A Comparative Study of Metaheuristic Algorithms for Reliability-Based Design Optimization Problems

2020 ◽  
Author(s):  
Zeng Meng ◽  
Gang Li ◽  
Xuan Wang ◽  
Sadiq M. Sait ◽  
Ali Rıza Yıldız
Keyword(s):  
Comparative Study ◽  
Design Optimization ◽  
Optimization Problems ◽  
Metaheuristic Algorithms ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

Reliability-based design optimization for vertical vibrations of a modified electric vehicle using fourth-moment polynomial standard transformation method

2020 ◽  
Vol 234 (10-11) ◽  
pp. 2649-2664
Author(s):  
Sheng Wang ◽  
Lin Hua ◽  
Xinghui Han ◽  
Zhuoyu Su
Keyword(s):  
Design Optimization ◽  
Electric Vehicle ◽  
Optimization Problems ◽  
Computing Time ◽  
Optimization Procedure ◽  
Transformation Method ◽  
Vertical Vibration ◽  
Fourth Moment ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

This article presents a new reliability-based design optimization procedure for the vertical vibration issues raised by a modified electric vehicle using fourth-moment polynomial standard transformation method. First, the fourth-moment polynomial standard transformation method with polynomial chaos expansion is used to obtain the reliability index of uncertain constraints in the reliability-based design optimization which is highly precise and saves computing time compared with other common methods. Next, the half-car model with nonlinear suspension parameters for the modified electric vehicle is investigated, and the response surface methodology is adopted to approximate the complex and time-consuming vertical vibration calculation to the polynomial expressions, and the approximation is validated for reliability-based design optimization results within permissible error level. Then, reliability-based design optimization results under both deterministic and uncertain load parameters are shown and analyzed. Unlike the traditional vertical vibration optimization that only considers one or several sets of load parameters, which lacks versatility, this article presents the reliability-based design optimization with uncertain load parameters which is more suitable for engineering. The results show that the proposed reliability-based design optimization procedure is an effective and efficient way to solve vertical vibration optimization problems for the modified electric vehicle, and the optimization statistics, including the maximum probability interval, can provide references for other suspension dynamical optimization.

scholarly journals Reliability-Based Design Optimization of Structures Using Complex-Step Approximation with Sensitivity Analysis

2021 ◽  
Vol 11 (10) ◽  
pp. 4708
Author(s):  
Junho Chun
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Design Optimization ◽  
Optimization Problems ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Step Size ◽  
First Derivative ◽  
Step Approximation ◽  
Reliability Based Design

Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.

A Hybrid Reliability Approach for Reliability-Based Design Optimization

2010 ◽  
Author(s):  
Po Ting Lin ◽  
Yogesh Jaluria ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Performance Measure ◽  
Accurate Solution ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Index Approach ◽  
Hybrid Reliability

Reliability-based Design Optimization problems have been solved by two well-known methods: Reliability Index Approach (RIA) and Performance Measure Approach (PMA). RIA generates first-order approximate probabilistic constraints using the measures of reliability indices. For infeasible design points, the traditional RIA method suffers from inaccurate evaluation of the reliability index. To overcome this problem, the Modified Reliability Index Approach (MRIA) has been proposed. The MRIA provides the accurate solution of the reliability index but also inherits some inefficiency characteristics from the Most Probable Failure Point (MPFP) search when nonlinear constraints are involved. In this paper, the benchmark examples have been utilized to examine the efficiency and stability of both PMA and MRIA. In our study, we found that the MRIA is capable of obtaining the correct optimal solutions regardless of the locations of design points but the PMA is much efficient in the inverse reliability analysis. To take advantages of the strengths of both methods, a Hybrid Reliability Approach (HRA) is proposed. The HRA uses a selection factor that can determine which method to use during optimization iterations. Numerical examples from the proposed method are presented and compared with the MRIA and the PMA.

scholarly journals Set Theoretical Variants of Optimization Algorithms for System Reliability-based Design of Truss Structures

2021 ◽  
Author(s):  
Ali Kaveh ◽  
Kiarash Biabani Hamedani ◽  
Mohammad Kamalinejad
Keyword(s):  
Design Optimization ◽  
System Reliability ◽  
Failure Modes ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
System Level ◽  
Truss Structures ◽  
Jaya Algorithm ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

In this paper, recently developed set theoretical variants of the teaching-learning-based optimization (TLBO) algorithm and the shuffled shepherd optimization algorithm (SSOA) are employed for system reliability-based design optimization (SRBDO) of truss structures. The set theoretical variants are designed based on a simple framework in which the population of candidate solutions is divided into some number of smaller well-arranged sub-populations. In addition, the framework is applied to the Jaya algorithm, leading to a set-theoretical variant of the Jaya algorithm. So far, most of the reliability-based design optimization studies have focused on the reliability of single structural members. This is due to the fact that the optimization problems with system reliability-based constraints are computationally expensive to solve. This is especially the case of statically redundant structures, where the number of failure modes is so high that it is impractical to identify all of them. System-level reliability analysis of truss structures is carried out by the branch and bound method by which the stochastically dominant failure paths are identified within a reasonable time. At last, three numerical examples, including size optimization of truss structures, are presented to illustrate the effectiveness of the proposed SRBDO approach. The results indicate the efficiency and applicability of the set theoretical optimization algorithms to solve the SRBDO problems of truss structures.

β-Pareto Set Prediction for Bi-Objective Reliability-Based Design Optimization

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Dong-Shin Lin ◽  
Chun-Min Ho ◽  
Kuei-Yuan Chan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Early Stage ◽  
Nonlinear Problems ◽  
Pareto Set ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Objective Space ◽  
Product Design Process ◽  
Linear Programming Problems

In this research, we investigate design optimization under uncertainties for problems with two objectives. Reliability-based design optimization (RBDO) that considers uncertainties as random variables and/or parameters and formulates constraints probabilistically has received extensive attention. However, research to date has focused primarily on single-objective problems only. We extend RBDO to problems for which multiple objectives are optimized simultaneously. Each constraint reliability value results in a Pareto set. The set of all Pareto frontiers at the various reliability values is denoted as the β-Pareto set. We study the relations between the deterministic Pareto set and the β-Pareto set and then develop a method to systematically determine the exact β-Pareto set of bi-objective linear programming problems. The method is also extended to predict the β-Pareto set of nonlinear problems using the sandwich technique. As a result, we are able to accurately predict the β-Pareto set in the objective space without solving multiple multi-objective optimization problems at various reliability levels. In the early stage of the product design process, the proposed approach can help decision-makers efficiently to determine how product performance varies with reliability level.

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