AbstractAbout AuthorsReferences
In practical problems of probabilistic reliability analysis, there is a need for accounting and modeling of aleatory and epistemic uncertainties of data. Modeling of aleatory uncertainty, as a rule, is based on well-known probabilistic and statistical methods of the structural reliability theory, while for effective and reliable modeling of epistemic uncertainty, it becomes necessary to use new mathematical theories of data analysis. The article demonstrates the p-box model as a tool for describing a random variable in the problems of structural reliability analysis. With a large number of random variables represented by p-boxes, the analytical solution of the problem becomes more complicated. To deal with this problem, the article presents two numerical approaches to solving it: the discretization of p-boxes into of the Dempster-Shafer structures and the Interval Monte Carlo method (IMC). Probabilistic analysis of the structural reliability allow to obtain a quantitative assessment of the safety level of buildings and structures, to forecast the residual life of structures according to the reliability criterion, as well as to solve the problems of risk assessing and optimization problems.
S.A. SOLOVEV1, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.),
A.A. SOLOVEVA1, Engineer (Graduate Student) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
N.P. UMNYAKOVA2,3, Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
A.A.KOCHKIN1, Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.)
A.A. SOLOVEVA1, Engineer (Graduate Student) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
N.P. UMNYAKOVA2,3, Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
A.A.KOCHKIN1, Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.)
1 Vologda State University (15, Lenin Street, Vologda, 160000, Russian Federation)
2 Scientific-Research Institute of Building Physics of RAACS (21, Lokomotivniy Driveway, Moscow, 127238, Russian Federation)
3 National Research Moscow State University of Civil Engineering (26, Yaroslavskoye Highway, Moscow, 129337, Russian Federation)
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1. Mkrtychev O.V., Shchedrin O.S., Lokhova E.M. Determination of individual coefficients on the basis of probabilistic analysis. Vestnik MSTU. 2022. Vol. 17 (10), pp. 1331–1346. (In Russian). DOI: 10.22227/1997-0935.2022.10.1331-1346
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2. Rzhanitsyn A.R. Application of statistical methods in calculations of structures for strength and safety. Stroitelnaya promishlennost. 1952. No. 6, pp. 22–25. (In Russian).
3. Der Kiureghian A., Ditlevsen O. Aleatory or epistemic? Does it matter? Structural safety. 2009. Vol. 31. Iss. 2, pp. 105–112. https://doi.org/10.1016/j.strusafe.2008.06.020
4. Xie H., Li J., Liao D. A new structural reliability analysis method under non-parameterized probability box variables. Structural and Multidisciplinary Optimization. 2022. Vol. 65. No. 11. 322. https://doi.org/10.1007/s00158-022-03408-5
5. Соловьев С.А., Соловьева А.А., Умнякова Н.П., Кочкин А.А. Анализ проблем оценки индекса надежности элементов строительных конструкций // Жилищное строительство. 2022. № 7. С. 32–39. DOI: https://doi.org/10.31659/0044-4472-2022-7-32-39
5. Soloviev S.A., Solovieva A.A., Umnyakova N.P., Kochkin A.A. Analysis of the problems of assessing the reliability index of elements of building structures. Zhilishchnoe Stroitel’stvo [Housing Construction]. 2022. No. 7, pp. 32–39. (In Russian). DOI: https://doi.org/10.31659/0044-4472-2022-7-32-39
6. Орлов А.И. Современное состояние непараметрической статистики // Политематический сетевой электронный научный журнал Кубанскогогосударственного аграрного университета. 2015. № 106. С. 239–269.
6. Orlov A.I. Current status of nonparametric statistics. Politematicheskij setevoj elektronnyj nauchnyj zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta. 2015. No. 106, pp. 239–269. (In Russian).
7. Zhang H., Dai H., Beer M., Wang W. Structural reliability analysis on the basis of small samples: an interval quasi-Monte Carlo method. Mechanical Systems and Signal Processing. 2013. Vol. 37 (1–2), pp. 137–151. https://doi.org/10.1016/j.ymssp.2012.03.001
8. Faes M.G., Daub M., Marelli S., Patelli E., Beer M. Engineering analysis with probability boxes: a review on computational methods. Structural Safety. 2021. Vol. 93. 102092. https://doi.org/10.1016/j.strusafe.2021.102092
9. Соловьев С.А. Вероятностная оценка промышленной безопасности при неполной статистической информации // Безопасность труда в промышленности. 2020. № 9. С. 88–93.DOI: 10.24000/0409-2961-2020-9-88-93.
9. Soloviev S.A. Probabilistic estimation of industrial safety with incomplete statistic data. Bezopasnost’ truda v promyshlennosti. 2020. No. 9, pp. 88–93. (In Russian). DOI: 10.24000/0409-2961-2020-9-88-93
10. Ferson S., Kreinovich V., Grinzburg L., Myers D., Sentz K. Constructing probability boxes and Dempster-Shafer structures (No. SAND-2015-4166J). Sandia National Lab (SNL-NM), Albuquerque, 2003. 132 p. DOI: 10.2172/809606
11. Karanki D.R., Kushwaha H.S., Verma A.K., Ajit S. Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Analysis: An International Journal. 2009. Vol. 29 (5). pp. 662–675. DOI: 10.1111/j.1539-6924.2009.01221.
