A Unified Framework for Integrated Optimization Under Uncertainty

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Zhonglai Wang ◽  
Hong-Zhong Huang ◽  
Yu Liu
Keyword(s):  
Objective Function ◽  
Robust Design ◽  
Taylor Series Expansion ◽  
Assessment Method ◽  
Optimization Under Uncertainty ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Design Stage ◽  
Unified Framework ◽  
Reliability Based Design

Reliability and robustness are two main attributes of design under uncertainty. Hence, it is necessary to combine reliability-based design and robust design at the design stage. In this paper, a unified framework for integrating reliability-based design and robust design is proposed. In the proposed framework, the probabilistic objective function is converted to a deterministic objective function by the Taylor series expansion or inverse reliability strategy with accounting for the probabilistic characteristic of the objective function. Therefore, with this unified framework, there is no need to deal with a multiobjective optimization problem to integrate reliability-based design and robust design any more. The probabilistic constraints are converted to deterministic constraints with inverse reliability strategy at the same time. In order to solve the unified framework, an improved sequential optimization and reliability assessment method is proposed. Three examples are given to illustrate the benefits of the proposed methods.

A Unified Optimization Design Model Under Uncertainty

2009 ◽  
Author(s):  
Zhonglai Wang ◽  
Hong-Zhong Huang ◽  
Huanwei Xu ◽  
Xiaoling Zhang
Keyword(s):  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Problem ◽  
Sequential Optimization ◽  
Multi Objective Optimization ◽  
Probabilistic Characteristic ◽  
Unified Framework ◽  
Reliability Based Design ◽  
Practical Engineering

It is necessary to combine reliability-based design and robust design in the practical engineering. In this paper, a unified framework for integrated reliability-based design and robust design is proposed. In the proposed framework, traditional multi-objective optimization problem is converted to a single objective optimization problem to integrate reliability-based design and robust design without weight factors. The conversion from probabilistic objective function to deterministic objective function is achieved by inverse reliability strategy under the consideration of the probabilistic characteristic of the objective function. After that, an improved sequential optimization and reliability assessment (SORA) method is proposed to deal with the unified framework. Overall, two examples are implemented to illustrate the benefits of the proposed methods.

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

2002 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Optimization Design ◽  
Reliability Assessment ◽  
Assessment Method ◽  
Side Impact ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Probabilistic Design ◽  
Probabilistic Optimization ◽  
Reliability Based Design

Probabilistic optimization design offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. In a probabilistic design, such as reliability-based design and robust design, the design feasibility is formulated probabilistically such that the probability of the constraint satisfaction (reliability) exceeds the desired limit. The reliability assessment for probabilistic constraints often involves an iterative procedure; therefore, two loops are involved in a probabilistic optimization. Due to the double-loop procedure, the computational demand is extremely high. To improve the efficiency of a probabilistic design, a novel method – sequential optimization and reliability assessment (SORA) is developed in this paper. The SORA method employs a single-loop strategy where a serial of cycles of optimization and reliability assessment is employed. In each cycle optimization and reliability assessment are decoupled from each other; no reliability assessment is required within optimization and the reliability assessment is only conducted after the optimization. The key concept of the proposed method is to shift the boundaries of violated deterministic constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. Hence the design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.

An Efficient Approach for Reliability-Based Design Optimization Combined Sequential Optimization with Approximate Models

2018 ◽  
Vol 15 (04) ◽  
pp. 1850018 ◽  
Author(s):  
Bao Quoc Doan ◽  
Guiping Liu ◽  
Can Xu ◽  
Minh Quang Chau
Keyword(s):  
Design Optimization ◽  
Reliability Assessment ◽  
Latin Hypercube Sampling ◽  
Assessment Method ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Efficient Approach ◽  
Reliability Based Design ◽  
Approximate Models

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints which can be time-consuming in engineering structural design problems. In this paper, an efficient approach combined sequential optimization with approximate models is suggested for RBDO. The radial basis functions and Latin hypercube sampling are used to construct approximate models of the probabilistic constraints. Then, a sequential optimization with approximate models is carried out by the sequential optimization and reliability assessment method which includes a serial of cycles of deterministic optimization and reliability assessment. Three numerical examples are presented to demonstrate the efficiency of the proposed approach.

