关键词: 可靠性, 马尔可夫链, 重要性抽样, 核密度估计, 蒙特卡罗模拟

Abstract: In the engineering practice of system reliability analysis, the strong nonlinearity of the limit state function is likely to cause large calculation error of the system failure probability and low efficiency. To solve the problems above, the Tree Markov Chain (TMC) algorithm and the system reliability analysis method based on TMC algorithm are proposed. The TMC is an improvement of the original Markov chain, and its state transition process is more flexible, with local multi-chain parallelism and adaptive exploration of the boundary of the failure domain. Applying multiple candidate states sampling, the TMC obtains as much additional failure domain information as possible, extracting the samples that fully reflect the failure distribution characteristics. The adaptive kernel density estimation of the sample is approximately optimal, improving the accuracy of the calculation results. At the end of the paper, two sets of numerical examples are used to verify the performance of the proposed algorithm. The calculation results show that the algorithm is not sensitive to the location of the design point and the sampling starting point. When dealing with strong nonlinear and complex series of system problems, the proposed method can get highly accurate calculation results with small sample size. When the sample size changes, the calculation result is relatively stable and reliable. The efficiency of the proposed method under practical problems is calculated in engineering examples, demonstrating its engineering application value.

Key words: reliability, Markov Chain, importance sampling, kernel density estimation, Monte Carlo simulation