12. Zhang H., Mullen R.L., Muhanna R.L. Interval Monte Carlo methods for structural reliability. Structural Safety. 2010. Vol. 32. Iss. 3, pp. 183–190. https://doi.org/10.1016/j.strusafe.2010.01.001
13. Timothy H., Ju Q., Van Emden M.H. Interval arithmetic: From principles to implementation. Journal of the ACM (JACM). 2001. Vol. 48. No. 5,pp. 1038–1068. DOI: 10.1145/502102.502106
1. Mkrtychev O.V., Shchedrin O.S., Lokhova E.M. Determination of individual coefficients on the basis of probabilistic analysis. Vestnik MSTU. 2022. Vol. 17 (10), pp. 1331–1346. (In Russian). DOI: 10.22227/1997-0935.2022.10.1331-1346
2. Ржаницын А.Р. Применение статистических методов в расчетах сооружений на прочность и безопасность // Строительная промышленность. 1952. № 6. С. 22–25.
2. Rzhanitsyn A.R. Application of statistical methods in calculations of structures for strength and safety. Stroitelnaya promishlennost. 1952. No. 6, pp. 22–25. (In Russian).
3. Der Kiureghian A., Ditlevsen O. Aleatory or epistemic? Does it matter? Structural safety. 2009. Vol. 31. Iss. 2, pp. 105–112. https://doi.org/10.1016/j.strusafe.2008.06.020
4. Xie H., Li J., Liao D. A new structural reliability analysis method under non-parameterized probability box variables. Structural and Multidisciplinary Optimization. 2022. Vol. 65. No. 11. 322. https://doi.org/10.1007/s00158-022-03408-5
5. Соловьев С.А., Соловьева А.А., Умнякова Н.П., Кочкин А.А. Анализ проблем оценки индекса надежности элементов строительных конструкций // Жилищное строительство. 2022. № 7. С. 32–39. DOI: https://doi.org/10.31659/0044-4472-2022-7-32-39
5. Soloviev S.A., Solovieva A.A., Umnyakova N.P., Kochkin A.A. Analysis of the problems of assessing the reliability index of elements of building structures. Zhilishchnoe Stroitel’stvo [Housing Construction]. 2022. No. 7, pp. 32–39. (In Russian). DOI: https://doi.org/10.31659/0044-4472-2022-7-32-39
6. Орлов А.И. Современное состояние непараметрической статистики // Политематический сетевой электронный научный журнал Кубанскогогосударственного аграрного университета. 2015. № 106. С. 239–269.
6. Orlov A.I. Current status of nonparametric statistics. Politematicheskij setevoj elektronnyj nauchnyj zhurnal Kubanskogo gosudarstvennogo agrarnogo universiteta. 2015. No. 106, pp. 239–269. (In Russian).
7. Zhang H., Dai H., Beer M., Wang W. Structural reliability analysis on the basis of small samples: an interval quasi-Monte Carlo method. Mechanical Systems and Signal Processing. 2013. Vol. 37 (1–2), pp. 137–151. https://doi.org/10.1016/j.ymssp.2012.03.001
8. Faes M.G., Daub M., Marelli S., Patelli E., Beer M. Engineering analysis with probability boxes: a review on computational methods. Structural Safety. 2021. Vol. 93. 102092. https://doi.org/10.1016/j.strusafe.2021.102092
9. Соловьев С.А. Вероятностная оценка промышленной безопасности при неполной статистической информации // Безопасность труда в промышленности. 2020. № 9. С. 88–93.DOI: 10.24000/0409-2961-2020-9-88-93.
9. Soloviev S.A. Probabilistic estimation of industrial safety with incomplete statistic data. Bezopasnost’ truda v promyshlennosti. 2020. No. 9, pp. 88–93. (In Russian). DOI: 10.24000/0409-2961-2020-9-88-93
10. Ferson S., Kreinovich V., Grinzburg L., Myers D., Sentz K. Constructing probability boxes and Dempster-Shafer structures (No. SAND-2015-4166J). Sandia National Lab (SNL-NM), Albuquerque, 2003. 132 p. DOI: 10.2172/809606
11. Karanki D.R., Kushwaha H.S., Verma A.K., Ajit S. Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Analysis: An International Journal. 2009. Vol. 29 (5). pp. 662–675. DOI: 10.1111/j.1539-6924.2009.01221.
12. Zhang H., Mullen R.L., Muhanna R.L. Interval Monte Carlo methods for structural reliability. Structural Safety. 2010. Vol. 32. Iss. 3, pp. 183–190. https://doi.org/10.1016/j.strusafe.2010.01.001
13. Timothy H., Ju Q., Van Emden M.H. Interval arithmetic: From principles to implementation. Journal of the ACM (JACM). 2001. Vol. 48. No. 5,pp. 1038–1068. DOI: 10.1145/502102.502106
For citation: Solovev S.A., Soloveva A.A., Umnyakova N.P., Kochkin A.A. Structural reliability analysis with epistemic uncertainty of data. Stroitel’nye Materialy [Construction Materials]. 2023. No. 6, pp. 45–50. (In Russian). DOI: https://doi.org/10.31659/0585-430X-2023-814-6-45-50