Optimization of Regularization in Inverse Heat Conduction Analysis

Inverse Heat Conduction Problems (IHCPs) are inherently ill-posed because their solution procedures are overly sensitive to small perturbations (errors) in the input data (measurements). To counter this characteristic, some form of regularization is incorporated in the solution, which provides the desired stability but at the expense of introducing unwanted bias in the results. The amount or degree of regularization to include in the solution is often not carefully selected; rather, the amount of regularization is chosen to please the eye of the analyst. This paper presents four different techniques for selecting the optimal degree of regularization: minimizing the mean squared error in the estimated heat flux, the Morozov Discrepancy Principle, the L-curve method, and Generalized Cross Validation. These techniques are illustrated using a simple one-dimensional heat conduction problem with a known exact analytical solution. The strengths and weaknesses of these four approaches are discussed. Practical application of these methods provide reliable techniques for determining the appropriate amount of regularization to use when IHCP solutions are employed in engineering experimentation.