Recovery of thermal load parameters by means of the Monte Carlo method with fixed and meshless random walks

The paper is focused on the numerical analysis of the two-point inverse stationary heat flow problem, namely the identification of the thermal load. Determination of selected parameters is possible on the basis of temperature measurements, done at specified few locations. This problem may be modelled as the optimization problem, standard numerical analysis of which requires multiple solutions of boundary value problems. However, the novel solution approach, proposed here, is based on the well-known concept of the Monte Carlo method with an appropriate random walk technique. It yields explicit stochastic relations combining computed temperatures and all load parameters. Such relations may be directly applied in most standard optimization algorithms, replacing time-consuming solutions of systems of algebraic equations. Moreover, one may construct the semi-analytical approach, in which the unknown load parameters are obtained explicitly, allowing for the elimination of sensitiveness to initial solutions or requirements for admissible load intervals. The paper is illustrated with results of several benchmark problems with simulated measurement data and various numbers of unknown load parameters. The results comparison, between standard element-free methods with selected optimization algorithms as well as the proposed Monte Carlo solution approach is presented and is especially focused on CPU times.