A hierarchical statistical sensitivity analysis method for complex engineering systems design

Xiaolei Yin, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 topdown 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.

Original languageEnglish (US)
Pages (from-to)714021-7140210
Number of pages6426190
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number7
StatePublished - Jul 2008


  • Aggregation of sensitivity index
  • Global statistical sensitivity index
  • Hierarchical modeling
  • Hierarchical system
  • Statistical sensitivity analysis
  • Top-down strategy

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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