A new and low cost proposed method for failure probability estimation based on Monte Carlo simulation

Document Type : Civil Article

Authors

civil engineering department, university of sistan and baluchestan, Zahedan Iran

Abstract

In recent years, evaluation of reliability analysis of structures has become a straightforward and interesting topic among structural researchers. In the field of civil engineering, estimation of structural failure probability is highly investigated, considering probabilistic uncertainties of resistance and load parameters during modeling and designing of structures. To obtain an accurate failure probability, researchers often perform Monte Carlo simulation (MCS) that requires numerous modeling and cost. In the present study, based on MCS, an enhanced technique is developed that efficiently reduces number of structural modeling. The approach works by employing the concept of First Order Reliability Methods (FORMs) to determine closest point to the mean of random variables in failure region. Afterward, by presenting sub-intervals in various layers, to group generated samples in MCS, the possibility of reducing number of structural modeling with well-disciplined error and acceptable accuracy is achieved. In order to investigate the efficiency and robustness of the method, various numerical and engineering examples with complex limit state functions were attempted and the obtained results were compared with those based on the conventional reliability methods in the literature. Results show the high accuracy of proposed approach while the number of requires structural modeling were substantially reduced.

Keywords

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References

[1] Nowak, A.S., Collins, K.R. (2012), “Reliability of structures“, Second Edition, CRC Press.
]2 [کاوه، ع.، کلات جاری ، و ، ر. (1373)، نظریه قابلیت اعتماد و کاربرد آن در مهندسی سازه، انتشارات دانشگاه علم و صنعت.
[3] Melchers, R.E., Beck, A.T. (2017), “Structural Reliability Analysis and Prediction“, Third Edition, John Wiley & Sons.
[4] Hasofer, A.M., Lind N.C. (1974), “Exact and Invariant Second-Moment Code Format”, Journal of Engineering Mechanics, Vol. 100, Issue 1, pp. 111-121.
[5] Rackwitz, R., Fiessler, B. (1978), “Structural reliability under combined random load sequences“, Computers & Structures, Vol. 9, No. 5, pp. 489-494.
[6] Zhao, Y.G., Ang, A.H.S. (2012), “On the first-order third-moment reliability method“, Structure and Infrastructure Engineering, Vol. 8, No. 5, pp. 517-527.
[7] Napa-Garcia, G.F., Beck, A.T., Celestino, T.B. (2017), “Reliability analyses of underground openings with the point estimate method “, Tunnelling and Underground Space Technology, Vol. 64, No. 1, pp. 154–163.
[8] Fiessler, B., Rackwitz, R., Neumann, H.J. (1979), “Quadratic Limit States in Structural Reliability”, Journal of the Engineering Mechanics Division, Vol. 105, No. 4, pp. 661-676.
[9] Breitung, K. (1984), “Asymptotic Approximations for Multinormal Integrals”, Journal of the Engineering Mechanics, Vol.110, No. 3, pp. 357-366.
[10]Lee, Y.K, Hwang, D.S. (2008), “A Study on The Techniques of Estimating The Probability of Failure”,  Journal of the Chungcheomg Mathematica Society, Vol. 21, No. 4, pp. 573-583.
[11] Lu, Z.H., Hu, D.Z., Zhao, Y.G. (2016), “Second-Order Fourth-Moment Method for Structural Reliability”, Journal of Engineering Mechanics, Vol. 143, No. 4, pp. 10-21.
[12] Chowdhury, R., Rao, B.N. (2008), “Structural failure probability estimation using HDMR and FFT“, Electronic Journal of Structural Engineering, Vol. 8, pp. 67–76.
[13] Guo, S. (2014), “An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures”, Applied Mathematical Modelling, Vol. 38, No. 1, pp. 221-232.
[14] Lemaire, M. (2013), “Structural reliability”, John Wiley & Sons.
