Parametric identification of technological thermophysics processes based on neural network approach

In this paper, the inverse problem of technological thermophysics under the influence of disturbing factors is under study. In the problem of identifying the process of nonstationary heat conduction, it is required to concretize its mathematical model by qualitatively and quantitatively expressing an unknown characteristic based on the results of experimental studies. It is necessary to determine the uncontrolled time-varying heat flux density on the surface of the heated product from the noisy temperature measurement results at a certain point inside the object. The problem is formulated in an extreme setting as a problem of optimal control of an object with distributed parameters, in which the quadratic value of the temperature discrepancy between experimental and model data is used as an optimality criterion. The preliminary parametrization of the desired control on a compact set of polynomial functions implements the reduction to the parametric optimization problem. Physically substantiated solutions to inverse heat conduction problems are found as a result of their sequential parametric optimization using an algorithmically accurate method based on optimal control theory. The proposed solution combines the advantages of an accurate analytical method, which allows taking into account the physical essence of the process of interest and artificial intelligence methods, which provide great opportunities to find an quasioptimal solution under conditions of uncertainty in the mathematical description of the process. The analytical method of sequential parameterization provides a search for solutions on a compact set of smooth functions, as a result of which there is a reduction to the problem of parametric optimization. Measurement errors lead to processing large amounts of data, which necessitates the use of artificial neural networks for parametric optimization of the identified characteristics. The attained results confirm the possibility of obtaining adequate solutions to the inverse problems of thermal conductivity with the intensity of the measurement noise in the range of 0-15 %. In the investigated class of solutions, with a suitable setting of the ranges of belonging of the parameters, the error in approximating the temperature state can be up to 2-5 %, and the error in restoring the unknown characteristic can be up to 7-10 %.