Identification of Impulse Responses in Heat Transfer: Parameterization, Doses, Partial Time Moments

Convolutive models, linking a local or average temperature to a thermal excitation in transient regime are as good as analytical or numerical solutions of the heat equation and of its associated boundary conditions, provided that the corresponding equations are linear with coefficients that do not depend on time, but with possible dependence on the space dimensions. These convolutive models are based on an impulse response function which can be identified, using measurements of input and output signals, together with some kind of regularization because of the ill-posed character of this inverse problem. Here, another exploratory approach is tested. It is based i) on a parameterization of the three functions involved by projection onto a Dirac comb basis to get a vector/matrix form of the convolution model derived in terms of doses, ii) on an alternate model based on an exact analytical relationship between the time moments of these functions and iii) on the different ways to use this last model in an inversion procedure using the parsimony principle. This is applied to a heat transfer configuration of one-dimensional heat diffusion in a slab, where conclusions and perspectives are drawn for this type of dosal-moment model.