Abstract
In this paper, we consider the inverse mathematical modelling problem for linear dynamic systems with multiple inputs and multiple outputs. The problem of this kind appears in chemical disintegration reactions and determines product concentration changing. In general case of dynamical system modelling, one needs to identify its parameters and initial values. The reason for this is the fact that a dynamical system output is a reaction on some input function and it depends on the initial state of the system. This means that changing initial values would cause parameter changing and vice versa. At the same time, statistical approximation of initial values does not give us a reliable result because in most of the cases data is noisy and flat. To provide simultaneous estimation of parameters and initial values we propose an approach based on the reduction of the inverse modelling problem to a two-criterion extremum problem and then approximating the Pareto front with specific evolution-based algorithms. Different algorithms, such as SPEA-II, PICEA-g and NSGA-2, were applied to solve the reduced multi-objective black-box optimization problem as well as their heterogeneous and homogeneous cooperations. We compared performance of these algorithms on solving inverse modelling problems for concentrations of hexadecane disintegration reaction products in case of diffusion and static reactions. On the base of numerical experiments, we provided the analysis of algorithm performances.
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Acknowledgement
The reported study was funded by Russian Foundation for Basic Research, Government of Krasnoyarsk Territory, Krasnoyarsk Region Science and Technology Support Fund to the research project â„– 16-41-243036. This research is supported by the Russian Foundation for Basic Research within project No 16-01-00767.
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Ryzhikov, I., Brester, C., Semenkin, E. (2020). Inverse Mathematical Modelling of Hexadecane Disintegration Reaction with Cooperative Multi-objective Genetic Algorithms. In: Gusikhin, O., Madani, K. (eds) Informatics in Control, Automation and Robotics . ICINCO 2017. Lecture Notes in Electrical Engineering, vol 495. Springer, Cham. https://doi.org/10.1007/978-3-030-11292-9_37
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