ارائه روشی موثر در تولید نمونه های تصادفی برای محاسبه احتمال خرابی سازه ها به روش مونت کارلو

نوع مقاله: مقاله پژوهشی

نویسندگان

1 پژوهشگاه مهندسی بحرانهای طبیعی ، اصفهان ، ایران.

2 استادیار، پژوهشگاه مهندسی بحران های طبیعی، اصفهان، ایران

3 استاد ، پژوهشگاه مهندسی بحران های طبیعی ، دانشگاه اصفهان ، ایران.

چکیده

نظریه قابلیت اطمینان، شاخه‌ای از تئوری عمومی احتمالات است که طی دهه‌های اخیر، به تدریج جایگاه ویژه‌ای در علوم مهندسی کسب کرده است. به‌طور کل، قابلیت اطمینان، مقیاسی است که می‌توان احتمال خرابی و یا سلامت یک سیستم را توسط آن سنجید. تاکنون روش‌های متنوعی در برآورد احتمال خرابی یک پدیده ارائه شده است که روش مونت‌کارلو یکی از مهم‌ترین و پرکاربردترین روش‌ها در این زمینه است. در پژوهش حاضر با ارائه یک روش بسیار مؤثر و ساده، تعداد زیادی از گام‌های مورد نیاز در تولید داده‌های تصادفی حذف خواهند شد. تولید داده در این روش، برمبنای نمودار هیستوگرام بوده و هیچ نیازی به آزمون‌های سازگار نمودن توابع مختلف با داده‌ها نمی‌باشد. این روش در مواردی بسیار پرکاربرد می‌باشد که داده‌های مربوط به پدیده مورد بررسی به تعداد کافی در دسترس بوده تا نمودار هیستوگرام پیوسته‌ای ایجاد شود. با گذراندن این نمودار از داده‌های یکنواخت پراکنده شده در فضای سه‌بعدی، می‌توان متغیرهایی با توزیع کاملا هماهنگ با داده‌ها به‌دست آورد. همچنین چهار مثال عملی در مورد برآورد احتمال خرابی یک تیر بتن مسلح یک دهانه و تیر فولادی چند دهانه، احتمال خرابی لغزشی و واژگونی سد بتنی وزنی شفارود و احتمال خرابی قوسی پل بوروکریگ ارائه شده که نتایج آن بیانگر کارآیی و دقت روش پیشنهادی می‌باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Expression an Effective Method in Generation of Random Samples to Calculate the Failure Probability of Structures With MCS Method

نویسندگان [English]

  • Mehdi Nikouei Mahani 1
  • Amir Mahmoudzade 2
  • Manuchehr Emamgholi Babadi 3
1 Department of Civil Engineering, Research Institute for Natural Disasters, Shakhes pajouh, Esfahan, Iran.
2 Department of Civil Engineering, Research Institute for Natural Disasters, Shakhes pajouh, Esfahan, Iran.
3 Department of Civil Engineering, Research Institute for Natural Disasters, Shakhes pajouh, Esfahan, Iran.
چکیده [English]

Reliability theory is a part of the general theory of probability that earned a special place in engineering science over recent decades. This theory has a logical framework. It provides the actual safety assessment possibility of a system by analyzing the uncertainties using mathematical methods. These uncertainties are caused by the statistical nature of engineering problems. Reliability is a scale that can measure the probability of failure or safety of a system. So far, various methods have been proposed to estimate the probability of failure of a phenomenon. MCS is one of the most important and most widely used approaches in this field. Many steps will be removed by providing a simple and effective method. The data generated in this method is based on the histogram. SGH, there is no need to curve fitting test. This method is very useful in case data on the studied phenomenon be available in sufficient number, and continuous histograms could be created. The general performance of SGH is passing the histogram of uniform data scattered in three-dimensional space and select samples in the diagram area. As well as, it provided three practical examples. The first one is estimating the failure probability of a concrete beam under moment load with four random variables. The second example expressed failure probability of a steel beam, and the third one is about sliding and overturning failure of SHAFAROUD concrete gravity dam. Results were compared with the usual method of sample generation and indicated the effectiveness and accuracy of the responses of the proposed method.

کلیدواژه‌ها [English]

  • Sample generation
  • Reliability
  • Histogram
  • Monte Carlo
  • Probability of failure
[1] Engelund, S., & Rackwitz, R. (1993). “A benchmark study on importance sampling techniques in structural reliability”, Structural Safety, 12(4), 255-276.

[2] Sorensen, J. D. (2004). “Structural Reliability Theory And Risk Analysis”, Institute of Building Technology and Structural Engineering, Aalborg University.

[3] Escuder-Bueno, I., Altarrejos-Garcia, L., & Serrano-Lombillo, A. (2012). “Methodology for estimating the probability of failure by sliding in concrete gravity dams in the context of risk analysis”, Structural Safety, 36, 1-13.

[4] Kiureghian, D. A., & Dakessian, T. (1998). “Multiple design points in first and second order reliability”, Struct Safety, 20, 37-49.

