روش پیشنهادی نوین و کم‌هزینه در محاسبه احتمال خرابی مسائل مبتنی بر روش مونت کارلو

نوع مقاله: مقاله عمران

نویسندگان

1 گروه مهندسی عمران، دانشگاه سیستان و بلوچستان، زاهدان، ایران

2 دانشگاه سیستان و بلوچستان

چکیده

در سال‌های اخیر ارزیابی قابلیت اطمینان سازه‌ها از جمله مباحث رو به گسترش و نیز مورد توجه پژوهشگران سازه بوده است. در این شاخه از مهندسی عمران، برآورد احتمال خرابی سازه با درنظرگرفتن عدم قطعیت‌های احتمالی درپارامترهای مقاومت و بار در فرآیند مدل‌سازی و طراحی سازه‌ها مورد بررسی قرار می‌گیرد. به شکل معمول، ارزیابی دقیق احتمال خرابی توسط روش شبیه‌سازی مونت کارلو انجام می‌پذیرد که مستلزم انجام مدل‌سازی و هزینه زیاد جهت شبیه‌سازی و متعاقباً برآورد احتمال خرابی سازه مورد بررسی است. در مقاله حاضر بر مبنای روش شبیه‌سازی مونت کارلو، روشی موثر ارائه شده است که دفعات انجام مدل‌سازی سازه جهت برآرود احتمال خرابی را به شکل مطلوبی کاهش داده است. در این روش از مفهوم حداقل فاصله ناحیه خرابی از مبدا، در روش FORM به عنوان معیاری برای تشخیص سلامت نمونه‌ها استفاده شده است. سپس با ارائه زیربازه‌هایی در لایه‌های مختلف جهت گروه‌بندی نمونه‌های تولید شده در روش مونت کارلو، امکان کاهش دفعات مدل‌سازی با کنترل خطای احتمالی و دقتی مناسب فراهم آورده شده است. به منظور بررسی کارایی و توانمندی روش پیشنهادی، مثال‌های عددی و مهندسی با توابع حالت حدی پیچیده توسط روش پیشنهادی مورد بررسی قرار گرفته و نتایج حاصله با روش‌های متداول قابلیت-اطمینان مقایسه گردیده‌اند. نتایج بیانگر دقت بالای روش پیشنهادی علی‌رغم کاهش زیاد دفعات مدل‌سازی سازه نسبت به شبیه‌سازی مونت کارلو می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

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

نویسندگان [English]

  • Hamed Ghohani Arab 1
  • Mohammad Reza Ghasemi 2
1 civil engineering department, university of sistan and baluchestan, Zahedan Iran
چکیده [English]

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.

کلیدواژه‌ها [English]

  • failure probability
  • Limit state function
  • Monte Carlo method
  • Sample elimination
  • Sub-interval
  • FORM method
[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.