Abstract
Traditional space-marching techniques for solving the inverse heat conduction problem are highly susceptible to both measurement and round-off error. This problem is exacerbated if the problem requires small time steps to resolve rapid changes in the surface condition, since this can cause instability. The inverse technique presented in this article utilizes a global time approach which eliminates the instability usually observed when using small time steps. It is demonstrated that a higher sampling rate (smaller time steps) in fact improves the inverse prediction. This is accomplished using a functional representation of the time derivative in the heat equation, and a physically based regularization scheme. A Gaussian low-pass filter is used with an analytically determined optimum cut-off frequency. The filter delivers an analytical function which has smooth, bounded derivatives. The inverse technique is demonstrated to accurately resolve the transient surface thermal condition in the presence of noise.
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