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

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.