Research Papers: Design Automation

A Hierarchical Statistical Sensitivity Analysis Method for Complex Engineering Systems Design

[+] Author and Article Information
Xiaolei Yin

Department of Mechanical Engineering,  Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111

Wei Chen1

Department of Mechanical Engineering,  Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111weichen@northwestern.edu


Corresponding author.

J. Mech. Des 130(7), 071402 (May 19, 2008) (10 pages) doi:10.1115/1.2918913 History: Received June 17, 2007; Revised December 12, 2007; Published May 19, 2008

Statistical sensitivity analysis (SSA) is playing an increasingly important role in engineering design, especially with the consideration of uncertainty. However, it is not straightforward to apply SSA to the design of complex engineering systems due to both computational and organizational difficulties. In this paper, to facilitate the application of SSA to the design of complex systems especially those that follow hierarchical modeling structures, a hierarchical statistical sensitivity analysis (HSSA) method containing a top-down strategy for SSA and an aggregation approach to evaluating the global statistical sensitivity index (GSSI) is developed. The top-down strategy for HSSA is introduced to invoke the SSA of the critical submodels based on the significance of submodel performances. A simplified formulation of the GSSI is studied to represent the effect of a lower-level submodel input on a higher-level model response by aggregating the submodel SSA results across intermediate levels. A sufficient condition under which the simplified formulation provides an accurate solution is derived. To improve the accuracy of the GSSI formulation for a general situation, a modified formulation is proposed by including an adjustment coefficient (AC) to capture the impact of the nonlinearities of the upper-level models. To improve the efficiency, the same set of samples used in submodel SSAs is used to evaluate the AC. The proposed HSSA method is examined through mathematical examples and a three-level hierarchical model used in vehicle suspension systems design.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

A demonstrative example of a hierarchical model

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Figure 2

A generalized two-level hierarchical model

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Figure 3

Flowchart of the HSSA method

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Figure 4

Linear approximation of the global trend of the upper-level function based on samples in prior upper level SSA

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Figure 5

Comparison of GSSIs for main effects in Example 1

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Figure 6

Linear regression with the consideration of submodel performance. The linear regression at the prior stage is performed with a prior uniform distribution of the submodel performance Y. When the real distribution of Y (the bottom-right plot) is obtained, the linear regression is executed at the posterior stage (the top-right plot).

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Figure 7

Hierarchical enterprise-driven multilevel vehicle suspension model

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Figure 8

Comparison of the GSSI for main effects using the HSSA method and the AIO method. The GSSIs of dR and DF are assumed as zero since the rear coil spring model is considered as an insignificant model. The figure shows the GSSI of all model input variables with respect to their impact on the system response—profit.

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Figure 9

Distribution of the top level response “profit” with different amount of information available from lower levels



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