Using Bayesian statistics in the estimation of heat source in radiation

By Jingbo Wang, Nicholas Zabaras. 2005

146 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aeb92ea023332ae25dbd9471a669254e65a49810

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In Aerospace Engineering

In Statistics and Probability

Citations in the corpus

A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems (2010, methodology): “The Bayesian approach has been widely used [15-18].”
Stochastic spectral methods for efficient Bayesian solution of inverse problems (2005, background): “Wang and Zabaras [10] use proper orthogonal decomposition (POD) [37] and Galerkin projection to speed forward model calculations in a radiative source inversion problem.”
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion (2012, methodology): “This is then used for posterior evaluation or sampling [3, 10, 16, 35, 46].”
Fast Numerical Methods for Stochastic Computations: A Review (2009, background): “1), and the examples are for linear problems, the gPC framework can be readily applied to complex problems including the time-dependent and nonlinear ones, for example, Burgers’ equation [34, 94], fluid dynamics [40, 41, 44, 46, 92], flow-structure interactions [96], hyperbolic problems [11,31], mat”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, methodology): “We first pursue Non-Destructive Evaluation (NDE) parameter estimation procedures [17,96, 154 ] — say by vibration or thermal transient analysis — to determine the location and configuration of the delamination crack in the support.”
Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Parabolic PDEs: Application to Real‐Time Bayesian Parameter Estimation (2010, methodology): “To reduce the computational cost of Bayesian inverse analysis Wang and Zabaras (2005) introduce POD–based model reduction.”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “In these cases, parametric model reduction over both state and parameter spaces can make tractable the solution of large-scale inverse problems that otherwise cannot be solved [80, 102, 156, 220, 72].”
Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7] (2010, methodology): “Wang and Zabaras (2005) use the POD to accelerate forward model calculations in a radiative source inversion problem.”
Bayesian inference with optimal maps (2011, background): “Keywords: Bayesian inference, optimal transport, measure-preserving maps, inverse problems, polynomial chaos, numerical optimization”
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems (2008, background): “Bayesian approaches to inverse problems have received much recent interest [4, 48, 49], with applications ranging from geophysics [50, 51] and climate modeling [52] to heat transfer [20, 53].”
A stochastic collocation approach to Bayesian inference in inverse problems (2009, background): “Several efforts at accelerating Bayesian inference in inverse problems have appeared in recent literature; these have relied largely on reductions or surrogates for the forward model [3, 14, 17, 24], or instead have sought more efﬁcient sampling from the posterior [4,5,11].”
Inverse Problems in Heat Transfer (2009, background): “Applications to non-linear problems can be found in [55], where identification of the time history of a heat source in radiation is discussed.”