Solution of inverse heat conduction problem using the Tikhonov regularization method

2017 ◽  
Vol 26 (1) ◽  
pp. 60-65 ◽  
Author(s):  
Piotr Duda
Keyword(s):  
Heat Conduction ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Conduction

scholarly journals Optimal Tikhonov approximation for a sideways parabolic equation

2005 ◽  
Vol 2005 (8) ◽  
pp. 1221-1237 ◽  
Author(s):  
Chu-Li Fu ◽  
Hong-Fang Li ◽  
Xiang-Tuan Xiong ◽  
Peng Fu
Keyword(s):  
Heat Conduction ◽  
Parabolic Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Conduction ◽  
Convection Term ◽  
Ill Posed

We consider an inverse heat conduction problem with convection term which appears in some applied subjects. This problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. A generalized Tikhonov regularization method for this problem is given, which realizes the best possible accuracy.

Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck
Keyword(s):  
Heat Conduction ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Regularization Methods ◽  
Inverse Heat Conduction ◽  
Random Errors ◽  
Internal Temperature ◽  
Inverse Heat Conduction Problems

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.

The Steady Inverse Heat Conduction Problem: A Comparison of Methods With Parameter Selection

2001 ◽  
Vol 123 (4) ◽  
pp. 633-644 ◽  
Author(s):  
Robert Throne ◽  
Lorraine Olson
Keyword(s):  
Heat Conduction ◽  
Tikhonov Regularization ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
True Solution ◽  
Sensitivity Method ◽  
Inverse Boundary Value Problems ◽  
Steady Heat Conduction

In the past we have developed the Generalized Eigensystem GESL techniques for solving inverse boundary value problems in steady heat conduction, and found that these vector expansion methods often give superior results to those obtained with standard Tikhonov regularization methods. However, these earlier comparisons were based on the optimal results for each method, which required that we know the true solution to set the value of the regularization parameter (t) for Tikhonov regularization and the number of mode clusters Nclusters for GESL. In this paper we introduce a sensor sensitivity method for estimating appropriate values of Nclusters for GESL. We compare those results with Tikhonov regularization using the Combined Residual and Smoothing Operator (CRESO) to estimate the appropriate values of t. We find that both methods are quite effective at estimating the appropriate parameters, and that GESL often gives superior results to Tikhonov regularization even when Nclusters is estimated from measured data.

A meshless method to the solution of an ill-posed problem

2016 ◽  
Vol 24 (5) ◽  
Author(s):  
Malihe Rostamian ◽  
Alimardan Shahrezaee
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Numerical Approximation ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Numerical Approach ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Conduction ◽  
Ill Posed

AbstractIn this paper, we consider an inverse heat conduction problem (IHCP). First, the existence, uniqueness and unstability solution of the inverse problem will be studied. Due to the ill-posedness of the inverse problem, we propose a meshless numerical approach based on basis function to solve this problem in the presence of noisy data. The Tikhonov regularization method with generalized discrepancy principle is applied to obtain a stable numerical approximation to the solution. The effectiveness of the algorithm is illustrated by some numerical examples.

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