[15] Piric, K. (2015), “Reliability analysis method based on determination of the performance function’s PDF using the univariate dimension reduction method”, Structural safety, Vol. 57, pp. 18-25.
[16] Zhang, X., Pandey, M.D. (2013), “Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method”, Structural Safety, Vol. 43, pp. 28-40.
[17] Xu, J, Lu, Z.H. (2017), “Evaluation of Moments of Performance Functions Based on Efficient Cubature Formulation”, Journal of Engineering Mechanics, Vol. 143, No. 8, pp. 27-39.
[18] Zio, E. (2013), The Monte Carlo simulation method for system reliability and risk analysis, London: Springer.
[19] Kang, F., Han, S., Salgado, R., Li, J. (2015), “System probabilistic stability analysis of soil slopes using Gaussian process regression with Latin hypercube sampling”, Computers and Geotechnics, Vol. 63, pp. 13-25.
[20] Bugallo, M.F., Elvira, V., Martino, L., Luengo, D., Miguez, J., Djuric, P.M. (2017), “Adaptive importance sampling: the past, the present, and the future”, IEEE Signal Processing Magazine, Vol. 34, No. 4, pp. 60-79.
[21] Echard, B., Gayton, N., Lemaire, M., Relun, N. (2013), “A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models”, Reliability Engineering & System Safety, Vol. 111, pp. 232-240.
[22] Zhu, Y., Zhou, H., Feng, X.T., Zhang, C.Q., Zhang, M.Q., Yang, F.J. (2017), “Directional simulation of failure probability of rock slope wedge”, Rock and Soil Mechanics, Vol. 38, No. S1, pp.151-157.
[23] Dubourg, V., Sudret, B. (2014), “Meta-model-based importance sampling for reliability sensitivity analysis”, Structural Safety, Vol. 49, pp. 27-36.
[24] de Angelis, M., Patelli, E., Beer, M. (2015), “Advanced line sampling for efficient robust reliability analysis”, Structural safety, Vol.52, pp. 170-182.
[25] Depina, I., Le, T.M.H., Fenton, G., Eiksund, G. (2016), “Reliability analysis with metamodel line sampling”, Structural Safety, Vol. 60, pp. 1-15.
[26] Papaioannou, I., Betz, W., Zwirglmaier, K., Straub, D. (2015), “MCMC algorithms for subset simulation”, Probabilistic Engineering Mechanics, Vol. 41, pp. 89-103.
[27] Huang, X., Chen, J., Zhu, H. (2016), “Assessing small failure probabilities by AK–SS: an active learning method combining Kriging and subset simulation”, Structural Safety, Vol. 59, pp. 86-95.
[28] Pradlwarter, H.J., Schuëller, G.I. (2010), “Local domain Monte Carlo simulation“, Structural Safety, Vol. 32, No. 5, pp. 275–280.
[29] Zhang, Y., Der Kiureghian, A. (1995), “Two improved algorithms for reliability analysis“, Editors: R. Rackwitz, G. Augusti, and A. Borr, In Proc. 6th IFIP WG7.5 ,Reliability and optimization of structural systems.
[30] Zhang, Y., Der Kiureghian, A. (1997), “Finite element reliability methods for inelastic structures“, Tech. Rep. no UCB/SEMM-97/05, University of California, Berkeley – Dpt of Civil Engineering.
[31] Wang, L.P., Grandhi, R.V. (1994), “Efficient safety index calculation for structural reliability analysis“, Computers & Structures, Vol. 52, pp.103–111.
[32] Rashki, M., Miri, M., Azhdary Moghaddam, M. (2012), “A new efficient simulation method to approximate the probability of failure and most probable point“, Structural Safety, Vol. 39, No. 1, pp. 22-29.
[33] Der Kiureghian, A., Dakessian, T. (1998), “Multiple design points in first and second order reliability“, Structural Safety, Vol. 20, No. 1, pp. 37-49.
[34] Ramu, P., Kim, N.H. and Haftka, R.T. (2006), “System Reliability Analysis Using Tail Modeling“, the 11th AIAA/ISSMO Multidisciplinary Analysis & Optimization Conference, 6 – 8 September, Portsmouth, VA.
[35] Mohammadi, S. (2008), “Extended finite element method for fracture analysis of structures“, Blackwell, Oxford.
 
 
Journal of Modeling in Engineering
Volume 16, Issue 54
October 2018
Pages 189-203

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History

  • Receive Date: 21 September 2013
  • Revise Date: 10 September 2017
  • Accept Date: 15 November 2017

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