aerosol Systems

NASA Astrophysics Data System (ADS)

Zagaynov, V. A.; Vasyanovich, M. E.; Maksimenko, V. V.; Lushnikov, A. A.; Biryukov, Yu. G.; Agranovskii, I. E.

2018-06-01

The distribution of highly dispersed aerosols is studied. Particular attention is given to the diffusion dynamic approach, as it is the best way to determine particle size distribution. It shown that the problem can be divided into two steps: directly measuring particle penetration through diffusion batteries and solving the inverse problem (obtaining a size distribution from the measured penetrations). No reliable way of solving the so-called inverse problem is found, but it can be done by introducing a parametrized size distribution (i.e., a gamma distribution). The integral equation is therefore reduced to a system of nonlinear equations that can be solved by elementary mathematical means. Further development of the method requires an increase in sensitivity (i.e., measuring the dimensions of molecular clusters with radioactive sources, along with the activity of diffusion battery screens).

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

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

Simonetto, Andrea; Dall'Anese, Emiliano

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

PubMed Central

Alexandridis, Alex; Stogiannos, Marios; Papaioannou, Nikolaos; Zois, Elias; Sarimveis, Haralambos

2018-01-01

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses. PMID:29361781

Generation of Look-Up Tables for Dynamic Job Shop Scheduling Decision Support Tool

NASA Astrophysics Data System (ADS)

Oktaviandri, Muchamad; Hassan, Adnan; Mohd Shaharoun, Awaluddin

2016-02-01

Majority of existing scheduling techniques are based on static demand and deterministic processing time, while most job shop scheduling problem are concerned with dynamic demand and stochastic processing time. As a consequence, the solutions obtained from the traditional scheduling technique are ineffective wherever changes occur to the system. Therefore, this research intends to develop a decision support tool (DST) based on promising artificial intelligent that is able to accommodate the dynamics that regularly occur in job shop scheduling problem. The DST was designed through three phases, i.e. (i) the look-up table generation, (ii) inverse model development and (iii) integration of DST components. This paper reports the generation of look-up tables for various scenarios as a part in development of the DST. A discrete event simulation model was used to compare the performance among SPT, EDD, FCFS, S/OPN and Slack rules; the best performances measures (mean flow time, mean tardiness and mean lateness) and the job order requirement (inter-arrival time, due dates tightness and setup time ratio) which were compiled into look-up tables. The well-known 6/6/J/Cmax Problem from Muth and Thompson (1963) was used as a case study. In the future, the performance measure of various scheduling scenarios and the job order requirement will be mapped using ANN inverse model.

The Source Inversion Validation (SIV) Initiative: A Collaborative Study on Uncertainty Quantification in Earthquake Source Inversions

NASA Astrophysics Data System (ADS)

Mai, P. M.; Schorlemmer, D.; Page, M.

2012-04-01

Earthquake source inversions image the spatio-temporal rupture evolution on one or more fault planes using seismic and/or geodetic data. Such studies are critically important for earthquake seismology in general, and for advancing seismic hazard analysis in particular, as they reveal earthquake source complexity and help (i) to investigate earthquake mechanics; (ii) to develop spontaneous dynamic rupture models; (iii) to build models for generating rupture realizations for ground-motion simulations. In applications (i - iii), the underlying finite-fault source models are regarded as "data" (input information), but their uncertainties are essentially unknown. After all, source models are obtained from solving an inherently ill-posed inverse problem to which many a priori assumptions and uncertain observations are applied. The Source Inversion Validation (SIV) project is a collaborative effort to better understand the variability between rupture models for a single earthquake (as manifested in the finite-source rupture model database) and to develop robust uncertainty quantification for earthquake source inversions. The SIV project highlights the need to develop a long-standing and rigorous testing platform to examine the current state-of-the-art in earthquake source inversion, and to develop and test novel source inversion approaches. We will review the current status of the SIV project, and report the findings and conclusions of the recent workshops. We will briefly discuss several source-inversion methods, how they treat uncertainties in data, and assess the posterior model uncertainty. Case studies include initial forward-modeling tests on Green's function calculations, and inversion results for synthetic data from spontaneous dynamic crack-like strike-slip earthquake on steeply dipping fault, embedded in a layered crustal velocity-density structure.

Parameter Selection Methods in Inverse Problem Formulation

DTIC Science & Technology

2010-11-03

clinical data and used for prediction and a model for the reaction of the cardiovascular system to an ergometric workload. Key Words: Parameter selection...model for HIV dynamics which has been successfully validated with clinical data and used for prediction and a model for the reaction of the...recently developed in-host model for HIV dynamics which has been successfully validated with clinical data and used for prediction [4, 8]; b) a global

Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.

PubMed

Negre, Christian F A; Mniszewski, Susan M; Cawkwell, Marc J; Bock, Nicolas; Wall, Michael E; Niklasson, Anders M N

2016-07-12

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive, iterative refinement of an initial guess of Z (inverse square root of the overlap matrix S). The initial guess of Z is obtained beforehand by using either an approximate divide-and-conquer technique or dynamical methods, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under the incomplete, approximate, iterative refinement of Z. Linear-scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables efficient shared-memory parallelization. As we show in this article using self-consistent density-functional-based tight-binding MD, our approach is faster than conventional methods based on the diagonalization of overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4158-atom water-solvated polyalanine system, we find an average speedup factor of 122 for the computation of Z in each MD step.

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

DOE PAGES

Negre, Christian F. A; Mniszewski, Susan M.; Cawkwell, Marc Jon; ...

2016-06-06

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance ismore » obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.« less

Inverse energy cascades in three-dimensional turbulence

NASA Technical Reports Server (NTRS)

Hossain, Murshed

1991-01-01

Fully three-dimensional magnetohydrodynamic (MHD) turbulence at large kinetic and low magnetic Reynolds numbers is considered in the presence of a strong uniform magnetic field. It is shown by numerical simulation of a model of MHD that the energy inverse cascades to longer length scales when the interaction parameter is large. While the steady-state dynamics of the driven problem is three-dimensional in character, the behavior has resemblance to two-dimensional hydrodynamics. These results have implications in turbulence theory, MHD power generator, planetary dynamos, and fusion reactor blanket design.

Efficient preconditioning of the electronic structure problem in large scale ab initio molecular dynamics simulations

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

Schiffmann, Florian; VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch

2015-06-28

We present an improved preconditioning scheme for electronic structure calculations based on the orbital transformation method. First, a preconditioner is developed which includes information from the full Kohn-Sham matrix but avoids computationally demanding diagonalisation steps in its construction. This reduces the computational cost of its construction, eliminating a bottleneck in large scale simulations, while maintaining rapid convergence. In addition, a modified form of Hotelling’s iterative inversion is introduced to replace the exact inversion of the preconditioner matrix. This method is highly effective during molecular dynamics (MD), as the solution obtained in earlier MD steps is a suitable initial guess. Filteringmore » small elements during sparse matrix multiplication leads to linear scaling inversion, while retaining robustness, already for relatively small systems. For system sizes ranging from a few hundred to a few thousand atoms, which are typical for many practical applications, the improvements to the algorithm lead to a 2-5 fold speedup per MD step.« less

Dynamics of omnidirectional unmanned rescue vehicle with mecanum wheels

NASA Astrophysics Data System (ADS)

Typiak, Andrzej; Łopatka, Marian Janusz; Rykała, Łukasz; Kijek, Magdalena

2018-01-01

The work presents the dynamic equations of motion of a unmanned six-wheeled vehicle with mecanum wheels for rescue applications derived with the of Lagrange equations of the second kind with multipliers. Analysed vehicle through using mecanum wheels has three degrees of freedom and can move on a flat ground in any direction with any configuration of platform's frame. In order to derive dynamic equations of motion of mentioned object, kinetic potential of the system and generalized forces affecting the system are determined. The results of a solution of inverse dynamics problem are also published.

A space-frequency multiplicative regularization for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

Dynamic forces reconstruction from vibration data is an ill-posed inverse problem. A standard approach to stabilize the reconstruction consists in using some prior information on the quantities to identify. This is generally done by including in the formulation of the inverse problem a regularization term as an additive or a multiplicative constraint. In the present article, a space-frequency multiplicative regularization is developed to identify mechanical forces acting on a structure. The proposed regularization strategy takes advantage of one's prior knowledge of the nature and the location of excitation sources, as well as that of their spectral contents. Furthermore, it has the merit to be free from the preliminary definition of any regularization parameter. The validity of the proposed regularization procedure is assessed numerically and experimentally. It is more particularly pointed out that properly exploiting the space-frequency characteristics of the excitation field to identify can improve the quality of the force reconstruction.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases.

The inverse problem of refraction travel times, part II: Quantifying refraction nonuniqueness using a three-layer model

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.

2005-01-01

This paper is the second of a set of two papers in which we study the inverse refraction problem. The first paper, "Types of Geophysical Nonuniqueness through Minimization," studies and classifies the types of nonuniqueness that exist when solving inverse problems depending on the participation of a priori information required to obtain reliable solutions of inverse geophysical problems. In view of the classification developed, in this paper we study the type of nonuniqueness associated with the inverse refraction problem. An approach for obtaining a realistic solution to the inverse refraction problem is offered in a third paper that is in preparation. The nonuniqueness of the inverse refraction problem is examined by using a simple three-layer model. Like many other inverse geophysical problems, the inverse refraction problem does not have a unique solution. Conventionally, nonuniqueness is considered to be a result of insufficient data and/or error in the data, for any fixed number of model parameters. This study illustrates that even for overdetermined and error free data, nonlinear inverse refraction problems exhibit exact-data nonuniqueness, which further complicates the problem of nonuniqueness. By evaluating the nonuniqueness of the inverse refraction problem, this paper targets the improvement of refraction inversion algorithms, and as a result, the achievement of more realistic solutions. The nonuniqueness of the inverse refraction problem is examined initially by using a simple three-layer model. The observations and conclusions of the three-layer model nonuniqueness study are used to evaluate the nonuniqueness of more complicated n-layer models and multi-parameter cell models such as in refraction tomography. For any fixed number of model parameters, the inverse refraction problem exhibits continuous ranges of exact-data nonuniqueness. Such an unfavorable type of nonuniqueness can be uniquely solved only by providing abundant a priori information. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.

Application of Dynamic Logic Algorithm to Inverse Scattering Problems Related to Plasma Diagnostics

NASA Astrophysics Data System (ADS)

Perlovsky, L.; Deming, R. W.; Sotnikov, V.

2010-11-01

In plasma diagnostics scattering of electromagnetic waves is widely used for identification of density and wave field perturbations. In the present work we use a powerful mathematical approach, dynamic logic (DL), to identify the spectra of scattered electromagnetic (EM) waves produced by the interaction of the incident EM wave with a Langmuir soliton in the presence of noise. The problem is especially difficult since the spectral amplitudes of the noise pattern are comparable with the amplitudes of the scattered waves. In the past DL has been applied to a number of complex problems in artificial intelligence, pattern recognition, and signal processing, resulting in revolutionary improvements. Here we demonstrate its application to plasma diagnostic problems. [4pt] Perlovsky, L.I., 2001. Neural Networks and Intellect: using model-based concepts. Oxford University Press, New York, NY.

Users manual for the Variable dimension Automatic Synthesis Program (VASP)

NASA Technical Reports Server (NTRS)

White, J. S.; Lee, H. Q.

1971-01-01

A dictionary and some problems for the Variable Automatic Synthesis Program VASP are submitted. The dictionary contains a description of each subroutine and instructions on its use. The example problems give the user a better perspective on the use of VASP for solving problems in modern control theory. These example problems include dynamic response, optimal control gain, solution of the sampled data matrix Ricatti equation, matrix decomposition, and pseudo inverse of a matrix. Listings of all subroutines are also included. The VASP program has been adapted to run in the conversational mode on the Ames 360/67 computer.

Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior.

PubMed

Hansen, Sofie Therese; Hansen, Lars Kai

2017-03-01

Electroencephalography (EEG) can capture brain dynamics in high temporal resolution. By projecting the scalp EEG signal back to its origin in the brain also high spatial resolution can be achieved. Source localized EEG therefore has potential to be a very powerful tool for understanding the functional dynamics of the brain. Solving the inverse problem of EEG is however highly ill-posed as there are many more potential locations of the EEG generators than EEG measurement points. Several well-known properties of brain dynamics can be exploited to alleviate this problem. More short ranging connections exist in the brain than long ranging, arguing for spatially focal sources. Additionally, recent work (Delorme et al., 2012) argues that EEG can be decomposed into components having sparse source distributions. On the temporal side both short and long term stationarity of brain activation are seen. We summarize these insights in an inverse solver, the so-called "Variational Garrote" (Kappen and Gómez, 2013). Using a Markov prior we can incorporate flexible degrees of temporal stationarity. Through spatial basis functions spatially smooth distributions are obtained. Sparsity of these are inherent to the Variational Garrote solver. We name our method the MarkoVG and demonstrate its ability to adapt to the temporal smoothness and spatial sparsity in simulated EEG data. Finally a benchmark EEG dataset is used to demonstrate MarkoVG's ability to recover non-stationary brain dynamics. Copyright © 2016 Elsevier Inc. All rights reserved.

Classical and quantum dynamics in an inverse square potential

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

Guillaumín-España, Elisa, E-mail: ege@correo.azc.uam.mx; Núñez-Yépez, H. N., E-mail: nyhn@xanum.uam.mx; Salas-Brito, A. L., E-mail: asb@correo.azc.uam.mx

2014-10-15

The classical motion of a particle in a 3D inverse square potential with negative energy, E, is shown to be geodesic, i.e., equivalent to the particle's free motion on a non-compact phase space manifold irrespective of the sign of the coupling constant. We thus establish that all its classical orbits with E < 0 are unbounded. To analyse the corresponding quantum problem, the Schrödinger equation is solved in momentum space. No discrete energy levels exist in the unrenormalized case and the system shows a complete “fall-to-the-center” with an energy spectrum unbounded by below. Such behavior corresponds to the non-existence ofmore » bound classical orbits. The symmetry of the problem is SO(3) × SO(2, 1) corroborating previously obtained results.« less

INFO-RNA--a fast approach to inverse RNA folding.

PubMed

Busch, Anke; Backofen, Rolf

2006-08-01

The structure of RNA molecules is often crucial for their function. Therefore, secondary structure prediction has gained much interest. Here, we consider the inverse RNA folding problem, which means designing RNA sequences that fold into a given structure. We introduce a new algorithm for the inverse folding problem (INFO-RNA) that consists of two parts; a dynamic programming method for good initial sequences and a following improved stochastic local search that uses an effective neighbor selection method. During the initialization, we design a sequence that among all sequences adopts the given structure with the lowest possible energy. For the selection of neighbors during the search, we use a kind of look-ahead of one selection step applying an additional energy-based criterion. Afterwards, the pre-ordered neighbors are tested using the actual optimization criterion of minimizing the structure distance between the target structure and the mfe structure of the considered neighbor. We compared our algorithm to RNAinverse and RNA-SSD for artificial and biological test sets. Using INFO-RNA, we performed better than RNAinverse and in most cases, we gained better results than RNA-SSD, the probably best inverse RNA folding tool on the market. www.bioinf.uni-freiburg.de?Subpages/software.html.

Algorithms and programs complex for solving inverse problems of artificial Earth satellite dynamics with using parallel computation. (Russian Title: Программно-математическое обеспечение для решения обратных задач динамики ИСЗ с использованием параллельных вычислений )

NASA Astrophysics Data System (ADS)

Chuvashov, I. N.

2011-07-01

In this paper complex of algorithms and programs for solving inverse problems of artificial earth satellite dynamics is described. Complex has been intended for satellite orbit improvement, calculation of motion model parameters and etc. Programs complex has been worked up for cluster "Skiff Cyberia". Results of numerical experiments obtained by using new complex in common the program "Numerical model of the system artificial satellites motion" is presented in this paper.

Modal resonant dynamics of cables with a flexible support: A modulated diffraction problem

NASA Astrophysics Data System (ADS)

Guo, Tieding; Kang, Houjun; Wang, Lianhua; Liu, Qijian; Zhao, Yueyu

2018-06-01

Modal resonant dynamics of cables with a flexible support is defined as a modulated (wave) diffraction problem, and investigated by asymptotic expansions of the cable-support coupled system. The support-cable mass ratio, which is usually very large, turns out to be the key parameter for characterizing cable-support dynamic interactions. By treating the mass ratio's inverse as a small perturbation parameter and scaling the cable tension properly, both cable's modal resonant dynamics and the flexible support dynamics are asymptotically reduced by using multiple scale expansions, leading finally to a reduced cable-support coupled model (i.e., on a slow time scale). After numerical validations of the reduced coupled model, cable-support coupled responses and the flexible support induced coupling effects on the cable, are both fully investigated, based upon the reduced model. More explicitly, the dynamic effects on the cable's nonlinear frequency and force responses, caused by the support-cable mass ratio, the resonant detuning parameter and the support damping, are carefully evaluated.

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

NASA Astrophysics Data System (ADS)

Yu, Jiang-Bo; Zhao, Yan; Wu, Yu-Qiang

2014-04-01

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.

Solving the inverse scattering problem in reflection-mode dynamic speckle-field phase microscopy (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zhou, Renjie; So, Peter T. C.; Yaqoob, Zahid; Jin, Di; Hosseini, Poorya; Kuang, Cuifang; Singh, Vijay Raj; Kim, Yang-Hyo; Dasari, Ramachandra R.

2017-02-01

Most of the quantitative phase microscopy systems are unable to provide depth-resolved information for measuring complex biological structures. Optical diffraction tomography provides a non-trivial solution to it by 3D reconstructing the object with multiple measurements through different ways of realization. Previously, our lab developed a reflection-mode dynamic speckle-field phase microscopy (DSPM) technique, which can be used to perform depth resolved measurements in a single shot. Thus, this system is suitable for measuring dynamics in a layer of interest in the sample. DSPM can be also used for tomographic imaging, which promises to solve the long-existing "missing cone" problem in 3D imaging. However, the 3D imaging theory for this type of system has not been developed in the literature. Recently, we have developed an inverse scattering model to rigorously describe the imaging physics in DSPM. Our model is based on the diffraction tomography theory and the speckle statistics. Using our model, we first precisely calculated the defocus response and the depth resolution in our system. Then, we further calculated the 3D coherence transfer function to link the 3D object structural information with the axially scanned imaging data. From this transfer function, we found that in the reflection mode excellent sectioning effect exists in the low lateral spatial frequency region, thus allowing us to solve the "missing cone" problem. Currently, we are working on using this coherence transfer function to reconstruct layered structures and complex cells.

Neural learning of constrained nonlinear transformations

NASA Technical Reports Server (NTRS)

Barhen, Jacob; Gulati, Sandeep; Zak, Michail

1989-01-01

Two issues that are fundamental to developing autonomous intelligent robots, namely, rudimentary learning capability and dexterous manipulation, are examined. A powerful neural learning formalism is introduced for addressing a large class of nonlinear mapping problems, including redundant manipulator inverse kinematics, commonly encountered during the design of real-time adaptive control mechanisms. Artificial neural networks with terminal attractor dynamics are used. The rapid network convergence resulting from the infinite local stability of these attractors allows the development of fast neural learning algorithms. Approaches to manipulator inverse kinematics are reviewed, the neurodynamics model is discussed, and the neural learning algorithm is presented.

Anthropic versus cosmological solutions to the coincidence problem

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

Barreira, A.; Avelino, P. P.; Departamento de Fisica da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto

2011-05-15

In this paper, we investigate possible solutions to the coincidence problem in flat phantom dark-energy models with a constant dark-energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the {Lambda} cold dark matter model. This relates a cosmological solution to the coincidence problem with a dynamical dark-energymore » component having an equation-of-state parameter not too close to -1 at the present time. We further show that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.« less

Dynamic data integration and stochastic inversion of a confined aquifer

NASA Astrophysics Data System (ADS)

Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.

2013-12-01

Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing and coarsening and therefore reducing the associated estimation uncertainty), a parallel LSQR solver was written and verified. For the 50×50 grid, the parallel solver sped up the serial solution time by 14X using 4 CPUs (research on parallel performance and scaling is ongoing). A sensitivity analysis was conducted to examine the relation between the observed data and the inversion outcomes, where measurement errors of increasing magnitudes (i.e., ×1, 2, 5, 10% of the total head variation and up to ×2% of the total flux variation) were imposed on the observed data. Inversion results were stable but the accuracy of Ks and boundary estimation degraded with increasing errors, as expected. In particular, quality of the observed heads is critical to hydraulic head recovery, while quality of the observed fluxes plays a dominant role in K estimation. References: Wang, D., Y. Zhang, J. Irsa, H. Huang, and L. Wang (2013), Data integration and stochastic inversion of a confined aquifer with high performance computing, Advances in Water Resources, in preparation. Paige, C. C., and M. A. Saunders (1982), LSQR: an algorithm for sparse linear equations and sparse least squares, ACM Transactions on Mathematical Software, 8(1), 43-71.

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

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.

Dynamic Source Inversion of a M6.5 Intraslab Earthquake in Mexico: Application of a New Parallel Genetic Algorithm

NASA Astrophysics Data System (ADS)

Díaz-Mojica, J. J.; Cruz-Atienza, V. M.; Madariaga, R.; Singh, S. K.; Iglesias, A.

2013-05-01

We introduce a novel approach for imaging the earthquakes dynamics from ground motion records based on a parallel genetic algorithm (GA). The method follows the elliptical dynamic-rupture-patch approach introduced by Di Carli et al. (2010) and has been carefully verified through different numerical tests (Díaz-Mojica et al., 2012). Apart from the five model parameters defining the patch geometry, our dynamic source description has four more parameters: the stress drop inside the nucleation and the elliptical patches; and two friction parameters, the slip weakening distance and the change of the friction coefficient. These parameters are constant within the rupture surface. The forward dynamic source problem, involved in the GA inverse method, uses a highly accurate computational solver for the problem, namely the staggered-grid split-node. The synthetic inversion presented here shows that the source model parameterization is suitable for the GA, and that short-scale source dynamic features are well resolved in spite of low-pass filtering of the data for periods comparable to the source duration. Since there is always uncertainty in the propagation medium as well as in the source location and the focal mechanisms, we have introduced a statistical approach to generate a set of solution models so that the envelope of the corresponding synthetic waveforms explains as much as possible the observed data. We applied the method to the 2012 Mw6.5 intraslab Zumpango, Mexico earthquake and determined several fundamental source parameters that are in accordance with different and completely independent estimates for Mexican and worldwide earthquakes. Our weighted-average final model satisfactorily explains eastward rupture directivity observed in the recorded data. Some parameters found for the Zumpango earthquake are: Δτ = 30.2+/-6.2 MPa, Er = 0.68+/-0.36x10^15 J, G = 1.74+/-0.44x10^15 J, η = 0.27+/-0.11, Vr/Vs = 0.52+/-0.09 and Mw = 6.64+/-0.07; for the stress drop, radiated energy, fracture energy, radiation efficiency, rupture velocity and moment magnitude, respectively. Mw6.5 intraslab Zumpango earthquake location, stations location and tectonic setting in central Mexico

Review: Optimization methods for groundwater modeling and management

NASA Astrophysics Data System (ADS)

Yeh, William W.-G.

2015-09-01

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

A Localized Ensemble Kalman Smoother

NASA Technical Reports Server (NTRS)

Butala, Mark D.

2012-01-01

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

An inverse problem for a mathematical model of aquaponic agriculture

NASA Astrophysics Data System (ADS)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

Improving rotorcraft survivability to RPG attack using inverse methods

NASA Astrophysics Data System (ADS)

Anderson, D.; Thomson, D. G.

2009-09-01

This paper presents the results of a preliminary investigation of optimal threat evasion strategies for improving the survivability of rotorcraft under attack by rocket propelled grenades (RPGs). The basis of this approach is the application of inverse simulation techniques pioneered for simulation of aggressive helicopter manoeuvres to the RPG engagement problem. In this research, improvements in survivability are achieved by computing effective evasive manoeuvres. The first step in this process uses the missile approach warning system camera (MAWS) on the aircraft to provide angular information of the threat. Estimates of the RPG trajectory and impact point are then estimated. For the current flight state an appropriate evasion response is selected then realised via inverse simulation of the platform dynamics. Results are presented for several representative engagements showing the efficacy of the approach.

Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems

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

Tupek, Michael R.

2016-06-30

In recent years there has been a proliferation of modeling techniques for forward predictions of crack propagation in brittle materials, including: phase-field/gradient damage models, peridynamics, cohesive-zone models, and G/XFEM enrichment techniques. However, progress on the corresponding inverse problems has been relatively lacking. Taking advantage of key features of existing modeling approaches, we propose a parabolic regularization of Barenblatt cohesive models which borrows extensively from previous phase-field and gradient damage formulations. An efficient explicit time integration strategy for this type of nonlocal fracture model is then proposed and justified. In addition, we present a C++ computational framework for computing in- putmore » parameter sensitivities efficiently for explicit dynamic problems using the adjoint method. This capability allows for solving inverse problems involving crack propagation to answer interesting engineering questions such as: 1) what is the optimal design topology and material placement for a heterogeneous structure to maximize fracture resistance, 2) what loads must have been applied to a structure for it to have failed in an observed way, 3) what are the existing cracks in a structure given various experimental observations, etc. In this work, we focus on the first of these engineering questions and demonstrate a capability to automatically and efficiently compute optimal designs intended to minimize crack propagation in structures.« less

Geomagnetic inverse problem and data assimilation: a progress report

NASA Astrophysics Data System (ADS)

Aubert, Julien; Fournier, Alexandre

2013-04-01

In this presentation I will present two studies recently undertaken by our group in an effort to bring the benefits of data assimilation to the study of Earth's magnetic field and the dynamics of its liquid iron core, where the geodynamo operates. In a first part I will focus on the geomagnetic inverse problem, which attempts to recover the fluid flow in the core from the temporal variation of the magnetic field (known as the secular variation). Geomagnetic data can be downward continued from the surface of the Earth down to the core-mantle boundary, but not further below, since the core is an electrical conductor. Historically, solutions to the geomagnetic inverse problem in such a sparsely observed system were thus found only for flow immediately below the core mantle boundary. We have recently shown that combining a numerical model of the geodynamo together with magnetic observations, through the use of Kalman filtering, now allows to present solutions for flow throughout the core. In a second part, I will present synthetic tests of sequential geomagnetic data assimilation aiming at evaluating the range at which the future of the geodynamo can be predicted, and our corresponding prospects to refine the current geomagnetic predictions. Fournier, Aubert, Thébault: Inference on core surface flow from observations and 3-D dynamo modelling, Geophys. J. Int. 186, 118-136, 2011, doi: 10.1111/j.1365-246X.2011.05037.x Aubert, Fournier: Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model, Nonlinear Proc. Geoph. 18, 657-674, 2011, doi:10.5194/npg-18-657-2011 Aubert: Flow throughout the Earth's core inverted from geomagnetic observations and numerical dynamo models, Geophys. J. Int., 2012, doi: 10.1093/gji/ggs051

Dynamic identification of axial force and boundary restraints in tie rods and cables with uncertainty quantification using Set Inversion Via Interval Analysis

NASA Astrophysics Data System (ADS)

Kernicky, Timothy; Whelan, Matthew; Al-Shaer, Ehab

2018-06-01

A methodology is developed for the estimation of internal axial force and boundary restraints within in-service, prismatic axial force members of structural systems using interval arithmetic and contractor programming. The determination of the internal axial force and end restraints in tie rods and cables using vibration-based methods has been a long standing problem in the area of structural health monitoring and performance assessment. However, for structural members with low slenderness where the dynamics are significantly affected by the boundary conditions, few existing approaches allow for simultaneous identification of internal axial force and end restraints and none permit for quantifying the uncertainties in the parameter estimates due to measurement uncertainties. This paper proposes a new technique for approaching this challenging inverse problem that leverages the Set Inversion Via Interval Analysis algorithm to solve for the unknown axial forces and end restraints using natural frequency measurements. The framework developed offers the ability to completely enclose the feasible solutions to the parameter identification problem, given specified measurement uncertainties for the natural frequencies. This ability to propagate measurement uncertainty into the parameter space is critical towards quantifying the confidence in the individual parameter estimates to inform decision-making within structural health diagnosis and prognostication applications. The methodology is first verified with simulated data for a case with unknown rotational end restraints and then extended to a case with unknown translational and rotational end restraints. A laboratory experiment is then presented to demonstrate the application of the methodology to an axially loaded rod with progressively increased end restraint at one end.

Tuning Fractures With Dynamic Data

NASA Astrophysics Data System (ADS)

Yao, Mengbi; Chang, Haibin; Li, Xiang; Zhang, Dongxiao

2018-02-01

Flow in fractured porous media is crucial for production of oil/gas reservoirs and exploitation of geothermal energy. Flow behaviors in such media are mainly dictated by the distribution of fractures. Measuring and inferring the distribution of fractures is subject to large uncertainty, which, in turn, leads to great uncertainty in the prediction of flow behaviors. Inverse modeling with dynamic data may assist to constrain fracture distributions, thus reducing the uncertainty of flow prediction. However, inverse modeling for flow in fractured reservoirs is challenging, owing to the discrete and non-Gaussian distribution of fractures, as well as strong nonlinearity in the relationship between flow responses and model parameters. In this work, building upon a series of recent advances, an inverse modeling approach is proposed to efficiently update the flow model to match the dynamic data while retaining geological realism in the distribution of fractures. In the approach, the Hough-transform method is employed to parameterize non-Gaussian fracture fields with continuous parameter fields, thus rendering desirable properties required by many inverse modeling methods. In addition, a recently developed forward simulation method, the embedded discrete fracture method (EDFM), is utilized to model the fractures. The EDFM maintains computational efficiency while preserving the ability to capture the geometrical details of fractures because the matrix is discretized as structured grid, while the fractures being handled as planes are inserted into the matrix grids. The combination of Hough representation of fractures with the EDFM makes it possible to tune the fractures (through updating their existence, location, orientation, length, and other properties) without requiring either unstructured grids or regridding during updating. Such a treatment is amenable to numerous inverse modeling approaches, such as the iterative inverse modeling method employed in this study, which is capable of dealing with strongly nonlinear problems. A series of numerical case studies with increasing complexity are set up to examine the performance of the proposed approach.

