An integrated framework for optimization under uncertainty using inverse reliability strategy

Xiaoping Du, Agus Sudjianto, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticle

235 Scopus citations


In this work, we propose an integrated framework for optimization under uncertainty that can bring both the design objective robustness and the probabilistic design constraints into account. The fundamental development of this work is the employment of an inverse reliability strategy that uses percentile performance for assessing both the objective robustness and probabilistic constraints. The percentile formulation for objective robustness provides us an accurate evaluation of the variation of an objective performance and a probabilistic measurement of the robustness. We can obtain more reasonable compound noise combinations for a robust design objective compared to using the traditional approach proposed by Taguchi. The proposed formulation is very efficient to solve since it only needs to evaluate the constraint functions at the required reliability levels. The other major development of this work is a new search algorithm for the Most Probable Point of Inverse Reliability (MPPIR) that can be used to efficiently evaluate percentile performances for both robustness and reliability assessments. Multiple strategies are employed in the MPPIR search, including using the steepest ascent direction and an arc search. The algorithm is applicable to general non-concave and non-convex performance functions of random variables following any continuous distributions. The effectiveness of the MPPIR search algorithm is verified using example problems. Overall, an engineering example on integrated robust and reliability design of a vehicle combustion engine piston is used to illustrate the benefits of our proposed method.

Original languageEnglish (US)
Pages (from-to)562-570
Number of pages9
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number4
StatePublished - Jul 1 2004

ASJC Scopus subject areas

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

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