Methodology for Comparison of Inverse Heat Conduction Methods

Abstract

The inverse heat conduction problem involves the calculation of the surface heat flux from transient measured temperatures inside solids. The deviation of the estimated heat flux from the true heat flux due to stabilization procedures is called the deterministic bias. This paper defines two test problems that show the tradeoff between deterministic bias and sensitivity to measurement errors of inverse methods. For a linear problem, with the statistical assumptions of additive and uncorrelated errors having constant variance and zero mean, the second test case gives the standard deviation of the estimated heat flux. A methodology for the quantitative comparison of deterministic bias and standard deviation of inverse methods is proposed. Four numerical inverse methods are compared.