Optimal Design with Probabilistic Objective and Constraints
Publication: Journal of Engineering Mechanics
Volume 132, Issue 1
Abstract
Significant challenges are associated with solving optimal structural design problems involving the failure probability in the objective and constraint functions. In this paper, we develop gradient-based optimization algorithms for estimating the solution of three classes of such problems in the case of continuous design variables. Our approach is based on a sequence of approximating design problems, which is constructed and then solved by a semiinfinite optimization algorithm. The construction consists of two steps: First, the failure probability terms in the objective function are replaced by auxiliary variables resulting in a simplified objective function. The auxiliary variables are determined automatically by the optimization algorithm. Second, the failure probability constraints are replaced by a parametrized first-order approximation. The parameter values are determined in an adaptive manner based on separate estimations of the failure probability. Any computational reliability method, including first-order reliability and second-order reliability methods and Monte Carlo simulation, can be used for this purpose. After repeatedly solving the approximating problem, an approximate solution of the original design problem is found, which satisfies the failure probability constraints at a precision level corresponding to the selected reliability method. The approach is illustrated by a series of examples involving optimal design and maintenance planning of a reinforced concrete bridge girder.
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Acknowledgments
Financial support from the Taisei Chair in Civil Engineering at the University of California Berkeley, the National Science Foundation under Grant No. NSFECS-9900985, and the University of California Berkeley Space Sciences Laboratory and Lockheed Martin Advanced Technology Center Mini-Grant Program is acknowledged. The writers thank doctoral student Morteza Mahyari for assistance in computing the examples.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 1 • January 2006
Pages: 107 - 118
Copyright
© 2006 ASCE.
History
Received: Jun 17, 2003
Accepted: Apr 14, 2005
Published online: Jan 1, 2006
Published in print: Jan 2006
Notes
Note. Associate Editor: Gerhart I. Schueller
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