可靠性全局灵敏度求解的Meta-IS-AK算法

Global Reliability Sensitivity (GRS) measures the average impact of input variable on the failure probability of a structural system, but there is still a lack of efficient algorithms with broad adaptability. For this issue, a new efficient algorithm is established based on meta-important sampling and the Bayesian algorithm of GRS. The proposed algorithm firstly utilizes the existing Bayesian method to convert the GRS into a form expressed by the unconditional failure probability and the conditional Probability Density Function (PDF) of the input variable on failure domains, and then the algorithm is organized in three steps. The first step is to extract the importance samples of the failure domain by using the iteration strategy of meta-important sampling. The second step is to embed the adaptive Kriging model in the existing meta-important sampling method to efficiently estimate the unconditional failure probability. The third step is to use the Metropolis-Hastings criterion to convert the importance samples in the failure domains into the samples of the original density function in the failure domains and simultaneously obtain the conditional PDF of each input variable on the failure domain, and finally the GRS can be obtained. As the proposed algorithm makes full use of the dimensional independence of the existing Bayesian algorithm of GRS, the adaptability of the meta-important sampling method and the efficiency of the embedded Kriging model, the proposed algorithm has wide adaptability and high efficiency. The above conclusions are verified by the results of the examples.