A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Yuanfu Tang ◽  
Jianqiao Chen ◽  
Junhong Wei
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Epistemic Uncertainty ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Sequential Algorithm ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Design Variables ◽  
Novel Concept

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

The Performance Moment Integration Method for Reliability-Based Robust Design Optimization

2004 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Product Quality ◽  
Robust Design ◽  
Mean Value ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Integration Scheme ◽  
Quality Loss ◽  
Reliability Based Design ◽  
Different Types

Reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability-based design and robust design. A reliability-based design optimization deals with the probability of failure, while a robust design optimization minimizes the product quality loss. In general, the product quality loss is described by using the first two statistical moments: mean and standard deviation. In this paper, a performance moment integration (PMI) method is proposed by using numerical integration scheme for output response to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the performance measure approach (PMA) and its numerical method, hybrid-mean value (HMV) method, are used. New formulations of reliability-based robust design optimization are presented for three different types of robust objectives, such as smaller-the-better, larger-the-better, and nominal-the-better types. Examples are used to demonstrate the effectiveness of reliability-based robust design optimization using the proposed PMI method for different types of robust objective.

scholarly journals Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shujuan Wang ◽  
Qiuyang Li ◽  
Gordon J. Savage
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Robust Design ◽  
Structural Reliability ◽  
Computational Cost ◽  
Optimization Process ◽  
Robust Design Optimization ◽  
Global Approximation ◽  
Design Variables ◽  
Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

A Sequential Algorithm for Possibility-Based Design Optimization

2006 ◽  
Author(s):  
Jun Zhou ◽  
Zissimos P. Mourelatos
Keyword(s):  
Design Optimization ◽  
Optimization Algorithm ◽  
Computational Cost ◽  
Possibility Theory ◽  
Sequential Optimization ◽  
Sequential Algorithm ◽  
Computationally Efficient ◽  
Worst Case ◽  
Reliability Based Design ◽  
Design Variables

Deterministic optimal designs that are obtained without taking into account uncertainty/variation are usually unreliable. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. After, the fundamentals of possibility theory and fuzzy measures are described, a double-loop, possibility-based design optimization algorithm is presented where all design constraints are expressed possibilistically. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. In order to reduce the high computational cost, a sequential algorithm for possibility-based design optimization is presented. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. Two examples demonstrate the accuracy and efficiency of the proposed sequential algorithm.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

2003 ◽  
Vol 125 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Charles D. McAllister ◽  
Timothy W. Simpson
Keyword(s):  
Internal Combustion Engine ◽  
Design Optimization ◽  
Robust Design ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Collaborative Optimization ◽  
Robust Design Optimization ◽  
Optimization Framework ◽  
Design Variables ◽  
Multiobjective Approach

In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed framework, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

2001 ◽  
Author(s):  
Charles D. McAllister ◽  
Timothy W. Simpson
Keyword(s):  
Internal Combustion Engine ◽  
Design Optimization ◽  
Robust Design ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Collaborative Optimization ◽  
Robust Design Optimization ◽  
Optimization Framework ◽  
Design Variables ◽  
Multiobjective Approach

Abstract In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed approach, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

Alternative Methods for Reliability-Based Robust Design Optimization Including Dimension Reduction Method

2006 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Reduction Method ◽  
Statistical Moments ◽  
Robust Design Optimization ◽  
Quality Loss ◽  
Dimension Reduction Method ◽  
Quality Loss Function ◽  
Performance Function ◽  
Design Variables

The objective of reliability-based robust design optimization (RBRDO) is to minimize the product quality loss function subject to probabilistic constraints. Since the quality loss function is usually expressed in terms of the first two statistical moments, mean and variance, many methods have been proposed to accurately and efficiently estimate the moments. Among the methods, the univariate dimension reduction method (DRM), performance moment integration (PMI), and percentile difference method (PDM) are recently proposed methods. In this paper, estimation of statistical moments and their sensitivities are carried out using DRM and compared with results obtained using PMI and PDM. In addition, PMI and DRM are also compared in terms of how accurately and efficiently they estimate the statistical moments and their sensitivities of a performance function. In this comparison, PDM is excluded since PDM could not even accurately estimate the statistical moments of the performance function. Also, robust design optimization using DRM is developed and then compared with the results of RBRDO using PMI and PDM. Several numerical examples are used for the two comparisons. The comparisons show that DRM is efficient when the number of design variables is small and PMI is efficient when the number of design variables is relatively large. For the inverse reliability analysis of reliability-based design, the enriched performance measure approach (PMA+) is used.

