关键词: Esscher’s近似, 卷积理论, 可靠性, 快速概率积分, 累积生成函数, 灵敏度

Abstract: A simple and effective computational procedure is presented for computing probability of failure of mechanical and structural systems with linear limit state function by using convolution theorem, fast probability integration and Esscher’s approximation. An efficient and accurate mean-value first order Esscher’s approximation method(MVFOEA) is proposed by approximating a performance function with the first order Taylor expansion at the mean-value point of random input variables. By combining MVFOEA with sensitivity analysis technique, a new reliability sensitivity analysis method is proposed. Because of the use of complete distribution information, MVFOEA is generally more accurate than mean value first order second moment(MVFOSM). MVFOEA requires the basic random variables should be independent for each other and have moment generating functions. The features of the proposed method are demonstrated with three numerical examples

Key words: Convolution theorem, Cumulant generating function, Esscher’s approximation, Fast probability integration, Reliability, Sensitivity