METHODS OF MATHEMATICAL SIMULATION AND MACHINE IDENTIFICATION OF ABNORMAL ENERGY PROCESSES

For the class of anomalous diffusion processes, the mathematical models of which are formalized in the form of variational inequalities in partial derivatives, a method of mathematical modeling based on the optimization procedure is proposed. The method is considered in relation to the generalized mathematical model of the studied class of anomalous diffusion processes. which made it possible to ensure the principle of unification and typification in the application of this method, as well as the correctness of using the generalized mathematical model in applied problems of mathematical modeling of known industrial and practically important natural cases of anomalous diffusion processes. At the same time, the task of implementing mathematical models of anomalous diffusion processes based on the proposed method is reduced to finding the maximum of the Hamiltonian function defined in the state space of the processes under consideration. A method of parametric identification of mathematical models of anomalous diffusion processes in the formulation of the problem of optimal control is also proposed. The method is reduced to the use of the optimization procedure of the gradient projection method. The possibility of solving the problem of parametric identification in cases of both linear and non-linear mathematical models of anomalous diffusion processes is proved. Moreover, the nonlinear formulation of the parametric identification problem does not lead to computational implementation complications, since the solution is based only on finding the gradient projection of the state function of the anomalous diffusion process. The proposed methods are presented in strict compliance with the provisions of functional analysis, which ensures their correctness and adequacy in solving a wide range of applied problems.