Improvement of the efficiency of numerical methods employed in corrosive constructions research

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Authors:

D.G. Zelentsov, Dr. Sci. (Tech.), Professor, State Higher Educational Institution “Ukrainian State University of Chemical Technology”, Head of the Information Systems Department, Dnepropetrovsk, Ukraine.

L.V. Novikova, State Higher Educational Institution “Ukrainian State University of Chemical Technology”, postgraduate student, Dnepropetrovsk, Ukraine.

Abstract:

Purpose. Creation of a neural network algorithm for determination of rational parameters for numeral analytical procedures for solving systems of differential equations that describe the corrosion process in multi-elemental rod-shaped constructions, in order to minimize the computational cost.

Methodology. To achieve this goal a new algorithm for the Euler method with irregular integration step (increment in time) was proposed. The algorithm assumes setting uniform increment of corrosion damage depth as a function of time, and using analytical formulas to determine the increment of the argument (time). The neural networks were employed to determine the minimum number of node points on integration interval that ensures the required accuracy of the solution.

Findings. The analysis of existing approaches to this problem was made and the ways to improve their effectiveness were identified. The influence of constructions parameters and corrosive environment on the accuracy of solution of differential equation systems which describe the corrosion process was investigated. Artificial neural network was used to formalize functional relationship between these parameters and the rational number of node points on integration interval that ensures the required accuracy of the solution. The technique of obtaining the training samples for various types of rod element cross-sections was described. The results of numerical experiments that confirm the high efficiency of the proposed approach were shown.

Originality. Use of neural network models of knowledge representation in numerical and analytical algorithms for solving systems of differential equations.

Practical value. The technique for solving systems of differential equations for modeling the behavior of multi-elemental constructions was proposed and justified. Its use allows the calculation of such structures with a specified accuracy at minimal computational cost.

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