Creation of High-Speed Methods for Solving Mathematical Models of Inverse Problems of Heat Power Engineering

Abstract

AbstractExperimental methods for studying thermophysical processes and their systems are the most reliable source of information about the thermal state of an object. The theory and practice of solving inverse problems acquire special significance in our time, when, due to the current circumstances, energy facilities, industry, transport, economy, communications, buildings and structures have worked out their planned resource and need to prevent man-made disasters, namely, they need urgent updating, modernization and reconstruction. The main problems in solving applied inverse heat conduction problems include the correctness of the formulation of the problem, the time of solving systems of algebraic equations for a discrete analogue of the heat conduction equation, the amount of calculations in the optimization of a quadratic functional in inverse problems (the number of calculations per iteration), stability and convergence of unconstrained optimization methods. In this chapter, a numerical analysis of series of methods of unconstrained optimization on nonlinear problems is carried out, which make it possible to reduce the search time for a numerical solution to a large class of nonlinear inverse heat conduction problems. Also, significant modifications of the classical Newton's method are proposed, which make it possible to obtain the desired numerical solution of nonlinear problems much faster than the classical Newton's method. Modifications of Newton's method with a variable step give a much faster convergence and make it possible to obtain fairly quickly solutions to nonlinear inverse heat conduction problems.KeywordsOptimization mathematical modelsNewton type methodsInverse heat conduction problemsSimulationMATLAB