Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty

[+] Author and Article Information
Wei Chen1

Integrated DEsign Automation Laboratory (IDEAL),  Northwestern University, Evanston, IL 60208-3111

Ruichen Jin

Ford Motor Company

Agus Sudjianto

Bank of America


Corresponding Author, weichen@northwestern.edu. Mechanical Engineering, Northwestern University, Evanston, IL 60208-3111, phone 847-491-17019, fax 847-491-3915.

J. Mech. Des 127(5), 875-886 (Dec 03, 2004) (12 pages) doi:10.1115/1.1904642 History: Received August 10, 2004; Revised December 03, 2004

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels. The approach is especially applicable to simulation-based design because metamodels are often created to replace expensive simulation programs, and therefore readily available to designers. In this work, we identify the needs of GSA in design under uncertainty, and then develop generalized analytical formulations that can provide GSA for a variety of metamodels commonly used in engineering applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results of univariate integrals can be constructed to calculate the multivariate integrals in GSA. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Main effects of illustrative example

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Figure 2

Interaction effects between two variables

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Figure 3

Sensitivity indices of 19 variables (D-design variable, N-noise variable)

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Figure 4

Subset contributions of noise, design variables, and interactions

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Figure 5

Main effects of variables (on rollover metric)

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Figure 6

Interaction between M123 and starṯbrake

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Figure 7

Interaction between M123 and enḏbrake



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