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research-article

Objective-Oriented Sequential Sampling for Simulation Based Robust Design Considering Multiple Sources of Uncertainty

[+] Author and Article Information
Paul D. Arendt

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Room B214, Evanston, IL 60208
e-mail: paularendt2012@u.northwestern.edu

Daniel W. Apley

Department of Industrial Engineering and Management Sciences,
Northwestern University,
2145 Sheridan Road,
Room C150, Evanston, IL 60208
e-mail: apley@northwestern.edu

Wei Chen

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Room A216, Evanston, IL 60208
e-mail: weichen@northwestern.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 11, 2012; final manuscript received February 24, 2013; published online April 23, 2013. Assoc. Editor: Michael Kokkolaras.

J. Mech. Des 135(5), 051005 (Apr 23, 2013) (10 pages) Paper No: MD-12-1307; doi: 10.1115/1.4023922 History: Received June 11, 2012; Revised February 24, 2013

Sequential sampling strategies have been developed for managing complexity when using computationally expensive computer simulations in engineering design. However, much of the literature has focused on objective-oriented sequential sampling methods for deterministic optimization. These methods cannot be directly applied to robust design, which must account for uncontrollable variations in certain input variables (i.e., noise variables). Obtaining a robust design that is insensitive to variations in the noise variables is more challenging. Even though methods exist for sequential sampling in design under uncertainty, the majority of the existing literature does not systematically take into account the interpolation uncertainty that results from limitations on the number of simulation runs, the effect of which is inherently more severe than in deterministic design. In this paper, we develop a systematic objective-oriented sequential sampling approach to robust design with consideration of both noise variable uncertainty and interpolation uncertainty. The method uses Gaussian processes to model the costly simulator and quantify the interpolation uncertainty within a robust design objective. We examine several criteria, including our own proposed criteria, for sampling the design and noise variables and provide insight into their performance behaviors. We show that for both of the examples considered in this paper the proposed sequential algorithm is more efficient in finding the robust design solution than a one-shot space filling design.

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Figures

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Fig. 1

Objective-oriented sequential sampling

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Fig. 2

(a) Response surface for y(d,w). (b) The robust design objective function for the open box example with d* = 1.34 m and f(d*) = $108.30.

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Fig. 3

Sequential sampling algorithm

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Fig. 4

The first iteration of the sequential sampling algorithm using the open box example

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Fig. 5

Sequential algorithm results for the open box example for (a) the location of dmin and fGW(dmin) and (b) the location of the sequentially added points (numbers indicate i) using the EI and MSE criteria

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Fig. 6

Convergence behavior for the engine piston design example. Note the error bars have been moved right slightly for improved visualization.

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