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

2004 ◽  
Vol 126 (2) ◽  
pp. 225-233 ◽  
Author(s):  
Xiaoping Du ◽  
Wei Chen
Keyword(s):  
Robust Design ◽  
Reliability Assessment ◽  
Simulation Models ◽  
Assessment Method ◽  
Side Impact ◽  
Sequential Optimization ◽  
Probabilistic Design ◽  
Deterministic Optimization ◽  
Probabilistic Optimization ◽  
Reliability Based Design

Probabilistic design, such as reliability-based design and robust design, offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. Since a probabilistic optimization often involves a double-loop procedure for the overall optimization and iterative probabilistic assessment, the computational demand is extremely high. In this paper, the sequential optimization and reliability assessment (SORA) is developed to improve the efficiency of probabilistic optimization. The SORA method employs a single-loop strategy with a serial of cycles of deterministic optimization and reliability assessment. In each cycle, optimization and reliability assessment are decoupled from each other; the reliability assessment is only conducted after the deterministic optimization to verify constraint feasibility under uncertainty. The key to the proposed method is to shift the boundaries of violated constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. The design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.

Reliability-Based Design Optimization Using Step Length Adjustment Algorithm and Sequential Optimization and Reliability Assessment Method

2019 ◽  
Vol 16 (07) ◽  
pp. 1850109 ◽  
Author(s):  
Ping Yi ◽  
Dongchi Xie ◽  
Zuo Zhu
Keyword(s):  
Design Optimization ◽  
Reliability Assessment ◽  
Step Length ◽  
Assessment Method ◽  
Sequential Optimization ◽  
Target Point ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Inverse Reliability Analysis ◽  
Minimum Performance Target Point

A step length adjustment (SLA) iterative algorithm was proposed for locating the minimum performance target point (MPTP) in the inverse reliability analysis. This paper elaborates SLA and two deliberately designed numerical examples are used to compare SLA with other algorithms appearing in recent literatures for locating MPTP. The results show that SLA is much more robust and efficient. Then SLA and sequential optimization and reliability assessment (SORA) are combined to solve reliability-based design optimization (RBDO) problems. In the reliability assessment of SORA, with the design obtained from the previous cycle, SLA is used to locate MPTP. Then in the deterministic optimization, the boundaries of violated constraints are shifted to the feasible direction according to the MPTP obtained in the reliability assessment. Several examples frequently cited in similar studies are used to compare SORA-SLA with other RBDO algorithms. The results indicate the effectiveness and robustness of SORA-SLA.

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.

A Quantile-Based SORA Method Using Maximum Entropy Method With Fractional Moments

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Wanxin He ◽  
Hua Yang ◽  
Gang Zhao ◽  
Yan Zeng ◽  
Gang Li
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Assessment Method ◽  
Entropy Method ◽  
Sequential Optimization ◽  
Target Point ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Fractional Moments ◽  
Minimum Performance Target Point

Abstract Reliability-based design optimization (RBDO) is receiving more attention from researchers because it can help to minimize cost reasonably in practical engineering. A large number of methods have been proposed to solve RBDO problems, most of which are based on the theory of the first-order reliability method (FORM). Therefore, the deficiencies of the FORM limit applications of general RBDO methods such as the dependency on the minimum performance target point (MPTP). In this study, we apply the fractional moment-based maximum entropy method to the RBDO problems for the first time and propose a novel RBDO method using the quantile-based sequential optimization and reliability assessment method. Because the proposed method is MPTP free, the shortcomings of FORM-based RBDO methods can be overcome. To demonstrate the performance of the proposed method, we test five numerical examples and one engineering example by the proposed method and three popular RBDO methods. The results show that the proposed method can balance the accuracy and the efficiency compared with other methods.

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