PARAMETRIC IDENTIFICATION OF DIFFERENTIAL-DIFFERENCE MODELS OF HEAT TRANSFER IN ONE-DIMENSIONAL BODIES BASED ON KALMAN FILTER ALGORITHMS

The paper considers the solution of the inverse heat conduction problem by parametric identification of differentialdifference models of heat transfer in one-dimensional bodies. Differential-difference models is a system of differential ordinary equations of the first order with respect to the state vector. In this case, the direct and inverse heat conduction problems are solved, and the Kalman recurrent digital filter algorithm is used in terms of parameters for discrepancy minimization between the measured and model parameters values. The paper considers the Kalman algorithm application for two specific problems, namely: an experiment estimation and planning for restoration of heat transfer boundary conditions for a system of bodies. When planning an experiment or during field studies, the task parametrization is carried out initially and then parametric identification, as well. To determine the confidence area for measuring the desired parameters, the Gram matrix (Fisher information matrix) is used, involving the components which are sensitivity functions that represent all significant factors of heat metering: the type of heat transfer in the system, the number and location of temperature measurement points, the quality of channels for recording measured values, and the features of input actions, time measurement section and the number of measurement time points in this section. The paper gives an example of Kalman recurrent digital filter, considers the battery transformer of unsteady heat flux, for which the creation of the differential-difference model is carried out, shows the results of unsteady heat flux restoration, changing according to an arbitrary law. Confidence areas of the desired parameters are established.