[5] Rahman, S., & Wei, D. (2006). “A univariate approximation at most probable point for higher-order reliability analysis”, International journal of solids and structures, 43(9), 2820-2839.

[6] Rackwitz, R. (1988). “Updating first and second-order reliability estimates by importance sampling”, Doboku Gakkai Ronbunshu, 1988(392), 53-59.

[7] Rackwitz, R., & Fiessler, B. (1978). “Structural reliability under combined random load sequences”, Computers & Structures, 9(5), 489-494.

[8] Kubler, O. (2007). Applied decision-making in civil engineering. Vol. 300, vdf Hochschulverlag AG.

[9] Cornell, A. (1969). “A probability based structural code”, Journal Proceedings, 66(12), 974-985.

[10] Hasofer, A. M., & Lind, N. C. (1974). “Exact and invariant second-moment code format”, Journal of the Engineering Mechanics division, 100(1), 111-121.

[11] Tu, J., Choi, K. K., & Park, Y. H. (1999). “A New Study on Reliability-Based Design Optimization”, Journal of Mechanical Design, 121(4), 557-564.

[12] Bartelt, P., Adams, E., Christen, M., Sack, R., & Sato, A. (2004). Snow Engineering V. Proceedings of the Fifth International Conference on Snow Engineering, Davos, Switzerland.

[13] Hohenbichler, M., & Rackwitz, R. (1986). “Sensitivity and importance measures in structural reliability”, Civil engineering systems, 3(4), 203-209.

[14] Fiessler, B., Neumann, H. J., & Rackwitz, R. (1979). “Quadratic limit states in structural reliability”, Journal of the Engineering Mechanics Division, 105(4), 661-676.

[15] McKay, M. D., Beckman, R. J., & Conover, W. J. (1979). “Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code”, Technometrics, 21(2), 239–245.

[16] Thoft-Cristensen, P., & Baker, M. J. (2012). Structural reliability theory and its applications. Springer Science & Business Media.

[17] Denny, M. (2001). “Introduction to importance sampling in rare-event simulations”, European Journal of Physics, 22(4), 403-411.

[18] Xu, Q., Chen, J., & Li, J. (2012). “A Study on the Functional Reliability of Gravity Dam”, Energy and Power Engineering, 4(2), 59-66.

[19] Bretas, E. M., Lemos, J. V., & Lourenco, P. B. (2014). “A DEM based tool for the safety analysis of masonry gravity dams”, Engineering Structures, 59, 248-260.

[20] Nowak, A. S., & Collins, K. R. (2012). Reliability of Structures. CRC Press.

[21] Khatibinia, M., & Khosravi, S. (2014). “A hybrid approach based on an improved gravitational search algorithm and orthogonal crossover for optimal shape design of concrete gravity dams”, Applied Soft Computing, 16, 223-233,

[22] USBR. (1976). Design of Gravity Dams. United States Department of the Interior, USA.

[23] FERC. (2002). “Manual for engineering guidelines for the evaluation of hydropower project”, (http://www.ferc.gov), USA.

[24] Su, H., & Wen, Z. (2013). “Interval risk analysis for gravity dam instability”, Engineering Failure Analysis, 33, 83-96.

[25] Teng-Fei, B., Miao, X., & Lan, C. (2012). “Stability Analysis of Concrete Gravity Dam Foundation Based on Catastrophe Model of Plastic Strain Energy”, Procedia engineering, 28, 825-830.

[26] Zhang, S., Wang, G., Wang, C., Pang, B., & Du, C. (2014). “Numerical simulation of failure modes of concrete gravity dams subjected to underwater explosion”, Engineering Failure Analysis, 36, 49-64.

[27] Kartal, M. E., Bayraktar, A., & Basaga. H. B. (2010). “Seismic failure probability of concrete slab on CFR dams with welded and friction contacts by response surface method”, Soil Dynamics and Earthquake Engineering, 30(11), 1383-1399.

[28] Jiang, S., Du. C., & Hong. Y. (2013). “Failure analysis of a cracked concrete gravity dam under earthquake”, Engineering Failure Analysis, 33, 265-280.

[29] Kartal, M. E., Basaga, H. B., & Bayraktar, A. (2011). “Probabilistic nonlinear analysis of CFR dams by MCS using Response Surface Method”, Applied Mathematical Modelling, 35(6), 2752-2770.

[30] Bretas, E. M., Léger, P., & Lemos, J. V. (2012). “3D Stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method”, Computers and Geotechnics, 44, 147-156.

[31] Zhang, J., Xiao, M., & Gao, L. (2019). “A new method for reliability analysis of structures with mixed random and convex variables”, Applied Mathematical Modelling, 70, 206-220.

[32] Xu, J., & Kong, F. (2019). “Adaptive scaled unscented transformation for highly efficient structural reliability analysis by maximum entropy method”, Structural Safety, 76, 123-134.

[33] Mustapha, A., & Abejide, O. (2019). “Probabilistic Strength of Steel Poles Used for Power Production and Transmissions”, Reliability Engineering and Resilience, 1(1), 29-41.

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