Solution to inverse heat conduction problems employing singular value decomposition and model-reduction

A new and simple method for solving linear, inverse heat conduction problems using temperature data containing significant noise is presented in this paper. The method consists in a straightforward application of singular-value decomposition to the matrix form of Duhamelʹs principle. A physical interpretation of the method is given by discussing the frequency-domain interpretation of the decomposition. Basically, rows and columns are removed from the decomposed matrices that are associated with small singular values that are shown to be associated with frequencies where the signal-to-noise ratio is small. The technique is demonstrated by considering a standard one-dimensional example. Advantages of the new method are reduction in matrix size, robust treatment of noisy temperature data, optimal in the least-squares sense, and lack of ad hoc parameters.