Parametric identification of differential-difference models of heat transfers in the systems of bodies

Abstract

The combined inverse heat conduction problem (IHCP) was solved to restore the boundary conditions of heat exchange, in particular, unsteady heat flux, while simultaneously refining the thermophysical properties of the object material by parametric identification of the differential - difference models (DDM) of heat transfer in the object of study. The differential-difference model is a system of first order ordinary differential equations with respect to the state vector. The type of feedback, control, and measurement matrices included in the DDM is established. A priori parametrization and parametric identification of the heat transfer model was performed. The parametrization involves approximation of the desired heat flux by B-splines of the first order for each piecewise-linear segment. With parametric identification, the discrepancy between the model and experimental values of the parameters is minimized using a recurrent linear Kalman filter. Taking into account the parametrization and parametric identification, the time-varying heat flux at the body boundary was restored and its thermal and physical properties, in particular, thermal conductivity, were simultaneously refined. The uncertainty of restoration of parameters based on the Gram matrix is estimated. The boundaries of confidence areas for determining the desired parameters based on the sensitivity functions, which are obtained by solving the heat transfer equations, are established. The results of model experiments, in which initial estimates of the desired parameters were set twice less than the true ones, are given.