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An efficient importance sampling algorithm is presented to analyze reliability of complex structural system with multiple failure modes and fuzzy-random uncertainties in basic variables and failure modes. In order to improve the sampling efficiency, the simulated annealing algorithm is adopted to optimize the density center of the importance sampling for each failure mode, and results that the more significant contribution the points make to fuzzy failure probability, the higher occurrence possibility the points are sampled. For the system with multiple fuzzy failure modes, a weighted and mixed importance sampling function is constructed. The contribution of each fuzzy failure mode to the system failure probability is represented by the appropriate factors, and the efficiency of sampling is improved furthermore. The variances and the coefficients of variation are derived for the failure probability estimations. Two examples are introduced to illustrate the rationality of the present method. Comparing with the direct Monte-Carlo method, the improved efficiency and the precision of the method are verified by the examples.
An efficient importance sampling algorithm is presented to analyze reliability of complex structural system with multiple failure modes and fuzzy-random uncertainties in basic variables and failure modes. In order to improve the sampling efficiency, the simulated annealing algorithm is adopted to optimize the density center of the importance sampling for each failure mode, and results that the more significant contribution the points make to fuzzy failure probability, the higher occurrence probability the points are sampled. . The contribution of each fuzzy failure mode to the system failure probability is represented by the appropriate factors, and the efficiency of sampling is improved more. The variances and the coefficients of variation are derived for the failure probability estimations. the rationality of the present me thod. Comparing with the direct Monte-Carlo method, the improved efficiency and the precision of the method are verified by the examples.