Localization of synchronous cortical neural sources.

PubMed

Zerouali, Younes; Herry, Christophe L; Jemel, Boutheina; Lina, Jean-Marc

2013-03-01

Neural synchronization is a key mechanism to a wide variety of brain functions, such as cognition, perception, or memory. High temporal resolution achieved by EEG recordings allows the study of the dynamical properties of synchronous patterns of activity at a very fine temporal scale but with very low spatial resolution. Spatial resolution can be improved by retrieving the neural sources of EEG signal, thus solving the so-called inverse problem. Although many methods have been proposed to solve the inverse problem and localize brain activity, few of them target the synchronous brain regions. In this paper, we propose a novel algorithm aimed at localizing specifically synchronous brain regions and reconstructing the time course of their activity. Using multivariate wavelet ridge analysis, we extract signals capturing the synchronous events buried in the EEG and then solve the inverse problem on these signals. Using simulated data, we compare results of source reconstruction accuracy achieved by our method to a standard source reconstruction approach. We show that the proposed method performs better across a wide range of noise levels and source configurations. In addition, we applied our method on real dataset and identified successfully cortical areas involved in the functional network underlying visual face perception. We conclude that the proposed approach allows an accurate localization of synchronous brain regions and a robust estimation of their activity.

Dynamic gamma knife radiosurgery

NASA Astrophysics Data System (ADS)

Luan, Shuang; Swanson, Nathan; Chen, Zhe; Ma, Lijun

2009-03-01

Gamma knife has been the treatment of choice for various brain tumors and functional disorders. Current gamma knife radiosurgery is planned in a 'ball-packing' approach and delivered in a 'step-and-shoot' manner, i.e. it aims to 'pack' the different sized spherical high-dose volumes (called 'shots') into a tumor volume. We have developed a dynamic scheme for gamma knife radiosurgery based on the concept of 'dose-painting' to take advantage of the new robotic patient positioning system on the latest Gamma Knife C™ and Perfexion™ units. In our scheme, the spherical high dose volume created by the gamma knife unit will be viewed as a 3D spherical 'paintbrush', and treatment planning reduces to finding the best route of this 'paintbrush' to 'paint' a 3D tumor volume. Under our dose-painting concept, gamma knife radiosurgery becomes dynamic, where the patient moves continuously under the robotic positioning system. We have implemented a fully automatic dynamic gamma knife radiosurgery treatment planning system, where the inverse planning problem is solved as a traveling salesman problem combined with constrained least-square optimizations. We have also carried out experimental studies of dynamic gamma knife radiosurgery and showed the following. (1) Dynamic gamma knife radiosurgery is ideally suited for fully automatic inverse planning, where high quality radiosurgery plans can be obtained in minutes of computation. (2) Dynamic radiosurgery plans are more conformal than step-and-shoot plans and can maintain a steep dose gradient (around 13% per mm) between the target tumor volume and the surrounding critical structures. (3) It is possible to prescribe multiple isodose lines with dynamic gamma knife radiosurgery, so that the treatment can cover the periphery of the target volume while escalating the dose for high tumor burden regions. (4) With dynamic gamma knife radiosurgery, one can obtain a family of plans representing a tradeoff between the delivery time and the dose distributions, thus giving the clinician one more dimension of flexibility of choosing a plan based on the clinical situations.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment

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

Manoli, Gabriele, E-mail: manoli@dmsa.unipd.it; Nicholas School of the Environment, Duke University, Durham, NC 27708; Rossi, Matteo

The modeling of unsaturated groundwater flow is affected by a high degree of uncertainty related to both measurement and model errors. Geophysical methods such as Electrical Resistivity Tomography (ERT) can provide useful indirect information on the hydrological processes occurring in the vadose zone. In this paper, we propose and test an iterated particle filter method to solve the coupled hydrogeophysical inverse problem. We focus on an infiltration test monitored by time-lapse ERT and modeled using Richards equation. The goal is to identify hydrological model parameters from ERT electrical potential measurements. Traditional uncoupled inversion relies on the solution of two sequentialmore » inverse problems, the first one applied to the ERT measurements, the second one to Richards equation. This approach does not ensure an accurate quantitative description of the physical state, typically violating mass balance. To avoid one of these two inversions and incorporate in the process more physical simulation constraints, we cast the problem within the framework of a SIR (Sequential Importance Resampling) data assimilation approach that uses a Richards equation solver to model the hydrological dynamics and a forward ERT simulator combined with Archie's law to serve as measurement model. ERT observations are then used to update the state of the system as well as to estimate the model parameters and their posterior distribution. The limitations of the traditional sequential Bayesian approach are investigated and an innovative iterative approach is proposed to estimate the model parameters with high accuracy. The numerical properties of the developed algorithm are verified on both homogeneous and heterogeneous synthetic test cases based on a real-world field experiment.« less

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

PubMed

Robinson, Katherine M; Ninowski, Jerilyn E

2003-12-01

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

Recurrent Neural Network for Computing the Drazin Inverse.

PubMed

Stanimirović, Predrag S; Zivković, Ivan S; Wei, Yimin

2015-11-01

This paper presents a recurrent neural network (RNN) for computing the Drazin inverse of a real matrix in real time. This recurrent neural network (RNN) is composed of n independent parts (subnetworks), where n is the order of the input matrix. These subnetworks can operate concurrently, so parallel and distributed processing can be achieved. In this way, the computational advantages over the existing sequential algorithms can be attained in real-time applications. The RNN defined in this paper is convenient for an implementation in an electronic circuit. The number of neurons in the neural network is the same as the number of elements in the output matrix, which represents the Drazin inverse. The difference between the proposed RNN and the existing ones for the Drazin inverse computation lies in their network architecture and dynamics. The conditions that ensure the stability of the defined RNN as well as its convergence toward the Drazin inverse are considered. In addition, illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network.

Constraining Mass Anomalies Using Trans-dimensional Gravity Inversions

NASA Astrophysics Data System (ADS)

Izquierdo, K.; Montesi, L.; Lekic, V.

2016-12-01

The density structure of planetary interiors constitutes a key constraint on their composition, temperature, and dynamics. This has motivated the development of non-invasive methods to infer 3D distribution of density anomalies within a planet's interior using gravity observations made from the surface or orbit. On Earth, this information can be supplemented by seismic and electromagnetic observations, but such data are generally not available on other planets and inferences must be made from gravity observations alone. Unfortunately, inferences of density anomalies from gravity are non-unique and even the dimensionality of the problem - i.e., the number of density anomalies detectable in the planetary interior - is unknown. In this project, we use the Reversible Jump Markov chain Monte Carlo (RJMCMC) algorithm to approach gravity inversions in a trans-dimensional way, that is, considering the magnitude of the mass, the latitude, longitude, depth and number of anomalies itself as unknowns to be constrained by the observed gravity field at the surface of a planet. Our approach builds upon previous work using trans-dimensional gravity inversions in which the density contrast between the anomaly and the surrounding material is known. We validate the algorithm by analyzing a synthetic gravity field produced by a known density structure and comparing the retrieved and input density structures. We find excellent agreement between the input and retrieved structure when working in 1D and 2D domains. However, in 3D domains, comprehensive exploration of the much larger space of possible models makes search efficiency a key ingredient in successful gravity inversion. We find that upon a sufficiently long RJMCMC run, it is possible to use statistical information to recover a predicted model that matches the real model. We argue that even more complex problems, such as those involving real gravity acceleration data of a planet as the constraint, our trans-dimensional gravity inversion algorithm provides a good option to overcome the problem of non-uniqueness while achieving parsimony in gravity inversions.

TOPEX/POSEIDON tides estimated using a global inverse model

NASA Technical Reports Server (NTRS)

Egbert, Gary D.; Bennett, Andrew F.; Foreman, Michael G. G.

1994-01-01

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better agreement with altimetric and ground truth data, than previously proposed tidal models. Relative to the 'default' tidal corrections provided with the TOPEX/POSEIDON GDR, the inverse solution reduces crossover difference variances significantly (approximately 20-30%), even though only a small number of free parameters (approximately equal to 1000) are actually fit to the crossover data.

Inversion for Refractivity Parameters Using a Dynamic Adaptive Cuckoo Search with Crossover Operator Algorithm

PubMed Central

Zhang, Zhihua; Sheng, Zheng; Shi, Hanqing; Fan, Zhiqiang

2016-01-01

Using the RFC technique to estimate refractivity parameters is a complex nonlinear optimization problem. In this paper, an improved cuckoo search (CS) algorithm is proposed to deal with this problem. To enhance the performance of the CS algorithm, a parameter dynamic adaptive operation and crossover operation were integrated into the standard CS (DACS-CO). Rechenberg's 1/5 criteria combined with learning factor were used to control the parameter dynamic adaptive adjusting process. The crossover operation of genetic algorithm was utilized to guarantee the population diversity. The new hybrid algorithm has better local search ability and contributes to superior performance. To verify the ability of the DACS-CO algorithm to estimate atmospheric refractivity parameters, the simulation data and real radar clutter data are both implemented. The numerical experiments demonstrate that the DACS-CO algorithm can provide an effective method for near-real-time estimation of the atmospheric refractivity profile from radar clutter. PMID:27212938

Fluid moments of the nonlinear Landau collision operator

DOE PAGES

Hirvijoki, E.; Lingam, M.; Pfefferle, D.; ...

2016-08-09

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. In conclusion, the proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

Children's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

Molecular structures and intramolecular dynamics of pentahalides

NASA Astrophysics Data System (ADS)

Ischenko, A. A.

2017-03-01

This paper reviews advances of modern gas electron diffraction (GED) method combined with high-resolution spectroscopy and quantum chemical calculations in studies of the impact of intramolecular dynamics in free molecules of pentahalides. Some recently developed approaches to the electron diffraction data interpretation, based on direct incorporation of the adiabatic potential energy surface parameters to the diffraction intensity are described. In this way, complementary data of different experimental and computational methods can be directly combined for solving problems of the molecular structure and its dynamics. The possibility to evaluate some important parameters of the adiabatic potential energy surface - barriers to pseudorotation and saddle point of intermediate configuration from diffraction intensities in solving the inverse GED problem is demonstrated on several examples. With increasing accuracy of the electron diffraction intensities and the development of the theoretical background of electron scattering and data interpretation, it has become possible to investigate complex nuclear dynamics in fluxional systems by the GED method. Results of other research groups are also included in the discussion.

Preliminary assessment of the robustness of dynamic inversion based flight control laws

NASA Technical Reports Server (NTRS)

Snell, S. A.

1992-01-01

Dynamic-inversion-based flight control laws present an attractive alternative to conventional gain-scheduled designs for high angle-of-attack maneuvering, where nonlinearities dominate the dynamics. Dynamic inversion is easily applied to the aircraft dynamics requiring a knowledge of the nonlinear equations of motion alone, rather than an extensive set of linearizations. However, the robustness properties of the dynamic inversion are questionable especially when considering the uncertainties involved with the aerodynamic database during post-stall flight. This paper presents a simple analysis and some preliminary results of simulations with a perturbed database. It is shown that incorporating integrators into the control loops helps to improve the performance in the presence of these perturbations.

Analysis and numerical modelling of eddy current damper for vibration problems

NASA Astrophysics Data System (ADS)

Irazu, L.; Elejabarrieta, M. J.

2018-07-01

This work discusses a contactless eddy current damper, which is used to attenuate structural vibration. Eddy currents can remove energy from dynamic systems without any contact and, thus, without adding mass or modifying the rigidity of the structure. An experimental modal analysis of a cantilever beam in the absence of and under a partial magnetic field is conducted in the bandwidth of 01 kHz. The results show that the eddy current phenomenon can attenuate the vibration of the entire structure without modifying the natural frequencies or the mode shapes of the structure itself. In this study, a new inverse method to numerically determine the dynamic properties of the contactless eddy current damper is proposed. The proposed inverse method and the eddy current model based on a lineal viscous force are validated by a practical application. The numerically obtained transfer function correlates with the experimental one, thus showing good agreement in the entire bandwidth of 01 kHz. The proposed method provides an easy and quick tool to model and predict the dynamic behaviour of the contactless eddy current damper, thereby avoiding the use of complex analytical models.

Dynamics and control of a multimode laser: Reduction of space-dependent rate equations to a low-dimensional system.

PubMed

Pyragas, K; Lange, F; Letz, T; Parisi, J; Kittel, A

2001-01-01

We suggest a quantitatively correct procedure for reducing the spatial degrees of freedom of the space-dependent rate equations of a multimode laser that describe the dynamics of the population inversion of the active medium and the mode intensities of the standing waves in the laser cavity. The key idea of that reduction is to take advantage of the small value of the parameter that defines the ratio between the population inversion decay rate and the cavity decay rate. We generalize the reduction procedure for the case of an intracavity frequency doubled laser. Frequency conversion performed by an optically nonlinear crystal placed inside the laser cavity may cause a pronounced instability in the laser performance, leading to chaotic oscillations of the output intensity. Based on the reduced equations, we analyze the dynamical properties of the system as well as the problem of stabilizing the steady state. The numerical analysis is performed considering the specific system of a Nd:YAG (neodymium-doped yttrium aluminum garnet) laser with an intracavity KTP (potassium titanyl phosphate) crystal.

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1995-01-01

During this year, we concentrated our efforts on the design of controllers for lateral/directional control using mu synthesis. This proved to be a more difficult task than we anticipated and we are still working on the designs. In the lateral-directional control problem, the inputs are pilot lateral stick and pedal commands and the outputs are roll rate about the velocity vector and side slip angle. The control effectors are ailerons, rudder deflection, and directional thrust vectoring vane deflection which produces a yawing moment about the body axis. Our math model does not contain any provision for thrust vectoring of rolling moment. This has resulted in limitations of performance at high angles of attack. During 1994-95, the following tasks for the lateral-directional controllers were accomplished: (1) Designed both inner and outer loop dynamic inversion controllers. These controllers are implemented using accelerometer outputs rather than an a priori model of the vehicle aerodynamics; (2) Used classical techniques to design controllers for the system linearized by dynamics inversion. These controllers acted to control roll rate and Dutch roll response; (3) Implemented the inner loop dynamic inversion and classical controllers on the six DOF simulation; (4) Developed a lateral-directional control allocation scheme based on minimizing required control effort among the ailerons, rudder, and directional thrust vectoring; and (5) Developed mu outer loop controllers combined with classical inner loop controllers.

Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.

PubMed

Cheng, Ching-An; Huang, Han-Pang

2016-12-01

We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Cellular Automata

NASA Astrophysics Data System (ADS)

Gutowitz, Howard

1991-08-01

Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices. Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole. Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.

Goal Directed Model Inversion: A Study of Dynamic Behavior

NASA Technical Reports Server (NTRS)

Colombano, Silvano P.; Compton, Michael; Raghavan, Bharathi; Lum, Henry, Jr. (Technical Monitor)

1994-01-01

Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome 0 "would have been right if the outcome had been the desired one." The algorithm then proceeds as follows: (1) store the action that produced the wrong outcome as a "target" (2) redefine the wrong outcome as a desired goal (3) submit the new desired goal to the system (4) compare the new action with the target action and modify the system by using a suitable algorithm for credit assignment (Back propagation in our example) (5) resubmit the original goal. Prior publications by our group in this area focused on demonstrating empirical results based on the inverse kinematic problem for a simulated robotic arm. In this paper we apply the inversion process to much simpler analytic functions in order to elucidate the dynamic behavior of the system and to determine the sensitivity of the learning process to various parameters. This understanding will be necessary for the acceptance of GDMI as a practical tool.

A 3D generic inverse dynamic method using wrench notation and quaternion algebra.

PubMed

Dumas, R; Aissaoui, R; de Guise, J A

2004-06-01

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.

Object-based inversion of crosswell radar tomography data to monitor vegetable oil injection experiments

USGS Publications Warehouse

Lane, John W.; Day-Lewis, Frederick D.; Versteeg, Roelof J.; Casey, Clifton C.

2004-01-01

Crosswell radar methods can be used to dynamically image ground-water flow and mass transport associated with tracer tests, hydraulic tests, and natural physical processes, for improved characterization of preferential flow paths and complex aquifer heterogeneity. Unfortunately, because the raypath coverage of the interwell region is limited by the borehole geometry, the tomographic inverse problem is typically underdetermined, and tomograms may contain artifacts such as spurious blurring or streaking that confuse interpretation.We implement object-based inversion (using a constrained, non-linear, least-squares algorithm) to improve results from pixel-based inversion approaches that utilize regularization criteria, such as damping or smoothness. Our approach requires pre- and post-injection travel-time data. Parameterization of the image plane comprises a small number of objects rather than a large number of pixels, resulting in an overdetermined problem that reduces the need for prior information. The nature and geometry of the objects are based on hydrologic insight into aquifer characteristics, the nature of the experiment, and the planned use of the geophysical results.The object-based inversion is demonstrated using synthetic and crosswell radar field data acquired during vegetable-oil injection experiments at a site in Fridley, Minnesota. The region where oil has displaced ground water is discretized as a stack of rectangles of variable horizontal extents. The inversion provides the geometry of the affected region and an estimate of the radar slowness change for each rectangle. Applying petrophysical models to these results and porosity from neutron logs, we estimate the vegetable-oil emulsion saturation in various layers.Using synthetic- and field-data examples, object-based inversion is shown to be an effective strategy for inverting crosswell radar tomography data acquired to monitor the emplacement of vegetable-oil emulsions. A principal advantage of object-based inversion is that it yields images that hydrologists and engineers can easily interpret and use for model calibration.

Shock Waves Propagation in Scope of the Nonlocal Theory of Dynamical Plasticity

NASA Astrophysics Data System (ADS)

Khantuleva, Tatyana A.

2004-07-01

From the point of view of the modern statistical mechanics the problems on shock compression of solids require a reformulation in terms of highly nonequilibrium effects arising inside the wave front. The self-organization during the multiscale and multistage momentum and energy exchange are originated by the correlation function. The theory of dynamic plasticity has been developed by the author on the base of the self-consistent nonlocal hydrodynamic approach had been applied to the shock wave propagation in solids. Nonlocal balance equations describe both the reversible wave type transport at the initial stage and the diffusive (dissipative) one in the end. The involved inverse influence of the mesoeffects on the wave propagation makes the formulation of problems self-consistent and involves a concept of the cybernetic control close-loop.

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

NASA Astrophysics Data System (ADS)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight into the nature of inverse problems and the appropriate mode of thought, chapter 1 offers historical vignettes, most of which have played an essential role in the development of natural science. These vignettes cover the first successful application of `non-destructive testing' by Archimedes (page 4) via Newton's laws of motion up to literary tomography, and readers will be able to enjoy a wide overview of inverse problems. Therefore, as the author asks, the reader should not skip this chapter. This may not be hard to do, since the headings of the sections are quite intriguing (`Archimedes' Bath', `Another World', `Got the Time?', `Head Games', etc). The author embarks on the technical approach to inverse problems in chapter 2. He has elegantly designed each section with a guide specifying course level, objective, mathematical and scientifical background and appropriate technology (e.g. types of calculators required). The guides are designed such that teachers may be able to construct effective and attractive courses by themselves. The book is not intended to offer one rigidly determined course, but should be used flexibly and independently according to the situation. Moreover, every section closes with activities which can be chosen according to the students' interests and levels of ability. Some of these exercises do not have ready solutions, but require long-term study, so readers are not required to solve all of them. After chapter 5, which contains discrete inverse problems such as the algebraic reconstruction technique and the Backus - Gilbert method, there are answers and commentaries to the activities. Finally, scripts in MATLAB are attached, although they can also be downloaded from the author's web page (http://math.uc.edu/~groetsch/). This book is aimed at students but it will be very valuable to researchers wishing to retain a wide overview of inverse problems in the midst of busy research activities. A Japanese version was published in 2002.

A dynamic processes study of PM retention by trees under different wind conditions.

PubMed

Xie, Changkun; Kan, Liyan; Guo, Jiankang; Jin, Sijia; Li, Zhigang; Chen, Dan; Li, Xin; Che, Shengquan

2018-02-01

Particulate matter (PM) is one of the most serious environmental problems, exacerbating respiratory and vascular illnesses. Plants have the ability to reduce non-point source PM pollution through retention on leaves and branches. Studies of the dynamic processes of PM retention by plants and the mechanisms influencing this process will help to improve the efficiency of urban greening for PM reduction. We examined dynamic processes of PM retention and the major factors influencing PM retention by six trees with different branch structure characteristics in wind tunnel experiments at three different wind speeds. The results showed that the changes of PM numbers retained by plant leaves over time were complex dynamic processes for which maximum values could exceed minimum values by over 10 times. The average value of PM measured in multiple periods and situations can be considered a reliable indicator of the ability of the plant to retain PM. The dynamic processes were similar for PM 10 and PM 2.5 . They could be clustered into three groups simulated by continually-rising, inverse U-shaped, and U-shaped polynomial functions, respectively. The processes were the synthetic effect of characteristics such as species, wind speed, period of exposure and their interactions. Continually-rising functions always explained PM retention in species with extremely complex branch structure. Inverse U-shaped processes explained PM retention in species with relatively simple branch structure and gentle wind. The U-shaped processes mainly explained PM retention at high wind speeds and in species with a relatively simple crown. These results indicate that using plants with complex crowns in urban greening and decreasing wind speed in plant communities increases the chance of continually-rising or inverse U-shaped relationships, which have a positive effect in reducing PM pollution. Copyright © 2017 Elsevier Ltd. All rights reserved.

Quench dynamics in SRF cavities: can we locate the quench origin with 2nd sound?

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

Maximenko, Yulia; /Moscow, MIPT; Segatskov, Dmitri A.

2011-03-01

A newly developed method of locating quenches in SRF cavities by detecting second-sound waves has been gaining popularity in SRF laboratories. The technique is based on measurements of time delays between the quench as determined by the RF system and arrival of the second-sound wave to the multiple detectors placed around the cavity in superfluid helium. Unlike multi-channel temperature mapping, this approach requires only a few sensors and simple readout electronics; it can be used with SRF cavities of almost arbitrary shape. One of its drawbacks is that being an indirect method it requires one to solve an inverse problemmore » to find the location of a quench. We tried to solve this inverse problem by using a parametric forward model. By analyzing the data we found that the approximation where the second-sound emitter is a near-singular source does not describe the physical system well enough. A time-dependent analysis of the quench process can help us to put forward a more adequate model. We present here our current algorithm to solve the inverse problem and discuss the experimental results.« less

Universal inverse design of surfaces with thin nematic elastomer sheets.

PubMed

Aharoni, Hillel; Xia, Yu; Zhang, Xinyue; Kamien, Randall D; Yang, Shu

2018-06-21

Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem-finding how to program a sheet in order for it to take an arbitrary desired 3D shape-is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers. We show how blueprints for arbitrary surface geometries can be generated using approximate numerical methods and how local extrinsic curvatures can be generated to assist in properly converting these geometries into shapes. Backed by faithfully alignable and rapidly lockable LCE chemistry, we precisely embed our designs in LCE sheets using advanced top-down microfabrication techniques. We thus successfully produce flat sheets that, upon thermal activation, take an arbitrary desired shape, such as a face. The general design principles presented here for creating an arbitrary 3D shape will allow for exploration of unmet needs in flexible electronics, metamaterials, aerospace and medical devices, and more.

A time domain inverse dynamic method for the end point tracking control of a flexible manipulator

NASA Technical Reports Server (NTRS)

Kwon, Dong-Soo; Book, Wayne J.

1991-01-01

The inverse dynamic equation of a flexible manipulator was solved in the time domain. By dividing the inverse system equation into the causal part and the anticausal part, we calculated the torque and the trajectories of all state variables for a given end point trajectory. The interpretation of this method in the frequency domain was explained in detail using the two-sided Laplace transform and the convolution integral. The open loop control of the inverse dynamic method shows an excellent result in simulation. For real applications, a practical control strategy is proposed by adding a feedback tracking control loop to the inverse dynamic feedforward control, and its good experimental performance is presented.

Network Inference via the Time-Varying Graphical Lasso

PubMed Central

Hallac, David; Park, Youngsuk; Boyd, Stephen; Leskovec, Jure

2018-01-01

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of such data, it is essential to understand the relationships between the different entities and how these relationships evolve over time. In this paper, we introduce the time-varying graphical lasso (TVGL), a method of inferring time-varying networks from raw time series data. We cast the problem in terms of estimating a sparse time-varying inverse covariance matrix, which reveals a dynamic network of interdependencies between the entities. Since dynamic network inference is a computationally expensive task, we derive a scalable message-passing algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in an efficient way. We also discuss several extensions, including a streaming algorithm to update the model and incorporate new observations in real time. Finally, we evaluate our TVGL algorithm on both real and synthetic datasets, obtaining interpretable results and outperforming state-of-the-art baselines in terms of both accuracy and scalability. PMID:29770256

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Hydrologic characterization of desert soils with varying degrees of pedogenesis: 2. Inverse modeling for eff ective properties

USGS Publications Warehouse

Mirus, B.B.; Perkins, K.S.; Nimmo, J.R.; Singha, K.

2009-01-01

To understand their relation to pedogenic development, soil hydraulic properties in the Mojave Desert were investi- gated for three deposit types: (i) recently deposited sediments in an active wash, (ii) a soil of early Holocene age, and (iii) a highly developed soil of late Pleistocene age. Eff ective parameter values were estimated for a simplifi ed model based on Richards' equation using a fl ow simulator (VS2D), an inverse algorithm (UCODE-2005), and matric pressure and water content data from three ponded infi ltration experiments. The inverse problem framework was designed to account for the eff ects of subsurface lateral spreading of infi ltrated water. Although none of the inverse problems converged on a unique, best-fi t parameter set, a minimum standard error of regression was reached for each deposit type. Parameter sets from the numerous inversions that reached the minimum error were used to develop probability distribu tions for each parameter and deposit type. Electrical resistance imaging obtained for two of the three infi ltration experiments was used to independently test fl ow model performance. Simulations for the active wash and Holocene soil successfully depicted the lateral and vertical fl uxes. Simulations of the more pedogenically developed Pleistocene soil did not adequately replicate the observed fl ow processes, which would require a more complex conceptual model to include smaller scale heterogeneities. The inverse-modeling results, however, indicate that with increasing age, the steep slope of the soil water retention curve shitis toward more negative matric pressures. Assigning eff ective soil hydraulic properties based on soil age provides a promising framework for future development of regional-scale models of soil moisture dynamics in arid environments for land-management applications. ?? Soil Science Society of America.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

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

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

DTIC Science & Technology

2017-03-07

please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics-based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics-based Inverse Problem to Deduce Marine...SUPPLEMENTARY NOTES 14. ABSTRACT This report describes research results related to the development and implementation of an inverse problem approach for

The inverse problem for definition of the shape of a molten contact bridge

NASA Astrophysics Data System (ADS)

Kharin, Stanislav N.; Sarsengeldin, Merey M.

2017-09-01

The paper presents the results of investigation of bridging phenomenon occurring at opening of electrical contacts. The mathematical model describing the dynamics of metal molten bridge takes into account the Thomson effect. It is based on the system of partial differential equations for temperature and electrical fields of the bridge in the domain containing two moving unknown boundaries. One of them is an interface between liquid and solid zones of the bridge and should be found by the solution of the corresponding Stefan problem. The second free boundary corresponds to the shape of the visible part of a bridge. Its definition is an inverse problem, for which solution it is necessary to find minimum of the energy consuming for the formation of the shape of a quasi-stationary bridge. Three components of this energy, namely surface tension, pinch effect and gravitation, are defined by the functional which minimum gives the required shape of the bridge. The solution of corresponding variation problem is found by the reduction of the problem to the solution of the system of ordinary differential equations. Calculated values of the voltage of the bridge rupture for various metals are in a good agreement with the experimental data. The criteria responsible for the mechanism of molten bridge rupture are introduced in the paper.

Simultaneous prediction of muscle and contact forces in the knee during gait.

PubMed

Lin, Yi-Chung; Walter, Jonathan P; Banks, Scott A; Pandy, Marcus G; Fregly, Benjamin J

2010-03-22

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process. Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Modified Dynamic Inversion to Control Large Flexible Aircraft: What's Going On?

NASA Technical Reports Server (NTRS)

Gregory, Irene M.

1999-01-01

High performance aircraft of the future will be designed lighter, more maneuverable, and operate over an ever expanding flight envelope. One of the largest differences from the flight control perspective between current and future advanced aircraft is elasticity. Over the last decade, dynamic inversion methodology has gained considerable popularity in application to highly maneuverable fighter aircraft, which were treated as rigid vehicles. This paper explores dynamic inversion application to an advanced highly flexible aircraft. An initial application has been made to a large flexible supersonic aircraft. In the course of controller design for this advanced vehicle, modifications were made to the standard dynamic inversion methodology. The results of this application were deemed rather promising. An analytical study has been undertaken to better understand the nature of the made modifications and to determine its general applicability. This paper presents the results of this initial analytical look at the modifications to dynamic inversion to control large flexible aircraft.

Studies of planetary upper atmospheres through occultations

NASA Technical Reports Server (NTRS)

Elliot, J. L.

1982-01-01

The structure, composition, dynamics and energy balance of planetary upper atmospheres through interpretation of steller occultation data from Uranus is discussed. The wave-optical problem of modelling strong scintillation for arbitrary turbulent atmospheres is studied, as well as influence of turbulence. It was concluded that quasi-global features of atmospheric structure are accurately determined by numerical inversion. Horizontally inhomogeneous structures are filtered out and have little effect on temperature profiles.

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

NASA Astrophysics Data System (ADS)

Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

2016-03-01

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Recursive mass matrix factorization and inversion: An operator approach to open- and closed-chain multibody dynamics

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Kreutz, K.

1988-01-01

This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.

