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Research Papers: Design Automation

An Approach to Identify Six Sigma Robust Solutions of Multi/Many-Objective Engineering Design Optimization Problems

[+] Author and Article Information
Tapabrata Ray

School of Engineering
and Information Technology,
University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: t.ray@adfa.edu.au

Md Asafuddoula

School of Engineering
and Information Technology,
University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: md.asaf@adfa.edu.au

Hemant Kumar Singh

School of Engineering
and Information Technology,
University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: h.singh@adfa.edu.au

Khairul Alam

School of Engineering
and Information Technology,
University of New South Wales,
Canberra, ACT 2600, Australia
e-mail: k.alam@adfa.edu.au

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received September 13, 2014; final manuscript received January 22, 2015; published online March 5, 2015. Assoc. Editor: Christopher Mattson.

J. Mech. Des 137(5), 051404 (May 01, 2015) (14 pages) Paper No: MD-14-1566; doi: 10.1115/1.4029704 History: Received September 13, 2014; Revised January 22, 2015; Online March 05, 2015

In order to be practical, solutions of engineering design optimization problems must be robust, i.e., competent and reliable in the face of uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this study focuses on problems where uncertainties emanate from the design variables. While approaches to identify robust optimal solutions of single and multi-objective optimization problems have been proposed in the past, we introduce a practical approach that is capable of solving robust optimization problems involving many objectives building on authors’ previous work. Two formulations of robustness have been considered in this paper, (a) feasibility robustness (FR), i.e., robustness against design failure and (b) feasibility and performance robustness (FPR), i.e., robustness against design failure and variation in performance. In order to solve such formulations, a decomposition based evolutionary algorithm (DBEA) relying on a generational model is proposed in this study. The algorithm is capable of identifying a set of uniformly distributed nondominated solutions with different sigma levels (feasibility and performance) simultaneously in a single run. Computational benefits offered by using polynomial chaos (PC) in conjunction with Latin hypercube sampling (LHS) for estimating expected mean and variance of the objective/constraint functions has also been studied in this paper. Last, the idea of redesign for robustness has been explored, wherein selective component(s) of an existing design are altered to improve its robustness. The performance of the strategies have been illustrated using two practical design optimization problems, namely, vehicle crash-worthiness optimization problem (VCOP) and a general aviation aircraft (GAA) product family design problem.

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Figures

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Fig. 1

Design variables for VCOP

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Fig. 2

Nondominated solutions obtained for VCOP (median run) using DF

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Fig. 3

Nondominated solutions obtained for VCOP (median run) using FR formulation

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Fig. 4

Nondominated solutions obtained for VCOP (median run) using FPR formulation

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Fig. 5

Sigmag and Sigmaf obtained from median run of DBEA-rg using FPR for VCOP

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Fig. 6

Obtained robust nondominated fronts for VCOP using FPR for redesign cases 1, 2, 3 for a median run

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Fig. 7

Sigmaf and Sigmag for obtained robust nondominated fronts for VCOP using FPR for redesign cases 1, 2, 3 for a median run

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Fig. 8

Nondominated solutions from median run of DBEA-rg using DF for GAA

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Fig. 9

Nondominated solutions from median run of DBEA-rg using FR for GAA

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Fig. 10

Nondominated solutions from median run of DBEA-rg using FPR for GAA

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Fig. 11

Sigmag and Sigmaf obtained from median run of DBEA-rg using FPR, Gaussian LHS with averaging, sample size 100

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