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A Polynomial Chaos Expansion Trust Region Method for Robust Optimization

Published online by Cambridge University Press:  03 June 2015

Samih Zein
Samih Zein*
Affiliation:
Samtech H.Q., 8 rue des chasseurs ardennais Angleur, Belgium
*
*Corresponding author.Email:samih.zein@lmsintl.com
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Abstract

Robust optimization is an approach for the design of a mechanical structure which takes into account the uncertainties of the design variables. It requires at each iteration the evaluation of some robust measures of the objective function and the constraints. In a previous work, the authors have proposed a method which efficiently generates a design of experiments with respect to the design variable uncertainties to compute the robust measures using the polynomial chaos expansion. This paper extends the proposed method to the case of the robust optimization. The generated design of experiments is used to build a surrogate model for the robust measures over a certain trust region. This leads to a trust region optimization method which only requires one evaluation of the design of experiments per iteration (single loop method). Unlike other single loop methods which are only based on a first order approximation of robust measure of the constraints and which does not handle a robust measure for the objective function, the proposed method can handle any approximation order and any choice for the robust measures. Some numerical experiments based on finite element functions are performed to show the efficiency of the method.

Keywords

60H1565K0562K2062K05Reliability based design optimizationpolynomial chaos expansiontrust region method

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 2 , August 2013 , pp. 412 - 424
Copyright
Copyright © Global Science Press Limited 2013

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