BEM Solution With Minimal Energy Technique for the Geometrical Inverse Heat Conduction Problem in a Doubly Connected Domain

2003 ◽  
Vol 125 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Chang-Yong Choi ◽  
Jong Chull Jo
Keyword(s):  
Heat Conduction ◽  
Boundary Element ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Boundary Surface ◽  
Inverse Heat Conduction Problem ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Minimal Energy ◽  
Element Analysis

This article addresses the use of boundary element method in conjunction with minimal energy technique for solving a geometrical inverse heat conduction problem. The problem considered in this study is to estimate the unknown inner boundary position in an irregular-shaped hollow body of which the inner boundary surface is subjected to a specified temperature condition. For solving the problem, first boundary element equations are converted into the quadratic programming problem by minimizing the energy functional with a constraint, next a hypothetical inner boundary is defined such that the actual inner boundary is located interior of the hypothetical solution domain, then temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error in inner surface temperatures, and finally boundary element analysis is performed for the position of an unknown boundary. Based on these main solution procedures, an effective detection algorithm is provided. In addition, the solution method is numerically tested to investigate the effects of measurement errors on the accuracy of estimation.

On Elliptic Inverse Heat Conduction Problems

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Initial Guess ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Robustness To Noise ◽  
Inverse Heat Conduction Problems ◽  
New Feature

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

Solution of the Inverse Heat Conduction Problem From Thermal Strain Measurements

1996 ◽  
Vol 118 (4) ◽  
pp. 842-849 ◽  
Author(s):  
G. Blanc ◽  
M. Raynaud
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Thermal Strain ◽  
Sensitivity Coefficient ◽  
Inverse Heat Conduction Problem ◽  
Temperature Measurements ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Numerical Predictions ◽  
Unknown Boundary Conditions

Another approach for the solution of the inverse heat conduction problem is presented. The unknown boundary conditions are recovered from thermal strain and temperature measurements instead of temperature measurements only. It is required to calculate both the temperature field and the strains induced by this field. The sensitivity coefficient analysis and the results of two benchmark test cases show that it is possible to recover higher temporal frequencies when the inversion is done from strains instead of temperatures. An experimental setup was specially designed to validate the numerical results. The numerical predictions are verified. Special attention is given to the strain gage measurements.

Methodology for Comparison of Inverse Heat Conduction Methods

1988 ◽  
Vol 110 (1) ◽  
pp. 30-37 ◽  
Author(s):  
M. Raynaud ◽  
J. V. Beck
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Standard Deviation ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Methods ◽  
Test Problems ◽  
Test Case ◽  
Inverse Heat Conduction

The inverse heat conduction problem involves the calculation of the surface heat flux from transient measured temperatures inside solids. The deviation of the estimated heat flux from the true heat flux due to stabilization procedures is called the deterministic bias. This paper defines two test problems that show the tradeoff between deterministic bias and sensitivity to measurement errors of inverse methods. For a linear problem, with the statistical assumptions of additive and uncorrelated errors having constant variance and zero mean, the second test case gives the standard deviation of the estimated heat flux. A methodology for the quantitative comparison of deterministic bias and standard deviation of inverse methods is proposed. Four numerical inverse methods are compared.

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