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Research Papers

Design Under Uncertainty: Balancing Expected Performance and Risk

[+] Author and Article Information
James A. Reneke

Department of Mathematical Sciences, Clemson University, Clemson, SC 29634reneke@clemson.edu

Margaret M. Wiecek

Department of Mathematical Sciences, Clemson University, Clemson, SC 29634wmalgor@clemson.edu

Georges M. Fadel

Department of Mechanical Engineering, Clemson University, Clemson, SC 29634geroges@clemson.edu

Sundeep Samson

Department of Mathematical Sciences, and Department of Mechanical Engineering, Clemson University, Clemson, SC 29634sundees@clemson.edu

Dimitri Nowak

Department of Mathematical Sciences, Clemson University, Clemson, SC 29634dimitrn@clemson.edu

J. Mech. Des 132(11), 111009 (Nov 15, 2010) (9 pages) doi:10.1115/1.4002836 History: Received May 23, 2009; Revised October 18, 2010; Published November 15, 2010; Online November 15, 2010

The problem of quantifying uncertainty in the design process is approached indirectly. Nonquantifiable variability resulting from lack of knowledge is treated as epistemic uncertainty and quantifiable variability caused by random influences is treated as aleatory uncertainty. The emphasis in this approach is on the effects of epistemic uncertainty, left unquantified, on design performance. Performance is treated as a random function of the epistemic uncertainties that are considered as independent variables, and a design decision is based on the mean and variance of design performance. Since the mean and variance are functions of the uncertainties, multicriteria decision methods are employed to determine the preferred design. The methodology is illustrated on a three-spring model with stochastic forcing and two uncertain damping coefficients. Based on the example, the concept of balancing expected performance and risk is explored in an engineering context. Risk is quantified using aleatory uncertainty for fixed values of epistemic uncertainty. The study shows the unique features of this approach in which risk-based design decisions are made under both aleatory and epistemic uncertainties without assuming a distribution for epistemic uncertainty.

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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Design
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Figures

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Figure 1

Three-spring system

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Figure 2

Simulation for the same designs (m1=m2=1.5) with two different uncertainty pairs: left (b1,b2)=(1.5,1.5); right (b1,b2)=(4.0,0.25). Initial conditions for displacement and velocity are y1(0)=−1, y2(0)=1, and y1′(0)=y2′(0)=0, respectively.

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Figure 3

Simulation for the same designs (m1=m2=1.5) with two different uncertainty pairs: left: (b1,b2)=(1.5,1.5); right: (b1,b2)=(4.0,0.25)

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Figure 4

Performance surfaces for the feasible designs. The two lowest surfaces represent the performances of design 4 (very dark gray) and design 5 (black).

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Figure 5

Expected performance surfaces μ¯i(b1,b2) (left) and variance surfaces σ¯i2(b1,b2) (right) for design 4 (light gray) and design 5 (dark gray)

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Figure 6

Decision surrogate surfaces μi(b1k,b2ℓ)+ασi(b1k,b2ℓ),k=1,…,m and ℓ=1,…,n for designs 4 (gray) and 5 (black)

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Figure 7

Histogram of a sample distribution of R¯(b1i,b2j,b1k,b2ℓ)

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