GRID-STEP OPTIMIZATION OF THE PARAMETERS OF THERMAL IMPACT ON THE TECHNICAL SYSTEM

Abstract

The article solves applied problems of optimizing the parameters of technical systems under the influence of concentrated, discrete sources of thermal load. To improve the accuracy and speed of solving applied optimization problems, the authors propose a generalized procedure for finding the optimal thermal load parameters. This procedure consists of well-known computational methods for solving boundary value problems and ensuring the optimization of the objective function and its parameters.

To calculate the values of the temperature field, it is necessary to solve a nonlocal boundary value problem of a system of nonlinear differential heat transfer equations. In order to find the conditions for the correctness of boundary value problems, the authors used the theory of pseudo-differential operators in the space of generalized slow power functions. This made it possible to guarantee the correctness of computational and applied optimization mathematical models.

The procedure for grid-step optimization of the parameters of thermal action on a multilayer material proposed by the authors is based on a grid approach with discretization of the main parameters of thermal load and grinding of a large uniform grid in the vicinity of the selected node of the large grid. The directed search for local extremes of the mesh model is carried out by the nodes of the crushed mesh. The search for local extrema is performed by selecting the next node of a large grid. This approach will increase the accuracy of solving applied optimization problems by allowing further mesh refinement and refinement of the values of local extremes, and, consequently, refinement of the values of the global extremum of the objective function. The optimization of the thermal impact parameters was carried out according to the criterion of reducing damage to the test material. This makes it possible to increase the accuracy of the technological process of thermal action on a multilayer material.