Spherical Harmonic Inductive Detection Coils and their use In Dynamic Pre-emphasis for Magnetic Resonance Imaging

NASA Astrophysics Data System (ADS)

Edler, Karl T.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field -- an inverse curl operation -- and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI. Keywords: magnetic resonance imaging, eddy currents, dynamic shimming, negative feedback, quasi-static fields, vector potential, inverse curl

Landslide caracteristics determination using bayesian inversion and seismic recording

NASA Astrophysics Data System (ADS)

Mangeney, A.; Moretti, L.; Capdeville, Y.; Stutzmann, E.; Bodin, T.; Bouchut, F.

2014-12-01

Gravitational instabilities, such as landslides, avalanches, or debris flows, play a key role in erosional processes and represent one of the major natural hazards in mountainous, coastal, and volcanic regions. Despite the great amount of field, experimental and numerical work devoted to this problem, the understanding of the physical processes at work in gravitational flows is still an open issue, in particular due to the lack of observations relevant to their dynamics. In this context, the seismic signal generated by gravitational flows is a unique opportunity to obtain information on their dynamics and characteristics. Here we present the study of the 1997 Boxing Day landslide that occurred in Montserrat. We accessed the force applied by the landslide to the ground surface responsible of the seismic waves by inverting the seismic waveform recorded (force-time function). This force was then used as a constraint in a bayesian inversion problem where the forward problem is the force-time function calculation obtained by simulating the landslide with the SHALTOP model (mangeney et al., 2007). With this method, we are able to give an estimate of the rheology (friction coefficient) and the initial shape of the collapsing mass. The volume retrieved is very similar to that obtained by field observations. The friction coefficient determined is also similar to that constrained by former studies or to that predicted by empirical laws (Lucas et al., 2014). Furthermore the method permits to give an estimate of the error made on these parameters.

A Forward Glimpse into Inverse Problems through a Geology Example

ERIC Educational Resources Information Center

Winkel, Brian J.

2012-01-01

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

Revealing physical interaction networks from statistics of collective dynamics

PubMed Central

Nitzan, Mor; Casadiego, Jose; Timme, Marc

2017-01-01

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system’s model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems. PMID:28246630

Static and dynamic pressure prediction for prosthetic socket fitting assessment utilising an inverse problem approach.

PubMed

Sewell, Philip; Noroozi, Siamak; Vinney, John; Amali, Ramin; Andrews, Stephen

2012-01-01

It has been recognised in a review of the developments of lower-limb prosthetic socket fitting processes that the future demands new tools to aid in socket fitting. This paper presents the results of research to design and clinically test an artificial intelligence approach, specifically inverse problem analysis, for the determination of the pressures at the limb/prosthetic socket interface during stance and ambulation. Inverse problem analysis is based on accurately calculating the external loads or boundary conditions that can generate a known amount of strain, stresses or displacements at pre-determined locations on a structure. In this study a backpropagation artificial neural network (ANN) is designed and validated to predict the interfacial pressures at the residual limb/socket interface from strain data collected from the socket surface. The subject of this investigation was a 45-year-old male unilateral trans-tibial (below-knee) traumatic amputee who had been using a prosthesis for 22 years. When comparing the ANN predicted interfacial pressure on 16 patches within the socket with actual pressures applied to the socket there is shown to be 8.7% difference, validating the methodology. Investigation of varying axial load through the subject's prosthesis, alignment of the subject's prosthesis, and pressure at the limb/socket interface during walking demonstrates that the validated ANN is able to give an accurate full-field study of the static and dynamic interfacial pressure distribution. To conclude, a methodology has been developed that enables a prosthetist to quantitatively analyse the distribution of pressures within the prosthetic socket in a clinical environment. This will aid in facilitating the "right first time" approach to socket fitting which will benefit both the patient in terms of comfort and the prosthetist, by reducing the time and associated costs of providing a high level of socket fit. Copyright © 2011 Elsevier B.V. All rights reserved.

Inverse modeling methods for indoor airborne pollutant tracking: literature review and fundamentals.

PubMed

Liu, X; Zhai, Z

2007-12-01

Reduction in indoor environment quality calls for effective control and improvement measures. Accurate and prompt identification of contaminant sources ensures that they can be quickly removed and contaminated spaces isolated and cleaned. This paper discusses the use of inverse modeling to identify potential indoor pollutant sources with limited pollutant sensor data. The study reviews various inverse modeling methods for advection-dispersion problems and summarizes the methods into three major categories: forward, backward, and probability inverse modeling methods. The adjoint probability inverse modeling method is indicated as an appropriate model for indoor air pollutant tracking because it can quickly find source location, strength and release time without prior information. The paper introduces the principles of the adjoint probability method and establishes the corresponding adjoint equations for both multi-zone airflow models and computational fluid dynamics (CFD) models. The study proposes a two-stage inverse modeling approach integrating both multi-zone and CFD models, which can provide a rapid estimate of indoor pollution status and history for a whole building. Preliminary case study results indicate that the adjoint probability method is feasible for indoor pollutant inverse modeling. The proposed method can help identify contaminant source characteristics (location and release time) with limited sensor outputs. This will ensure an effective and prompt execution of building management strategies and thus achieve a healthy and safe indoor environment. The method can also help design optimal sensor networks.

Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

NASA Astrophysics Data System (ADS)

Hendzel, Z.; Rykała, Ł.

2017-02-01

The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

Next Generation Robots for STEM Education andResearch at Huston Tillotson University

DTIC Science & Technology

2017-11-10

dynamics through the following command: roslaunch mtb_lab6_feedback_linearization gravity_compensation.launch Part B: Gravity Inversion : After...understood the system’s natural dynamics. roslaunch mtb_lab6_feedback_linearization gravity_compensation.launch Part B: Gravity Inversion ...is created using the following command: roslaunch mtb_lab6_feedback_linearization gravity_inversion.launch Gravity inversion is just one

Using a pseudo-dynamic source inversion approach to improve earthquake source imaging

NASA Astrophysics Data System (ADS)

Zhang, Y.; Song, S. G.; Dalguer, L. A.; Clinton, J. F.

2014-12-01

Imaging a high-resolution spatio-temporal slip distribution of an earthquake rupture is a core research goal in seismology. In general we expect to obtain a higher quality source image by improving the observational input data (e.g. using more higher quality near-source stations). However, recent studies show that increasing the surface station density alone does not significantly improve source inversion results (Custodio et al. 2005; Zhang et al. 2014). We introduce correlation structures between the kinematic source parameters: slip, rupture velocity, and peak slip velocity (Song et al. 2009; Song and Dalguer 2013) in the non-linear source inversion. The correlation structures are physical constraints derived from rupture dynamics that effectively regularize the model space and may improve source imaging. We name this approach pseudo-dynamic source inversion. We investigate the effectiveness of this pseudo-dynamic source inversion method by inverting low frequency velocity waveforms from a synthetic dynamic rupture model of a buried vertical strike-slip event (Mw 6.5) in a homogeneous half space. In the inversion, we use a genetic algorithm in a Bayesian framework (Moneli et al. 2008), and a dynamically consistent regularized Yoffe function (Tinti, et al. 2005) was used for a single-window slip velocity function. We search for local rupture velocity directly in the inversion, and calculate the rupture time using a ray-tracing technique. We implement both auto- and cross-correlation of slip, rupture velocity, and peak slip velocity in the prior distribution. Our results suggest that kinematic source model estimates capture the major features of the target dynamic model. The estimated rupture velocity closely matches the target distribution from the dynamic rupture model, and the derived rupture time is smoother than the one we searched directly. By implementing both auto- and cross-correlation of kinematic source parameters, in comparison to traditional smoothing constraints, we are in effect regularizing the model space in a more physics-based manner without loosing resolution of the source image. Further investigation is needed to tune the related parameters of pseudo-dynamic source inversion and relative weighting between the prior and the likelihood function in the Bayesian inversion.

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.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Exact finite element method analysis of viscoelastic tapered structures to transient loads

NASA Technical Reports Server (NTRS)

Spyrakos, Constantine Chris

1987-01-01

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

On seismological moments and magnitudes

USGS Publications Warehouse

Bolt, B. A.

1991-01-01

My approach to seismology over the years has always been from the point of view of applied mathematics, as exemplified broadly by the work of the late Sir Harold Jeffreys and Professor K. E. Bullen. Both stresses the development of mathematics in the context of physical systems and of modeling, with an eye always on the side of inference. Seismology provided for them and still provides today the almost perfect paradigm; the problem is the resolution of the detailed consitution of the Earth and its geologically short-term dynamics. The latter part, includes, of course, seismic-risk estimation. The last 20 years have seen the construction of a brilliant theoretical  formalism for linear inverse problems in seismology , although, oddly enough, the current popular Earth models do not take account it. It is interesting too that the narrow opinion, prevelent a decade ago, to the effect that the traditional seismic body-wave approaches to structural definition were superceded, has been largely abandoned under today's banner of tomography-as though the Oldham-Jeffreys-Gutenbery inversions were not tomography. 

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft

NASA Technical Reports Server (NTRS)

Snell, Antony

1993-01-01

Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

Distributed micro-releases of bioterror pathogens : threat characterizations and epidemiology from uncertain patient observables.

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

Wolf, Michael M.; Marzouk, Youssef M.; Adams, Brian M.

2008-10-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern since the anthrax attacks of 2001. The ability to characterize the parameters of such attacks, i.e., to estimate the number of people infected, the time of infection, the average dose received, and the rate of disease spread in contemporary American society (for contagious diseases), is important when planning a medical response. For non-contagious diseases, we address the characterization problem by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To keep the approach relevant for response planning, we limitmore » ourselves to 3.5 days of data. In computational tests performed for anthrax, we usually find these observation windows sufficient, especially if the outbreak model employed in the inverse problem is accurate. For contagious diseases, we formulated a Bayesian inversion technique to infer both pathogenic transmissibility and the social network from outbreak observations, ensuring that the two determinants of spreading are identified separately. We tested this technique on data collected from a 1967 smallpox epidemic in Abakaliki, Nigeria. We inferred, probabilistically, different transmissibilities in the structured Abakaliki population, the social network, and the chain of transmission. Finally, we developed an individual-based epidemic model to realistically simulate the spread of a rare (or eradicated) disease in a modern society. This model incorporates the mixing patterns observed in an (American) urban setting and accepts, as model input, pathogenic transmissibilities estimated from historical outbreaks that may have occurred in socio-economic environments with little resemblance to contemporary society. Techniques were also developed to simulate disease spread on static and sampled network reductions of the dynamic social networks originally in the individual-based model, yielding faster, though approximate, network-based epidemic models. These reduced-order models are useful in scenario analysis for medical response planning, as well as in computationally intensive inverse problems.« less

Real-time characterization of partially observed epidemics using surrogate models.

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

Safta, Cosmin; Ray, Jaideep; Lefantzi, Sophia

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiologicalmore » parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.« less

Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

USGS Publications Warehouse

Chen, C.; Xia, J.; Liu, J.; Feng, G.

2006-01-01

Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant result is that final solution is determined by the average model derived from multiple trials instead of one computation due to the randomness in a genetic algorithm procedure. These advantages were demonstrated by synthetic and real-world examples of inversion of potential-field data. ?? 2005 Elsevier Ltd. All rights reserved.

Edge remap for solids

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

Kamm, James R.; Love, Edward; Robinson, Allen C.

We review the edge element formulation for describing the kinematics of hyperelastic solids. This approach is used to frame the problem of remapping the inverse deformation gradient for Arbitrary Lagrangian-Eulerian (ALE) simulations of solid dynamics. For hyperelastic materials, the stress state is completely determined by the deformation gradient, so remapping this quantity effectively updates the stress state of the material. A method, inspired by the constrained transport remap in electromagnetics, is reviewed, according to which the zero-curl constraint on the inverse deformation gradient is implicitly satisfied. Open issues related to the accuracy of this approach are identified. An optimization-based approachmore » is implemented to enforce positivity of the determinant of the deformation gradient. The efficacy of this approach is illustrated with numerical examples.« less

Probabilistic dual heuristic programming-based adaptive critic

NASA Astrophysics Data System (ADS)

Herzallah, Randa

2010-02-01

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

NASA Astrophysics Data System (ADS)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in atmospheric sciences and oceanography. Last but not least is our gratitude. As editors we would like to express our sincere thanks to all the plenary and invited speakers, the members of the International Scientific Committee and the Advisory Board for the success of the conference, which has given rise to this present volume of selected papers. We would also like to thank Mr Wang Yanbo, Miss Wan Xiqiong and the graduate students at Fudan University for their effective work to make this conference a success. The conference was financially supported by the NFS of China, the Mathematical Center of Ministry of Education of China, E-Institutes of Shanghai Municipal Education Commission (No E03004) and Fudan University, Grant 15340027 from the Japan Society for the Promotion of Science, and Grant 15654015 from the Ministry of Education, Cultures, Sports and Technology.

Inverse Problems for Nonlinear Delay Systems

DTIC Science & Technology

2011-03-15

population dynamics. We consider the delay between birth and adulthood for neonate pea aphids and present a mathematical model that treats this delay as...which there is currently no known cure. For HIV, the core of the virus is composed of single-stranded viral RNA and protein components. As depicted in...at a CD4 receptor site and the viral core is injected into the cell. Once inside, the protein components enable transcription and integration of the

Current Problems in Turbomachinery Fluid Dynamics.

DTIC Science & Technology

1982-05-21

Research Center. It is thought to result from the termination of the 3-D bow shock as the relAtive blade Mach decreases ,.zom tip to hub. This low...project emphasized development of at least a plausible inverse scheme for mixed supersonic, subsonic flow with the possibility of shock waves appearing...Calculation Procedure for Shock -Free or Strong Passage Shock Turbomachinery Cascades," ASME paper 82-GT-220. The next phase of this project was expected to

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

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

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

The Inverse Contagion Problem (ICP) vs.. Predicting site contagion in real time, when network links are not observable

NASA Astrophysics Data System (ADS)

Mushkin, I.; Solomon, S.

2017-10-01

We study the inverse contagion problem (ICP). As opposed to the direct contagion problem, in which the network structure is known and the question is when each node will be contaminated, in the inverse problem the links of the network are unknown but a sequence of contagion histories (the times when each node was contaminated) is observed. We consider two versions of the ICP: The strong problem (SICP), which is the reconstruction of the network and has been studied before, and the weak problem (WICP), which requires "only" the prediction (at each time step) of the nodes that will be contaminated at the next time step (this is often the real life situation in which a contagion is observed and predictions are made in real time). Moreover, our focus is on analyzing the increasing accuracy of the solution, as a function of the number of contagion histories already observed. For simplicity, we discuss the simplest (deterministic and synchronous) contagion dynamics and the simplest solution algorithm, which we have applied to different network types. The main result of this paper is that the complex problem of the convergence of the ICP for a network can be reduced to an individual property of pairs of nodes: the "false link difficulty". By definition, given a pair of unlinked nodes i and j, the difficulty of the false link (i,j) is the probability that in a random contagion history, the nodes i and j are not contaminated at the same time step (or at consecutive time steps). In other words, the "false link difficulty" of a non-existing network link is the probability that the observations during a random contagion history would not rule out that link. This probability is relatively straightforward to calculate, and in most instances relies only on the relative positions of the two nodes (i,j) and not on the entire network structure. We have observed the distribution of false link difficulty for various network types, estimated it theoretically and confronted it (successfully) with the numerical simulations. Based on it, we estimated analytically the convergence of the ICP solution (as a function of the number of contagion histories observed), and found it to be in perfect agreement with simulation results. Finally, the most important insight we obtained is that SICP and WICP are have quite different properties: if one in interested only in the operational aspect of predicting how contagion will spread, the links which are most difficult to decide about are the least influential on contagion dynamics. In other words, the parts of the network which are harder to reconstruct are also least important for predicting the contagion dynamics, up to the point where a (large) constant number of false links in the network (i.e. non-convergence of the network reconstruction procedure) implies a zero rate of the node contagion prediction errors (perfect convergence of the WICP). Thus, the contagion prediction problem (WICP) difficulty is very different from the network reconstruction problem (SICP), in as far as links which are difficult to reconstruct are quite harmless in terms of contagion prediction capability (WICP).

Simulation of the Tsunami Resulting from the M 9.2 2004 Sumatra-Andaman Earthquake - Dynamic Rupture vs. Seismic Inversion Source Model

NASA Astrophysics Data System (ADS)

Vater, Stefan; Behrens, Jörn

2017-04-01

Simulations of historic tsunami events such as the 2004 Sumatra or the 2011 Tohoku event are usually initialized using earthquake sources resulting from inversion of seismic data. Also, other data from ocean buoys etc. is sometimes included in the derivation of the source model. The associated tsunami event can often be well simulated in this way, and the results show high correlation with measured data. However, it is unclear how the derived source model compares to the particular earthquake event. In this study we use the results from dynamic rupture simulations obtained with SeisSol, a software package based on an ADER-DG discretization solving the spontaneous dynamic earthquake rupture problem with high-order accuracy in space and time. The tsunami model is based on a second-order Runge-Kutta discontinuous Galerkin (RKDG) scheme on triangular grids and features a robust wetting and drying scheme for the simulation of inundation events at the coast. Adaptive mesh refinement enables the efficient computation of large domains, while at the same time it allows for high local resolution and geometric accuracy. The results are compared to measured data and results using earthquake sources based on inversion. With the approach of using the output of actual dynamic rupture simulations, we can estimate the influence of different earthquake parameters. Furthermore, the comparison to other source models enables a thorough comparison and validation of important tsunami parameters, such as the runup at the coast. This work is part of the ASCETE (Advanced Simulation of Coupled Earthquake and Tsunami Events) project, which aims at an improved understanding of the coupling between the earthquake and the generated tsunami event.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Gaussian process-based Bayesian nonparametric inference of population size trajectories from gene genealogies.

PubMed

Palacios, Julia A; Minin, Vladimir N

2013-03-01

Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state-of-the-art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data, we demonstrate that our method has better accuracy and precision. Next, we analyze two genealogies reconstructed from real sequences of hepatitis C and human Influenza A viruses. In both cases, we recover more believed aspects of the viral demographic histories than the GMRF approach. We also find that our GP method produces more reasonable uncertainty estimates than the GMRF method. Copyright © 2013, The International Biometric Society.

Retrodicting the Cenozoic evolution of the mantle: Implications for dynamic surface topography

NASA Astrophysics Data System (ADS)

Glišović, Petar; Forte, Alessandro; Rowley, David; Simmons, Nathan; Grand, Stephen

2014-05-01

Seismic tomography is the essential starting ingredient for constructing realistic models of the mantle convective flow and for successfully predicting a wide range of convection-related surface observables. However, the lack of knowledge of the initial thermal state of the mantle in the geological past is still an outstanding problem in mantle convection. The resolution of this problem requires models of 3-D mantle evolution that yield maximum consistency with a wide suite of geophysical constraints. Quantifying the robustness of the reconstructed thermal evolution is another major concern. We have carried out mantle dynamic simulations (Glišović & Forte, EPSL 2014) using a pseudo-spectral solution for compressible-flow thermal convection in 3-D spectral geometry that directly incorporate: 1) joint seismic-geodynamic inversions of mantle density structure with constraints provided by mineral physics data (Simmons et al., GJI 2009); and 2) constraints on mantle viscosity inferred by inversion of a suite of convection-related and glacial isostatic adjustment data sets (Mitrovica & Forte, EPSL 2004) characterised by Earth-like Rayleigh numbers. These time-reversed convection simulations reveal how the buoyancy associated with hot, active upwellings is a major driver of the mantle-wide convective circulation and the changes in dynamic topography at the Earth's surface. These simulations reveal, for example, a stable and long-lived superplume under the East Pacific Rise (centred under the Easter and Pitcairn hotspots) that was previously identified by Rowley et al. (AGU 2011, Nature in review) on the basis of plate kinematic data. We also present 65 Myr reconstructions of the Reunion plume that gave rise to the Deccan Traps.

Inverse Problems in Geodynamics Using Machine Learning Algorithms

NASA Astrophysics Data System (ADS)

Shahnas, M. H.; Yuen, D. A.; Pysklywec, R. N.

2018-01-01

During the past few decades numerical studies have been widely employed to explore the style of circulation and mixing in the mantle of Earth and other planets. However, in geodynamical studies there are many properties from mineral physics, geochemistry, and petrology in these numerical models. Machine learning, as a computational statistic-related technique and a subfield of artificial intelligence, has rapidly emerged recently in many fields of sciences and engineering. We focus here on the application of supervised machine learning (SML) algorithms in predictions of mantle flow processes. Specifically, we emphasize on estimating mantle properties by employing machine learning techniques in solving an inverse problem. Using snapshots of numerical convection models as training samples, we enable machine learning models to determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at midmantle depths. Employing support vector machine algorithms, we show that SML techniques can successfully predict the magnitude of mantle density anomalies and can also be used in characterizing mantle flow patterns. The technique can be extended to more complex geodynamic problems in mantle dynamics by employing deep learning algorithms for putting constraints on properties such as viscosity, elastic parameters, and the nature of thermal and chemical anomalies.

Children's Understanding of the Inverse Relation between Multiplication and Division

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

NASA Astrophysics Data System (ADS)

Zaikin, Oleg; Petrov, Pavel; Posypkin, Mikhail; Bulavintsev, Vadim; Kurochkin, Ilya

2017-12-01

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

An evolutive real-time source inversion based on a linear inverse formulation

NASA Astrophysics Data System (ADS)

Sanchez Reyes, H. S.; Tago, J.; Cruz-Atienza, V. M.; Metivier, L.; Contreras Zazueta, M. A.; Virieux, J.

2016-12-01

Finite source inversion is a steppingstone to unveil earthquake rupture. It is used on ground motion predictions and its results shed light on seismic cycle for better tectonic understanding. It is not yet used for quasi-real-time analysis. Nowadays, significant progress has been made on approaches regarding earthquake imaging, thanks to new data acquisition and methodological advances. However, most of these techniques are posterior procedures once seismograms are available. Incorporating source parameters estimation into early warning systems would require to update the source build-up while recording data. In order to go toward this dynamic estimation, we developed a kinematic source inversion formulated in the time-domain, for which seismograms are linearly related to the slip distribution on the fault through convolutions with Green's functions previously estimated and stored (Perton et al., 2016). These convolutions are performed in the time-domain as we progressively increase the time window of records at each station specifically. Selected unknowns are the spatio-temporal slip-rate distribution to keep the linearity of the forward problem with respect to unknowns, as promoted by Fan and Shearer (2014). Through the spatial extension of the expected rupture zone, we progressively build-up the slip-rate when adding new data by assuming rupture causality. This formulation is based on the adjoint-state method for efficiency (Plessix, 2006). The inverse problem is non-unique and, in most cases, underdetermined. While standard regularization terms are used for stabilizing the inversion, we avoid strategies based on parameter reduction leading to an unwanted non-linear relationship between parameters and seismograms for our progressive build-up. Rise time, rupture velocity and other quantities can be extracted later on as attributs from the slip-rate inversion we perform. Satisfactory results are obtained on a synthetic example (FIgure 1) proposed by the Source Inversion Validation project (Mai et al. 2011). A real case application is currently being explored. Our specific formulation, combined with simple prior information, as well as numerical results obtained so far, yields interesting perspectives for a real-time implementation.

Enhancing Autonomy of Aerial Systems Via Integration of Visual Sensors into Their Avionics Suite

DTIC Science & Technology

2016-09-01

aerial platform for subsequent visual sensor integration. 14. SUBJECT TERMS autonomous system, quadrotors, direct method, inverse ...CONTROLLER ARCHITECTURE .....................................................43 B. INVERSE DYNAMICS IN THE VIRTUAL DOMAIN ......................45 1...control station GPS Global-Positioning System IDVD inverse dynamics in the virtual domain ILP integer linear program INS inertial-navigation system

Adaptive online inverse control of a shape memory alloy wire actuator using a dynamic neural network

NASA Astrophysics Data System (ADS)

Mai, Huanhuan; Song, Gangbing; Liao, Xiaofeng

2013-01-01

Shape memory alloy (SMA) actuators exhibit severe hysteresis, a nonlinear behavior, which complicates control strategies and limits their applications. This paper presents a new approach to controlling an SMA actuator through an adaptive inverse model based controller that consists of a dynamic neural network (DNN) identifier, a copy dynamic neural network (CDNN) feedforward term and a proportional (P) feedback action. Unlike fixed hysteresis models used in most inverse controllers, the proposed one uses a DNN to identify online the relationship between the applied voltage to the actuator and the displacement (the inverse model). Even without a priori knowledge of the SMA hysteresis and without pre-training, the proposed controller can precisely control the SMA wire actuator in various tracking tasks by identifying online the inverse model of the SMA actuator. Experiments were conducted, and experimental results demonstrated real-time modeling capabilities of DNN and the performance of the adaptive inverse controller.

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

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

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

A "Kane's Dynamics" Model for the Active Rack Isolation System Part Two: Nonlinear Model Development, Verification, and Simplification

NASA Technical Reports Server (NTRS)

Beech, G. S.; Hampton, R. D.; Rupert, J. K.

2004-01-01

Many microgravity space-science experiments require vibratory acceleration levels that are unachievable without active isolation. The Boeing Corporation's active rack isolation system (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station. Effective model-based vibration isolation requires: (1) An isolation device, (2) an adequate dynamic; i.e., mathematical, model of that isolator, and (3) a suitable, corresponding controller. This Technical Memorandum documents the validation of that high-fidelity dynamic model of ARIS. The verification of this dynamics model was achieved by utilizing two commercial off-the-shelf (COTS) software tools: Deneb's ENVISION(registered trademark), and Online Dynamics Autolev(trademark). ENVISION is a robotics software package developed for the automotive industry that employs three-dimensional computer-aided design models to facilitate both forward and inverse kinematics analyses. Autolev is a DOS-based interpreter designed, in general, to solve vector-based mathematical problems and specifically to solve dynamics problems using Kane's method. The simplification of this model was achieved using the small-angle theorem for the joint angle of the ARIS actuators. This simplification has a profound effect on the overall complexity of the closed-form solution while yielding a closed-form solution easily employed using COTS control hardware.

A comprehensive inversion approach for feedforward compensation of piezoactuator system at high frequency

NASA Astrophysics Data System (ADS)

Tian, Lizhi; Xiong, Zhenhua; Wu, Jianhua; Ding, Han

2016-09-01

Motion control of the piezoactuator system over broadband frequencies is limited due to its inherent hysteresis and system dynamics. One of the suggested ways is to use feedforward controller to linearize the input-output relationship of the piezoactuator system. Although there have been many feedforward approaches, it is still a challenge to develop feedforward controller for the piezoactuator system at high frequency. Hence, this paper presents a comprehensive inversion approach in consideration of the coupling of hysteresis and dynamics. In this work, the influence of dynamics compensation on the input-output relationship of the piezoactuator system is investigated first. With system dynamics compensation, the input-output relationship of the piezoactuator system will be further represented as rate-dependent nonlinearity due to the inevitable dynamics compensation error, especially at high frequency. Base on this result, the feedforward controller composed by a cascade of linear dynamics inversion and rate-dependent nonlinearity inversion is developed. Then, the system identification of the comprehensive inversion approach is proposed. Finally, experimental results show that the proposed approach can improve the performance on tracking of both periodic and non-periodic trajectories at medium and high frequency compared with the conventional feedforward approaches.

Joint Loads and Cartilage Stress in Intact Joints of Military Transtibial Amputees: Enhancing Quality of Life

DTIC Science & Technology

2017-04-01

crosstalk); analysis of tested subjects underway. 4) Developed analytical methods to obtain knee joint loads using EMG-driven inverse dynamics; analysis of...13/2018. Completion %: 40. Task 1.3: EMG-driven inverse dynamic (ID) analyses with OpenSim for amputee and control group subjects. Target date: 1...predicted by EMG-driven inverse dynamics. Two-three conference papers are being prepared for submission in February 2017. Other achievements. None

Evolution of the regions of the 3D particle motion in the regular polygon problem of (N+1) bodies with a quasi-homogeneous potential

NASA Astrophysics Data System (ADS)

Fakis, Demetrios; Kalvouridis, Tilemahos

2017-09-01

The regular polygon problem of (N+1) bodies deals with the dynamics of a small body, natural or artificial, in the force field of N big bodies, the ν=N-1 of which have equal masses and form an imaginary regular ν -gon, while the Nth body with a different mass is located at the center of mass of the system. In this work, instead of considering Newtonian potentials and forces, we assume that the big bodies create quasi-homogeneous potentials, in the sense that we insert to the inverse square Newtonian law of gravitation an inverse cube corrective term, aiming to approximate various phenomena due to their shape or to the radiation emitting from the primaries. Based on this new consideration, we apply a general methodology in order to investigate by means of the zero-velocity surfaces, the regions where 3D motions of the small body are allowed, their evolutions and parametric variations, their topological bifurcations, as well as the existing trapping domains of the particle. Here we note that this process is definitely a fundamental step of great importance in the study of many dynamical systems characterized by a Jacobian-type integral of motion in the long way of searching for solutions of any kind.

A New Paradigm for Satellite Retrieval of Hydrologic Variables: The CDRD Methodology

NASA Astrophysics Data System (ADS)

Smith, E. A.; Mugnai, A.; Tripoli, G. J.

2009-09-01

Historically, retrieval of thermodynamically active geophysical variables in the atmosphere (e.g., temperature, moisture, precipitation) involved some time of inversion scheme - embedded within the retrieval algorithm - to transform radiometric observations (a vector) to the desired geophysical parameter(s) (either a scalar or a vector). Inversion is fundamentally a mathematical operation involving some type of integral-differential radiative transfer equation - often resisting a straightforward algebraic solution - in which the integral side of the equation (typically the right-hand side) contains the desired geophysical vector, while the left-hand side contains the radiative measurement vector often free of operators. Inversion was considered more desirable than forward modeling because the forward model solution had to be selected from a generally unmanageable set of parameter-observation relationships. However, in the classical inversion problem for retrieval of temperature using multiple radiative frequencies along the wing of an absorption band (or line) of a well-mixed radiatively active gas, in either the infrared or microwave spectrums, the inversion equation to be solved consists of a Fredholm integral equation of the 2nd kind - a specific type of transform problem in which there are an infinite number of solutions. This meant that special treatment of the transform process was required in order to obtain a single solution. Inversion had become the method of choice for retrieval in the 1950s because it appealed to the use of mathematical elegance, and because the numerical approaches used to solve the problems (typically some type of relaxation or perturbation scheme) were computationally fast in an age when computers speeds were slow. Like many solution schemes, inversion has lingered on regardless of the fact that computer speeds have increased many orders of magnitude and forward modeling itself has become far more elegant in combination with Bayesian averaging procedures given that the a priori probabilities of occurrence in the true environment of the parameter(s) in question can be approximated (or are actually known). In this presentation, the theory of the more modern retrieval approach using a combination of cloud, radiation and other specialized forward models in conjunction with Bayesian weighted averaging will be reviewed in light of a brief history of inversion. The application of the theory will be cast in the framework of what we call the Cloud-Dynamics-Radiation-Database (CDRD) methodology - which we now use for the retrieval of precipitation from spaceborne passive microwave radiometers. In a companion presentation, we will specifically describe the CDRD methodology and present results for its application within the Mediterranean basin.

