Reliability-based design optimization with equality constraints

2007 ◽  
Vol 72 (11) ◽  
pp. 1314-1331 ◽  
Author(s):  
Xiaoping Du ◽  
Beiqing Huang
Keyword(s):  
Design Optimization ◽  
Equality Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

Modified Reduced Gradient With Realizations Sorting for Hard Equality Constraints in Reliability-Based Design Optimization

2010 ◽  
Author(s):  
Chun-Min Ho ◽  
Kuei-Yuan Chan
Keyword(s):  
Design Optimization ◽  
Gradient Methods ◽  
Equality Constraints ◽  
Reliability Based Design Optimization ◽  
Reduced Gradient Method ◽  
Reliability Based Design ◽  
Reduced Gradient ◽  
Solution Efficiency ◽  
Inverse Functions ◽  
Reduced Gradient Methods

In this work, the presence of equality constraints in reliability-based design optimization (RBDO) problems is studied. Relaxation of soft equality constraints in RBDO and its challenges are briefly discussed while the main focus is on hard equalities that can not be violated even under uncertainty. Direct elimination of hard equalities to reduce problem dimensions is usually suggested; however, for nonlinear or black-box functions, variable elimination requires expensive root-finding processes or inverse functions that are generally unavailable. We extend the reduced gradient methods in deterministic optimization to handle hard equalities in RBDO. The efficiency and accuracy of the first and the second order predictions in reduced gradient methods are compared. Results show the first order prediction being more efficient when realizations of random variables are available. A gradient-weighted sorting with these random samples is proposed to further improve the solution efficiency of the reduced gradient method. Feasible design realizations subject to hard equality constraints are then available to be implemented with the state-of-the-art sampling techniques for RBDO problems. Numerical and engineering examples show the strength and simplicity of the proposed method.

Modified Reduced Gradient With Realization Sorting for Hard Equality Constraints in Reliability-Based Design Optimization

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Chun-Min Ho ◽  
Kuei-Yuan Chan
Keyword(s):  
Design Optimization ◽  
Gradient Methods ◽  
Equality Constraints ◽  
Reliability Based Design Optimization ◽  
Reduced Gradient Method ◽  
Reliability Based Design ◽  
Reduced Gradient ◽  
Solution Efficiency ◽  
Inverse Functions ◽  
Reduced Gradient Methods

In this work, the presence of equality constraints in reliability-based design optimization (RBDO) problems is studied. Relaxation of soft equality constraints in RBDO and its challenges are briefly discussed, while the main focus is on hard equalities that cannot be violated even under uncertainty. Direct elimination of hard equalities to reduce problem dimensions is usually suggested; however, for nonlinear or black-box functions, variable elimination requires expensive root- finding processes or inverse functions that are generally unavailable. We extend the reduced gradient methods in deterministic optimization to handle hard equalities in RBDO. The efficiency and accuracy of the first- and second-order predictions in reduced gradient methods are compared. Results show that the first-order prediction is more efficient when realizations of random variables are available. Gradient-weighted sorting with these random samples is proposed to further improve the solution efficiency of the reduced gradient method. Feasible design realizations subject to hard equality constraints are then available to be implemented with state-of-the-art sampling techniques for RBDO problems. Numerical and engineering examples show the strength and simplicity of the proposed method.

An Approach for Uni-Level Reliability Based Design Optimization Using Cross-Entropy Method

2012 ◽  
Author(s):  
Pugazhendhi Kanakasabai ◽  
Anoop K. Dhingra
Keyword(s):  
Design Optimization ◽  
Equality Constraints ◽  
Problem Definition ◽  
Kkt Conditions ◽  
Cross Entropy ◽  
Reliability Based Design Optimization ◽  
Single Level ◽  
Reliability Based Design ◽  
Cross Entropy Method ◽  
Level Problem

In this paper a novel approach is proposed to solve the reliability based design optimization (RBDO) problem, which is translated into a single-level problem using Karush-Kuhn-Tucker (KKT) conditions. The transformation of a bi-level RBDO problem into a single-level problem using KKT conditions introduces several equality constraints in the single-level problem definition. Presence of multiple equality constraints poses numerical difficulty to the gradient based optimizers, hence a robust algorithm to solve the single-level RBDO problem is proposed in this paper using an alternative approach. The proposed approach uses an exterior penalty based cross-entropy (CE) method to solve the uni-level RBDO problem. This approach is shown to be robust in handling equality constraints. The three example problems solved in this paper also shows that the algorithm works well with different starting points used for the design variables.

Sign in / Sign up

Export Citation Format

Share Document