Random - weighted Monte Carlo Simulation Method for Structural Reliability Analysis
Authors
Abstract
The computational burdens and more accurate approximations for the estimation of the failure probability are the main concerns in the structural reliability analyses. The Monte Carlo simulation (MCS) method can simply provide an accurate estimation for the failure probability, but it is a time-consuming method for complex reliability engineering problems with a low failure probability and may efficiently approximate the failure probability. In this paper, the efficiency of MCS for the computations of the performance function is improved using a random-weighted method known as the random-weighted MCS (RWMC) method. By using the weighted exponential function, the weights of random data points generated by MCS are adjusted by selecting the random point in the design space. The convergence performances including the computational burdens for evaluating the limit sate function and the accuracy of failure probabilities of RWMC are compared with MCS by using several nonlinear and complex mathematical and structural problems with normal and no-normal random variables. The results indicate that the proposed RWMC method can estimate the accurate results with the less computational burdens, about 100 to 1000 times faster than MCS
Keywords
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2. Li, J, and Chen, J., “Probability Density Evolution Method for Dynamic Response Analysis of Structures with Uncertain Parameters”, Computational Mechanics, Vol. 34, No. 5, pp. 400-409, 2004.
3. Li, J., and Chen, J., Stochastic Dynamics of Structures, John Wiley & Sons, 2009.
4. Sørensen, J. D., Notes in Structural Reliability Theory and Risk Analysis, Aalborg University, 2004.
5. Breitung, K., “Asymptotic Approximations for Multinormal Integrals”, Engineering Mechanics, Vol. 110, No. 3, pp. 357-366, 1984.
6. Yuan, X., and Zeng, L., “Weighted Simulation for Failure Probability Function Estimation”, Second International Conference on Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management, ASCE, pp. 2053-2062, 2014.
7. Sørensen, J. D., Structural Reliability Theory And Risk Analysis, Aalborg, February, 2004.
8. Bedford, T., and van Gelder, P. H. A. J. M., “Safety and Reliability”, Proceedings of European Safety and Reliability Conference, Maastricht, the Netherlands, 15-18 June, 2003.
9. Zio, E., and Pedroni, N., “How to Effectively Compute the Reliability of a Thermal-hydraulic Nuclear Passive System”, Nuclear Engineering and Design, Vol. 241, pp. 310-327, 2011.
10. Rocco, S. C. M., “A Rule Induction Approach to Improve Monte Carlo System Reliability Assessment”, Reliability Engineering and System Safety, Vol. 82, pp. 85-92, 2003.
11. Naess, A., Leira, B. J., and Batsevych, O., “System Reliability Analysis by Enhanced Monte Carlo Simulation”, Structural Safety, Vol. 3, No. 1, pp. 349-355, 2009.
12. Rashki, M., Miri, M., and Moghaddam, M. A., “A New Efficient Simulation Method to Approximate the Probability of Failure and Most Probable Point”, Structural Safety, Vol. 46, pp. 15-26, 2012.
13. Okasha, N. M., “An Improved Weighted Average Simulation Approach for Solving Reliability-based Analysis and Design Optimization Problems”, Structural Safety, Vol. 60, pp. 47-55, 2016.
14. Xu, J., Zhang, W., and Sun, R., “Efficient Reliability Assessment of Structural Dynamic Systems with Unequal Weighted Quasi-monte Carlo Simulation”, Computers and Structures, Vol. 175, pp. 37-51, 2016.
15. Das, P., and Zheng, Y., “Cumulative Formation of Response Surface and Its Use in Reliability Analysis”, Probabilistic Engineering Mechanics, Vol. 15, No. 4, pp. 309-315, 2000.
16. Kim, S. H., and Na, S. -W., “Response Surface Method using Vector Projected Sampling Points”, Structural Safety, Vol. 19, No. 1, pp. 3-19, 1997.
17. Papadrakakis, M., and Lagaros, N. D., “Reliability-based Structural Optimization using Neural Networks and Monte Carlo Simulation”, Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 32, pp. 3491-3507, 2002.
18. Kaymaz, I., “Application of Kriging Method to Structural Reliability Problems”, Structural Safety, Vol. 27. No. 2, pp. 133-151, 2005.
19. Nowak, A. S., and Collins, K. R., Reliability of Structures, McGrawHill, United States, 2000.
20. Melchers, R., Structural Reliability: Analisis and Prediction, Ellis Horwood, John Wiley. 1987.
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22. Csenki, A., “An Improved Monte Carlo Method in Structural Reliability”, Reliability Engineering and System Safety, Vol. 24, No. 3, pp. 275-292, 1989.
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24. Keshtegar, B., and Chakraborty, S., “A hybrid Self-adaptive Conjugate First Order Reliability Method for Robust Structural Reliability Analysis”, Applied Mathematical Modelling, Vol. 53, pp. 319-332, 2018.
25. Pan, Q., and Dias, D., “An Efficient Reliability Method Combining Adaptive Support Vector Machine and Monte Carlo Simulation”, Structural Safety, Vol. 67, pp. 85-95, 2017.
26. Keshtegar, B., “Limited Conjugate Gradient Method for Structural Reliability Analysis”, Engineering with Computers, Vol. 33, No. 3, pp. 621-629, 2017.
27. Zhu, Z, and Du, X., “Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions”, Journal of Mechanical Design, Vol. 138, No. 12, pp. 11-22.
28. Keshtegar, B., and Kisi, O.,“M5 Model Tree and Monte Carlo Simulation for Efficient Structural Reliability Analysis”, Applied Mathematical Modelling, Vol. 48, pp. 899-910, 2017.
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