A Saddlepoint Approximation Based Simulation Method for Uncertainty Analysis

Uncertainty analysis, which assesses the impact of the uncertainty of input random variables on performance functions, is an important and indispensable component in engineering design under uncertainty. In this paper, a simulation method based on the Saddlepoint Approximation (SPA) is proposed to estimate accurately and efficiently the distribution of a response variable. The proposed method combines both simulation and analytical techniques and involves three main steps: (1) sampling on input random variables, (2) approximating the cumulant generating function (cgf) of the response variable with its first four cumulants and (3) estimating the cumulant distribution function (cdf) and probability density function (pdf) of the response variable using the SPA. This method provides more computationally efficient solutions than the general Monte Carlo Simulation (MCS) while maintaining high accuracy. The effectiveness of the proposed method is illustrated with a mathematical example and two engineering analysis problems.

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