Reliability‐based design optimization with equality constraints

Abstract

SUMMARYEquality 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.

Efficient strategies for reliability‐based design optimisation of a superconducting magnetic energy storage system‐based on reliability index approach

“…3. Such a double-loop optimisation structure inherently demands very high computational cost because the sub-optimisation problem of (5) has to be solved for each probabilistic constraint function given at every design point [11][12][13][14][15].…”

Lifetime cost optimization with time-dependent reliability

“…One is the reliability analysis (Rackwitz 2001;Du and Sudjianto 2004;Mahadevan and Smith 2006;Guo and Du 2010) where the reliability is predicted, and the other is reliability-based design optimization (RBDO) (Du, Sudjianto, and Huang 2005;Du and Huang 2007;Du 2008;Du, Guo, and Beeram 2008) where the reliability target is achieved by selecting appropriate design variables. For a given design, to evaluate whether its reliability is satisfactory, reliability analysis needs to be performed to obtain the reliability prediction.…”

“…Many physics-based reliability methodologies have been developed in recent decades (Huang, Chan, and Lou 2012;Hurtado and Alvarez 2012;Jensen, Kusanovic, and Valdebenito 2012;Kang et al 2012;Sanchez-Silva, Klutke, and Rosowsky 2012). Design optimization with physics-based reliability (Du, Sudjianto, and Huang 2005;Du and Huang 2007;Du 2008;Du, Guo, and Beeram 2008) has been applied in various engineering fields to ensure that a design meets a specified reliability requirement.The major drawback of traditional physics-based RBDO (Du, Sudjianto, and Huang 2005;Du and Huang 2007;Du 2008;Du, Guo, and Beeram 2008) is that in many applications the reliability is a constant with respect to time. The reason is that the limit-state functions are time independent, e.g.…”

“…The major drawback of traditional physics-based RBDO (Du, Sudjianto, and Huang 2005;Du and Huang 2007;Du 2008;Du, Guo, and Beeram 2008) is that in many applications the reliability is a constant with respect to time. The reason is that the limit-state functions are time independent, e.g.…”

An incremental shifting vector approach for reliability-based design optimization

“…The second category is decoupling methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. The basic idea of this type of method is to decouple the nested optimization in RBDO into a series of iterative processes that are composed of deterministic design optimization and reliability analysis; the design optimization and reliability analysis are completed alternately and converge to the optimal solution.…”