Date(s) - 02/26/2021
3:00 pm - 4:00 pm
“Introduction to the Inverse Heat Conduction Problem (IHCP) and Solution”
By: Dr. Keith A. Woodbury
Professor of Mechanical Engineering, Director of Alabama Industrial Assessment Center at the University of Alabama
The Inverse Heat Conduction Problem is the task of identifying an unknown surface disturbance (heat flux) using temperature measurements inside a heat conducting body.
This presentation begins with presentation of a simple mathematical model for solution of (forward) linear heat conduction problems. The IHCP is outlined, and a discussion is given about ill posedness of inverse problems and the need for regularization. Regularization is presented as a classic compromise between reducing sensitivity to random error at the cost of intentionally adding bias to the solution procedure.
A one-dimensional version of the forward solution is used as a vehicle for demonstrating and comparing several IHCP solution methods. Stoltz’s method, function specification, Tikhonov regularization, conjugate gradient method, and truncated singular value decomposition are reviewed. Each one of these methods offers a different form of regularization for the IHCP.
Proper selection of the degree of regularization for any IHCP solution method is essential. Three different techniques for optimization of regularization are considered: the discrepancy principle, the L curve method, and minimizing the expected value of the residuals in estimated heat flux history.
Keith A. Woodbury is Professor of Mechanical Engineering at the University of Alabama and Director of the Alabama Industrial Assessment Center. He is the author or co-author of 40+ journal articles and 60+ conference papers
Dr. Woodbury’s academic research in inverse problems in heat transfer has included applications to metal casting and investigation of measurement error effects on inversion. Recent research under his direction has focused on development of algorithms for near real-time solution of the inverse heat conduction problem. He is the editor of the Inverse Engineering Handbook (CRC Press, 2005).
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