An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints

[+] Author and Article Information
Kuei-Yuan Chan

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwanchanky@mail.ncku.edu.tw

Steven J. Skerlos

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

Panos Papalambros

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

J. Mech. Des 129(2), 140-149 (Jan 23, 2006) (10 pages) doi:10.1115/1.2337312 History: Received June 20, 2005; Revised January 23, 2006

Optimal design problems with probabilistic constraints, often referred to as reliability-based design optimization problems, have been the subject of extensive recent studies. Solution methods to date have focused more on improving efficiency rather than accuracy and the global convergence behavior of the solution. A new strategy utilizing an adaptive sequential linear programming (SLP) algorithm is proposed as a promising approach to balance accuracy, efficiency, and convergence. The strategy transforms the nonlinear probabilistic constraints into equivalent deterministic ones using both first order and second order approximations, and applies a filter-based SLP algorithm to reach the optimum. Simple numerical examples show promise for increased accuracy without sacrificing efficiency.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Algorithm flow chart

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Figure 2

Small versus large input variation

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Figure 3

Example of Ej variations with respect to β and κ values

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Figure 4

Switch between FORM and SORM

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Figure 5

FORM/SORM switch at μXA

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Figure 6

FORM/SORM switch

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Figure 7

Non-dominated entries in the filter

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Figure 11

Example 4: Passive vehicle suspension




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