Session: K20-W2: WORKSHOP ON INVERSE PROBLEMS AND PARAMETER ESTIMATION IN HEAT TRANSFER II

Paper Number: 138639

138639 - Inverse Heat Conduction Problem: Optimization and Comparisons 

Abstract: 

Regularization introduces stability to the IHCP solution at the expense of introducing bias in the estimation, and balancing these effects is a challenge for the IHCP analyst.  Two figures of merit are defined characterizing the effectiveness of a regularized IHCP solution:  mean squared error in heat flux and mean squared error in measured temperature.  Optimization can performed in either a design setting (through numerical experiments) or an experimental setting (using experimental data).  In design settings, the expected value of the heat flux or temperature mean squared error can be used to optimize regularization.  In experimental settings, Morozov discrepancy principle, L-curve method, or Generalized Cross Validation may be used.  Most methods require specification of the expected standard deviation of the measurements (s_Y), but GCV can be applied without knowing s_Y.

Test problems are defined to generate exact data for IHCPs.  Standard numerical noise is generated to add to the exact values, and the resulting noisy data are processed using IHCP solution techniques:  Function Specification (FSM), Tikhonov Regularization (TR), Conjugate Gradient Method (CGM), and Truncated Singular Value Decomposition (SVD) Method.  The expected value of the mean squared error in the estimated heat flux is minimized to define the optimal degree of regularization. A summary comparison of the results from these methods with focus on accuracy of the heat flux estimates is given.

Presenting Author: Keith Woodbury The University of Alabama

Presenting Author Biography: Keith A. Woodbury is Professor Emeritus of Mechanical Engineering at the University of Alabama, where his research in inverse heat conduction supported investigations into quenching and metal casting. Dr. Woodbury is a life-long member of ASME and has organized numerous technical sessions on inverse problems through the Heat Transfer Division’s K-20 Committee. He is the editor of the Inverse Engineering Handbook (2003) and lead author of Inverse Heat Conduction: Ill-posed Problems (2nd Edition, 2023).

Authors:

Keith Woodbury The University of Alabama