Level-set techniques for facies identification in reservoir modeling

NASA Astrophysics Data System (ADS)

Iglesias, Marco A.; McLaughlin, Dennis

2011-03-01

In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil-water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301-29 2004 Inverse Problems 20 259-82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg-Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush-Kuhn-Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Mass, heat and nutrient fluxes in the Atlantic Ocean determined by inverse methods. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rintoul, Stephen Rich

1988-01-01

Inverse methods are applied to historical hydrographic data to address two aspects of the general circulation of the Atlantic Ocean. The method allows conservation statements for mass and other properties, along with a variety of other constraints, to be combined in a dynamically consistent way to estimate the absolute velocity field and associated property transports. The method was first used to examine the exchange of mass and heat between the South Atlantic and the neighboring ocean basins. The second problem addressed concerns the circulation and property fluxes across the 24 and 36 deg N in the subtropical North Atlantic. Conservation statements are considered for the nutrients as well as mass, and the nutrients are found to contribute significant information independent of temperature and salinity.

Simulation of Forward and Inverse X-ray Scattering From Shocked Materials

NASA Astrophysics Data System (ADS)

Barber, John; Marksteiner, Quinn; Barnes, Cris

2012-02-01

The next generation of high-intensity, coherent light sources should generate sufficient brilliance to perform in-situ coherent x-ray diffraction imaging (CXDI) of shocked materials. In this work, we present beginning-to-end simulations of this process. This includes the calculation of the partially-coherent intensity profiles of self-amplified stimulated emission (SASE) x-ray free electron lasers (XFELs), as well as the use of simulated, shocked molecular-dynamics-based samples to predict the evolution of the resulting diffraction patterns. In addition, we will explore the corresponding inverse problem by performing iterative phase retrieval to generate reconstructed images of the simulated sample. The development of these methods in the context of materials under extreme conditions should provide crucial insights into the design and capabilities of shocked in-situ imaging experiments.

The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.

2005-01-01

In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.

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

USGS Publications Warehouse

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

1980-01-01

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

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Robust state preparation in quantum simulations of Dirac dynamics

NASA Astrophysics Data System (ADS)

Song, Xue-Ke; Deng, Fu-Guo; Lamata, Lucas; Muga, J. G.

2017-02-01

A nonrelativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

Forward and inverse functional variations in rotationally inelastic scattering

NASA Astrophysics Data System (ADS)

Guzman, Robert; Rabitz, Herschel

1986-09-01

This paper considers the response of various rotational energy transfer processes to functional variations about an assumed model intermolecular potential. Attention is focused on the scattering of an atom and a linear rigid rotor. The collision dynamics are approximated by employing both the infinite order sudden (IOS) and exponential distorted wave (EDW) methods to describe Ar-N2 and He-H2, respectively. The following cross sections are considered: state-to-state differential and integral, final state summed differential and integral, and effective diffusion and viscosity cross sections. Attention is first given to the forward sensitivity densities δ0/δV(R,r) where 0 denotes any of the aforementioned cross sections, R is the intermolecular distance, and r is the internal coordinates. These forward sensitivity densities (functional derivatives) offer a quantitative measure of the importance of different regions of the potential surface to a chosen cross section. Via knowledge of the forward sensitivities and a particular variation δV(R,r) the concomitant response δ0 is generated. It was found that locally a variation in the potential can give rise to a large response in the cross sections as measured by these forward densities. In contrast, a unit percent change in the overall potential produced a 1%-10% change in the cross sections studied indicating that the large + and - responses to local variations tend to cancel. In addition, inverse sensitivity densities δV(R,r)/δ0 are obtained. These inverse densities are of interest since they are the exact solution to the infinitesimal inverse scattering problem. Although the inverse sensitivity densities do not in themselves form an inversion algorithm, they do offer a quantitative measure of the importance of performing particular measurements for the ultimate purpose of inversion. Using a set of state-to-state integral cross sections we found that the resultant responses from the infinitesimal inversion were typically small such that ‖δV(R,r)‖≪‖V(R,r)‖. From the viewpoint of an actual inversion, these results indicate that only through an extensive effort will significant knowledge of the potential be gained from the cross sections. All of these calculations serve to illustrate the methodology, and other observables as well as dynamical schemes could be explored as desired.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

Motion control of musculoskeletal systems with redundancy.

PubMed

Park, Hyunjoo; Durand, Dominique M

2008-12-01

Motion control of musculoskeletal systems for functional electrical stimulation (FES) is a challenging problem due to the inherent complexity of the systems. These include being highly nonlinear, strongly coupled, time-varying, time-delayed, and redundant. The redundancy in particular makes it difficult to find an inverse model of the system for control purposes. We have developed a control system for multiple input multiple output (MIMO) redundant musculoskeletal systems with little prior information. The proposed method separates the steady-state properties from the dynamic properties. The dynamic control uses a steady-state inverse model and is implemented with both a PID controller for disturbance rejection and an artificial neural network (ANN) feedforward controller for fast trajectory tracking. A mechanism to control the sum of the muscle excitation levels is also included. To test the performance of the proposed control system, a two degree of freedom ankle-subtalar joint model with eight muscles was used. The simulation results show that separation of steady-state and dynamic control allow small output tracking errors for different reference trajectories such as pseudo-step, sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against system parameter and controller parameter variations. A possible application of this control algorithm is FES control using multiple contact cuff electrodes where mathematical modeling is not feasible and the redundancy makes the control of dynamic movement difficult.

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Mantle viscosity structure constrained by joint inversions of seismic velocities and density

NASA Astrophysics Data System (ADS)

Rudolph, M. L.; Moulik, P.; Lekic, V.

2017-12-01

The viscosity structure of Earth's deep mantle affects the thermal evolution of Earth, the ascent of mantle upwellings, sinking of subducted oceanic lithosphere, and the mixing of compositional heterogeneities in the mantle. Modeling the long-wavelength dynamic geoid allows us to constrain the radial viscosity profile of the mantle. Typically, in inversions for the mantle viscosity structure, wavespeed variations are mapped into density variations using a constant- or depth-dependent scaling factor. Here, we use a newly developed joint model of anisotropic Vs, Vp, density and transition zone topographies to generate a suite of solutions for the mantle viscosity structure directly from the seismologically constrained density structure. The density structure used to drive our forward models includes contributions from both thermal and compositional variations, including important contributions from compositionally dense material in the Large Low Velocity Provinces at the base of the mantle. These compositional variations have been neglected in the forward models used in most previous inversions and have the potential to significantly affect large-scale flow and thus the inferred viscosity structure. We use a transdimensional, hierarchical, Bayesian approach to solve the inverse problem, and our solutions for viscosity structure include an increase in viscosity below the base of the transition zone, in the shallow lower mantle. Using geoid dynamic response functions and an analysis of the correlation between the observed geoid and mantle structure, we demonstrate the underlying reason for this inference. Finally, we present a new family of solutions in which the data uncertainty is accounted for using covariance matrices associated with the mantle structure models.

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

NASA Astrophysics Data System (ADS)

Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

2017-07-01

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

An integrated collision prediction and avoidance scheme for mobile robots in non-stationary environments

NASA Technical Reports Server (NTRS)

Kyriakopoulos, K. J.; Saridis, G. N.

1993-01-01

A formulation that makes possible the integration of collision prediction and avoidance stages for mobile robots moving in general terrains containing moving obstacles is presented. A dynamic model of the mobile robot and the dynamic constraints are derived. Collision avoidance is guaranteed if the distance between the robot and a moving obstacle is nonzero. A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. A feedback control is developed and local asymptotic stability is proved if the velocity of the moving obstacle is bounded. Furthermore, a solution to the problem of inverse dynamics for the mobile robot is given. Simulation results verify the value of the proposed strategy.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

NASA Technical Reports Server (NTRS)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Towards inverse modeling of turbidity currents: The inverse lock-exchange problem

NASA Astrophysics Data System (ADS)

Lesshafft, Lutz; Meiburg, Eckart; Kneller, Ben; Marsden, Alison

2011-04-01

A new approach is introduced for turbidite modeling, leveraging the potential of computational fluid dynamics methods to simulate the flow processes that led to turbidite formation. The practical use of numerical flow simulation for the purpose of turbidite modeling so far is hindered by the need to specify parameters and initial flow conditions that are a priori unknown. The present study proposes a method to determine optimal simulation parameters via an automated optimization process. An iterative procedure matches deposit predictions from successive flow simulations against available localized reference data, as in practice may be obtained from well logs, and aims at convergence towards the best-fit scenario. The final result is a prediction of the entire deposit thickness and local grain size distribution. The optimization strategy is based on a derivative-free, surrogate-based technique. Direct numerical simulations are performed to compute the flow dynamics. A proof of concept is successfully conducted for the simple test case of a two-dimensional lock-exchange turbidity current. The optimization approach is demonstrated to accurately retrieve the initial conditions used in a reference calculation.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

On the Use of Nonlinear Regularization in Inverse Methods for the Solar Tachocline Profile Determination

NASA Astrophysics Data System (ADS)

Corbard, T.; Berthomieu, G.; Provost, J.; Blanc-Feraud, L.

Inferring the solar rotation from observed frequency splittings represents an ill-posed problem in the sense of Hadamard and the traditional approach used to override this difficulty consists in regularizing the problem by adding some a priori information on the global smoothness of the solution defined as the norm of its first or second derivative. Nevertheless, inversions of rotational splittings (e.g. Corbard et al., 1998; Schou et al., 1998) have shown that the surface layers and the so-called solar tachocline (Spiegel & Zahn 1992) at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. %there exist high gradients in the solar rotation profile near %the surface and at the base of the convection zone (e.g. Corbard et al. 1998) %in the so-called solar tachocline (Spiegel & Zahn 1992). Therefore, the global smoothness a-priori which tends to smooth out every high gradient in the solution may not be appropriate for the study of a zone like the tachocline which is of particular interest for the study of solar dynamics (e.g. Elliot 1997). In order to infer the fine structure of such regions with high gradients by inverting helioseismic data, we have to find a way to preserve these zones in the inversion process. Setting a more adapted constraint on the solution leads to non-linear regularization methods that are in current use for edge-preserving regularization in computed imaging (e.g. Blanc-Feraud et al. 1995). In this work, we investigate their use in the helioseismic context of rotational inversions.

Assessing when chromosomal rearrangements affect the dynamics of speciation: implications from computer simulations

PubMed Central

Feder, Jeffrey L.; Nosil, Patrik; Flaxman, Samuel M.

2014-01-01

Many hypotheses have been put forth to explain the origin and spread of inversions, and their significance for speciation. Several recent genic models have proposed that inversions promote speciation with gene flow due to the adaptive significance of the genes contained within them and because of the effects inversions have on suppressing recombination. However, the consequences of inversions for the dynamics of genome wide divergence across the speciation continuum remain unclear, an issue we examine here. We review a framework for the genomics of speciation involving the congealing of the genome into alternate adaptive states representing species (“genome wide congealing”). We then place inversions in this context as examples of how genetic hitchhiking can potentially hasten genome wide congealing. Specifically, we use simulation models to (i) examine the conditions under which inversions may speed genome congealing and (ii) quantify predicted magnitudes of these effects. Effects of inversions on promoting speciation were most common and pronounced when inversions were initially fixed between populations before secondary contact and adaptation involved many genes with small fitness effects. Further work is required on the role of underdominance and epistasis between a few loci of major effect within inversions. The results highlight five important aspects of the roles of inversions in speciation: (i) the geographic context of the origins and spread of inversions, (ii) the conditions under which inversions can facilitate divergence, (iii) the magnitude of that facilitation, (iv) the extent to which the buildup of divergence is likely to be biased within vs. outside of inversions, and (v) the dynamics of the appearance and disappearance of exceptional divergence within inversions. We conclude by discussing the empirical challenges in showing that inversions play a central role in facilitating speciation with gene flow. PMID:25206365

Efficient robust reconstruction of dynamic PET activity maps with radioisotope decay constraints.

PubMed

Gao, Fei; Liu, Huafeng; Shi, Pengcheng

2010-01-01

Dynamic PET imaging performs sequence of data acquisition in order to provide visualization and quantification of physiological changes in specific tissues and organs. The reconstruction of activity maps is generally the first step in dynamic PET. State space Hinfinity approaches have been proved to be a robust method for PET image reconstruction where, however, temporal constraints are not considered during the reconstruction process. In addition, the state space strategies for PET image reconstruction have been computationally prohibitive for practical usage because of the need for matrix inversion. In this paper, we present a minimax formulation of the dynamic PET imaging problem where a radioisotope decay model is employed as physics-based temporal constraints on the photon counts. Furthermore, a robust steady state Hinfinity filter is developed to significantly improve the computational efficiency with minimal loss of accuracy. Experiments are conducted on Monte Carlo simulated image sequences for quantitative analysis and validation.

Field dynamics inference via spectral density estimation

NASA Astrophysics Data System (ADS)

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A.

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Field dynamics inference via spectral density estimation.

PubMed

Frank, Philipp; Steininger, Theo; Enßlin, Torsten A

2017-11-01

Stochastic differential equations are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to solve, e.g., when modeling Brownian motion. In some cases, the equations governing the dynamics of a physical system on macroscopic scales occur to be unknown since they typically cannot be deduced from general principles. In this work, we describe how the underlying laws of a stochastic process can be approximated by the spectral density of the corresponding process. Furthermore, we show how the density can be inferred from possibly very noisy and incomplete measurements of the dynamical field. Generally, inverse problems like these can be tackled with the help of Information Field Theory. For now, we restrict to linear and autonomous processes. To demonstrate its applicability, we employ our reconstruction algorithm on a time-series and spatiotemporal processes.

Estimating the Earthquake Source Time Function by Markov Chain Monte Carlo Sampling

NASA Astrophysics Data System (ADS)

Dȩbski, Wojciech

2008-07-01

Many aspects of earthquake source dynamics like dynamic stress drop, rupture velocity and directivity, etc. are currently inferred from the source time functions obtained by a deconvolution of the propagation and recording effects from seismograms. The question of the accuracy of obtained results remains open. In this paper we address this issue by considering two aspects of the source time function deconvolution. First, we propose a new pseudo-spectral parameterization of the sought function which explicitly takes into account the physical constraints imposed on the sought functions. Such parameterization automatically excludes non-physical solutions and so improves the stability and uniqueness of the deconvolution. Secondly, we demonstrate that the Bayesian approach to the inverse problem at hand, combined with an efficient Markov Chain Monte Carlo sampling technique, is a method which allows efficient estimation of the source time function uncertainties. The key point of the approach is the description of the solution of the inverse problem by the a posteriori probability density function constructed according to the Bayesian (probabilistic) theory. Next, the Markov Chain Monte Carlo sampling technique is used to sample this function so the statistical estimator of a posteriori errors can be easily obtained with minimal additional computational effort with respect to modern inversion (optimization) algorithms. The methodological considerations are illustrated by a case study of the mining-induced seismic event of the magnitude M L ≈3.1 that occurred at Rudna (Poland) copper mine. The seismic P-wave records were inverted for the source time functions, using the proposed algorithm and the empirical Green function technique to approximate Green functions. The obtained solutions seem to suggest some complexity of the rupture process with double pulses of energy release. However, the error analysis shows that the hypothesis of source complexity is not justified at the 95% confidence level. On the basis of the analyzed event we also show that the separation of the source inversion into two steps introduces limitations on the completeness of the a posteriori error analysis.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Extracting motor synergies from random movements for low-dimensional task-space control of musculoskeletal robots.

PubMed

Fu, Kin Chung Denny; Dalla Libera, Fabio; Ishiguro, Hiroshi

2015-10-08

In the field of human motor control, the motor synergy hypothesis explains how humans simplify body control dimensionality by coordinating groups of muscles, called motor synergies, instead of controlling muscles independently. In most applications of motor synergies to low-dimensional control in robotics, motor synergies are extracted from given optimal control signals. In this paper, we address the problems of how to extract motor synergies without optimal data given, and how to apply motor synergies to achieve low-dimensional task-space tracking control of a human-like robotic arm actuated by redundant muscles, without prior knowledge of the robot. We propose to extract motor synergies from a subset of randomly generated reaching-like movement data. The essence is to first approximate the corresponding optimal control signals, using estimations of the robot's forward dynamics, and to extract the motor synergies subsequently. In order to avoid modeling difficulties, a learning-based control approach is adopted such that control is accomplished via estimations of the robot's inverse dynamics. We present a kernel-based regression formulation to estimate the forward and the inverse dynamics, and a sliding controller in order to cope with estimation error. Numerical evaluations show that the proposed method enables extraction of motor synergies for low-dimensional task-space control.

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

FAST: a framework for simulation and analysis of large-scale protein-silicon biosensor circuits.

PubMed

Gu, Ming; Chakrabartty, Shantanu

2013-08-01

This paper presents a computer aided design (CAD) framework for verification and reliability analysis of protein-silicon hybrid circuits used in biosensors. It is envisioned that similar to integrated circuit (IC) CAD design tools, the proposed framework will be useful for system level optimization of biosensors and for discovery of new sensing modalities without resorting to laborious fabrication and experimental procedures. The framework referred to as FAST analyzes protein-based circuits by solving inverse problems involving stochastic functional elements that admit non-linear relationships between different circuit variables. In this regard, FAST uses a factor-graph netlist as a user interface and solving the inverse problem entails passing messages/signals between the internal nodes of the netlist. Stochastic analysis techniques like density evolution are used to understand the dynamics of the circuit and estimate the reliability of the solution. As an example, we present a complete design flow using FAST for synthesis, analysis and verification of our previously reported conductometric immunoassay that uses antibody-based circuits to implement forward error-correction (FEC).

Inverse dynamics of underactuated mechanical systems: A simple case study and experimental verification

NASA Astrophysics Data System (ADS)

Blajer, W.; Dziewiecki, K.; Kołodziejczyk, K.; Mazur, Z.

2011-05-01

Underactuated systems are featured by fewer control inputs than the degrees-of-freedom, m < n. The determination of an input control strategy that forces such a system to complete a set of m specified motion tasks is a challenging task, and the explicit solution existence is conditioned to differential flatness of the problem. The flatness-based solution denotes that all the 2 n states and m control inputs can be algebraically expressed in terms of the m specified outputs and their time derivatives up to a certain order, which is in practice attainable only for simple systems. In this contribution the problem is posed in a more practical way as a set of index-three differential-algebraic equations, and the solution is obtained numerically. The formulation is then illustrated by a two-degree-of-freedom underactuated system composed of two rotating discs connected by a torsional spring, in which the pre-specified motion of one of the discs is actuated by the torque applied to the other disc, n = 2 and m = 1. Experimental verification of the inverse simulation control methodology is reported.

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein. PMID:23043260

First Calderón Prize

NASA Astrophysics Data System (ADS)

Rundell, William; Somersalo, Erkki

2008-07-01

The Inverse Problems International Association (IPIA) awarded the first Calderón Prize to Matti Lassas for his outstanding contributions to the field of inverse problems, especially in geometric inverse problems. The Calderón Prize is given to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined. The first Calderón Prize Committee consisted of Professors Adrian Nachman, Lassi Päivärinta, William Rundell (chair), and Michael Vogelius. William Rundell For the Calderón Prize Committee Prize ceremony The ceremony awarding the Calderón Prize. Matti Lassas is on the left. He and William Rundell are on the right. Photos by P Stefanov. Brief Biography of Matti Lassas Matti Lassas was born in 1969 in Helsinki, Finland, and studied at the University of Helsinki. He finished his Master's studies in 1992 in three years and earned his PhD in 1996. His PhD thesis, written under the supervision of Professor Erkki Somersalo was entitled `Non-selfadjoint inverse spectral problems and their applications to random bodies'. Already in his thesis, Matti demonstrated a remarkable command of different fields of mathematics, bringing together the spectral theory of operators, geometry of Riemannian surfaces, Maxwell's equations and stochastic analysis. He has continued to develop all of these branches in the framework of inverse problems, the most remarkable results perhaps being in the field of differential geometry and inverse problems. Matti has always been a very generous researcher, sharing his ideas with his numerous collaborators. He has authored over sixty scientific articles, among which a monograph on inverse boundary spectral problems with Alexander Kachalov and Yaroslav Kurylev and over forty articles in peer reviewed journals of the highest standards. To get an idea of the wide range of Matti's interests, it is enough to say that he also has three US patents on medical imaging applications. Matti is currently professor of mathematics at Helsinki University of Technology, where he has created his own line of research with young talented researchers around him. He is a central person in the Centre of Excellence in Inverse Problems Research of the Academy of Finland. Previously, Matti Lassas has won several awards in his home country, including the prestigious Vaisala price of the Finnish Academy of Science and Letters in 2004. He is a highly esteemed colleague, teacher and friend, and the Great Diving Beetle of the Finnish Inverse Problems Society (http://venda.uku.fi/research/FIPS/), an honorary title for a person who has no fear of the deep. Erkki Somersalo

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

NASA Astrophysics Data System (ADS)

Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro

2007-06-01

These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this flourishing time, it is necessary to carefully analyse the current status of inverse problems for further development. Thus we have opened with the panel discussion entitled `Future of Inverse Problems' with panelists: Professors J Cheng, H W Engl, V Isakov, R Kress, J-K Seo, G Uhlmann and the commentator: Elaine Longden-Chapman from IOP Publishing. The aims of the panel discussion were to examine the current research status from various viewpoints, to discuss how we can overcome any difficulties and how we can promote young researchers and open new possibilities for inverse problems such as industrial linkages. As one output, the panel discussion has triggered the organization of the Inverse Problems International Association (IPIA) which has led to its first international congress in the summer of 2007. Another remarkable outcome of the conference is, of course, the present volume: this is the very high quality online proceedings volume of Journal of Physics: Conference Series. Readers can see in these proceedings very well written tutorial lecture notes, and very high quality original research and review papers all of which show what was achieved by the time the conference was held. The electronic publication of the proceedings is a new way of publicizing the achievement of the conference. It has the advantage of wide circulation and cost reduction. We believe this is a most efficient method for our needs and purposes. We would like to take this opportunity to acknowledge all the people who helped to organize the conference. Guest Editors Jin Cheng, Fudan University, Shanghai, China Yuusuke Iso, Kyoto University, Kyoto, Japan Gen Nakamura, Hokkaido University, Sapporo, Japan Masahiro Yamamoto, University of Tokyo, Tokyo, Japan

The Earthquake Source Inversion Validation (SIV) - Project: Summary, Status, Outlook

NASA Astrophysics Data System (ADS)

Mai, P. M.

2017-12-01

Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, this kinematic source inversion is ill-posed and returns non-unique solutions, as seen for instance in multiple source models for the same earthquake, obtained by different research teams, that often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversions and to understand strengths and weaknesses of various methods, the Source Inversion Validation (SIV) project developed a set of forward-modeling exercises and inversion benchmarks. Several research teams then use these validation exercises to test their codes and methods, but also to develop and benchmark new approaches. In this presentation I will summarize the SIV strategy, the existing benchmark exercises and corresponding results. Using various waveform-misfit criteria and newly developed statistical comparison tools to quantify source-model (dis)similarities, the SIV platforms is able to rank solutions and identify particularly promising source inversion approaches. Existing SIV exercises (with related data and descriptions) and all computational tools remain available via the open online collaboration platform; additional exercises and benchmark tests will be uploaded once they are fully developed. I encourage source modelers to use the SIV benchmarks for developing and testing new methods. The SIV efforts have already led to several promising new techniques for tackling the earthquake-source imaging problem. I expect that future SIV benchmarks will provide further innovations and insights into earthquake source kinematics that will ultimately help to better understand the dynamics of the rupture process.

Parsimony and goodness-of-fit in multi-dimensional NMR inversion

NASA Astrophysics Data System (ADS)

Babak, Petro; Kryuchkov, Sergey; Kantzas, Apostolos

2017-01-01

Multi-dimensional nuclear magnetic resonance (NMR) experiments are often used for study of molecular structure and dynamics of matter in core analysis and reservoir evaluation. Industrial applications of multi-dimensional NMR involve a high-dimensional measurement dataset with complicated correlation structure and require rapid and stable inversion algorithms from the time domain to the relaxation rate and/or diffusion domains. In practice, applying existing inverse algorithms with a large number of parameter values leads to an infinite number of solutions with a reasonable fit to the NMR data. The interpretation of such variability of multiple solutions and selection of the most appropriate solution could be a very complex problem. In most cases the characteristics of materials have sparse signatures, and investigators would like to distinguish the most significant relaxation and diffusion values of the materials. To produce an easy to interpret and unique NMR distribution with the finite number of the principal parameter values, we introduce a new method for NMR inversion. The method is constructed based on the trade-off between the conventional goodness-of-fit approach to multivariate data and the principle of parsimony guaranteeing inversion with the least number of parameter values. We suggest performing the inversion of NMR data using the forward stepwise regression selection algorithm. To account for the trade-off between goodness-of-fit and parsimony, the objective function is selected based on Akaike Information Criterion (AIC). The performance of the developed multi-dimensional NMR inversion method and its comparison with conventional methods are illustrated using real data for samples with bitumen, water and clay.

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

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

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David

2000-01-01

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

Sensing of the atmospheric variation using Low Cost GNSS Receiver

NASA Astrophysics Data System (ADS)

Bramanto, Brian; Gumilar, Irwan; Sidiq, Teguh P.; Kuntjoro, Wedyanto; Tampubolon, Daniel A.

2018-05-01

As the GNSS signals transmitted through the atmosphere, they are delayed by interference of TEC (Total Electron Content) in the ionosphere and water vapor in the troposphere. By using inverse-problem, name GNSS Meteorology, those parameters can be obtained precisely and several researches has approved and supported that method. However, the geodetic GNSS receivers are relatively high cost (30,000 to 70,000 each) to be established on a regular and uniform network. This research aims to investigate the potential use of low cost GNSS receiver (less than 2,000) to observe the atmospheric dynamic both in ionosphere and troposphere. Results indicated that low cost GNSS receiver is a promising tools to sensing the atmospheric dynamic, however, further processing is needed to enhance the data quality. It is found that both of ionosphere and troposphere dynamic has diurnal periodic component.

Acoustic Inversion in Optoacoustic Tomography: A Review

PubMed Central

Rosenthal, Amir; Ntziachristos, Vasilis; Razansky, Daniel

2013-01-01

Optoacoustic tomography enables volumetric imaging with optical contrast in biological tissue at depths beyond the optical mean free path by the use of optical excitation and acoustic detection. The hybrid nature of optoacoustic tomography gives rise to two distinct inverse problems: The optical inverse problem, related to the propagation of the excitation light in tissue, and the acoustic inverse problem, which deals with the propagation and detection of the generated acoustic waves. Since the two inverse problems have different physical underpinnings and are governed by different types of equations, they are often treated independently as unrelated problems. From an imaging standpoint, the acoustic inverse problem relates to forming an image from the measured acoustic data, whereas the optical inverse problem relates to quantifying the formed image. This review focuses on the acoustic aspects of optoacoustic tomography, specifically acoustic reconstruction algorithms and imaging-system practicalities. As these two aspects are intimately linked, and no silver bullet exists in the path towards high-performance imaging, we adopt a holistic approach in our review and discuss the many links between the two aspects. Four classes of reconstruction algorithms are reviewed: time-domain (so called back-projection) formulae, frequency-domain formulae, time-reversal algorithms, and model-based algorithms. These algorithms are discussed in the context of the various acoustic detectors and detection surfaces which are commonly used in experimental studies. We further discuss the effects of non-ideal imaging scenarios on the quality of reconstruction and review methods that can mitigate these effects. Namely, we consider the cases of finite detector aperture, limited-view tomography, spatial under-sampling of the acoustic signals, and acoustic heterogeneities and losses. PMID:24772060

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

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

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

Inverse Transformation: Unleashing Spatially Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis.

PubMed

Andrews, Ross N; Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-02-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables probing dynamics in a broad array of materials with XPCS, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fails. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. In this paper, we propose an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, we demonstrate the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.

Inverse Transformation: Unleashing Spatially Heterogeneous Dynamics with an Alternative Approach to XPCS Data Analysis

PubMed Central

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-01-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables probing dynamics in a broad array of materials with XPCS, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fails. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. In this paper, we propose an alternative analysis scheme based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. Using XPCS data measured from colloidal gels, we demonstrate the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS. PMID:29875506

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Inferring Muscle-Tendon Unit Power from Ankle Joint Power during the Push-Off Phase of Human Walking: Insights from a Multiarticular EMG-Driven Model

PubMed Central

2016-01-01

Introduction Inverse dynamics joint kinetics are often used to infer contributions from underlying groups of muscle-tendon units (MTUs). However, such interpretations are confounded by multiarticular (multi-joint) musculature, which can cause inverse dynamics to over- or under-estimate net MTU power. Misestimation of MTU power could lead to incorrect scientific conclusions, or to empirical estimates that misguide musculoskeletal simulations, assistive device designs, or clinical interventions. The objective of this study was to investigate the degree to which ankle joint power overestimates net plantarflexor MTU power during the Push-off phase of walking, due to the behavior of the flexor digitorum and hallucis longus (FDHL)–multiarticular MTUs crossing the ankle and metatarsophalangeal (toe) joints. Methods We performed a gait analysis study on six healthy participants, recording ground reaction forces, kinematics, and electromyography (EMG). Empirical data were input into an EMG-driven musculoskeletal model to estimate ankle power. This model enabled us to parse contributions from mono- and multi-articular MTUs, and required only one scaling and one time delay factor for each subject and speed, which were solved for based on empirical data. Net plantarflexing MTU power was computed by the model and quantitatively compared to inverse dynamics ankle power. Results The EMG-driven model was able to reproduce inverse dynamics ankle power across a range of gait speeds (R2 ≥ 0.97), while also providing MTU-specific power estimates. We found that FDHL dynamics caused ankle power to slightly overestimate net plantarflexor MTU power, but only by ~2–7%. Conclusions During Push-off, FDHL MTU dynamics do not substantially confound the inference of net plantarflexor MTU power from inverse dynamics ankle power. However, other methodological limitations may cause inverse dynamics to overestimate net MTU power; for instance, due to rigid-body foot assumptions. Moving forward, the EMG-driven modeling approach presented could be applied to understand other tasks or larger multiarticular MTUs. PMID:27764110

Inferring Muscle-Tendon Unit Power from Ankle Joint Power during the Push-Off Phase of Human Walking: Insights from a Multiarticular EMG-Driven Model.