Time-Dependent Reliability-Based Robust Design Optimization via Extreme Value Moment Method

2018 ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Robust Design ◽  
Moment Method ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Integrated Framework ◽  
Multi Objective

During the product design and development stage, design engineers often encounter reliability and robustness of dynamic uncertain structures. Meanwhile, time-varying and high nonlinear performance are the basic characteristics of reliability analysis and design. Hence, the time-dependent reliability analysis and integrating reliability-based design with robust design become a primary challenge in reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The multi-objective integrated framework, which minimizes the mean value and coefficient of variation for the objective function at the same time subject to time-dependent probabilistic constraints, is first established. The time-dependent probabilistic constraints are then converted into deterministic constraints using a combination of moment method and the sparse grid based stochastic collocation method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

scholarly journals Robust Design Optimization with Penalty Function for Electric Oil Pumps with BLDC Motors

Energies ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 153 ◽  
Author(s):  
Keun-Young Yoon ◽  
Soo-Whang Baek
Keyword(s):  
Optimal Design ◽  
Design Optimization ◽  
Robust Design ◽  
Penalty Function ◽  
Block Diagram ◽  
Robust Design Optimization ◽  
Bldc Motor ◽  
Control Block ◽  
Element Analysis ◽  
Design Variables

In this paper, we propose and evaluate a robust design optimization (RDO) algorithm for the shape of a brushless DC (BLDC) motor used in an electric oil pump (EOP). The components of the EOP system and the control block diagram for driving the BLDC motor are described. Although the conventional deterministic design optimization (DDO) method derives an appropriate combination of design goals and target performance, DDO does not allow free searching of the entire design space because it is confined to preset experimental combinations of parameter levels. To solve this problem, we propose an efficient RDO method that improves the torque characteristics of BLDC motors by considering design variable uncertainties. The dimensions of the stator and the rotor were selected as the design variables for the optimal design and a penalty function was applied to address the disadvantages of the conventional Taguchi method. The optimal design results obtained through the proposed RDO algorithm were confirmed by finite element analysis, and the improvement in torque and output performance was confirmed through experimental dynamometer tests of a BLDC motor fabricated according to the optimization results.

Reliability-Based Robust Design Optimization in Consideration of Manufacturing Tolerance by Multi-Objective Evolutionary Optimization with Repair Algorithm

2021 ◽  
pp. 2150005
Author(s):  
Gang Li ◽  
Ye Liu ◽  
Gang Zhao ◽  
Yan Zeng
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Robust Design Optimization ◽  
Manufacturing Cost ◽  
Multi Objective Optimization ◽  
Random Design ◽  
Multi Objective ◽  
Design Variables ◽  
Objective Robustness ◽  
Repair Operator

There are inherently various uncertainties in practical engineering, and reliability-based design optimization (RBDO) and robust design optimization (RDO) are two well-established methodologies when considering the uncertainties. Naturally, reliability-based robust design optimization (RBRDO) is a methodology developed recently by combining RBDO and RDO, in which the tolerances of random design variables are always assumed as constants. However, the tolerance of random design variables is a key factor for the objective robustness and manufacturing cost, and the tolerance allocation is the core problem in mechanical manufacturing. Inspired by the cost–tolerance relationship in mechanical manufacturing, this paper presents an integrated framework to simultaneously find the optimal design variable and the corresponding tolerance in the multi-objective RBRDO, with the trade-off between objective robustness and manufacturing cost. The failure mechanism of the constraint handling strategy of the constrained reference vector-guided evolutionary algorithm (C-RVEA) is discussed to solve the multi-objective optimization formulation. Then the robust repair operator and reliability-based repair operator are proposed to transform unfeasible solutions to the feasible ones under reliability constraints. Numerical results reveal that the proposed repair algorithm is effective. By solving the integrated multi-objective optimization problem, the Pareto front with the compromised solutions between the objective robustness and manufacturing cost could be obtained, from which decision makers can select the satisfying solution conveniently according to the preferred requirements.

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