DOI: https://doi.org/10.15802/stp2018/141008

### OPTIMAL STRUCTURAL RESERVATION OF TECHNICAL SYSTEMS

S. N. Semenets, S. S. Nasonova, G. I. Semenets

#### Abstract

Purpose. The purpose of the article is to give designers of highly reliable technical systems that do not have special knowledge in the field of optimization and programming skills, a simple and accessible mathematical tool for choosing the optimal solution for structural redundancy of systems. Methodology. The article poses the problem of optimal structural redundancy of technical systems. Two typical redundancy schemes are considered: a) a separate "hot" backup scheme; b) a separate "cold" backup scheme. The computational models for estimating the reliability of redundant systems are formulated. We offer optimization models that allow us to find a rational option for reserving a system that is being designed, taking into account conflicting requirements for its reliability and cost. These models are numerically implemented in the operating environment of the Excel spreadsheet as applied to the main object, consisting of 7 elements. The optimal variants of reserving this object according to the "hot" and "cold" separate reservation schemes are given. Findings. Calculated models for estimating reliability, as well as models for optimizing the systems reserved for the "hot" and "cold" separate backup schemes, have been developed. With the use of the Excel spreadsheet, the optimal options for reserving 7 element objects are found for separate "hot" and "cold" backups. Originality. New computational models for estimating the reliability of redundant systems are proposed, as well as optimization models developed on the basis of these, which are formulated using the decomposition of unknown initial problem of structural redundancy into binary components. In this case, the obtained optimization models belong to the class of problems of non-linear mathematical programming with binary variables, for the numerical solution of which (even for a sufficiently large dimension) well-known packages of applied computer programs, in particular, the MS Excel spreadsheet, are well adapted. Thus, the process of solving the initially very complicated problem of optimal structural redundancy is much simpler and reduced to performing elementary actions in the corresponding software interfaces. Practical value. The proposed calculation models for estimating the reliability of redundant systems, models for optimal structural redundancy, and the methodology for their formation, in order to simplify further numerical implementation, can be useful in solving problems of ensuring the reliability of technical systems in the early stages of their design.

#### Keywords

system; design; reliability; structural reservation; model; optimization; binary variables

#### Full Text:

PDF TRANSLATION (Русский) HTML

#### References

Afanasev, V. P., & Semenets, G. I. (2006). Reliability of a thin-walled shell under conditions of corrosive wear. Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. La-zaryan, 11, 171-174. (in Russin)

Aleksandrovskaya, L. N., Aronov, I. Z., & Kruglov, V. I. (2017). Bezopasnost i nadezhnost slozhnykh sistem: uchebnoe posobie. Moscow: Logos. (in Russian)

Borodin, A. V. (2015). Tekhniko-ekonomicheskoe obosnovanie varianta rezervirovaniya setevoy komponenty ot-kazoustoychivoy masshtabiruemoy vychislitelnoy sistemy spetsialnogo naznacheniya. Kibernetika i programmirovanie, 6(6), 55-70. doi: 10.7256/2306-4196.2015.6.17523 (in Russian)

Kapur, K., & Lamberson, L. (1980). Reliability in engineering design. Moscow: Peace. (in Russian)

Kashtanov, V. A., & Medvedev, A. I. (2010). Teoriya nadezhnosti slozhnykh system. Moscow: Fizmatlit. (in Russian)

Nasonova, S. S. (2008). The optimization of failure risk in management tasks reliability of steel storage tanks for petroleum products. Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, 20, 126-130. (in Russian)

Dorokhov, A. N., Kernozhitskiy, V. A., Mironov, A. N., & Shestopalova, O. L. (2011). Obespechenie nadezhnosti slozhnykh tekhnicheskikh system. Saint Petersburg: Lan. (in Russian)

Polovko, A. M., & Gurov, S.V. (2006). Fundamentals of the theory of reliability. Saint Petersburg: BHV. (in Russian)

