MATHEMATICAL MODELS OF CONTROLLING AND MONITORING IN ENERGY MANAGEMENT OF TECHNOLOGICAL SYSTEMS

Abstract

The article is devoted to the development of mathematical models and improvement of numerical methods by increasing the detailing of simulated systems for the optimization of technological processes in conditions of uncertainty. A characteristic feature of the research is the division of mathematical models into computational and applied optimization models. By increasing iterations on the construction and solution of boundary tasks underlying computational mathematical models, an increase in the accuracy of the implementation of the main optimization problem of improving the quality of the technological process of welding sheet metal is achieved. Due to the specific features of the process under study, the authors propose to use the theory of differential operators in the space of generalized functions for proving the conditions of correctness of boundary value problems.

The main task set in the article is to provide monitoring and controlling in energy management to increase the accuracy and speed of implementation of the technological process of metal welding. A methodological approach for calculating the action temperature, time and energy cost optimization is proposed. Its basis includes boundary problems of differential equations of heat conduction and approximate ways of embodiment of optimization. Optimization of the control characteristics was carried out in a step-by-step manner using uniform grid nodes. To calculate the percentage of sheet metal damage, the ratio of the damaged material volume to the volume of the whole material was used. Optimization of the time and energy of the thermal action is carried out until the specified accuracy of the parameter optimization is achieved or the time allocated for optimization is exhausted. According to the authors of the article, the research results can be used for prediction and control of possible risks in solving many applied problems of economic mathematical modeling.