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Reliability-Based Design Optimization with Equality Constraints
International Journal for Numerical Methods in Engineering
  • Xiaoping Du, Missouri University of Science and Technology
  • Beiqing Huang
Equality constraints have been well studied and widely used in deterministic optimization, but they have rarely been addressed in reliability-based design optimization (RBDO). The inclusion of an equality constraint in RBDO results in dependency among random variables. Theoretically, one random variable can be substituted in terms of remaining random variables given an equality constraint; and the equality constraint can then be eliminated. However, in practice, eliminating an equality constraint may be difficult or impossible because of complexities such as coupling, recursion, high dimensionality, non-linearity, implicit formats, and high computational costs. The objective of this work is to develop a methodology to model equality constraints and a numerical procedure to solve a RBDO problem with equality constraints. Equality constraints are classified into demand-based type and physics-based type. A sequential optimization and reliability analysis strategy is used to solve RBDO with physics-based equality constraints. The first-order reliability method is employed for reliability analysis. The proposed method is illustrated by a mathematical example and a two-member frame design problem. Copyright © 2007 John Wiley & Sons, Ltd.
Mechanical and Aerospace Engineering
National Science Foundation (U.S.)
University of Missouri--Rolla. Intelligent Systems Center
Keywords and Phrases
  • Equality Constraints,
  • Optimization,
  • Probabilistic Constraints,
  • Reliability
Document Type
Article - Journal
Document Version
File Type
© 2007 John Wiley & Sons, All rights reserved.
Publication Date
Citation Information
Xiaoping Du and Beiqing Huang. "Reliability-Based Design Optimization with Equality Constraints" International Journal for Numerical Methods in Engineering (2007)
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