A Study of Heat Conduction in Structural Ceramic Materials. Part IV. The Method of Descriptive Identification of Heat Conduction

Abstract

Methods of descriptive identification of heat conduction in structural ceramic materials are described. The method of descriptive regularization is applied in an algorithm of implicit identification. The optimization problem is predominantly solved for thermal conductivity as a function of the temperature in the convex part of the space of possible solutions. The main regularization criteria of the solution of the inverse optimization problem are the geometrical characteristics of the dependence of the thermal conductivity on the temperature, which is represented by a parabolic function. The position of the minimum of the dependence of the thermal conductivity on the temperature is determined by progressive displacement of the temperature range to the region of high temperatures. The results of the determination of the temperature dependence of the thermal conductivity were chosen under the assumption that the difference between the curves describing individual measurements is minimum. The results of the numerical solutions of the model problem show that the experimental data modeled in the computational process at a specified value of comparatively high intensity of normally distributed noise do not bear information about systematic errors. The computation is performed for various positions of temperature constraints and provides curves that are close to the exact solution of the problem.