PubMed

Honert, Eric C; Zelik, Karl E

2016-01-01

Inverse dynamics joint kinetics are often used to infer contributions from underlying groups of muscle-tendon units (MTUs). However, such interpretations are confounded by multiarticular (multi-joint) musculature, which can cause inverse dynamics to over- or under-estimate net MTU power. Misestimation of MTU power could lead to incorrect scientific conclusions, or to empirical estimates that misguide musculoskeletal simulations, assistive device designs, or clinical interventions. The objective of this study was to investigate the degree to which ankle joint power overestimates net plantarflexor MTU power during the Push-off phase of walking, due to the behavior of the flexor digitorum and hallucis longus (FDHL)-multiarticular MTUs crossing the ankle and metatarsophalangeal (toe) joints. We performed a gait analysis study on six healthy participants, recording ground reaction forces, kinematics, and electromyography (EMG). Empirical data were input into an EMG-driven musculoskeletal model to estimate ankle power. This model enabled us to parse contributions from mono- and multi-articular MTUs, and required only one scaling and one time delay factor for each subject and speed, which were solved for based on empirical data. Net plantarflexing MTU power was computed by the model and quantitatively compared to inverse dynamics ankle power. The EMG-driven model was able to reproduce inverse dynamics ankle power across a range of gait speeds (R2 ≥ 0.97), while also providing MTU-specific power estimates. We found that FDHL dynamics caused ankle power to slightly overestimate net plantarflexor MTU power, but only by ~2-7%. During Push-off, FDHL MTU dynamics do not substantially confound the inference of net plantarflexor MTU power from inverse dynamics ankle power. However, other methodological limitations may cause inverse dynamics to overestimate net MTU power; for instance, due to rigid-body foot assumptions. Moving forward, the EMG-driven modeling approach presented could be applied to understand other tasks or larger multiarticular MTUs.

Analytic semigroups: Applications to inverse problems for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rebnord, D. A.

1990-01-01

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

Turbulent Equilibria for Charged Particles in Space

NASA Astrophysics Data System (ADS)

Yoon, Peter

2017-04-01

The solar wind electron distribution function is apparently composed of several components including non-thermal tail population. The electron distribution that contains energetic tail feature is well fitted with the kappa distribution function. The solar wind protons also possess quasi power-law tail distribution function that is well fitted with an inverse power law model. The present paper discusses the latest theoretical development regarding the dynamical steady-state solution of electrons and Langmuir turbulence that are in turbulent equilibrium. According to such a theory, the Maxwellian and kappa distribution functions for the electrons emerge as the only two possible solution that satisfy the steady-state weak turbulence plasma kinetic equation. For the proton inverse power-law tail problem, a similar turbulent equilibrium solution can be conceived of, but instead of high-frequency Langmuir fluctuation, the theory involves low-frequency kinetic Alfvenic turbulence. The steady-state solution of the self-consistent proton kinetic equation and wave kinetic equation for Alfvenic waves can be found in order to obtain a self-consistent solution for the inverse power law tail distribution function.

Characterization of dynamic changes of current source localization based on spatiotemporal fMRI constrained EEG source imaging

NASA Astrophysics Data System (ADS)

Nguyen, Thinh; Potter, Thomas; Grossman, Robert; Zhang, Yingchun

2018-06-01

Objective. Neuroimaging has been employed as a promising approach to advance our understanding of brain networks in both basic and clinical neuroscience. Electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) represent two neuroimaging modalities with complementary features; EEG has high temporal resolution and low spatial resolution while fMRI has high spatial resolution and low temporal resolution. Multimodal EEG inverse methods have attempted to capitalize on these properties but have been subjected to localization error. The dynamic brain transition network (DBTN) approach, a spatiotemporal fMRI constrained EEG source imaging method, has recently been developed to address these issues by solving the EEG inverse problem in a Bayesian framework, utilizing fMRI priors in a spatial and temporal variant manner. This paper presents a computer simulation study to provide a detailed characterization of the spatial and temporal accuracy of the DBTN method. Approach. Synthetic EEG data were generated in a series of computer simulations, designed to represent realistic and complex brain activity at superficial and deep sources with highly dynamical activity time-courses. The source reconstruction performance of the DBTN method was tested against the fMRI-constrained minimum norm estimates algorithm (fMRIMNE). The performances of the two inverse methods were evaluated both in terms of spatial and temporal accuracy. Main results. In comparison with the commonly used fMRIMNE method, results showed that the DBTN method produces results with increased spatial and temporal accuracy. The DBTN method also demonstrated the capability to reduce crosstalk in the reconstructed cortical time-course(s) induced by neighboring regions, mitigate depth bias and improve overall localization accuracy. Significance. The improved spatiotemporal accuracy of the reconstruction allows for an improved characterization of complex neural activity. This improvement can be extended to any subsequent brain connectivity analyses used to construct the associated dynamic brain networks.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Gravity inversion of a fault by Particle swarm optimization (PSO).

PubMed

Toushmalani, Reza

2013-01-01

Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult optimization problems. The technique proved to work efficiently when tested to a number of models.

The Inverse Problem in Jet Acoustics

NASA Technical Reports Server (NTRS)

Wooddruff, S. L.; Hussaini, M. Y.

2001-01-01

The inverse problem for jet acoustics, or the determination of noise sources from far-field pressure information, is proposed as a tool for understanding the generation of noise by turbulence and for the improved prediction of jet noise. An idealized version of the problem is investigated first to establish the extent to which information about the noise sources may be determined from far-field pressure data and to determine how a well-posed inverse problem may be set up. Then a version of the industry-standard MGB code is used to predict a jet noise source spectrum from experimental noise data.

Inverse kinematics problem in robotics using neural networks

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.; Lawrence, Charles

1992-01-01

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

NASA Astrophysics Data System (ADS)

Fedele, Micaela; Vernia, Cecilia

2017-10-01

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

CONTIN XPCS: Software for Inverse Transform Analysis of X-Ray Photon Correlation Spectroscopy Dynamics

PubMed Central

Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-01-01

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) both reveal dynamics using coherent scattering, but X-rays permit investigating of dynamics in a much more diverse array of materials. Heterogeneous dynamics occur in many such materials, and we showed how classic tools employed in analysis of heterogeneous DLS dynamics extend to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. This work presents the software implementation of inverse transform analysis of XPCS data called CONTIN XPCS, an extension of traditional CONTIN that accommodates dynamics encountered in equilibrium XPCS measurements. PMID:29875507

CONTIN XPCS: Software for Inverse Transform Analysis of X-Ray Photon Correlation Spectroscopy Dynamics.

PubMed

Andrews, Ross N; Narayanan, Suresh; Zhang, Fan; Kuzmenko, Ivan; Ilavsky, Jan

2018-02-01

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) both reveal dynamics using coherent scattering, but X-rays permit investigating of dynamics in a much more diverse array of materials. Heterogeneous dynamics occur in many such materials, and we showed how classic tools employed in analysis of heterogeneous DLS dynamics extend to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. This work presents the software implementation of inverse transform analysis of XPCS data called CONTIN XPCS, an extension of traditional CONTIN that accommodates dynamics encountered in equilibrium XPCS measurements.

Approximation methods for inverse problems involving the vibration of beams with tip bodies

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1984-01-01

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Utilizing High-Performance Computing to Investigate Parameter Sensitivity of an Inversion Model for Vadose Zone Flow and Transport

NASA Astrophysics Data System (ADS)

Fang, Z.; Ward, A. L.; Fang, Y.; Yabusaki, S.

2011-12-01

High-resolution geologic models have proven effective in improving the accuracy of subsurface flow and transport predictions. However, many of the parameters in subsurface flow and transport models cannot be determined directly at the scale of interest and must be estimated through inverse modeling. A major challenge, particularly in vadose zone flow and transport, is the inversion of the highly-nonlinear, high-dimensional problem as current methods are not readily scalable for large-scale, multi-process models. In this paper we describe the implementation of a fully automated approach for addressing complex parameter optimization and sensitivity issues on massively parallel multi- and many-core systems. The approach is based on the integration of PNNL's extreme scale Subsurface Transport Over Multiple Phases (eSTOMP) simulator, which uses the Global Array toolkit, with the Beowulf-Cluster inspired parallel nonlinear parameter estimation software, BeoPEST in the MPI mode. In the eSTOMP/BeoPEST implementation, a pre-processor generates all of the PEST input files based on the eSTOMP input file. Simulation results for comparison with observations are extracted automatically at each time step eliminating the need for post-process data extractions. The inversion framework was tested with three different experimental data sets: one-dimensional water flow at Hanford Grass Site; irrigation and infiltration experiment at the Andelfingen Site; and a three-dimensional injection experiment at Hanford's Sisson and Lu Site. Good agreements are achieved in all three applications between observations and simulations in both parameter estimates and water dynamics reproduction. Results show that eSTOMP/BeoPEST approach is highly scalable and can be run efficiently with hundreds or thousands of processors. BeoPEST is fault tolerant and new nodes can be dynamically added and removed. A major advantage of this approach is the ability to use high-resolution geologic models to preserve the spatial structure in the inverse model, which leads to better parameter estimates and improved predictions when using the inverse-conditioned realizations of parameter fields.

A Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

PubMed Central

Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrell J; Wang, Dafang F; Steffen, Michael; Brooks, Dana H; van Dam, Peter M; Macleod, Rob S

2012-01-01

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems. PMID:22254301

The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography.

PubMed

Dushaw, Brian D; Sagen, Hanne

2017-12-01

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

Joint Geophysical Inversion With Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelievre, P. G.; Bijani, R.; Farquharson, C. G.

2015-12-01

Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem is essentially a geometry inversion, which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.

Location identification for indoor instantaneous point contaminant source by probability-based inverse Computational Fluid Dynamics modeling.

PubMed

Liu, X; Zhai, Z

2008-02-01

Indoor pollutions jeopardize human health and welfare and may even cause serious morbidity and mortality under extreme conditions. To effectively control and improve indoor environment quality requires immediate interpretation of pollutant sensor readings and accurate identification of indoor pollution history and source characteristics (e.g. source location and release time). This procedure is complicated by non-uniform and dynamic contaminant indoor dispersion behaviors as well as diverse sensor network distributions. This paper introduces a probability concept based inverse modeling method that is able to identify the source location for an instantaneous point source placed in an enclosed environment with known source release time. The study presents the mathematical models that address three different sensing scenarios: sensors without concentration readings, sensors with spatial concentration readings, and sensors with temporal concentration readings. The paper demonstrates the inverse modeling method and algorithm with two case studies: air pollution in an office space and in an aircraft cabin. The predictions were successfully verified against the forward simulation settings, indicating good capability of the method in finding indoor pollutant sources. The research lays a solid ground for further study of the method for more complicated indoor contamination problems. The method developed can help track indoor contaminant source location with limited sensor outputs. This will ensure an effective and prompt execution of building control strategies and thus achieve a healthy and safe indoor environment. The method can also assist the design of optimal sensor networks.

Time-reversal and Bayesian inversion

NASA Astrophysics Data System (ADS)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

NASA Astrophysics Data System (ADS)

Uhlmann, Gunther

2008-07-01

This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology, Finland), Masahiro Yamamoto (University of Tokyo, Japan), Gunther Uhlmann (University of Washington) and Jun Zou (Chinese University of Hong Kong). IPIA is a recently formed organization that intends to promote the field of inverse problem at all levels. See http://www.inverse-problems.net/. IPIA awarded the first Calderón prize at the opening of the conference to Matti Lassas (see first article in the Proceedings). There was also a general meeting of IPIA during the workshop. This was probably the largest conference ever on IP with 350 registered participants. The program consisted of 18 invited speakers and the Calderón Prize Lecture given by Matti Lassas. Another integral part of the program was the more than 60 mini-symposia that covered a broad spectrum of the theory and applications of inverse problems, focusing on recent developments in medical imaging, seismic exploration, remote sensing, industrial applications, numerical and regularization methods in inverse problems. Another important related topic was image processing in particular the advances which have allowed for significant enhancement of widely used imaging techniques. For more details on the program see the web page: http://www.pims.math.ca/science/2007/07aip. These proceedings reflect the broad spectrum of topics covered in AIP 2007. The conference and these proceedings would not have happened without the contributions of many people. I thank all my fellow organizers, the invited speakers, the speakers and organizers of mini-symposia for making this an exciting and vibrant event. I also thank PIMS, NSF and MITACS for their generous financial support. I take this opportunity to thank the PIMS staff, particularly Ken Leung, for making the local arrangements. Also thanks are due to Stephen McDowall for his help in preparing the schedule of the conference and Xiaosheng Li for the help in preparing these proceedings. I also would like to thank the contributors of this volume and the referees. Finally, many thanks are due to Graham Douglas and Elaine Longden-Chapman for suggesting publication in Journal of Physics: Conference Series.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

Compensation of significant parametric uncertainties using sliding mode online learning

NASA Astrophysics Data System (ADS)

Schnetter, Philipp; Kruger, Thomas

An augmented nonlinear inverse dynamics (NID) flight control strategy using sliding mode online learning for a small unmanned aircraft system (UAS) is presented. Because parameter identification for this class of aircraft often is not valid throughout the complete flight envelope, aerodynamic parameters used for model based control strategies may show significant deviations. For the concept of feedback linearization this leads to inversion errors that in combination with the distinctive susceptibility of small UAS towards atmospheric turbulence pose a demanding control task for these systems. In this work an adaptive flight control strategy using feedforward neural networks for counteracting such nonlinear effects is augmented with the concept of sliding mode control (SMC). SMC-learning is derived from variable structure theory. It considers a neural network and its training as a control problem. It is shown that by the dynamic calculation of the learning rates, stability can be guaranteed and thus increase the robustness against external disturbances and system failures. With the resulting higher speed of convergence a wide range of simultaneously occurring disturbances can be compensated. The SMC-based flight controller is tested and compared to the standard gradient descent (GD) backpropagation algorithm under the influence of significant model uncertainties and system failures.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

Combined Parameter and State Estimation Problem in a Complex Domain: RF Hyperthermia Treatment Using Nanoparticles

NASA Astrophysics Data System (ADS)

Bermeo Varon, L. A.; Orlande, H. R. B.; Eliçabe, G. E.

2016-09-01

The particle filter methods have been widely used to solve inverse problems with sequential Bayesian inference in dynamic models, simultaneously estimating sequential state variables and fixed model parameters. This methods are an approximation of sequences of probability distributions of interest, that using a large set of random samples, with presence uncertainties in the model, measurements and parameters. In this paper the main focus is the solution combined parameters and state estimation in the radiofrequency hyperthermia with nanoparticles in a complex domain. This domain contains different tissues like muscle, pancreas, lungs, small intestine and a tumor which is loaded iron oxide nanoparticles. The results indicated that excellent agreements between estimated and exact value are obtained.

Ship dynamics for maritime ISAR imaging.

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

Doerry, Armin Walter

2008-02-01

Demand is increasing for imaging ships at sea. Conventional SAR fails because the ships are usually in motion, both with a forward velocity, and other linear and angular motions that accompany sea travel. Because the target itself is moving, this becomes an Inverse- SAR, or ISAR problem. Developing useful ISAR techniques and algorithms is considerably aided by first understanding the nature and characteristics of ship motion. Consequently, a brief study of some principles of naval architecture sheds useful light on this problem. We attempt to do so here. Ship motions are analyzed for their impact on range-Doppler imaging using Inversemore » Synthetic Aperture Radar (ISAR). A framework for analysis is developed, and limitations of simple ISAR systems are discussed.« less

Quantization of Non-Lagrangian Systems

NASA Astrophysics Data System (ADS)

Kochan, Denis

A novel method for quantization of non-Lagrangian (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (Lagrangian) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.

General Theory and Algorithms for the Non-Casual Inversion, Slewing and Control of Space-Based Articulated Structures

DTIC Science & Technology

1993-10-01

Structures: Simultaneous Trajectory Tracking and Vibration Reduction ... 10 3 . Buckling Control of a Flexible Beam Using Piezoelectric Actuators...bounded solution for the inverse dynamic torque has to be non-causal. Bayo, et. al. [ 3 ], extended the inverse dynamics to planar, multiple-link systems...presented by &ayo and Moulin [4] for the single link system, with provisions for 3 extension to multiple link systems. An equivalent time domain approach for

Getting in shape: Reconstructing three-dimensional long-track speed skating kinematics by comparing several body pose reconstruction techniques.

PubMed

van der Kruk, E; Schwab, A L; van der Helm, F C T; Veeger, H E J

2018-03-01

In gait studies body pose reconstruction (BPR) techniques have been widely explored, but no previous protocols have been developed for speed skating, while the peculiarities of the skating posture and technique do not automatically allow for the transfer of the results of those explorations to kinematic skating data. The aim of this paper is to determine the best procedure for body pose reconstruction and inverse dynamics of speed skating, and to what extend this choice influences the estimation of joint power. The results show that an eight body segment model together with a global optimization method with revolute joint in the knee and in the lumbosacral joint, while keeping the other joints spherical, would be the most realistic model to use for the inverse kinematics in speed skating. To determine joint power, this method should be combined with a least-square error method for the inverse dynamics. Reporting on the BPR technique and the inverse dynamic method is crucial to enable comparison between studies. Our data showed an underestimation of up to 74% in mean joint power when no optimization procedure was applied for BPR and an underestimation of up to 31% in mean joint power when a bottom-up inverse dynamics method was chosen instead of a least square error approach. Although these results are aimed at speed skating, reporting on the BPR procedure and the inverse dynamics method, together with setting a golden standard should be common practice in all human movement research to allow comparison between studies. Copyright © 2018 Elsevier Ltd. All rights reserved.

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

DOE PAGES

Butler, Troy; Graham, L.; Estep, D.; ...

2015-02-03

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in amore » shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.« less

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

What you feel is what you see: inverse dynamics estimation underlies the resistive sensation of a delayed cursor.

PubMed

Takamuku, Shinya; Gomi, Hiroaki

2015-07-22

How our central nervous system (CNS) learns and exploits relationships between force and motion is a fundamental issue in computational neuroscience. While several lines of evidence have suggested that the CNS predicts motion states and signals from motor commands for control and perception (forward dynamics), it remains controversial whether it also performs the 'inverse' computation, i.e. the estimation of force from motion (inverse dynamics). Here, we show that the resistive sensation we experience while moving a delayed cursor, perceived purely from the change in visual motion, provides evidence of the inverse computation. To clearly specify the computational process underlying the sensation, we systematically varied the visual feedback and examined its effect on the strength of the sensation. In contrast to the prevailing theory that sensory prediction errors modulate our perception, the sensation did not correlate with errors in cursor motion due to the delay. Instead, it correlated with the amount of exposure to the forward acceleration of the cursor. This indicates that the delayed cursor is interpreted as a mechanical load, and the sensation represents its visually implied reaction force. Namely, the CNS automatically computes inverse dynamics, using visually detected motions, to monitor the dynamic forces involved in our actions. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Off-axis impact of unidirectional composites with cracks: Dynamic stress intensification

NASA Technical Reports Server (NTRS)

Sih, G. C.; Chen, E. P.

1979-01-01

The dynamic response of unidirectional composites under off axis (angle loading) impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. The analytical method utilizes Fourier transform for the space variable and Laplace transform for the time variable. The off axis impact is separated into two parts, one being symmetric and the other skew-symmetric with reference to the crack plane. Transient boundary conditions of normal and shear tractions are applied to a crack embedded in the matrix of the unidirectional composite. The two boundary conditions are solved independently and the results superimposed. Mathematically, these conditions reduce the problem to a system of dual integral equations which are solved in the Laplace transform plane for the transformation of the dynamic stress intensity factor. The time inversion is carried out numerically for various combinations of the material properties of the composite and the results are displayed graphically.

Wavelet-based spectral finite element dynamic analysis for an axially moving Timoshenko beam

NASA Astrophysics Data System (ADS)

Mokhtari, Ali; Mirdamadi, Hamid Reza; Ghayour, Mostafa

2017-08-01

In this article, wavelet-based spectral finite element (WSFE) model is formulated for time domain and wave domain dynamic analysis of an axially moving Timoshenko beam subjected to axial pretension. The formulation is similar to conventional FFT-based spectral finite element (SFE) model except that Daubechies wavelet basis functions are used for temporal discretization of the governing partial differential equations into a set of ordinary differential equations. The localized nature of Daubechies wavelet basis functions helps to rule out problems of SFE model due to periodicity assumption, especially during inverse Fourier transformation and back to time domain. The high accuracy of WSFE model is then evaluated by comparing its results with those of conventional finite element and SFE results. The effects of moving beam speed and axial tensile force on vibration and wave characteristics, and static and dynamic stabilities of moving beam are investigated.

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

PubMed Central

Van Regenmortel, Marc H. V.

2018-01-01

Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly rational design process. This is why the complexity of the human immune system prevents us from rationally designing an HIV vaccine by solving inverse problems. PMID:29387066

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

Evaluation of uncertainty for regularized deconvolution: A case study in hydrophone measurements.

PubMed

Eichstädt, S; Wilkens, V

2017-06-01

An estimation of the measurand in dynamic metrology usually requires a deconvolution based on a dynamic calibration of the measuring system. Since deconvolution is, mathematically speaking, an ill-posed inverse problem, some kind of regularization is required to render the problem stable and obtain usable results. Many approaches to regularized deconvolution exist in the literature, but the corresponding evaluation of measurement uncertainties is, in general, an unsolved issue. In particular, the uncertainty contribution of the regularization itself is a topic of great importance, because it has a significant impact on the estimation result. Here, a versatile approach is proposed to express prior knowledge about the measurand based on a flexible, low-dimensional modeling of an upper bound on the magnitude spectrum of the measurand. This upper bound allows the derivation of an uncertainty associated with the regularization method in line with the guidelines in metrology. As a case study for the proposed method, hydrophone measurements in medical ultrasound with an acoustic working frequency of up to 7.5 MHz are considered, but the approach is applicable for all kinds of estimation methods in dynamic metrology, where regularization is required and which can be expressed as a multiplication in the frequency domain.

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

NASA Technical Reports Server (NTRS)

Kent, James; Holdaway, Daniel

2015-01-01

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis

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

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis schememore » based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. In conclusion, using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.« less

Inverse transformation: unleashing spatially heterogeneous dynamics with an alternative approach to XPCS data analysis

DOE PAGES

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; ...

2018-02-01

X-ray photon correlation spectroscopy (XPCS), an extension of dynamic light scattering (DLS) in the X-ray regime, detects temporal intensity fluctuations of coherent speckles and provides scattering-vector-dependent sample dynamics at length scales smaller than DLS. The penetrating power of X-rays enables XPCS to probe the dynamics in a broad array of materials, including polymers, glasses and metal alloys, where attempts to describe the dynamics with a simple exponential fit usually fail. In these cases, the prevailing XPCS data analysis approach employs stretched or compressed exponential decay functions (Kohlrausch functions), which implicitly assume homogeneous dynamics. This paper proposes an alternative analysis schememore » based upon inverse Laplace or Gaussian transformation for elucidating heterogeneous distributions of dynamic time scales in XPCS, an approach analogous to the CONTIN algorithm widely accepted in the analysis of DLS from polydisperse and multimodal systems. In conclusion, using XPCS data measured from colloidal gels, it is demonstrated that the inverse transform approach reveals hidden multimodal dynamics in materials, unleashing the full potential of XPCS.« less

First quantification of relationship between dune orientation and sediment availability, Olympia Undae, Mars

NASA Astrophysics Data System (ADS)

Fernandez-Cascales, Laura; Lucas, Antoine; Rodriguez, Sébastien; Gao, Xin; Spiga, Aymeric; Narteau, Clément

2018-05-01

Dunes provide unique information about wind regimes on planetary bodies where there is no direct meteorological data. At the eastern margin of Olympia Undae on Mars, dune orientation is measured from satellite imagery and sediment cover is estimated using the high contrast between the dune material and substrate. The analysis of these data provide the first quantification of relationship between sediment availability and dune orientation. Abrupt and smooth dune reorientations are associated with inward and outward dynamics of dunes approaching and ejecting from major sedimentary bodies, respectively. These reorientation patterns along sediment transport pathways are interpreted using a new generation dune model based on the coexistence of two dune growth mechanisms. This model also permits solving of the inverse problem of predicting the wind regime from dune orientation. For bidirectional wind regimes, solutions of this inverse problem show substantial differences in the distributions of sediment flux orientation, which can be attributed to atmospheric flow variations induced by changes in albedo at the boundaries of major dune fields. Then, we conclude that relationships between sediment cover and dune orientation can be used to constrain wind regime and dune field development on Mars and other planetary surfaces.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Control of a flexible bracing manipulator: Integration of current research work to realize the bracing manipulator

NASA Technical Reports Server (NTRS)

Kwon, Dong-Soo

1991-01-01

All research results about flexible manipulator control were integrated to show a control scenario of a bracing manipulator. First, dynamic analysis of a flexible manipulator was done for modeling. Second, from the dynamic model, the inverse dynamic equation was derived, and the time domain inverse dynamic method was proposed for the calculation of the feedforward torque and the desired flexible coordinate trajectories. Third, a tracking controller was designed by combining the inverse dynamic feedforward control with the joint feedback control. The control scheme was applied to the tip position control of a single link flexible manipulator for zero and non-zero initial condition cases. Finally, the contact control scheme was added to the position tracking control. A control scenario of a bracing manipulator is provided and evaluated through simulation and experiment on a single link flexible manipulator.

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

Geodynamic inversion to constrain the non-linear rheology of the lithosphere

NASA Astrophysics Data System (ADS)

Baumann, T. S.; Kaus, Boris J. P.

2015-08-01

One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology, we first perform a geodynamic inversion of a synthetic forward model of intraoceanic subduction with known parameters. This requires solving an inverse problem with 14-16 parameters, depending on whether temperature is assumed to be known or not. With the help of a massively parallel direct-search combined with a Markov Chain Monte Carlo method, solving the inverse problem becomes feasible. Results show that the rheological parameters and particularly the effective viscosity structure of the lithosphere can be reconstructed in a probabilistic sense. This also holds, with somewhat larger uncertainties, for the case where the temperature distribution is parametrized. Finally, we apply the method to a cross-section of the India-Asia collision system. In this case, the number of parameters is larger, which requires solving around 1.9 × 106 forward models. The resulting models fit the data within their respective uncertainty bounds, and show that the Indian mantle lithosphere must have a high viscosity. Results for the Tibetan plateau are less clear, and both models with a weak Asian mantle lithosphere and with a weak Asian lower crust fit the data nearly equally well.

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

NASA Astrophysics Data System (ADS)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

The inverse Wiener polarity index problem for chemical trees.

PubMed

Du, Zhibin; Ali, Akbar

2018-01-01

The Wiener polarity number (which, nowadays, known as the Wiener polarity index and usually denoted by Wp) was devised by the chemist Harold Wiener, for predicting the boiling points of alkanes. The index Wp of chemical trees (chemical graphs representing alkanes) is defined as the number of unordered pairs of vertices (carbon atoms) at distance 3. The inverse problems based on some well-known topological indices have already been addressed in the literature. The solution of such inverse problems may be helpful in speeding up the discovery of lead compounds having the desired properties. This paper is devoted to solving a stronger version of the inverse problem based on Wiener polarity index for chemical trees. More precisely, it is proved that for every integer t ∈ {n - 3, n - 2,…,3n - 16, 3n - 15}, n ≥ 6, there exists an n-vertex chemical tree T such that Wp(T) = t.

Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

Novel Infrared Dynamics of Cold Atoms on Hot Graphene

NASA Astrophysics Data System (ADS)

Sengupta, Sanghita; Kotov, Valeri; Clougherty, Dennis

The low-energy dynamics of cold atoms interacting with macroscopic graphene membranes exhibits severe infrared divergences when treated perturbatively. These infrared problems are even more pronounced at finite temperature due to the (infinitely) many flexural phonons excited in graphene. We have devised a technique to take account (resummation) of such processes in the spirit of the well-known exact solution of the independent boson model. Remarkably, there is also similarity to the infrared problems and their treatment (via the Bloch-Nordsieck scheme) in finite temperature ``hot'' quantum electrodynamics and chromodynamics due to the long-range, unscreened nature of gauge interactions. The method takes into account correctly the strong damping provided by the many emitted phonons at finite temperature. In our case, the inverse membrane size plays the role of an effective low-energy scale, and, unlike the above mentioned field theories, there remains an unusual, highly nontrivial dependence on that scale due to the 2D nature of the problem. We present detailed results for the sticking (atomic damping rate) rate of cold atomic hydrogen as a function of the membrane temperature and size. We find that the rate is very strongly dependent on both quantities.

