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RESEARCH PAPERS

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

[+] Author and Article Information
Kuei-Yuan Chan

Department of Mechanical Engineering, University of Michigan, G.G. Brown Bldg., Ann Arbor, MI 48109chanky@umich.edu

Steven Skerlos

Department of Mechanical Engineering, University of Michigan, G.G. Brown Bldg., Ann Arbor, MI 48109skerlos@umich.edu

Panos Y. Papalambros

Department of Mechanical Engineering, University of Michigan, G.G. Brown Bldg., Ann Arbor, MI 48109pyp@umich.edu

J. Mech. Des 128(4), 893-900 (Jan 05, 2006) (8 pages) doi:10.1115/1.2202887 History: Received September 15, 2005; Revised January 05, 2006

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Extended active set concept

Grahic Jump Location
Figure 2

Extended active set approximation

Grahic Jump Location
Figure 3

Active set strategy for SLP (15) with added step in active sets update

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