Inverse heat conduction problem: Sensitivity coefficient insights, filter coefficients, and intrinsic verification

The inverse heat conduction problem is the estimation of the time and/or space dependence of the surface heat flux or temperature utilizing interior temperature measurements at discrete times and/or locations. This problem is ill-posed since it is very sensitive to omnipresent measurement errors. Many solution methods have been proposed including exact-matching, function specification, Tikhonov regularization, iterative regularization, conjugate gradient, steepest descent and singular value decomposition. In this paper, the tools provided by the scaled sensitivity coefficients, digital filter coefficients, and intrinsic verification are used to investigate and compare several of these methods. The utility of digital filters designed for on-line instrumentation for “continuous” measurements of the surface heat flux and temperature in manufacturing settings is also demonstrated.