508 research outputs found
A variational Bayesian method for inverse problems with impulsive noise
We propose a novel numerical method for solving inverse problems subject to
impulsive noises which possibly contain a large number of outliers. The
approach is of Bayesian type, and it exploits a heavy-tailed t distribution for
data noise to achieve robustness with respect to outliers. A hierarchical model
with all hyper-parameters automatically determined from the given data is
described. An algorithm of variational type by minimizing the Kullback-Leibler
divergence between the true posteriori distribution and a separable
approximation is developed. The numerical method is illustrated on several one-
and two-dimensional linear and nonlinear inverse problems arising from heat
conduction, including estimating boundary temperature, heat flux and heat
transfer coefficient. The results show its robustness to outliers and the fast
and steady convergence of the algorithm.Comment: 20 pages, to appear in J. Comput. Phy
Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence
A finite dimensional abstract approximation and convergence theory is
developed for estimation of the distribution of random parameters in infinite
dimensional discrete time linear systems with dynamics described by regularly
dissipative operators and involving, in general, unbounded input and output
operators. By taking expectations, the system is re-cast as an equivalent
abstract parabolic system in a Gelfand triple of Bochner spaces wherein the
random parameters become new space-like variables. Estimating their
distribution is now analogous to estimating a spatially varying coefficient in
a standard deterministic parabolic system. The estimation problems are
approximated by a sequence of finite dimensional problems. Convergence is
established using a state space-varying version of the Trotter-Kato semigroup
approximation theorem. Numerical results for a number of examples involving the
estimation of exponential families of densities for random parameters in a
diffusion equation with boundary input and output are presented and discussed
Sequential particle filter estimation of a time-dependent heat transfer coefficient in a multidimensional nonlinear inverse heat conduction problem
In the applied mathematical modelling of heat transfer systems, the heat transfer coefficient (HTC) is one of the most important parameters. This paper proposes a combination of the Method of Fundamental Solutions (MFS) with particle filter Sequential Importance Resampling (PF-SIR) to estimate the time-dependent HTC in two-dimensional transient inverse heat conduction problems from non-standard boundary integral measurements. These measurements ensure the unique solvability of the boundary coefficient identification problem. Numerical results show high performance on several test cases with both linear and nonlinear Robin boundary conditions, supporting the synergy between the MFS and simulation-based particle filter sequential analysis methods
Reconstruction of a Robin Coefficient by a Predictor-Corrector Method
The present paper is devoted to solving a nonlinear inverse problem of identifying a Robin coefficient from boundary temperature measurement. A numerical algorithm on the basis of the predictor-corrector method is designed to restore the approximate solution and the performance of the method is verified by simulating several examples. The convergence with respect to the amount of noise in the data is also investigated
Proceedings of the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory
This book is a collection of 15 reviewed technical reports summarizing the presentations at the 2011 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory. The covered topics include image processing, optical signal processing, visual inspection, pattern recognition and classification, human-machine interaction, world and situation modeling, autonomous system localization and mapping, information fusion, and trust propagation in sensor networks
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