Geodesic
Construction of approximate mathematical models on results of numerical experiments
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 1, pp. 76-87

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A mathematical model of an artillery shot is represented as a system of non-stationary one- and two-dimensional differential equations of the multiphase gas dynamics and heat transfer. Conjunction Euler-Lagrange method is used for the numerical solution of gas-dynamic equations. The initial mathematical model is approximated by a system of ordinary differential equations using a vector of correction functions. Correction functions are found from solutions of multiobjective optimal control problem. Multiobjective optimization is carried out using a hybrid genetic algorithm. The resulting model is adequate and allows doing more processing series of calculations the main process parameters (projectile velocity and maximum pressure) depending on the input parameters. Comparative analysis of different approximators (linear multiple regression, support vector machines, multi-layer neural network, radial network, the method of fuzzy decision trees) showed that an acceptable accuracy 0,4–0,5% is provided by only non-linear approximation methods, such as multi-layer and radial neural networks. Constructed approximate models are not require much computing time and can be implemented in the control systems.
Keywords: mathematical model of the shot; multi-phase gas dynamics; approximate models; multi-objective optimization. 
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     title = {Construction of approximate mathematical models on results of numerical experiments},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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V. A. Tenenev; I. G. Rusyak; V. G. Sufiyanov; M. A. Ermolaev; D. G. Nefedov. Construction of approximate mathematical models on results of numerical experiments. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 1, pp. 76-87. http://geodesic.mathdoc.fr/item/VYURU_2015_8_1_a5/