POSSIBLE RISKS CONTROL METHODOLOGY IN SOLVING APPLIED PROBLEMS - KRAVTSOV, ANDRII; LEVKIN, DMYTRO; BEREZHNAJA, NATALIJA (Herald of Khmelnytskyi National University. Technical sciences, 2022)
The article deals with developed mathematical models and improved computational methods in terms of taking into account the specifics of the simulated processes to predict and control possible risks in order to increase the efficiency of solving applied problems. The authors propose a method of technological innovations managing to improve the efficiency of complex systems. As a demonstration of its universality, the article calculates and optimizes the technical parameters of laser emitters to increase the speed and accuracy of laser separation of the embryo. Due to the technical characteristics of the emitters and the geometry of the embryo, nonlocal boundary value problems of systems of multidimensional, non-linear differential equations of thermal conductivity are used to describe the state of the simulated system. Methods from the theory of differential equations in the space of generalized functions are used to prove the conditions of existence and the uniqueness of their solution. This allowed to guarantee the correctness of computational and applied optimization mathematical models. The authors have formed a grid model of discretization of optimized parameters, solved boundary value problems using the method of directed search of local extremums, compared to the trauma of cells, which is achieved at the nodes of the grid model. In order to increase the accuracy of optimization, the steps of the grid model were ground. Grinding and spot analysis of embryonic cell injury continues until the time allotted for optimization is exhausted or the specified optimization accuracy is achieved. According to the authors of the article, the research allowed to expand the range of tasks of economic and mathematical modeling for forecasting and control of possible risks to improve the efficiency of calculation and optimization of control parameters of complex systems.