Solving a Linear Inverse Problem by Using an $L^{\infty}$ Fitting and a Hybrid Penalty with an Application to an Inverse Heat Conduction Problem

2013 ◽  
Vol 10 (18) ◽  
pp. 5935-5943
Author(s):  
Yixin Dou
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Linear Inverse Problem

Identification of Contact Failures in Multi-Layered Composites

2011 ◽  
Author(s):  
L. A. Abreu ◽  
H. R. B. Orlande ◽  
C. P. Naveira-Cotta ◽  
J. N. N. Quaresma ◽  
R. M. Cotta ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Markov Chain ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Layered Composites ◽  
Simulated Temperature ◽  
Prior Models

This paper deals with the solution of an inverse heat conduction problem, aiming at the identification of contact failures in composites formed by layers of different materials. The inverse problem is solved within the Bayesian framework, with a Markov chain Monte Carlo method. The effects of the prior models, for the unknown contact conductance at the interface of a plate with two layers, are examined. The solution of the inverse problem is performed with simulated temperature measurements.

An Initial Value Approach to the Inverse Heat Conduction Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 248-256 ◽  
Author(s):  
E. Hensel ◽  
R. G. Hills
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Initial Value ◽  
Surface Conditions ◽  
One Dimensional ◽  
The One

The one-dimensional linear inverse problem of heat conduction is considered. An initial value technique is developed which solves the inverse problem without need for iteration. Simultaneous estimates of the surface temperature and heat flux histories are obtained from measurements taken at a subsurface location. Past and future measurement times are inherently used in the analysis. The tradeoff that exists between resolution and variance of the estimates of the surface conditions is discussed quantitatively. A stabilizing matrix is introduced to the analysis, and its effect on the resolution and variance of the estimates is quantified. The technique is applied to “exact” and “noisy” numerically simulated experimental data. Results are presented which indicate the technique is capable of handling both exact and noisy data.

scholarly journals Application of the Finite Element Method to the Nonlinear Inverse Heat Conduction Problem Using Beck’s Second Method

1980 ◽  
Vol 102 (2) ◽  
pp. 168-176 ◽  
Author(s):  
B. R. Bass
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Finite Element ◽  
Heat Conduction ◽  
Interior Point ◽  
Surface Heat Flux ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Surface Heat ◽  
Inverse Heat Conduction

The calculation of the surface temperature and surface heat flux from a measured temperature history at an interior point of a body is identified in the literature as the inverse heat conduction problem. This paper presents, to the author’s knowledge, the first application of a solution technique for the inverse problem that utilizes a finite element heat conduction model and Beck’s nonlinear estimation procedure. The technique is applicable to the one-dimensional nonlinear model with temperature-dependent thermophysical properties. The formulation is applied first to a numerical example with a known solution. The example treated is that of a periodic heat flux imposed on the surface of a rod. The computed surface heat flux is compared with the imposed heat flux to evaluate the performance of the technique in solving the inverse problem. Finally, the technique is applied to an experimentally determined temperature transient taken from an interior point of an electrically-heated composite rod. The results are compared with those obtained by applying a finite difference inverse technique to the same data.

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