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

A new version of variational integrated technology for environmental modeling with assimilation of available data

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Aleksey

2014-05-01

A modeling technology based on coupled models of atmospheric dynamics and chemistry are presented [1-3]. It is the result of application of variational methods in combination with the methods of decomposition and splitting. The idea of Euler's integrating factors combined with technique of adjoint problems is also used. In online technologies, a significant part of algorithmic and computational work consist in solving the problems like convection-diffusion-reaction and in organizing data assimilation techniques based on them. For equations of convection-diffusion, the methodology gives us the unconditionally stable and monotone discrete-analytical schemes in the frames of methods of decomposition and splitting. These schemes are exact for locally one-dimensional problems respect to the spatial variables. For stiff systems of equations describing transformation of gas and aerosol substances, the monotone and stable schemes are also obtained. They are implemented by non- iterative algorithms. By construction, all schemes for different components of state functions are structurally uniform. They are coordinated among themselves in the sense of forward and inverse modeling. Variational principles are constructed taking into account the fact that the behavior of the different dynamic and chemical components of the state function is characterized by high variability and uncertainty. Information on the parameters of models, sources and emission impacts is also not determined precisely. Therefore, to obtain the consistent solutions, we construct methods of the sensitivity theory taking into account the influence of uncertainty. For this purpose, new methods of data assimilation of hydrodynamic fields and gas-aerosol substances measured by different observing systems are proposed. Optimization criteria for data assimilation problems are defined so that they include a set of functionals evaluating the total measure of uncertainties. The latter are explicitly introduced into the equations of the model of processes as desired deterministic control functions. This method of data assimilation with control functions is implemented by direct algorithms. The modeling technology presented here focuses on various scientific and applied problems of environmental prediction and design, including risk assessment in relation to existing and potential sources of natural and anthropogenic influences. The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS; by RFBR projects NN 11-01-00187 and 14-01-31482; by Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References 1. V. Penenko, A.Baklanov, E. Tsvetova and A. Mahura. Direct and Inverse Problems in a Variational Concept of Environmental Modeling, Pure and Applied Geoph. 2012.V.169:447-465. 2. A.V. Penenko, Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods, Numerical Analysis and Applications, 2012. V. 5:326-341. 3. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models, Numerical analysis and applications, 2013. V. 6: 210-220.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Performance impact of mutation operators of a subpopulation-based genetic algorithm for multi-robot task allocation problems.

PubMed

Liu, Chun; Kroll, Andreas

2016-01-01

Multi-robot task allocation determines the task sequence and distribution for a group of robots in multi-robot systems, which is one of constrained combinatorial optimization problems and more complex in case of cooperative tasks because they introduce additional spatial and temporal constraints. To solve multi-robot task allocation problems with cooperative tasks efficiently, a subpopulation-based genetic algorithm, a crossover-free genetic algorithm employing mutation operators and elitism selection in each subpopulation, is developed in this paper. Moreover, the impact of mutation operators (swap, insertion, inversion, displacement, and their various combinations) is analyzed when solving several industrial plant inspection problems. The experimental results show that: (1) the proposed genetic algorithm can obtain better solutions than the tested binary tournament genetic algorithm with partially mapped crossover; (2) inversion mutation performs better than other tested mutation operators when solving problems without cooperative tasks, and the swap-inversion combination performs better than other tested mutation operators/combinations when solving problems with cooperative tasks. As it is difficult to produce all desired effects with a single mutation operator, using multiple mutation operators (including both inversion and swap) is suggested when solving similar combinatorial optimization problems.

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Performance recovery of a class of uncertain non-affine systems with unmodelled dynamics: an indirect dynamic inversion method

NASA Astrophysics Data System (ADS)

Yi, Bowen; Lin, Shuyi; Yang, Bo; Zhang, Weidong

2018-02-01

This paper presents an output feedback indirect dynamic inversion (IDI) approach for a class of uncertain nonaffine systems with input unmodelled dynamics. Compared with previous approaches to achieve performance recovery, the proposed method aims at dealing with a broader class of nonaffine-in-control systems with triangular structure. An IDI state feedback law is designed first, in which less knowledge of the model plant is needed compared to earlier approximate dynamic inversion methods, thus yielding more robust performance. After that, an extended high-gain observer is designed to accomplish the task with output feedback. Finally, we prove that the designed IDI controller is equivalent to an adaptive proportional-integral (PI) controller, with respect to both time response equivalence and robustness equivalence. The conclusion implies that for the studied strict-feedback non-affine systems with unmodelled dynamics, there always exits a PI controller to stabilise the systems. The effectiveness and benefits of the designed approach are verified by three examples.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

The inverse electroencephalography pipeline

NASA Astrophysics Data System (ADS)

Weinstein, David Michael

The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.

Efficacy of an ankle brace with a subtalar locking system in inversion control in dynamic movements.

PubMed

Zhang, Songning; Wortley, Michael; Chen, Qingjian; Freedman, Julia

2009-12-01

Controlled laboratory study. To examine effectiveness of an ankle brace with a subtalar locking system in restricting ankle inversion during passive and dynamic movements. Semirigid ankle braces are considered more effective in restricting ankle inversion than other types of brace, but a semirigid brace with a subtalar locking system may be even more effective. Nineteen healthy subjects with no history of major lower extremity injuries were included in the study. Participants performed 5 trials of an ankle inversion drop test and a lateral-cutting movement without wearing a brace and while wearing either the Element (with the subtalar locking system), a Functional ankle brace, or an ASO ankle brace. A 2-way repeated-measures analysis of variance (ANOVA) was used to assess brace differences (P?.05). All 3 braces significantly reduced total passive ankle frontal plane range of motion (ROM), with the Element ankle brace being the most effective. For the inversion drop the results showed significant reductions in peak ankle inversion angle and inversion ROM for all 3 braces compared to the no brace condition; and the peak inversion velocity was also reduced for the Element brace and the Functional brace. In the lateral-cutting movement, a small but significant reduction of the peak inversion angle in early foot contact and the peak eversion velocity at push-off were seen when wearing the Element and the Functional ankle braces compared to the no brace condition. Peak vertical ground reaction force was reduced for the Element brace compared to the ASO brace and the no brace conditions. These results suggest that the tested ankle braces, especially the Element brace, provided effective restriction of ankle inversion during both passive and dynamic movements.

Real-time Fatigue and Free-Living Physical Activity in Hematopoietic Stem Cell Transplantation Cancer Survivors and Healthy Controls: A Preliminary Examination of the Temporal, Dynamic Relationship.

PubMed

Hacker, Eileen Danaher; Kim, Inah; Park, Chang; Peters, Tara

Fatigue and physical inactivity, critical problems facing cancer survivors, impact overall health and functioning. Our group designed a novel methodology to evaluate the temporal, dynamic patterns in real-world settings. Using real-time technology, the temporal, dynamic relationship between real-time fatigue and free-living is described and compared in cancer survivors who were treated with hematopoietic stem cell transplantation (n = 25) and age- and gender-matched healthy controls (n = 25). Subjects wore wrist actigraphs on their nondominant hand to assess free-living physical activity, measured in 1-minute epochs, over 7 days. Subjects entered real-time fatigue assessments directly into the subjective event marker of the actigraph 5 times per day. Running averages of mean 1-minute activity counts 30, 60, and 120 minutes before and after each real-time fatigue score were correlated with real-time fatigue using generalized estimating equations, RESULTS:: A strong inverse relationship exists between real-time fatigue and subsequent free-living physical activity. This inverse relationship suggests that increasing real-time fatigue limits subsequent physical activity (B range= -0.002 to -0.004; P < .001). No significant differences in the dynamic patterns of real-time fatigue and free-living physical activity were found between groups. To our knowledge, this is the first study to document the temporal and potentially causal relationship between real-time fatigue and free-living physical activity in real-world setting. These findings suggest that fatigue drives the subsequent physical activity and the relationship may not be bidirectional. Understanding the temporal, dynamic relationship may have important health implications for developing interventions to address fatigue in cancer survivors.

IPDO-2007: Inverse Problems, Design and Optimization Symposium

DTIC Science & Technology

2007-08-01

Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

Machine learning in motion control

NASA Technical Reports Server (NTRS)

Su, Renjeng; Kermiche, Noureddine

1989-01-01

The existing methodologies for robot programming originate primarily from robotic applications to manufacturing, where uncertainties of the robots and their task environment may be minimized by repeated off-line modeling and identification. In space application of robots, however, a higher degree of automation is required for robot programming because of the desire of minimizing the human intervention. We discuss a new paradigm of robotic programming which is based on the concept of machine learning. The goal is to let robots practice tasks by themselves and the operational data are used to automatically improve their motion performance. The underlying mathematical problem is to solve the problem of dynamical inverse by iterative methods. One of the key questions is how to ensure the convergence of the iterative process. There have been a few small steps taken into this important approach to robot programming. We give a representative result on the convergence problem.

A preprocessing strategy for helioseismic inversions

NASA Astrophysics Data System (ADS)

Christensen-Dalsgaard, J.; Thompson, M. J.

1993-05-01

Helioseismic inversion in general involves considerable computational expense, due to the large number of modes that is typically considered. This is true in particular of the widely used optimally localized averages (OLA) inversion methods, which require the inversion of one or more matrices whose order is the number of modes in the set. However, the number of practically independent pieces of information that a large helioseismic mode set contains is very much less than the number of modes, suggesting that the set might first be reduced before the expensive inversion is performed. We demonstrate with a model problem that by first performing a singular value decomposition the original problem may be transformed into a much smaller one, reducing considerably the cost of the OLA inversion and with no significant loss of information.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE PAGES

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

2017-10-29

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

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

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Final Report: Resolving and Discriminating Overlapping Anomalies from Multiple Objects in Cluttered Environments

DTIC Science & Technology

2015-12-15

UXO community . NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Irma Shamatava 0.50 0.50 1 Resolving and Discriminating...Distinguishing an object of interest from innocuous items is the main problem that the UXO community is facing currently. This inverse problem...innocuous items is the main problem that the UXO community is facing currently. This inverse problem demands fast and accurate representation of

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Nonlinear Inversion for Dynamic Rupture Parameters from the 2004 Mw6.0 Parkfield Earthquake

NASA Astrophysics Data System (ADS)

Jimenez, R. M.; Olsen, K. B.

2007-12-01

The Parkfield section of the San Andreas Fault has produced repeated moderate-size earthquakes at fairly regular intervals and is therefore an important target for investigations of rupture initiation, propagation and arrest, which could eventually lead to clues on earthquake prediction. The most recent member of the Parkfield series of earthquakes, the 2004 Mw6.0 event, produced a considerable amount of high-resolution strong motion data, and provides an ideal test bed for analysis of the dynamic rupture propagation. Here, we use a systematic nonlinear direct-search method to invert strong-ground motion data (less than 1 Hz) at 37 stations to obtain models of the slip weakening distance and spatially-varying stress drop (8 by 4 subfaults) on the (vertical) causative segment of the San Andreas fault (40 km long by 15 km wide), along with spatial-temporal coseismic slip distributions. The rupture and wave propagation modeling is performed by a three-dimensional finite-difference method with a slip- weakening friction law and the stress-glut dynamic-rupture formulation (Andrews, 1999), and the inversion is carried out by a neighborhood algorithm (Sambridge, 1999), minimizing the least-squares misfit between the calculated and observed seismograms. The dynamic rupture is nucleated artificially by lowering the yield stress in a 3 km by 3 km patch centered at the location of the hypocenter estimated from strong motion data. Outside the nucleation patch the yield stress is kept constant (5-10 MPa), and we constrain the slip-weakening distance to values less than 1 m. We compare the inversion results for two different velocity models: (1) a 3-D model based on the P-wave velocity structure by Thurber (2006), with S-wave and density relations based on Brocher (2005), and (2) a combination of two different 1-D layered velocity structures on either side of the fault, as proposed by Liu et al. (2006). Due to the non-uniqueness of the problem, the inversion provides an ensemble of equally valid rupture models that produce synthetics with comparable fit to the observed strong motion data. Our preliminary results with the smallest misfits, out of about 3000 tested rupture models, suggest an average slip-weakening distance of 19-81 cm and an average stress drop across the fault of 6.7 - 8.4 MPa. Compared to the kinematic inversion results by Liu et al. (2006) our models with the smallest misfits produce a larger maximum slip (up to about 81 cm) and smaller rupture area, but similar rupture duration (5-7s). The inversions carried out for the layered models tend to produce smaller misfit between data and synthetics as compared to the results using the 3D structure. This suggests that our 3D structure needs improvement, including the Vs-Vp and density-Vp relation. We expect further decrease in the misfit values by increasing the number of tested rupture models.

Full analogue electronic realisation of the Hodgkin-Huxley neuronal dynamics in weak-inversion CMOS.

PubMed

Lazaridis, E; Drakakis, E M; Barahona, M

2007-01-01

This paper presents a non-linear analog synthesis path towards the modeling and full implementation of the Hodgkin-Huxley neuronal dynamics in silicon. The proposed circuits have been realized in weak-inversion CMOS technology and take advantage of both log-domain and translinear transistor-level techniques.

CONTIN XPCS: software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics

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

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, calledCONTIN XPCS, is an extension of traditionalCONTINanalysis and accommodates the various dynamics encountered inmore » equilibrium XPCS measurements.« less

CONTIN XPCS: software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics

DOE PAGES

Andrews, Ross N.; Narayanan, Suresh; Zhang, Fan; ...

2018-02-01

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, calledCONTIN XPCS, is an extension of traditionalCONTINanalysis and accommodates the various dynamics encountered inmore » equilibrium XPCS measurements.« less

Studies of phosphatidylcholine vesicles by spectroturbidimetric and dynamic light scattering methods

NASA Astrophysics Data System (ADS)

Khlebtsov, B. N.; Kovler, L. A.; Bogatyrev, V. A.; Khlebtsov, N. G.; Shchyogolev, S. Yu.

2003-09-01

A spectroturbidimetric method for the determination of the average size and thickness of the shell in polydisperse suspensions of liposome particles is discussed. The method is based on measuring the wavelength exponent of a suspension (a slope of the logarithmic turbidity spectrum) and the specific turbidity (the turbidity per unit mass concentration of the dispersed substance). The inverse problem was solved using an exact calculation of characteristics of light scattering for polydisperse suspensions of spherical bilayer particles with allowance for the spectral dependence of optical constants. A practical realization of this method is illustrated by the experimental determinations of the structural parameters of liposomes prepared from egg lecithin. Comparison experiments to determine the liposome size by the dynamic (quasielastic) light scattering method were performed as an independent control.

Packaging stiff polymers in small containers: A molecular dynamics study

NASA Astrophysics Data System (ADS)

Rapaport, D. C.

2016-09-01

The question of how stiff polymers are able to pack into small containers is particularly relevant to the study of DNA packaging in viruses. A reduced version of the problem based on coarse-grained representations of the main components of the system—the DNA polymer and the spherical viral capsid—has been studied by molecular dynamics simulation. The results, involving longer polymers than in earlier work, show that as polymers become more rigid there is an increasing tendency to self-organize as spools that wrap from the inside out, rather than the inverse direction seen previously. In the final state, a substantial part of the polymer is packed into one or more coaxial spools, concentrically layered with different orientations, a form of packaging achievable without twisting the polymer.

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

A multi-frequency iterative imaging method for discontinuous inverse medium problem

NASA Astrophysics Data System (ADS)

Zhang, Lei; Feng, Lixin

2018-06-01

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

Phase Inversion of EPDM/PP Blends: Effect of Viscosity Ratio

NASA Astrophysics Data System (ADS)

Machado, Ana Vera; Antunes, Carla Filipa; van Duin, Martin

2011-07-01

EPDM/PP blends and TPVs with and without crosslinking, respectively, were prepared, in a batch mixer, using three different EPDM rubbers. EPDM/PP based TPVs were dynamic vulcanised using the resol/SnCl2 system. Samples were collected along the time in order to get information on the morphology evolution and crosslinking density during dynamic vulcanisation. The morphology was studied by SEM and the crosslink density by gel content. In the case of low viscosity EPDMs, crosslinking of the EPDM phase was retarded due to its low crosslinking efficiency. This delay on crosslinking reaction enables the observation of the various stages of the morphological mechanism that takes place during dynamic vulcanisation. It could be observed that phase inversion takes place via lamellar mechanism. More detailed insight on phase inversion mechanism during dynamic vulcanisation was accomplished.

Stability Result For Dynamic Inversion Devised to Control Large Flexible Aircraft

NASA Technical Reports Server (NTRS)

Gregory, Irene M.

2001-01-01

High performance aircraft of the future will be designed lighter, more maneuverable, and operate over an ever expanding flight envelope. One of the largest differences from the flight control perspective between current and future advanced aircraft is elasticity. Over the last decade, dynamic inversion methodology has gained considerable popularity in application to highly maneuverable fighter aircraft, which were treated as rigid vehicles. This paper is an initial attempt to establish global stability results for dynamic inversion methodology as applied to a large, flexible aircraft. This work builds on a previous result for rigid fighter aircraft and adds a new level of complexity that is the flexible aircraft dynamics, which cannot be ignored even in the most basic flight control. The results arise from observations of the control laws designed for a new generation of the High-Speed Civil Transport aircraft.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

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

Liu, Yun; Zhang, Yin

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as smallmore » as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.« less

Inferior olive mirrors joint dynamics to implement an inverse controller.

PubMed

Alvarez-Icaza, Rodrigo; Boahen, Kwabena

2012-10-01

To produce smooth and coordinated motion, our nervous systems need to generate precisely timed muscle activation patterns that, due to axonal conduction delay, must be generated in a predictive and feedforward manner. Kawato proposed that the cerebellum accomplishes this by acting as an inverse controller that modulates descending motor commands to predictively drive the spinal cord such that the musculoskeletal dynamics are canceled out. This and other cerebellar theories do not, however, account for the rich biophysical properties expressed by the olivocerebellar complex's various cell types, making these theories difficult to verify experimentally. Here we propose that a multizonal microcomplex's (MZMC) inferior olivary neurons use their subthreshold oscillations to mirror a musculoskeletal joint's underdamped dynamics, thereby achieving inverse control. We used control theory to map a joint's inverse model onto an MZMC's biophysics, and we used biophysical modeling to confirm that inferior olivary neurons can express the dynamics required to mirror biomechanical joints. We then combined both techniques to predict how experimentally injecting current into the inferior olive would affect overall motor output performance. We found that this experimental manipulation unmasked a joint's natural dynamics, as observed by motor output ringing at the joint's natural frequency, with amplitude proportional to the amount of current. These results support the proposal that the cerebellum-in particular an MZMC-is an inverse controller; the results also provide a biophysical implementation for this controller and allow one to make an experimentally testable prediction.

Transient reaction of an elastic half-plane on a source of a concentrated boundary disturbance

NASA Astrophysics Data System (ADS)

Okonechnikov, A. S.; Tarlakovski, D. V.; Ul'yashina, A. N.; Fedotenkov, G. V.

2016-11-01

One of the key problems in studying the non-stationary processes of solid mechanics is obtaining of influence functions. These functions serve as solutions for the problems of effect of sudden concentrated loads on a body with linear elastic properties. Knowledge of the influence functions allows us to obtain the solutions for the problems with non-mixed boundary and initial conditions in the form of quadrature formulae with the help of superposition principle, as well as get the integral governing equations for the problems with mixed boundary and initial conditions. This paper offers explicit derivations for all nonstationary surface influence functions of an elastic half-plane in a plane strain condition. It is achieved with the help of combined inverse transform of a Fourier-Laplace integral transformation. The external disturbance is both dynamic and kinematic. The derived functions in xτ-domain are studied to find and describe singularities and are supplemented with graphs.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Movement Characteristics Analysis and Dynamic Simulation of Collaborative Measuring Robot

NASA Astrophysics Data System (ADS)

guoqing, MA; li, LIU; zhenglin, YU; guohua, CAO; yanbin, ZHENG

2017-03-01

Human-machine collaboration is becoming increasingly more necessary, and so collaborative robot applications are also in high demand. We selected a UR10 robot as our research subject for this study. First, we applied D-H coordinate transformation of the robot to establish a link system, and we then used inverse transformation to solve the robot’s inverse kinematics and find all the joints. Use Lagrange method to analysis UR robot dynamics; use ADAMS multibody dynamics simulation software to dynamic simulation; verifying the correctness of the derived kinetic models.

Viscoelastic material inversion using Sierra-SD and ROL

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

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis

2014-11-01

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

Integrated Analytic and Linearized Inverse Kinematics for Precise Full Body Interactions

NASA Astrophysics Data System (ADS)

Boulic, Ronan; Raunhardt, Daniel

Despite the large success of games grounded on movement-based interactions the current state of full body motion capture technologies still prevents the exploitation of precise interactions with complex environments. This paper focuses on ensuring a precise spatial correspondence between the user and the avatar. We build upon our past effort in human postural control with a Prioritized Inverse Kinematics framework. One of its key advantage is to ease the dynamic combination of postural and collision avoidance constraints. However its reliance on a linearized approximation of the problem makes it vulnerable to the well-known full extension singularity of the limbs. In such context the tracking performance is reduced and/or less believable intermediate postural solutions are produced. We address this issue by introducing a new type of analytic constraint that smoothly integrates within the prioritized Inverse Kinematics framework. The paper first recalls the background of full body 3D interactions and the advantages and drawbacks of the linearized IK solution. Then the Flexion-EXTension constraint (FLEXT in short) is introduced for the partial position control of limb-like articulated structures. Comparative results illustrate the interest of this new type of integrated analytical and linearized IK control.

An interactive Bayesian geostatistical inverse protocol for hydraulic tomography

USGS Publications Warehouse

Fienen, Michael N.; Clemo, Tom; Kitanidis, Peter K.

2008-01-01

Hydraulic tomography is a powerful technique for characterizing heterogeneous hydrogeologic parameters. An explicit trade-off between characterization based on measurement misfit and subjective characterization using prior information is presented. We apply a Bayesian geostatistical inverse approach that is well suited to accommodate a flexible model with the level of complexity driven by the data and explicitly considering uncertainty. Prior information is incorporated through the selection of a parameter covariance model characterizing continuity and providing stability. Often, discontinuities in the parameter field, typically caused by geologic contacts between contrasting lithologic units, necessitate subdivision into zones across which there is no correlation among hydraulic parameters. We propose an interactive protocol in which zonation candidates are implied from the data and are evaluated using cross validation and expert knowledge. Uncertainty introduced by limited knowledge of dynamic regional conditions is mitigated by using drawdown rather than native head values. An adjoint state formulation of MODFLOW-2000 is used to calculate sensitivities which are used both for the solution to the inverse problem and to guide protocol decisions. The protocol is tested using synthetic two-dimensional steady state examples in which the wells are located at the edge of the region of interest.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

PubMed Central

Louis, A. K.

2006-01-01

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts. PMID:23165060

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Multiple estimation channel decoupling and optimization method based on inverse system

NASA Astrophysics Data System (ADS)

Wu, Peng; Mu, Rongjun; Zhang, Xin; Deng, Yanpeng

2018-03-01

This paper addressed the intelligent autonomous navigation request of intelligent deformation missile, based on the intelligent deformation missile dynamics and kinematics modeling, navigation subsystem solution method and error modeling, and then focuses on the corresponding data fusion and decision fusion technology, decouples the sensitive channel of the filter input through the inverse system of design dynamics to reduce the influence of sudden change of the measurement information on the filter input. Then carrying out a series of simulation experiments, which verified the feasibility of the inverse system decoupling algorithm effectiveness.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Analysis of 3D poroelastodynamics using BEM based on modified time-step scheme

NASA Astrophysics Data System (ADS)

Igumnov, L. A.; Petrov, A. N.; Vorobtsov, I. V.

2017-10-01

The development of 3d boundary elements modeling of dynamic partially saturated poroelastic media using a stepping scheme is presented in this paper. Boundary Element Method (BEM) in Laplace domain and the time-stepping scheme for numerical inversion of the Laplace transform are used to solve the boundary value problem. The modified stepping scheme with a varied integration step for quadrature coefficients calculation using the symmetry of the integrand function and integral formulas of Strongly Oscillating Functions was applied. The problem with force acting on a poroelastic prismatic console end was solved using the developed method. A comparison of the results obtained by the traditional stepping scheme with the solutions obtained by this modified scheme shows that the computational efficiency is better with usage of combined formulas.

Frechet derivatives for shallow water ocean acoustic inverse problems

NASA Astrophysics Data System (ADS)

Odom, Robert I.

2003-04-01

For any inverse problem, finding a model fitting the data is only half the problem. Most inverse problems of interest in ocean acoustics yield nonunique model solutions, and involve inevitable trade-offs between model and data resolution and variance. Problems of uniqueness and resolution and variance trade-offs can be addressed by examining the Frechet derivatives of the model-data functional with respect to the model variables. Tarantola [Inverse Problem Theory (Elsevier, Amsterdam, 1987), p. 613] published analytical formulas for the basic derivatives, e.g., derivatives of pressure with respect to elastic moduli and density. Other derivatives of interest, such as the derivative of transmission loss with respect to attenuation, can be easily constructed using the chain rule. For a range independent medium the analytical formulas involve only the Green's function and the vertical derivative of the Green's function for the medium. A crucial advantage of the analytical formulas for the Frechet derivatives over numerical differencing is that they can be computed with a single pass of any program which supplies the Green's function. Various derivatives of interest in shallow water ocean acoustics are presented and illustrated by an application to the sensitivity of measured pressure to shallow water sediment properties. [Work supported by ONR.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

NASA Astrophysics Data System (ADS)

Marinoni, Marianna; Delay, Frederick; Ackerer, Philippe; Riva, Monica; Guadagnini, Alberto

2016-08-01

We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A. In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy's law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg-Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

Coupling of Large Amplitude Inversion with Other States

NASA Astrophysics Data System (ADS)

Pearson, John; Yu, Shanshan

2016-06-01

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

An approach to quantum-computational hydrologic inverse analysis

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

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

A useful observable for estimating keff in fast subcritical systems

NASA Astrophysics Data System (ADS)

Saracco, Paolo; Borreani, Walter; Chersola, Davide; Lomonaco, Guglielmo; Ricco, Gianni; Ripani, Marco

2017-09-01

The neutron multiplication factor keff is a key quantity to characterize subcritical neutron multiplying devices and for understanting their physical behaviour, being related to the fundamental eigenvalue of Boltzmann transport equation. Both the maximum available power - and all quantities related to it, like, e.g. the effectiveness in burning nuclear wastes - as well as reactor kinetics and dynamics depend on keff. Nevertheless, keff is not directly measurable and its determination results from the solution of an inverse problem: minimizing model dependence of the solution for keff then becomes a critical issue, relevant both for practical and theoretical reasons.

Feedback control laws for highly maneuverable aircraft

NASA Technical Reports Server (NTRS)

Garrard, William L.; Balas, Gary J.

1994-01-01

During the first half of the year, the investigators concentrated their efforts on completing the design of control laws for the longitudinal axis of the HARV. During the second half of the year they concentrated on the synthesis of control laws for the lateral-directional axes. The longitudinal control law design efforts can be briefly summarized as follows. Longitudinal control laws were developed for the HARV using mu synthesis design techniques coupled with dynamic inversion. An inner loop dynamic inversion controller was used to simplify the system dynamics by eliminating the aerodynamic nonlinearities and inertial cross coupling. Models of the errors resulting from uncertainties in the principal longitudinal aerodynamic terms were developed and included in the model of the HARV with the inner loop dynamic inversion controller. This resulted in an inner loop transfer function model which was an integrator with the modeling errors characterized as uncertainties in gain and phase. Outer loop controllers were then designed using mu synthesis to provide robustness to these modeling errors and give desired response to pilot inputs. Both pitch rate and angle of attack command following systems were designed. The following tasks have been accomplished for the lateral-directional controllers: inner and outer loop dynamic inversion controllers have been designed; an error model based on a linearized perturbation model of the inner loop system was derived; controllers for the inner loop system have been designed, using classical techniques, that control roll rate and Dutch roll response; the inner loop dynamic inversion and classical controllers have been implemented on the six degree of freedom simulation; and lateral-directional control allocation scheme has been developed based on minimizing required control effort.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

DTIC Science & Technology

1988-09-14

Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

What you feel is what you see: inverse dynamics estimation underlies the resistive sensation of a delayed cursor

PubMed Central

Takamuku, Shinya; Gomi, Hiroaki

2015-01-01

How our central nervous system (CNS) learns and exploits relationships between force and motion is a fundamental issue in computational neuroscience. While several lines of evidence have suggested that the CNS predicts motion states and signals from motor commands for control and perception (forward dynamics), it remains controversial whether it also performs the ‘inverse’ computation, i.e. the estimation of force from motion (inverse dynamics). Here, we show that the resistive sensation we experience while moving a delayed cursor, perceived purely from the change in visual motion, provides evidence of the inverse computation. To clearly specify the computational process underlying the sensation, we systematically varied the visual feedback and examined its effect on the strength of the sensation. In contrast to the prevailing theory that sensory prediction errors modulate our perception, the sensation did not correlate with errors in cursor motion due to the delay. Instead, it correlated with the amount of exposure to the forward acceleration of the cursor. This indicates that the delayed cursor is interpreted as a mechanical load, and the sensation represents its visually implied reaction force. Namely, the CNS automatically computes inverse dynamics, using visually detected motions, to monitor the dynamic forces involved in our actions. PMID:26156766

Comparison of dynamic treatment regimes via inverse probability weighting.

PubMed

Hernán, Miguel A; Lanoy, Emilie; Costagliola, Dominique; Robins, James M

2006-03-01

Appropriate analysis of observational data is our best chance to obtain answers to many questions that involve dynamic treatment regimes. This paper describes a simple method to compare dynamic treatment regimes by artificially censoring subjects and then using inverse probability weighting (IPW) to adjust for any selection bias introduced by the artificial censoring. The basic strategy can be summarized in four steps: 1) define two regimes of interest, 2) artificially censor individuals when they stop following one of the regimes of interest, 3) estimate inverse probability weights to adjust for the potential selection bias introduced by censoring in the previous step, 4) compare the survival of the uncensored individuals under each regime of interest by fitting an inverse probability weighted Cox proportional hazards model with the dichotomous regime indicator and the baseline confounders as covariates. In the absence of model misspecification, the method is valid provided data are available on all time-varying and baseline joint predictors of survival and regime discontinuation. We present an application of the method to compare the AIDS-free survival under two dynamic treatment regimes in a large prospective study of HIV-infected patients. The paper concludes by discussing the relative advantages and disadvantages of censoring/IPW versus g-estimation of nested structural models to compare dynamic regimes.

