An efficient method for analyzing local reliability sensitivity by moment method and extended failure probability

The moment method can effectively estimate the structure reliability and its local reliability sensitivity (LRS). But the existing moment method has two limitations. The first one is that error may exist in computing LRS due to the LRS is derived on the numerical approximation of failure probability (FP). The second one is the computational cost increases exponentially with the dimension of random input. To solve these limitations, a simple and efficient method for LRS is proposed in this paper. Firstly, the proposed method uses integral transformation to equivalently derive the LRS as the weighted sum of FP and several extended FPs, and these FPs have the same performance function but different probability density functions (PDFs), in which no assumption is introduced in case of normal input. Secondly, by taking advantage of the derived FPs with the same performance function and different PDFs, where these different PDFs have an explicit and specific relationship, a strategy of sharing integral nodes is dexterously designed on the multiplicative dimensional reduction procedure to simultaneously estimate the moments, which are required by estimating the FP and the extended FPs with moment-based method, of performance function with different PDFs. After the derived FPs are estimated by their corresponding moments, the LRS can be estimated as a byproduct. Compared with the existing moment method for LRS, the proposed method avoids its first limitation by equivalently deriving the LRS as a series of FPs without introducing error in case of normal input. Moreover, because of the designed strategy of sharing integral nodes, the computational cost of the proposed method increases linearly with the dimension of random input, which avoids the second limitation of the existing method for LRS. The superiority of the proposed method over the existing method is verified by numerical and engineering examples.