Науковий вісник НГУ

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

• 
• 

User Rating:  / 0

PoorBest 

Details

Category: Information technologies, systems analysis and administration

Last Updated on 30 October 2015

Published on 30 October 2015

Hits: 3404

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.

References:

Овчинников И.Г. Тонкостенные конструкции в условиях коррозионного износа. Расчёт и оптимизация / Овчинников И.Г., Почтман Ю.М. – Днепропетровск: ДГУ, 1995 – 192 с.

Ovchinnikov, I.G. and Pochtman, Yu.M. (1995), Tonkostennye konstruktsyi v usloviyakh korrozionnogo iznosa. Raschet i optimizatsyya [Thin-Walled Structures under Corrosive Wear. Calculation and Optimization], DNU, Dnepropetrovsk, Ukraine.

Корниенко В.И. Комплексная оценка, идентификация и прогнозирование сложных нелинейных процессов./ В.И.Корниенко, И.Г. Гулина, Л.В. Будкова // Науковий вісник НГУ. – 2013. – № 6 (138). – С. 124–131.

Korniienko, V.I., Gulina, I.G. and Budkova, L.V. (2013), “Complex estimation, identification and prediction of difficult nonlinear processes”, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 6 (138), рp. 124–131.

Зеленцов Д.Г. Расчет конструкций с изменяющейся геометрией в агрессивных средах. Стержневые системы: монография /Д.Г. Зеленцов – Днепропетровск: УГХТУ, 2002. – 168 с.

Zelentsov, D.G. (2002), Raschet konstruktsyi s izmenyayushcheysya geometriyey v agressivnykh sredakh [Calculation of Structures with Variable Geometry in Aggressive Environments. Rod Systems], Monograph, UDHTU, Dnepropetrovsk, Ukraine.

Зеленцов Д.Г. Информационное обеспечение расчётов корродирующих объектов. Математические модели и концепция проектирования систем / Зеленцов Д.Г., Ляшенко О.А., Науменко Н.Ю. – Днепропетровск:УГХТУ, 2012. – 264 с.

Zelentsov, D.G., Lyashenko, O.A. and Naumenko, N.Yu. (2012), Informatsyonnoye obespecheniye raschetov korrodiruyushchikh obyektov [Dataware Calculations Corrosive Objects. Mathematical Models and the Concept of System Design], UDHTU, Dnepropetrovsk, Ukraine.

Иванова А.П. Исследование долговечности центрально сжатых стержней с изменяющимися геометрическими характеристиками / А.П. Иванова //Науковий вісник НГУ. – 2013. – №3(135). – С.87–92

Ivanova, A.P. “Research of durability of the centrally compressed bars with changing geometrical”, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (2013), Vol. 3 (135), pp .87–92.

Науменко Н.Ю. Математичні моделі процесу корозії в задачах будівельної механіки кородуючих конструкцій / Н.Ю.Науменко, О.А.Ляшенко // Вопросы химии и хи-мической технологи. – 2010. – № 6. – С. 144–147.

Naumenko, N.Yu. and Lyashenko, O.A. (2010), “Mathematical models of corrosion process in the tasks of structural mechanics of corrosive constructions”, Voprosy Khimii i Khimicheskoy Tekhnologii, no. 6, pp. 144–147.

Короткая Л.И. Численное решение некоторых классов систем дифференциальных уравнений с использованием нейронних сетей: тезисы докл. ХIX международной научно-технической конференции (12–16 сентября 2011г. / Л.И. Короткая // Прикладные задачи математики и механики. – Севастополь: СевНТУ, 2011. – С. 226–228.

Korotkaya, L.I. (2011), “Numeral root-finding in some classes of differential equation systems using neural networks”, Proc. of the 19th Int. Scientific and Technical Conference “Applied Tasks Of Mathematics And Mechanics”, September 12-16, 2011, SEVNTU, Sevastopol, pp. 226–228.

Барский А.Б. Нейронные сети: распознавание, управление, принятие решений / Барский А.Б. – М.: Финансы и статистика, 2004. – 176 с.

Barskiy, A.B. (2004), [Neural Networks: Recognition, Management, Decision Making], Finansy i statistika, Moscow, Russia.

Калан Р. Основные концепции нейронных сетей. / Роберт Калан; пер с англ. А.Г. Сивак. – М.: Издательский дом «Вильямс», 2001. – 287 с.

Kalan, R. (2001), Osnovnye kontseptsyi neyronnykh setey [Basic Concept of Neural Networks], Translated from English by A.G. Sivak, Publishing House "Williams", Moscow, Russia.

Емельянов В. В. Теория и практика эволюционного моделирования / Емельянов В. В., Курейчик В. М., Курейчик В. В. – М.: ФИЗМАТЛИТ, 2003. – 432 с.

Emelyanov, V.V., Kureychik, V.M. and Kureychik, V.V. (2003), Teoriya i praktika evolyutsyonnogo modelirovaniya [Theory and Practice of Evolutional Modelling], FIZMATLIT, Moscow, Russia.

2015_03_zelentsov
2015-10-29  419.6 KB  996

• Next >