Ryabinin, I. A. (2000). Reliability and safety of structurally complicated systems. Saint Petersburg: Politekhnika. (in Russian)

Troshin, A. V. (2017). Optimizatsiya rezervirovaniya v kommutiruemykh paketnykh setyakh. Infokommunikatsionnye tekhnologii, 15(4), 354-360. (in Russian)

Shishmarev, V. Y. (2018). Nadezhnost tekhnicheskikh sistem: uchebnik dlya bakalavriata i magistratury. Moscow: Yurayt. (in Russian)

Chanda, N. (2015). Redundant Transmitting System in Aircraft (RTSA). SAE Technical Paper Series, 2015-01-2443. doi: 10.4271/2015-01-2443 (in English)

Jaberipur, G. (2017). Redundant Number System-Based Arithmetic Circuits. In Arithmetic Circuits for DSP Applications (рр. 273-312). Hoboken: John Wiley & Sons. doi: 10.1002/9781119206804.ch8 (in English)

#### GOST Style Citations

1. Афанасьев, В. П. Надежность тонкостенной оболочки в условиях коррозионного износа / В. П. Афанасьев, Г. И. Семенец // Вісн. Дніпропетр. нац. ун-ту залізн. трансп. ім. акад. В. Лазаряна. – Дніпропетровськ, 2006. – Вип. 11. – С. 171–174.
2. Безопасность и надежность сложных систем : учеб. пособие / Л. Н. Александровская, И. З. Аронов,
В. И. Круглов [и др.]. – Москва : Логос, 2017. – 376 с.
3. Бородин, А. В. Технико-экономическое обоснование варианта резервирования сетевой компоненты отказоустойчивой масштабируемой вычислительной системы специального назначения / А. В. Бородин // Кибернетика и программирование. – 2015. – № 6. – С. 55–70.
4. Капур, К. Надежность и проектирование систем : [пер. с англ.] / К. Капур, Л. Ламберсон. – Москва : Мир, 1980. – 604 с.
5. Каштанов, В. А. Теория надежности сложных систем / В. А. Каштанов, А. И. Медведев. – Москва : Физматлит, 2010. – 606 с.
6. Насонова, С. С. Оптимизация риска отказа в задачах управления надежностью стальных резервуаров для нефтепродуктов / С. С. Насонова // Вісн. Дніпропетр. нац. ун-ту залізн. трансп. ім. акад. В. Лазаряна. – Дніпропетровськ, 2008. – Вип. 20. – С. 126–130.
7. Обеспечение надежности сложных технических систем / А. Н. Дорохов, В. А. Керножицкий, А. Н. Миронов, О. Л. Шестопалова. – Санкт-Петербург : Лань, 2011. – 352 с.
8. Половко, А. М. Основы теории надежности / А. М. Половко, С. В. Гуров. – Санкт-Петербург : БХВ, 2006. – 704 с.
9. Рябинин, И. А. Надежность и безопасность структурно-сложных систем / И. А. Рябинин. – Санкт-Петербург : Политехника, 2000. – 248 с.
10. Трошин, А. В. Оптимизация резервирования в коммутируемых пакетных сетях / А. В. Трошин // Инфокоммуникационные технологии. – 2017. – Т. 15, № 4. – С. 354–360.
11. Шишмарев, В. Ю. Надёжность технических систем : учебник / В. Ю. Шишмарев. – Москва : Юрайт, 2018. – 306 с.
12. Chanda, N. Redundant Transmitting System in Aircraft (RTSA) / N. Chanda // SAE Technical Paper Series 2015-01-2443. – 2015. doi: 10.4271/2015-01-2443
13. Jaberipur, G. Redundant Number System-Based Arithmetic Circuits / G. Jaberipur // Arithmetic Circuits for DSP Applications. – Hoboken : John Wiley & Sons, 2017. – P. 273–312. doi: 10.1002/9781119206804.ch8