A sequential algorithm of inverse heat conduction problems using singular value decomposition

This paper examines numerically and theoretically the application of truncated Singular Value Decomposition (SVD) in a sequential form. The Sequential SVD algorithm presents two tunable hyperparameters: the number of future temperature (r) and the rank of the truncated sensitivity matrix (p). The regularization effect of both hyperparameters is consistent with the data filtering interpretation by truncated SVD (reported by Shenefelt [Internat. J. Heat Mass Transfer 45 (2002) 67]). This study reveals that the most suitable reduced rank is “one”. Under this assumption (p=1), the sequential procedure proposed, presents several advantages with respect to the standard whole-domain procedure: The search of the optimum rank value is not required. The simplification of the model is the maximum that can be achieved. The unique tunable hyperparameter is the number of future temperatures, and a very simple algorithm is obtained. This algorithm has been compared to: Function Specification Method (FSM) proposed by Beck and the standard whole-domain SVD. In this comparative study, the parameters considered have been: the shape of the input, the noise level of measurement and the size of time step. In all cases, the FSM and sequential SVD algorithm give very similar results. In one case, the results obtained by the sequential SVD algorithm are clearly superior to the ones obtained by the whole-domain algorithm.