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

Carlin, E. S.; Ramos, A. Asensio, E-mail: escarlin@irsol.es

This paper presents a synthetic tomography of the quiet solar chromosphere formed by spatial maps of scattering polarization. It has been calculated for the Ca II 8498, 8542, and 3934 Å lines by solving the non-LTE radiative transfer problem of the second kind in a three-dimensional atmosphere model obtained from realistic magneto-hydrodynamical simulations. Our investigation focuses on the linear polarization signals induced by kinematics, radiation field anisotropy, and the Hanle effect in forward-scattering geometry. Thus, instead of considering slit profiles at the limb as normally done in the study of the second solar spectrum, we synthesize and analyze spatial mapsmore » of polarization at the disk center. This allows us to understand the spatial signatures of dynamics and magnetic field in the linear polarization in order to discriminate them observationally. Our results suggest some ideas for chromospheric diagnosis that will be developed throughout a series of papers. In particular, Hanle polarity inversion lines and dynamic Hanle diagrams are two concepts introduced in the present work. We find that chromospheric dynamics and magnetic field topology create spatial polarization fingerprints that trace the dynamic situation of the plasma and the magnetic field. This allows us to reconstruct the magnetic field intensity in the middle chromosphere using Stokes V along grooves of null linear polarization. We finally address the problems of diagnosing Hanle saturation and kinematic amplification of scattering signals using Hanle diagrams.« less

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Deconvolution using a neural network

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

Lehman, S.K.

1990-11-15

Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.

Genetics Home Reference: Koolen-de Vries syndrome

MedlinePlus

... of Koolen-de Vries syndrome , has undergone an inversion . An inversion involves two breaks in a chromosome; the resulting ... lineage have no health problems related to the inversion. However, genetic material can be lost or duplicated ...

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Ultrasound viscoelasticity assessment using an adaptive torsional shear wave propagation method

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

Ouared, Abderrahmane; Kazemirad, Siavash; Montagnon, Emmanuel

2016-04-15

Purpose: Different approaches have been used in dynamic elastography to assess mechanical properties of biological tissues. Most techniques are based on a simple inversion based on the measurement of the shear wave speed to assess elasticity, whereas some recent strategies use more elaborated analytical or finite element method (FEM) models. In this study, a new method is proposed for the quantification of both shear storage and loss moduli of confined lesions, in the context of breast imaging, using adaptive torsional shear waves (ATSWs) generated remotely with radiation pressure. Methods: A FEM model was developed to solve the inverse wave propagationmore » problem and obtain viscoelastic properties of interrogated media. The inverse problem was formulated and solved in the frequency domain and its robustness to noise and geometric constraints was evaluated. The proposed model was validated in vitro with two independent rheology methods on several homogeneous and heterogeneous breast tissue-mimicking phantoms over a broad range of frequencies (up to 400 Hz). Results: Viscoelastic properties matched benchmark rheology methods with discrepancies of 8%–38% for the shear modulus G′ and 9%–67% for the loss modulus G″. The robustness study indicated good estimations of storage and loss moduli (maximum mean errors of 19% on G′ and 32% on G″) for signal-to-noise ratios between 19.5 and 8.5 dB. Larger errors were noticed in the case of biases in lesion dimension and position. Conclusions: The ATSW method revealed that it is possible to estimate the viscoelasticity of biological tissues with torsional shear waves when small biases in lesion geometry exist.« less

Individual differences in children's understanding of inversion and arithmetical skill.

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables

NASA Astrophysics Data System (ADS)

Kamynin, V. L.; Bukharova, T. I.

2017-01-01

We prove the estimates of stability with respect to perturbations of input data for the solutions of inverse problems for degenerate parabolic equations with unbounded coefficients. An important feature of these estimates is that the constants in these estimates are written out explicitly by the input data of the problem.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

Three-dimensional tomographic imaging for dynamic radiation behavior study using infrared imaging video bolometers in large helical device plasma

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

Sano, Ryuichi; Iwama, Naofumi; Peterson, Byron J.

A three-dimensional (3D) tomography system using four InfraRed imaging Video Bolometers (IRVBs) has been designed with a helical periodicity assumption for the purpose of plasma radiation measurement in the large helical device. For the spatial inversion of large sized arrays, the system has been numerically and experimentally examined using the Tikhonov regularization with the criterion of minimum generalized cross validation, which is the standard solver of inverse problems. The 3D transport code EMC3-EIRENE for impurity behavior and related radiation has been used to produce phantoms for numerical tests, and the relative calibration of the IRVB images has been carried outmore » with a simple function model of the decaying plasma in a radiation collapse. The tomography system can respond to temporal changes in the plasma profile and identify the 3D dynamic behavior of radiation, such as the radiation enhancement that starts from the inboard side of the torus, during the radiation collapse. The reconstruction results are also consistent with the output signals of a resistive bolometer. These results indicate that the designed 3D tomography system is available for the 3D imaging of radiation. The first 3D direct tomographic measurement of a magnetically confined plasma has been achieved.« less

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

On parameterization of the inverse problem for estimating aquifer properties using tracer data

NASA Astrophysics Data System (ADS)

Kowalsky, M. B.; Finsterle, S.; Williams, K. H.; Murray, C.; Commer, M.; Newcomer, D.; Englert, A.; Steefel, C. I.; Hubbard, S. S.

2012-06-01

In developing a reliable approach for inferring hydrological properties through inverse modeling of tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance, as errors in the model structure are partly compensated for by estimating biased property values during the inversion. These biased estimates, while potentially providing an improved fit to the calibration data, may lead to wrong interpretations and conclusions and reduce the ability of the model to make reliable predictions. We consider the estimation of spatial variations in permeability and several other parameters through inverse modeling of tracer data, specifically synthetic and actual field data associated with the 2007 Winchester experiment from the Department of Energy Rifle site. Characterization is challenging due to the real-world complexities associated with field experiments in such a dynamic groundwater system. Our aim is to highlight and quantify the impact on inversion results of various decisions related to parameterization, such as the positioning of pilot points in a geostatistical parameterization; the handling of up-gradient regions; the inclusion of zonal information derived from geophysical data or core logs; extension from 2-D to 3-D; assumptions regarding the gradient direction, porosity, and the semivariogram function; and deteriorating experimental conditions. This work adds to the relatively limited number of studies that offer guidance on the use of pilot points in complex real-world experiments involving tracer data (as opposed to hydraulic head data).

Control of a high beta maneuvering reentry vehicle using dynamic inversion.

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

Watts, Alfred Chapman

2005-05-01

The design of flight control systems for high performance maneuvering reentry vehicles presents a significant challenge to the control systems designer. These vehicles typically have a much higher ballistic coefficient than crewed vehicles like as the Space Shuttle or proposed crew return vehicles such as the X-38. Moreover, the missions of high performance vehicles usually require a steeper reentry flight path angle, followed by a pull-out into level flight. These vehicles then must transit the entire atmosphere and robustly perform the maneuvers required for the mission. The vehicles must also be flown with small static margins in order to performmore » the required maneuvers, which can result in highly nonlinear aerodynamic characteristics that frequently transition from being aerodynamically stable to unstable as angle of attack increases. The control system design technique of dynamic inversion has been applied successfully to both high performance aircraft and low beta reentry vehicles. The objective of this study was to explore the application of this technique to high performance maneuvering reentry vehicles, including the basic derivation of the dynamic inversion technique, followed by the extension of that technique to the use of tabular trim aerodynamic models in the controller. The dynamic inversion equations are developed for high performance vehicles and augmented to allow the selection of a desired response for the control system. A six degree of freedom simulation is used to evaluate the performance of the dynamic inversion approach, and results for both nominal and off nominal aerodynamic characteristics are presented.« less

Solving inversion problems with neural networks

NASA Technical Reports Server (NTRS)

Kamgar-Parsi, Behzad; Gualtieri, J. A.

1990-01-01

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Inverse problems and coherence

NASA Astrophysics Data System (ADS)

Baltes, H. P.; Ferwerda, H. A.

1981-03-01

A summary of current inverse problems of statistical optics is presented together with a short guide to the pertinent review-type literature. The retrieval of structural information from the far-zone degree of coherence and the average intensity distribution of radiation scattered by a superposition of random and periodic scatterers is discussed.

Dynamic Hop Service Differentiation Model for End-to-End QoS Provisioning in Multi-Hop Wireless Networks

NASA Astrophysics Data System (ADS)

Youn, Joo-Sang; Seok, Seung-Joon; Kang, Chul-Hee

This paper presents a new QoS model for end-to-end service provisioning in multi-hop wireless networks. In legacy IEEE 802.11e based multi-hop wireless networks, the fixed assignment of service classes according to flow's priority at every node causes priority inversion problem when performing end-to-end service differentiation. Thus, this paper proposes a new QoS provisioning model called Dynamic Hop Service Differentiation (DHSD) to alleviate the problem and support effective service differentiation between end-to-end nodes. Many previous works for QoS model through the 802.11e based service differentiation focus on packet scheduling on several service queues with different service rate and service priority. Our model, however, concentrates on a dynamic class selection scheme, called Per Hop Class Assignment (PHCA), in the node's MAC layer, which selects a proper service class for each packet, in accordance with queue states and service requirement, in every node along the end-to-end route of the packet. The proposed QoS solution is evaluated using the OPNET simulator. The simulation results show that the proposed model outperforms both best-effort and 802.11e based strict priority service models in mobile ad hoc environments.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

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

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

SIAM conference on inverse problems: Geophysical applications. Final technical report

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

NONE

1995-12-31

This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devotedmore » to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.« less

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Robust inverse kinematics using damped least squares with dynamic weighting

NASA Technical Reports Server (NTRS)

Schinstock, D. E.; Faddis, T. N.; Greenway, R. B.

1994-01-01

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Investigation into the Effects of Weapon Setback on Various Materials and Geometries.

DTIC Science & Technology

1978-07-01

taking the Laplace Transform of the dynamic equation, rearrangement and taking the inverse transform to find the time-dependent strain. The "dynamic...taking the inverse transform of the above equation: ■»-«fa-to*« 1 E’ ♦ ¥®*> B’ (s+-fj- )(S2+f )T If we neglect the residual strain on the system...partial fractions yields: *t) --f (fr JC-> K, K2 —L_ + + K3 »+-^ s+i(f) s-i(f) performing the inverse transform yields: 4©[K,^> ♦ K2

Inverse problem of the vibrational band gap of periodically supported beam

NASA Astrophysics Data System (ADS)

Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei

2017-04-01

The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.

Quantitative Description of Crystal Nucleation and Growth from in Situ Liquid Scanning Transmission Electron Microscopy.

PubMed

Ievlev, Anton V; Jesse, Stephen; Cochell, Thomas J; Unocic, Raymond R; Protopopescu, Vladimir A; Kalinin, Sergei V

2015-12-22

Recent advances in liquid cell (scanning) transmission electron microscopy (S)TEM has enabled in situ nanoscale investigations of controlled nanocrystal growth mechanisms. Here, we experimentally and quantitatively investigated the nucleation and growth mechanisms of Pt nanostructures from an aqueous solution of K2PtCl6. Averaged statistical, network, and local approaches have been used for the data analysis and the description of both collective particles dynamics and local growth features. In particular, interaction between neighboring particles has been revealed and attributed to reduction of the platinum concentration in the vicinity of the particle boundary. The local approach for solving the inverse problem showed that particles dynamics can be simulated by a stationary diffusional model. The obtained results are important for understanding nanocrystal formation and growth processes and for optimization of synthesis conditions.

A controlled ac Stark echo for quantum memories.

PubMed

Ham, Byoung S

2017-08-09

A quantum memory protocol of controlled ac Stark echoes (CASE) based on a double rephasing photon echo scheme via controlled Rabi flopping is proposed. The double rephasing scheme of photon echoes inherently satisfies the no-population inversion requirement for quantum memories, but the resultant absorptive echo remains a fundamental problem. Herein, it is reported that the first echo in the double rephasing scheme can be dynamically controlled so that it does not affect the second echo, which is accomplished by using unbalanced ac Stark shifts. Then, the second echo is coherently controlled to be emissive via controlled coherence conversion. Finally a near perfect ultralong CASE is presented using a backward echo scheme. Compared with other methods such as dc Stark echoes, the present protocol is all-optical with advantages of wavelength-selective dynamic control of quantum processing for erasing, buffering, and channel multiplexing.

Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

NASA Astrophysics Data System (ADS)

Xia, Jake Jiqing

The electromagnetic inverse scattering problems concerned in this thesis are to find unknown inhomogeneous permittivity and conductivity profiles in a medium from the scattering data. Both analytical and numerical methods are studied in the thesis. The inverse methods can be applied to geophysical medium probing, non-destructive testing, medical imaging, optical waveguide synthesis and material characterization. An introduction is given in Chapter 1. The first part of the thesis presents inhomogeneous media probing. The Riccati equation approach is discussed in Chapter 2 for a one-dimensional planar profile inversion problem. Two types of the Riccati equations are derived and distinguished. New renormalized formulae based inverting one specific type of the Riccati equation are derived. Relations between the inverse methods of Green's function, the Riccati equation and the Gel'fand-Levitan-Marchenko (GLM) theory are studied. In Chapter 3, the renormalized source-type integral equation (STIE) approach is formulated for inversion of cylindrically inhomogeneous permittivity and conductivity profiles. The advantages of the renormalized STIE approach are demonstrated in numerical examples. The cylindrical profile inversion problem has an application for borehole inversion. In Chapter 4 the renormalized STIE approach is extended to a planar case where the two background media are different. Numerical results have shown fast convergence. This formulation is applied to inversion of the underground soil moisture profiles in remote sensing. The second part of the thesis presents the synthesis problem of inhomogeneous dielectric waveguides using the electromagnetic inverse methods. As a particular example, the rational function representation of reflection coefficients in the GLM theory is used. The GLM method is reviewed in Chapter 5. Relations between modal structures and transverse reflection coefficients of an inhomogeneous medium are established in Chapter 6. A stratified medium model is used to derive the guidance condition and the reflection coefficient. Results obtained in Chapter 6 provide the physical foundation for applying the inverse methods for the waveguide design problem. In Chapter 7, a global guidance condition for continuously varying medium is derived using the Riccati equation. It is further shown that the discrete modes in an inhomogeneous medium have the same wave vectors as the poles of the transverse reflection coefficient. An example of synthesizing an inhomogeneous dielectric waveguide using a rational reflection coefficient is presented. A summary of the thesis is given in Chapter 8. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Geophysical approaches to inverse problems: A methodological comparison. Part 1: A Posteriori approach

NASA Technical Reports Server (NTRS)

Seidman, T. I.; Munteanu, M. J.

1979-01-01

The relationships of a variety of general computational methods (and variances) for treating illposed problems such as geophysical inverse problems are considered. Differences in approach and interpretation based on varying assumptions as to, e.g., the nature of measurement uncertainties are discussed along with the factors to be considered in selecting an approach. The reliability of the results of such computation is addressed.

Layer Stripping Solutions of Inverse Seismic Problems.

DTIC Science & Technology

1985-03-21

problems--more so than has generally been recognized. The subject of this thesis is the theoretical development of the . layer-stripping methodology , and...medium varies sharply at each interface, which would be expected to cause difficulties for the algorithm, since it was designed for a smoothy varying... methodology was applied in a novel way. The inverse problem considered in this chapter was that of reconstructing a layered medium from measurement of its

Hydromagnetic conditions near the core-mantle boundary

NASA Technical Reports Server (NTRS)

Backus, George E.

1995-01-01

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

NASA Technical Reports Server (NTRS)

Fijany, Amir

1993-01-01

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

Dynamic experiment design regularization approach to adaptive imaging with array radar/SAR sensor systems.

PubMed

Shkvarko, Yuriy; Tuxpan, José; Santos, Stewart

2011-01-01

We consider a problem of high-resolution array radar/SAR imaging formalized in terms of a nonlinear ill-posed inverse problem of nonparametric estimation of the power spatial spectrum pattern (SSP) of the random wavefield scattered from a remotely sensed scene observed through a kernel signal formation operator and contaminated with random Gaussian noise. First, the Sobolev-type solution space is constructed to specify the class of consistent kernel SSP estimators with the reproducing kernel structures adapted to the metrics in such the solution space. Next, the "model-free" variational analysis (VA)-based image enhancement approach and the "model-based" descriptive experiment design (DEED) regularization paradigm are unified into a new dynamic experiment design (DYED) regularization framework. Application of the proposed DYED framework to the adaptive array radar/SAR imaging problem leads to a class of two-level (DEED-VA) regularized SSP reconstruction techniques that aggregate the kernel adaptive anisotropic windowing with the projections onto convex sets to enforce the consistency and robustness of the overall iterative SSP estimators. We also show how the proposed DYED regularization method may be considered as a generalization of the MVDR, APES and other high-resolution nonparametric adaptive radar sensing techniques. A family of the DYED-related algorithms is constructed and their effectiveness is finally illustrated via numerical simulations.

Physical parameter estimation from porcine ex vivo vocal fold dynamics in an inverse problem framework.

PubMed

Gómez, Pablo; Schützenberger, Anne; Kniesburges, Stefan; Bohr, Christopher; Döllinger, Michael

2018-06-01

This study presents a framework for a direct comparison of experimental vocal fold dynamics data to a numerical two-mass-model (2MM) by solving the corresponding inverse problem of which parameters lead to similar model behavior. The introduced 2MM features improvements such as a variable stiffness and a modified collision force. A set of physiologically sensible degrees of freedom is presented, and three optimization algorithms are compared on synthetic vocal fold trajectories. Finally, a total of 288 high-speed video recordings of six excised porcine larynges were optimized to validate the proposed framework. Particular focus lay on the subglottal pressure, as the experimental subglottal pressure is directly comparable to the model subglottal pressure. Fundamental frequency, amplitude and objective function values were also investigated. The employed 2MM is able to replicate the behavior of the porcine vocal folds very well. The model trajectories' fundamental frequency matches the one of the experimental trajectories in [Formula: see text] of the recordings. The relative error of the model trajectory amplitudes is on average [Formula: see text]. The experiments feature a mean subglottal pressure of 10.16 (SD [Formula: see text]) [Formula: see text]; in the model, it was on average 7.61 (SD [Formula: see text]) [Formula: see text]. A tendency of the model to underestimate the subglottal pressure is found, but the model is capable of inferring trends in the subglottal pressure. The average absolute error between the subglottal pressure in the model and the experiment is 2.90 (SD [Formula: see text]) [Formula: see text] or [Formula: see text]. A detailed analysis of the factors affecting the accuracy in matching the subglottal pressure is presented.

Identification of an internal combustion engine model by nonlinear multi-input multi-output system identification. Ph.D. Thesis

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

Luh, G.C.

1994-01-01

This thesis presents the application of advanced modeling techniques to construct nonlinear forward and inverse models of internal combustion engines for the detection and isolation of incipient faults. The NARMAX (Nonlinear Auto-Regressive Moving Average modeling with eXogenous inputs) technique of system identification proposed by Leontaritis and Billings was used to derive the nonlinear model of a internal combustion engine, over operating conditions corresponding to the I/M240 cycle. The I/M240 cycle is a standard proposed by the United States Environmental Protection Agency to measure tailpipe emissions in inspection and maintenance programs and consists of a driving schedule developed for the purposemore » of testing compliance with federal vehicle emission standards for carbon monoxide, unburned hydrocarbons, and nitrogen oxides. The experimental work for model identification and validation was performed on a 3.0 liter V6 engine installed in an engine test cell at the Center for Automotive Research at The Ohio State University. In this thesis, different types of model structures were proposed to obtain multi-input multi-output (MIMO) nonlinear NARX models. A modification of the algorithm proposed by He and Asada was used to estimate the robust orders of the derived MIMO nonlinear models. A methodology for the analysis of inverse NARX model was developed. Two methods were proposed to derive the inverse NARX model: (1) inversion from the forward NARX model; and (2) direct identification of inverse model from the output-input data set. In this thesis, invertibility, minimum-phase characteristic of zero dynamics, and stability analysis of NARX forward model are also discussed. Stability in the sense of Lyapunov is also investigated to check the stability of the identified forward and inverse models. This application of inverse problem leads to the estimation of unknown inputs and to actuator fault diagnosis.« less

The Relationship Between Non-Symbolic Multiplication and Division in Childhood

PubMed Central

McCrink, Koleen; Shafto, Patrick; Barth, Hilary

2016-01-01

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b − b = a). The current study examines children’s ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8 * 4 / 4) or did not (e.g., 8 * 4 / 2). Children’s performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a * b / b structure, suggesting they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems. PMID:26880261

Numerical Modeling in Geodynamics: Success, Failure and Perspective

NASA Astrophysics Data System (ADS)

Ismail-Zadeh, A.

2005-12-01

A real success in numerical modeling of dynamics of the Earth can be achieved only by multidisciplinary research teams of experts in geodynamics, applied and pure mathematics, and computer science. The success in numerical modeling is based on the following basic, but simple, rules. (i) People need simplicity most, but they understand intricacies best (B. Pasternak, writer). Start from a simple numerical model, which describes basic physical laws by a set of mathematical equations, and move then to a complex model. Never start from a complex model, because you cannot understand the contribution of each term of the equations to the modeled geophysical phenomenon. (ii) Study the numerical methods behind your computer code. Otherwise it becomes difficult to distinguish true and erroneous solutions to the geodynamic problem, especially when your problem is complex enough. (iii) Test your model versus analytical and asymptotic solutions, simple 2D and 3D model examples. Develop benchmark analysis of different numerical codes and compare numerical results with laboratory experiments. Remember that the numerical tool you employ is not perfect, and there are small bugs in every computer code. Therefore the testing is the most important part of your numerical modeling. (iv) Prove (if possible) or learn relevant statements concerning the existence, uniqueness and stability of the solution to the mathematical and discrete problems. Otherwise you can solve an improperly-posed problem, and the results of the modeling will be far from the true solution of your model problem. (v) Try to analyze numerical models of a geological phenomenon using as less as possible tuning model variables. Already two tuning variables give enough possibilities to constrain your model well enough with respect to observations. The data fitting sometimes is quite attractive and can take you far from a principal aim of your numerical modeling: to understand geophysical phenomena. (vi) If the number of tuning model variables are greater than two, test carefully the effect of each of the variables on the modeled phenomenon. Remember: With four exponents I can fit an elephant (E. Fermi, physicist). (vii) Make your numerical model as accurate as possible, but never put the aim to reach a great accuracy: Undue precision of computations is the first symptom of mathematical illiteracy (N. Krylov, mathematician). How complex should be a numerical model? A model which images any detail of the reality is as useful as a map of scale 1:1 (J. Robinson, economist). This message is quite important for geoscientists, who study numerical models of complex geodynamical processes. I believe that geoscientists will never create a model of the real Earth dynamics, but we should try to model the dynamics such a way to simulate basic geophysical processes and phenomena. Does a particular model have a predictive power? Each numerical model has a predictive power, otherwise the model is useless. The predictability of the model varies with its complexity. Remember that a solution to the numerical model is an approximate solution to the equations, which have been chosen in believe that they describe dynamic processes of the Earth. Hence a numerical model predicts dynamics of the Earth as well as the mathematical equations describe this dynamics. What methodological advances are still needed for testable geodynamic modeling? Inverse (time-reverse) numerical modeling and data assimilation are new methodologies in geodynamics. The inverse modeling can allow to test geodynamic models forward in time using restored (from present-day observations) initial conditions instead of unknown conditions.

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

3D and 4D magnetic susceptibility tomography based on complex MR images

DOEpatents

Chen, Zikuan; Calhoun, Vince D

2014-11-11

Magnetic susceptibility is the physical property for T2*-weighted magnetic resonance imaging (T2*MRI). The invention relates to methods for reconstructing an internal distribution (3D map) of magnetic susceptibility values, .chi. (x,y,z), of an object, from 3D T2*MRI phase images, by using Computed Inverse Magnetic Resonance Imaging (CIMRI) tomography. The CIMRI technique solves the inverse problem of the 3D convolution by executing a 3D Total Variation (TV) regularized iterative convolution scheme, using a split Bregman iteration algorithm. The reconstruction of .chi. (x,y,z) can be designed for low-pass, band-pass, and high-pass features by using a convolution kernel that is modified from the standard dipole kernel. Multiple reconstructions can be implemented in parallel, and averaging the reconstructions can suppress noise. 4D dynamic magnetic susceptibility tomography can be implemented by reconstructing a 3D susceptibility volume from a 3D phase volume by performing 3D CIMRI magnetic susceptibility tomography at each snapshot time.

Inverse Jacobi multiplier as a link between conservative systems and Poisson structures

NASA Astrophysics Data System (ADS)

García, Isaac A.; Hernández-Bermejo, Benito

2017-08-01

Some aspects of the relationship between conservativeness of a dynamical system (namely the preservation of a finite measure) and the existence of a Poisson structure for that system are analyzed. From the local point of view, due to the flow-box theorem we restrict ourselves to neighborhoods of singularities. In this sense, we characterize Poisson structures around the typical zero-Hopf singularity in dimension 3 under the assumption of having a local analytic first integral with non-vanishing first jet by connecting with the classical Poincaré center problem. From the global point of view, we connect the property of being strictly conservative (the invariant measure must be positive) with the existence of a Poisson structure depending on the phase space dimension. Finally, weak conservativeness in dimension two is introduced by the extension of inverse Jacobi multipliers as weak solutions of its defining partial differential equation and some of its applications are developed. Examples including Lotka-Volterra systems, quadratic isochronous centers, and non-smooth oscillators are provided.

The deep Peru 2015 doublet earthquakes

NASA Astrophysics Data System (ADS)

Ruiz, S.; Tavera, H.; Poli, P.; Herrera, C.; Flores, C.; Rivera, E.; Madariaga, R.

2017-11-01

On 24 November 2015 two events of magnitude Mw 7.5 and Mw 7.6 occurred at 600 km depth under the Peru-Brazil boundary. These two events were separated in time by 300 s. Deep event doublets occur often under South America. The characteristics that control these events and the dynamic interaction between them are an unresolved problem. We used teleseismic and regional data, situated above the doublet, to perform source inversion in order to characterize their ruptures. The overall resemblance between these two events suggests that they share similar rupture process. They are not identical but occur on the same fault surface dipping westward. Using a P-wave stripping and stretching method we determine rupture speed of 2.25 km/s. From regional body wave inversion we find that stress drop is similar for both events, they differ by a factor of two. The similarity in geometry, rupture velocity, stress drop and radiated energy, suggests that these two events looked like simple elliptical ruptures that propagated like classical sub-shear brittle cracks.

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

Exploring image data assimilation in the prospect of high-resolution satellite data

NASA Astrophysics Data System (ADS)

Verron, J. A.; Duran, M.; Gaultier, L.; Brankart, J. M.; Brasseur, P.

2016-02-01

Many recent works show the key importance of studying the ocean at fine scales including the meso- and submesoscales. Satellite observations such as ocean color data provide informations on a wide range of scales but do not directly provide information on ocean dynamics. Satellite altimetry provide informations on the ocean dynamic topography (SSH) but so far with a limited resolution in space and even more, in time. However, in the near future, high-resolution SSH data (e.g. SWOT) will give a vision of the dynamic topography at such fine space resolution. This raises some challenging issues for data assimilation in physical oceanography: develop reliable methodology to assimilate high resolution data, make integrated use of various data sets including biogeochemical data, and even more simply, solve the challenge of handling large amont of data and huge state vectors. In this work, we propose to consider structured information rather than pointwise data. First, we take an image data assimilation approach in studying the feasibility of inverting tracer observations from Sea Surface Temperature and/or Ocean Color datasets, to improve the description of mesoscale dynamics provided by altimetric observations. Finite Size Lyapunov Exponents are used as an image proxy. The inverse problem is formulated in a Bayesian framework and expressed in terms of a cost function measuring the misfits between the two images. Second, we explore the inversion of SWOT-like high resolution SSH data and more especially the various possible proxies of the actual SSH that could be used to control the ocean circulation at various scales. One focus is made on controlling the subsurface ocean from surface only data. A key point lies in the errors and uncertainties that are associated to SWOT data.

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

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

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

ERIC Educational Resources Information Center

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations

NASA Technical Reports Server (NTRS)

Meyer, G.; Cicolani, L.

1981-01-01

A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

The experimental identification of magnetorheological dampers and evaluation of their controllers

NASA Astrophysics Data System (ADS)

Metered, H.; Bonello, P.; Oyadiji, S. O.

2010-05-01

Magnetorheological (MR) fluid dampers are semi-active control devices that have been applied over a wide range of practical vibration control applications. This paper concerns the experimental identification of the dynamic behaviour of an MR damper and the use of the identified parameters in the control of such a damper. Feed-forward and recurrent neural networks are used to model both the direct and inverse dynamics of the damper. Training and validation of the proposed neural networks are achieved by using the data generated through dynamic tests with the damper mounted on a tensile testing machine. The validation test results clearly show that the proposed neural networks can reliably represent both the direct and inverse dynamic behaviours of an MR damper. The effect of the cylinder's surface temperature on both the direct and inverse dynamics of the damper is studied, and the neural network model is shown to be reasonably robust against significant temperature variation. The inverse recurrent neural network model is introduced as a damper controller and experimentally evaluated against alternative controllers proposed in the literature. The results reveal that the neural-based damper controller offers superior damper control. This observation and the added advantages of low-power requirement, extended service life of the damper and the minimal use of sensors, indicate that a neural-based damper controller potentially offers the most cost-effective vibration control solution among the controllers investigated.

