A Saddlepoint Approximation Based Simulation Method for Uncertainty Analysis

Abstract

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.

Department(s)

Mechanical and Aerospace Engineering

Sponsor(s)

National Science Foundation (U.S.)
University of Missouri--Rolla. Intelligent Systems Center

Keywords and Phrases

MCS; Monte Carlo Simulation; SPA; Cgf; Cumulant Generating Function; Engineering Analysis; Reliability Analysis; Saddlepoint Approximation; Uncertainty Analysis; Engineering design

International Standard Serial Number (ISSN)

1479-389X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Inderscience, All rights reserved.

Publication Date

01 Jan 2006

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