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Inverse Heat Conduction: Ill-Posed Problems
02 Oct 1985-
TL;DR: In this paper, the Inverse Heat Conduction Problem (IHCP) is formulated as a two-dimensional Inverse Convolutional Problem (ICP) and the solution of the one-dimensional IHCP is described.
Abstract: Description of the Inverse Heat Conduction Problem Exact Solutions of the Inverse Heat Conduction Problem Approximate Methods for Direct Heat Conduction Problems Inverse Heat Conduction Estimation Procedures Inverse Convolution Procedures Difference Methods for Solution of the One Dimensional Inverse Heat Conduction Problem Multiple Heat Flux Estimation Heat Transfer Coefficient Estimation Index
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TL;DR: The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Abstract: The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.
1,695 citations
TL;DR: This work presents a reformulation of the Bayesian approach to inverse problems, that seeks to accelerate Bayesian inference by using polynomial chaos expansions to represent random variables, and evaluates the utility of this technique on a transient diffusion problem arising in contaminant source inversion.
484 citations
01 Jan 2003
465 citations
TL;DR: In this article, the state of the art in sensitivity analysis for linear elliptic systems is reviewed and a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses.
Abstract: Design sensitivity plays a critical role in inverse and identification studies, as well as numerical optimization, and reliability analysis. Herein, we review the state of design sensitivity analysis as it applies to linear elliptic systems. Both first- and second-order sensitivities are derived as well as first-order sensitivities for symmetric positive definite eigenvalue systems. Although these results are not new, some of the derivations offer a different perspective than those previously presented. This article is meant as a tutorial, and as such, a simple two-degree-of-freedom spring system is employed to exemplify the sensitivity analyses. However, the concepts presented in this trivial example may be readily extended to compute sensitivities for complex systems via numerical techniques such as the finite element, boundary element, and finite difference methods.
362 citations
Cites background from "Inverse Heat Conduction: Ill-Posed ..."
...Likewise, sensitivities appear in nondestrucive evaluation [127, 128], modal identification [129, 130] chaos prediction [131], nonlinear programming [132, 133, 134] and reliability, probability and stochastic analyses [135, 136, 137, 138, 139, 140]....
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01 Jan 2013
TL;DR: In this paper, the inverse heat transfer analysis (INTA) problem is studied, where the necessary geometry, temperatures, and radiative properties are known, enabling us to calculate the radiative intensity and heat fluxes in such enclosures.
Abstract: Up to this point we have concerned ourselves with radiative heat transfer problems, where the necessary geometry, temperatures, and radiative properties are known, enabling us to calculate the radiative intensity and radiative heat fluxes in such enclosures. Such cases are sometimes called “direct” heat transfer problems. However, there are many important engineering applications where knowledge of one or more input parameters is desired that cause a certain radiative intensity field. For example, it may be desired to control the temperatures of heating elements in a furnace, in order to achieve a specified temperature distribution or radiative heat load on an object being heated. Or the aim may be to deduce difficult to measure parameters (such as radiative properties, temperature fields inside a furnace, etc.) based on measurements of radiative intensity or radiative flux. Such calculations are known as inverse heat transfer analyses.
354 citations