NDLI: An efficient method of solving design optimization problems with arbitrary random distributions in gradient-based design spaces

Content Provider	Springer Nature Link
Author	Lin, Po Ting
Copyright Year	2016
Abstract	Reliability-Based Design Optimization (RBDO) algorithms, such as Reliability Index Approach (RIA) and Performance Measure Approach (PMA), have been developed to solve engineering optimization problems under design uncertainties. In some existing methods, the random design space is transformed to standard normal design space and the reliability assessment, such as reliability index from RIA or performance measure from PMA, is estimated in order to evaluate the failure probability. When the random variable is arbitrarily distributed and cannot be properly fitted to any known form of probability density function, the existing RBDO methods cannot perform reliability analysis in the original design space. This paper proposes a novel Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) to evaluate the failure probability of any arbitrarily distributed random variables in the original design space. The arbitrary distribution of the random variable is approximated by a merger of multiple Gaussian kernel functions in a single-variate coordinate that is directed toward the gradient of the constraint function. The failure probability is then estimated using the ensemble of each kernel reliability analysis. This paper further derives a linearly approximated probabilistic constraint at the design point with allowable reliability level in the original design space using the aforementioned fundamentals and techniques. Numerical examples with generated random distributions show that existing RBDO algorithms can improperly approximate the uncertainties as Gaussian distributions and provide solutions with poor assessments of reliabilities. On the other hand, the numerical results show EGTRA is capable of efficiently solving the RBDO problems with arbitrarily distributed uncertainties.
Starting Page	1653
Ending Page	1670
Page Count	18
File Format	PDF
ISSN	1615147X
Journal	Structural and Multidisciplinary Optimization
Volume Number	54
Issue Number	6
e-ISSN	16151488
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-07-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Reliability-Based Design Optimization (RBDO) Arbitrarily distributed uncertainties Gradient-based transformation Gaussian kernel density estimation Theoretical and Applied Mechanics Computational Mathematics and Numerical Analysis Engineering Design
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Computer Graphics and Computer-Aided Design Control and Systems Engineering Computer Science Applications Software

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