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 differential-difference models (DDM) of heat transfer in one-dimensional bodies. The DDM is a system of ordinary differential equations of the first order with respect to the state vector. In this case, the direct and inverse heat conduction problems are solved, and to minimize the residual function between the measured and model values of the parameters, the Kalman recurrent digital filter (KF) algorithm is used. The paper considers its application for solving two specific problems, namely: evaluating and planning of an experiment to restore the boundary conditions of heat transfer of a system of bodies. When planning an experiment, or during field studies, the task is first parameterized, and then parametric identification is carried out. To determine the confidence region for measuring the desired parameters, the Gram matrix (Fisher information matrix) is used, the components of which are sensitivity functions that reflect all significant factors of heat metering. The paper gives an example of the use of the KF, considers the non-stationary heat flux transducer (HFT), for which the construction of the DDM is carried out. Also, the results of the restoration of the non-stationary heat flux are shown, and the confidence regions of the desired parameters are defined.