Integration of Gravitational Torques in Cerebellar Pathways Allows for the Dynamic Inverse Computation of Vertical Pointing Movements of a Robot Arm

PubMed Central

Gentili, Rodolphe J.; Papaxanthis, Charalambos; Ebadzadeh, Mehdi; Eskiizmirliler, Selim; Ouanezar, Sofiane; Darlot, Christian

2009-01-01

Background Several authors suggested that gravitational forces are centrally represented in the brain for planning, control and sensorimotor predictions of movements. Furthermore, some studies proposed that the cerebellum computes the inverse dynamics (internal inverse model) whereas others suggested that it computes sensorimotor predictions (internal forward model). Methodology/Principal Findings This study proposes a model of cerebellar pathways deduced from both biological and physical constraints. The model learns the dynamic inverse computation of the effect of gravitational torques from its sensorimotor predictions without calculating an explicit inverse computation. By using supervised learning, this model learns to control an anthropomorphic robot arm actuated by two antagonists McKibben artificial muscles. This was achieved by using internal parallel feedback loops containing neural networks which anticipate the sensorimotor consequences of the neural commands. The artificial neural networks architecture was similar to the large-scale connectivity of the cerebellar cortex. Movements in the sagittal plane were performed during three sessions combining different initial positions, amplitudes and directions of movements to vary the effects of the gravitational torques applied to the robotic arm. The results show that this model acquired an internal representation of the gravitational effects during vertical arm pointing movements. Conclusions/Significance This is consistent with the proposal that the cerebellar cortex contains an internal representation of gravitational torques which is encoded through a learning process. Furthermore, this model suggests that the cerebellum performs the inverse dynamics computation based on sensorimotor predictions. This highlights the importance of sensorimotor predictions of gravitational torques acting on upper limb movements performed in the gravitational field. PMID:19384420

Estimating uncertainty of Full Waveform Inversion with Ensemble-based methods

NASA Astrophysics Data System (ADS)

Thurin, J.; Brossier, R.; Métivier, L.

2017-12-01

Uncertainty estimation is one key feature of tomographic applications for robust interpretation. However, this information is often missing in the frame of large scale linearized inversions, and only the results at convergence are shown, despite the ill-posed nature of the problem. This issue is common in the Full Waveform Inversion community.While few methodologies have already been proposed in the literature, standard FWI workflows do not include any systematic uncertainty quantifications methods yet, but often try to assess the result's quality through cross-comparison with other results from seismic or comparison with other geophysical data. With the development of large seismic networks/surveys, the increase in computational power and the more and more systematic application of FWI, it is crucial to tackle this problem and to propose robust and affordable workflows, in order to address the uncertainty quantification problem faced for near surface targets, crustal exploration, as well as regional and global scales.In this work (Thurin et al., 2017a,b), we propose an approach which takes advantage of the Ensemble Transform Kalman Filter (ETKF) proposed by Bishop et al., (2001), in order to estimate a low-rank approximation of the posterior covariance matrix of the FWI problem, allowing us to evaluate some uncertainty information of the solution. Instead of solving the FWI problem through a Bayesian inversion with the ETKF, we chose to combine a conventional FWI, based on local optimization, and the ETKF strategies. This scheme allows combining the efficiency of local optimization for solving large scale inverse problems and make the sampling of the local solution space possible thanks to its embarrassingly parallel property. References:Bishop, C. H., Etherton, B. J. and Majumdar, S. J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), 420-436.Thurin, J., Brossier, R. and Métivier, L. 2017,a.: Ensemble-Based Uncertainty Estimation in Full Waveform Inversion. 79th EAGE Conference and Exhibition 2017, (12 - 15 June, 2017)Thurin, J., Brossier, R. and Métivier, L. 2017,b.: An Ensemble-Transform Kalman Filter - Full Waveform Inversion scheme for Uncertainty estimation; SEG Technical Program Expanded Abstracts 2012

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

The inverse resonance problem for CMV operators

NASA Astrophysics Data System (ADS)

Weikard, Rudi; Zinchenko, Maxim

2010-05-01

We consider the class of CMV operators with super-exponentially decaying Verblunsky coefficients. For these we define the concept of a resonance. Then we prove the existence of Jost solutions and a uniqueness theorem for the inverse resonance problem: given the location of all resonances, taking multiplicities into account, the Verblunsky coefficients are uniquely determined.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Analysis of the Hessian for Inverse Scattering Problems. Part 1: Inverse Shape Scattering of Acoustic Waves

DTIC Science & Technology

2011-06-01

in giving us of a copy of his habilitation thesis, without which this article would not have been possible. We also thank Prof. Karsten Eppler for...John Wiley & Sons, 1983. [19] Andreas Kirsch. Generalized boundary value- and control problems for the Helmholtz equation. Habilitation thesis, 1984

A posteriori error estimates in voice source recovery

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2017-12-01

The inverse problem of voice source pulse recovery from a segment of a speech signal is under consideration. A special mathematical model is used for the solution that relates these quantities. A variational method of solving inverse problem of voice source recovery for a new parametric class of sources, that is for piecewise-linear sources (PWL-sources), is proposed. Also, a technique for a posteriori numerical error estimation for obtained solutions is presented. A computer study of the adequacy of adopted speech production model with PWL-sources is performed in solving the inverse problems for various types of voice signals, as well as corresponding study of a posteriori error estimates. Numerical experiments for speech signals show satisfactory properties of proposed a posteriori error estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes is about 7-8% for the investigated speech material. It is noted that a posteriori error estimates can be used as a criterion of the quality for obtained voice source pulses in application to speaker recognition.

Solving ill-posed inverse problems using iterative deep neural networks

NASA Astrophysics Data System (ADS)

Adler, Jonas; Öktem, Ozan

2017-12-01

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the ‘gradient’ component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Full Waveform Inversion for Seismic Velocity And Anelastic Losses in Heterogeneous Structures

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

Askan, A.; /Carnegie Mellon U.; Akcelik, V.

2009-04-30

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to amore » variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.« less

Trimming and procrastination as inversion techniques

NASA Astrophysics Data System (ADS)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Dynamics and Novel Mechanisms of SN2 Reactions on ab Initio Analytical Potential Energy Surfaces.

PubMed

Szabó, István; Czakó, Gábor

2017-11-30

We describe a novel theoretical approach to the bimolecular nucleophilic substitution (S N 2) reactions that is based on analytical potential energy surfaces (PESs) obtained by fitting a few tens of thousands high-level ab initio energy points. These PESs allow computing millions of quasi-classical trajectories thereby providing unprecedented statistical accuracy for S N 2 reactions, as well as performing high-dimensional quantum dynamics computations. We developed full-dimensional ab initio PESs for the F - + CH 3 Y [Y = F, Cl, I] systems, which describe the direct and indirect, complex-forming Walden-inversion, the frontside attack, and the new double-inversion pathways as well as the proton-transfer channels. Reaction dynamics simulations on the new PESs revealed (a) a novel double-inversion S N 2 mechanism, (b) frontside complex formation, (c) the dynamics of proton transfer, (d) vibrational and rotational mode specificity, (e) mode-specific product vibrational distributions, (f) agreement between classical and quantum dynamics, (g) good agreement with measured scattering angle and product internal energy distributions, and (h) significant leaving group effect in accord with experiments.

A general approach to regularizing inverse problems with regional data using Slepian wavelets

NASA Astrophysics Data System (ADS)

Michel, Volker; Simons, Frederik J.

2017-12-01

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

NASA Astrophysics Data System (ADS)

Pulkkinen, Aki; Cox, Ben T.; Arridge, Simon R.; Kaipio, Jari P.; Tarvainen, Tanja

2016-03-01

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

NASA Astrophysics Data System (ADS)

Wang, Jun; Wang, Yang; Zeng, Hui

2016-01-01

A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

The Self-Organization of a Spoken Word

PubMed Central

Holden, John G.; Rajaraman, Srinivasan

2012-01-01

Pronunciation time probability density and hazard functions from large speeded word naming data sets were assessed for empirical patterns consistent with multiplicative and reciprocal feedback dynamics – interaction dominant dynamics. Lognormal and inverse power law distributions are associated with multiplicative and interdependent dynamics in many natural systems. Mixtures of lognormal and inverse power law distributions offered better descriptions of the participant’s distributions than the ex-Gaussian or ex-Wald – alternatives corresponding to additive, superposed, component processes. The evidence for interaction dominant dynamics suggests fundamental links between the observed coordinative synergies that support speech production and the shapes of pronunciation time distributions. PMID:22783213

Inverse Tone Mapping Based upon Retina Response

PubMed Central

Huo, Yongqing; Yang, Fan; Brost, Vincent

2014-01-01

The development of high dynamic range (HDR) display arouses the research of inverse tone mapping methods, which expand dynamic range of the low dynamic range (LDR) image to match that of HDR monitor. This paper proposed a novel physiological approach, which could avoid artifacts occurred in most existing algorithms. Inspired by the property of the human visual system (HVS), this dynamic range expansion scheme performs with a low computational complexity and a limited number of parameters and obtains high-quality HDR results. Comparisons with three recent algorithms in the literature also show that the proposed method reveals more important image details and produces less contrast loss and distortion. PMID:24744678

Dynamic motion planning of 3D human locomotion using gradient-based optimization.

PubMed

Kim, Hyung Joo; Wang, Qian; Rahmatalla, Salam; Swan, Colby C; Arora, Jasbir S; Abdel-Malek, Karim; Assouline, Jose G

2008-06-01

Since humans can walk with an infinite variety of postures and limb movements, there is no unique solution to the modeling problem to predict human gait motions. Accordingly, we test herein the hypothesis that the redundancy of human walking mechanisms makes solving for human joint profiles and force time histories an indeterminate problem best solved by inverse dynamics and optimization methods. A new optimization-based human-modeling framework is thus described for predicting three-dimensional human gait motions on level and inclined planes. The basic unknowns in the framework are the joint motion time histories of a 25-degree-of-freedom human model and its six global degrees of freedom. The joint motion histories are calculated by minimizing an objective function such as deviation of the trunk from upright posture that relates to the human model's performance. A variety of important constraints are imposed on the optimization problem, including (1) satisfaction of dynamic equilibrium equations by requiring the model's zero moment point (ZMP) to lie within the instantaneous geometrical base of support, (2) foot collision avoidance, (3) limits on ground-foot friction, and (4) vanishing yawing moment. Analytical forms of objective and constraint functions are presented and discussed for the proposed human-modeling framework in which the resulting optimization problems are solved using gradient-based mathematical programming techniques. When the framework is applied to the modeling of bipedal locomotion on level and inclined planes, acyclic human walking motions that are smooth and realistic as opposed to less natural robotic motions are obtained. The aspects of the modeling framework requiring further investigation and refinement, as well as potential applications of the framework in biomechanics, are discussed.

Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

NASA Astrophysics Data System (ADS)

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

AN ADJOINT-BASED METHOD FOR THE INVERSION OF THE JUNO AND CASSINI GRAVITY MEASUREMENTS INTO WIND FIELDS

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

Galanti, Eli; Kaspi, Yohai, E-mail: eli.galanti@weizmann.ac.il

2016-04-01

During 2016–17, the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. These data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus only allowing the calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model is developed tomore » relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for the examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, also taking into account measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-mid-latitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths. Therefore, we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini.« less

Model-Based Heterogeneous Data Fusion for Reliable Force Estimation in Dynamic Structures under Uncertainties

PubMed Central

Khodabandeloo, Babak; Melvin, Dyan; Jo, Hongki

2017-01-01

Direct measurements of external forces acting on a structure are infeasible in many cases. The Augmented Kalman Filter (AKF) has several attractive features that can be utilized to solve the inverse problem of identifying applied forces, as it requires the dynamic model and the measured responses of structure at only a few locations. But, the AKF intrinsically suffers from numerical instabilities when accelerations, which are the most common response measurements in structural dynamics, are the only measured responses. Although displacement measurements can be used to overcome the instability issue, the absolute displacement measurements are challenging and expensive for full-scale dynamic structures. In this paper, a reliable model-based data fusion approach to reconstruct dynamic forces applied to structures using heterogeneous structural measurements (i.e., strains and accelerations) in combination with AKF is investigated. The way of incorporating multi-sensor measurements in the AKF is formulated. Then the formulation is implemented and validated through numerical examples considering possible uncertainties in numerical modeling and sensor measurement. A planar truss example was chosen to clearly explain the formulation, while the method and formulation are applicable to other structures as well. PMID:29149088

Behavioral pattern identification for structural health monitoring in complex systems

NASA Astrophysics Data System (ADS)

Gupta, Shalabh

Estimation of structural damage and quantification of structural integrity are critical for safe and reliable operation of human-engineered complex systems, such as electromechanical, thermofluid, and petrochemical systems. Damage due to fatigue crack is one of the most commonly encountered sources of structural degradation in mechanical systems. Early detection of fatigue damage is essential because the resulting structural degradation could potentially cause catastrophic failures, leading to loss of expensive equipment and human life. Therefore, for reliable operation and enhanced availability, it is necessary to develop capabilities for prognosis and estimation of impending failures, such as the onset of wide-spread fatigue crack damage in mechanical structures. This dissertation presents information-based online sensing of fatigue damage using the analytical tools of symbolic time series analysis ( STSA). Anomaly detection using STSA is a pattern recognition method that has been recently developed based upon a fixed-structure, fixed-order Markov chain. The analysis procedure is built upon the principles of Symbolic Dynamics, Information Theory and Statistical Pattern Recognition. The dissertation demonstrates real-time fatigue damage monitoring based on time series data of ultrasonic signals. Statistical pattern changes are measured using STSA to monitor the evolution of fatigue damage. Real-time anomaly detection is presented as a solution to the forward (analysis) problem and the inverse (synthesis) problem. (1) the forward problem - The primary objective of the forward problem is identification of the statistical changes in the time series data of ultrasonic signals due to gradual evolution of fatigue damage. (2) the inverse problem - The objective of the inverse problem is to infer the anomalies from the observed time series data in real time based on the statistical information generated during the forward problem. A computer-controlled special-purpose fatigue test apparatus, equipped with multiple sensing devices (e.g., ultrasonics and optical microscope) for damage analysis, has been used to experimentally validate the STSA method for early detection of anomalous behavior. The sensor information is integrated with a software module consisting of the STSA algorithm for real-time monitoring of fatigue damage. Experiments have been conducted under different loading conditions on specimens constructed from the ductile aluminium alloy 7075 - T6. The dissertation has also investigated the application of the STSA method for early detection of anomalies in other engineering disciplines. Two primary applications include combustion instability in a generic thermal pulse combustor model and whirling phenomenon in a typical misaligned shaft.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

Inverse algorithms for 2D shallow water equations in presence of wet dry fronts: Application to flood plain dynamics

NASA Astrophysics Data System (ADS)

Monnier, J.; Couderc, F.; Dartus, D.; Larnier, K.; Madec, R.; Vila, J.-P.

2016-11-01

The 2D shallow water equations adequately model some geophysical flows with wet-dry fronts (e.g. flood plain or tidal flows); nevertheless deriving accurate, robust and conservative numerical schemes for dynamic wet-dry fronts over complex topographies remains a challenge. Furthermore for these flows, data are generally complex, multi-scale and uncertain. Robust variational inverse algorithms, providing sensitivity maps and data assimilation processes may contribute to breakthrough shallow wet-dry front dynamics modelling. The present study aims at deriving an accurate, positive and stable finite volume scheme in presence of dynamic wet-dry fronts, and some corresponding inverse computational algorithms (variational approach). The schemes and algorithms are assessed on classical and original benchmarks plus a real flood plain test case (Lèze river, France). Original sensitivity maps with respect to the (friction, topography) pair are performed and discussed. The identification of inflow discharges (time series) or friction coefficients (spatially distributed parameters) demonstrate the algorithms efficiency.

X-38 Experimental Controls Laws

NASA Technical Reports Server (NTRS)

Munday, Steve; Estes, Jay; Bordano, Aldo J.

2000-01-01

X-38 Experimental Control Laws X-38 is a NASA JSC/DFRC experimental flight test program developing a series of prototypes for an International Space Station (ISS) Crew Return Vehicle, often called an ISS "lifeboat." X- 38 Vehicle 132 Free Flight 3, currently scheduled for the end of this month, will be the first flight test of a modem FCS architecture called Multi-Application Control-Honeywell (MACH), originally developed by the Honeywell Technology Center. MACH wraps classical P&I outer attitude loops around a modem dynamic inversion attitude rate loop. The dynamic inversion process requires that the flight computer have an onboard aircraft model of expected vehicle dynamics based upon the aerodynamic database. Dynamic inversion is computationally intensive, so some timing modifications were made to implement MACH on the slower flight computers of the subsonic test vehicles. In addition to linear stability margin analyses and high fidelity 6-DOF simulation, hardware-in-the-loop testing is used to verify the implementation of MACH and its robustness to aerodynamic and environmental uncertainties and disturbances.

Elastic Cherenkov effects in transversely isotropic soft materials-I: Theoretical analysis, simulations and inverse method

NASA Astrophysics Data System (ADS)

Li, Guo-Yang; Zheng, Yang; Liu, Yanlin; Destrade, Michel; Cao, Yanping

2016-11-01

A body force concentrated at a point and moving at a high speed can induce shear-wave Mach cones in dusty-plasma crystals or soft materials, as observed experimentally and named the elastic Cherenkov effect (ECE). The ECE in soft materials forms the basis of the supersonic shear imaging (SSI) technique, an ultrasound-based dynamic elastography method applied in clinics in recent years. Previous studies on the ECE in soft materials have focused on isotropic material models. In this paper, we investigate the existence and key features of the ECE in anisotropic soft media, by using both theoretical analysis and finite element (FE) simulations, and we apply the results to the non-invasive and non-destructive characterization of biological soft tissues. We also theoretically study the characteristics of the shear waves induced in a deformed hyperelastic anisotropic soft material by a source moving with high speed, considering that contact between the ultrasound probe and the soft tissue may lead to finite deformation. On the basis of our theoretical analysis and numerical simulations, we propose an inverse approach to infer both the anisotropic and hyperelastic parameters of incompressible transversely isotropic (TI) soft materials. Finally, we investigate the properties of the solutions to the inverse problem by deriving the condition numbers in analytical form and performing numerical experiments. In Part II of the paper, both ex vivo and in vivo experiments are conducted to demonstrate the applicability of the inverse method in practical use.

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

NASA Technical Reports Server (NTRS)

Newman, Dava J.

1995-01-01

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m.

Appraisal of geodynamic inversion results: a data mining approach

NASA Astrophysics Data System (ADS)

Baumann, T. S.

2016-11-01

Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB code is provided to perform the appraisal analysis.

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Group-theoretic models of the inversion process in bacterial genomes.

PubMed

Egri-Nagy, Attila; Gebhardt, Volker; Tanaka, Mark M; Francis, Andrew R

2014-07-01

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

DOE PAGES

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2017-07-10

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2 (Data Assimilation Linked Ecosystem Carbon). Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. We recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their advantage through a linear analysis. By using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matricesmore » to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non-linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.« less

An improved self-adaptive ant colony algorithm based on genetic strategy for the traveling salesman problem

NASA Astrophysics Data System (ADS)

Wang, Pan; Zhang, Yi; Yan, Dong

2018-05-01

Ant Colony Algorithm (ACA) is a powerful and effective algorithm for solving the combination optimization problem. Moreover, it was successfully used in traveling salesman problem (TSP). But it is easy to prematurely converge to the non-global optimal solution and the calculation time is too long. To overcome those shortcomings, a new method is presented-An improved self-adaptive Ant Colony Algorithm based on genetic strategy. The proposed method adopts adaptive strategy to adjust the parameters dynamically. And new crossover operation and inversion operation in genetic strategy was used in this method. We also make an experiment using the well-known data in TSPLIB. The experiment results show that the performance of the proposed method is better than the basic Ant Colony Algorithm and some improved ACA in both the result and the convergence time. The numerical results obtained also show that the proposed optimization method can achieve results close to the theoretical best known solutions at present.

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

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

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2 (Data Assimilation Linked Ecosystem Carbon). Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. We recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their advantage through a linear analysis. By using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matricesmore » to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non-linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.« less

Angular dependence of multiangle dynamic light scattering for particle size distribution inversion using a self-adapting regularization algorithm

NASA Astrophysics Data System (ADS)

Li, Lei; Yu, Long; Yang, Kecheng; Li, Wei; Li, Kai; Xia, Min

2018-04-01

The multiangle dynamic light scattering (MDLS) technique can better estimate particle size distributions (PSDs) than single-angle dynamic light scattering. However, determining the inversion range, angular weighting coefficients, and scattering angle combination is difficult but fundamental to the reconstruction for both unimodal and multimodal distributions. In this paper, we propose a self-adapting regularization method called the wavelet iterative recursion nonnegative Tikhonov-Phillips-Twomey (WIRNNT-PT) algorithm. This algorithm combines a wavelet multiscale strategy with an appropriate inversion method and could self-adaptively optimize several noteworthy issues containing the choices of the weighting coefficients, the inversion range and the optimal inversion method from two regularization algorithms for estimating the PSD from MDLS measurements. In addition, the angular dependence of the MDLS for estimating the PSDs of polymeric latexes is thoroughly analyzed. The dependence of the results on the number and range of measurement angles was analyzed in depth to identify the optimal scattering angle combination. Numerical simulations and experimental results for unimodal and multimodal distributions are presented to demonstrate both the validity of the WIRNNT-PT algorithm and the angular dependence of MDLS and show that the proposed algorithm with a six-angle analysis in the 30-130° range can be satisfactorily applied to retrieve PSDs from MDLS measurements.

A practical method to assess model sensitivity and parameter uncertainty in C cycle models

NASA Astrophysics Data System (ADS)

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2015-04-01

The carbon cycle combines multiple spatial and temporal scales, from minutes to hours for the chemical processes occurring in plant cells to several hundred of years for the exchange between the atmosphere and the deep ocean and finally to millennia for the formation of fossil fuels. Together with our knowledge of the transformation processes involved in the carbon cycle, many Earth Observation systems are now available to help improving models and predictions using inverse modelling techniques. A generic inverse problem consists in finding a n-dimensional state vector x such that h(x) = y, for a given N-dimensional observation vector y, including random noise, and a given model h. The problem is well posed if the three following conditions hold: 1) there exists a solution, 2) the solution is unique and 3) the solution depends continuously on the input data. If at least one of these conditions is violated the problem is said ill-posed. The inverse problem is often ill-posed, a regularization method is required to replace the original problem with a well posed problem and then a solution strategy amounts to 1) constructing a solution x, 2) assessing the validity of the solution, 3) characterizing its uncertainty. The data assimilation linked ecosystem carbon (DALEC) model is a simple box model simulating the carbon budget allocation for terrestrial ecosystems. Intercomparison experiments have demonstrated the relative merit of various inverse modelling strategies (MCMC, ENKF) to estimate model parameters and initial carbon stocks for DALEC using eddy covariance measurements of net ecosystem exchange of CO2 and leaf area index observations. Most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. While other studies have tried to overcome this difficulty by adding complementary data streams or by considering longer observation windows no systematic analysis has been carried out so far to explain the large differences among results. We consider adjoint based methods to investigate inverse problems using DALEC and various data streams. Using resolution matrices we study the nature of the inverse problems (solution existence, uniqueness and stability) and show how standard regularization techniques affect resolution and stability properties. Instead of using standard prior information as a penalty term in the cost function to regularize the problems we constraint the parameter space using ecological balance conditions and inequality constraints. The efficiency and rapidity of this approach allows us to compute ensembles of solutions to the inverse problems from which we can establish the robustness of the variational method and obtain non Gaussian posterior distributions for the model parameters and initial carbon stocks.

Inverse Symmetry in Complete Genomes and Whole-Genome Inverse Duplication

PubMed Central

Kong, Sing-Guan; Fan, Wen-Lang; Chen, Hong-Da; Hsu, Zi-Ting; Zhou, Nengji; Zheng, Bo; Lee, Hoong-Chien

2009-01-01

The cause of symmetry is usually subtle, and its study often leads to a deeper understanding of the bearer of the symmetry. To gain insight into the dynamics driving the growth and evolution of genomes, we conducted a comprehensive study of textual symmetries in 786 complete chromosomes. We focused on symmetry based on our belief that, in spite of their extreme diversity, genomes must share common dynamical principles and mechanisms that drive their growth and evolution, and that the most robust footprints of such dynamics are symmetry related. We found that while complement and reverse symmetries are essentially absent in genomic sequences, inverse–complement plus reverse–symmetry is prevalent in complex patterns in most chromosomes, a vast majority of which have near maximum global inverse symmetry. We also discovered relations that can quantitatively account for the long observed but unexplained phenomenon of -mer skews in genomes. Our results suggest segmental and whole-genome inverse duplications are important mechanisms in genome growth and evolution, probably because they are efficient means by which the genome can exploit its double-stranded structure to enrich its code-inventory. PMID:19898631

Remote monitoring of environmental particulate pollution - A problem in inversion of first-kind integral equations

NASA Technical Reports Server (NTRS)

Fymat, A. L.

1975-01-01

The determination of the microstructure, chemical nature, and dynamical evolution of scattering particulates in the atmosphere is considered. A description is given of indirect sampling techniques which can circumvent most of the difficulties associated with direct sampling techniques, taking into account methods based on scattering, extinction, and diffraction of an incident light beam. Approaches for reconstructing the particulate size distribution from the direct and the scattered radiation are discussed. A new method is proposed for determining the chemical composition of the particulates and attention is given to the relevance of methods of solution involving first kind Fredholm integral equations.

A synergic simulation-optimization approach for analyzing biomolecular dynamics in living organisms.

PubMed

Sadegh Zadeh, Kouroush

2011-01-01

A synergic duo simulation-optimization approach was developed and implemented to study protein-substrate dynamics and binding kinetics in living organisms. The forward problem is a system of several coupled nonlinear partial differential equations which, with a given set of kinetics and diffusion parameters, can provide not only the commonly used bleached area-averaged time series in fluorescence microscopy experiments but more informative full biomolecular/drug space-time series and can be successfully used to study dynamics of both Dirac and Gaussian fluorescence-labeled biomacromolecules in vivo. The incomplete Cholesky preconditioner was coupled with the finite difference discretization scheme and an adaptive time-stepping strategy to solve the forward problem. The proposed approach was validated with analytical as well as reference solutions and used to simulate dynamics of GFP-tagged glucocorticoid receptor (GFP-GR) in mouse cancer cell during a fluorescence recovery after photobleaching experiment. Model analysis indicates that the commonly practiced bleach spot-averaged time series is not an efficient approach to extract physiological information from the fluorescence microscopy protocols. It was recommended that experimental biophysicists should use full space-time series, resulting from experimental protocols, to study dynamics of biomacromolecules and drugs in living organisms. It was also concluded that in parameterization of biological mass transfer processes, setting the norm of the gradient of the penalty function at the solution to zero is not an efficient stopping rule to end the inverse algorithm. Theoreticians should use multi-criteria stopping rules to quantify model parameters by optimization. Copyright © 2010 Elsevier Ltd. All rights reserved.

Volume effect of non-polar solvent towards the synthesis of hydrophilic polymer nanoparticles prepares via inverse miniemulsion polymerization

NASA Astrophysics Data System (ADS)

Kamaruddin, Nur Nasyita; Kassim, Syara; Harun, Noor Aniza

2017-09-01

Polymeric nanoparticles have drawn tremendous attention to researchers and have utilized in diverse fields especially in biomedical applications. Nevertheless, question has raised about the safety and hydrophilicity of the nanoparticles to be utilized in medical and biological applications. One promising solution to this problem is to develop biodegradable polymeric nanoparticles with improve hydrophilicity. This study is focusing to develop safer and "greener" polymeric nanoparticles via inverse miniemulsion polymerization techniques, a robust and convenient method to produce water-soluble polymer nanoparticles. Acrylamide (Am), acrylic acid (AA) and methacrylic acid (MAA) monomers have chosen, as they are biocompatible, non-toxic and ecological. The effect of different volumes of cyclohexane towards the formation of polymer nanoparticles, particle size, particle size distribution and morphology of polymer nanoparticles are investigated. The formation and morphology of polymer nanoparticles are determined using FTIR and SEM respectively. The mean diameters of the polymer nanoparticles were in a range of 80 - 250 nm and with broad particle size distributions as determined by dynamic light scattering (DLS). Hydrophilic polyacrylamide (pAm), poly(acrylic acid) (pAA) and poly(methacrylic acid) (pMAA) nanoparticles were successfully achieved by inverse miniemulsion polymerization and have potentiality to be further utilized in the fabrication of hybrid polymer composite nanoparticles especially in biological and medical applications.

Propeller sheet cavitation noise source modeling and inversion

NASA Astrophysics Data System (ADS)

Lee, Keunhwa; Lee, Jaehyuk; Kim, Dongho; Kim, Kyungseop; Seong, Woojae

2014-02-01

Propeller sheet cavitation is the main contributor to high level of noise and vibration in the after body of a ship. Full measurement of the cavitation-induced hull pressure over the entire surface of the affected area is desired but not practical. Therefore, using a few measurements on the outer hull above the propeller in a cavitation tunnel, empirical or semi-empirical techniques based on physical model have been used to predict the hull-induced pressure (or hull-induced force). In this paper, with the analytic source model for sheet cavitation, a multi-parameter inversion scheme to find the positions of noise sources and their strengths is suggested. The inversion is posed as a nonlinear optimization problem, which is solved by the optimization algorithm based on the adaptive simplex simulated annealing algorithm. Then, the resulting hull pressure can be modeled with boundary element method from the inverted cavitation noise sources. The suggested approach is applied to the hull pressure data measured in a cavitation tunnel of the Samsung Heavy Industry. Two monopole sources are adequate to model the propeller sheet cavitation noise. The inverted source information is reasonable with the cavitation dynamics of the propeller and the modeled hull pressure shows good agreement with cavitation tunnel experimental data.

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

USGS Publications Warehouse

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only concentration observations. Permeability, freshwater inflow, solute molecular diffusivity, and porosity can be estimated with roughly equivalent confidence using observations of only the logarithm of concentration. Furthermore, covariance analysis allows a logical reduction of the number of estimated parameters for ill-posed inverse seawater intrusion problems. Ill-posed problems may exhibit poor estimation convergence, have a non-unique solution, have multiple minima, or require excessive computational effort, and the condition often occurs when estimating too many or co-dependent parameters. For the Henry problem, such analysis allows selection of the two parameters that control system physics from among all possible system parameters. ?? 2005 Elsevier Ltd. All rights reserved.

Solving the Inverse-Square Problem with Complex Variables

ERIC Educational Resources Information Center

Gauthier, N.

2005-01-01

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…