Identification methods in nonlinear heat conduction. Part I: Model reduction

An original method for the identification of Reduced Models (RM) of nonlinear diffusive thermal systems is proposed in this numerical study. This method derives from the Modal Identification Method developed for linear systems in previous works. Starting from a Detailed Model (DM) under matrix form, a RM structure is defined. RM's matrices are then identified through the minimization of a squared residues functional built with the discrepancy between system responses (DM outputs in this study) on the one hand and RM outputs on the other hand, when a specific input signal is applied. A tridimensional example with thermal conductivity depending linearly on temperature illustrates the method. In comparison with DM, computing time is drastically reduced (division by a factor greater than 1000 in the proposed example) without significant loss of accuracy.