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Reliability-Based Design Optimization in X-Space Using Ensemble of Gaussian Reliability Analyses (EoGRA)

[+] Author Affiliations
Po Ting Lin, Shu-Ping Lin

Chung Yuan Christian University, Chungli, Taoyuan, Taiwan

Paper No. DETC2015-46130, pp. V02BT03A048; 13 pages
doi:10.1115/DETC2015-46130
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2B: 41st Design Automation Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5708-3
  • Copyright © 2015 by ASME

abstract

Reliability-Based Design Optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the Modified Reliability Index Approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the Performance Measure Approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. To this end, a new algorithm, Ensemble of Gaussian Reliability Analyses (EoGRA), was developed to estimate the failure probability using Gaussian-based Kernel Density Estimation (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations. Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The results showed EoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods.

Copyright © 2015 by ASME

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