scholarly journals An Efficient Integrated Framework of Reliability-Based Robust Design Optimization for Computation-Intensive Structures

2021 ◽  
Author(s):  
xiongming lai ◽  
Ju Huang ◽  
Cheng Wang ◽  
Yong Zhang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Engineering Structures ◽  
Integrated Framework ◽  
Finite Element Software

Abstract When carrying out robust design optimization for complex engineering structures, they are computed by finite element software and are always computation-intensive. Aim at this problem, the paper proposes an efficient integrated framework of Reliability-based Robust Design Optimization (RBRDO). Firstly, the conventional RBRDO problem is changed as percentile form, that is, the improved percentile formulation of computing the objective robustness and probabilistic constraints is presented by resorting to the employment of Performance Measure Approach (PMA). Secondly, the above improved RBRDO problem is simplified by a series of new approximation methods due to the need of reducing computation. An efficient approximation method is proposed to estimate PMA functions of the RBRDO formulation. Based on it, the above improved RBRDO problem can be transformed into a sequence of approximate deterministic sub-optimization problems, whose objective function and constraints are expressed as the approximate explicit form only in relation to the design variables. Furthermore, use the trust region method to solve the above sequence of sub-optimization. Lastly, several examples are used to demonstrate the effectiveness and efficiency of the proposed method.

Time-Dependent Reliability-Based Robust Design Optimization Using Evolutionary Algorithm

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Shui Yu ◽  
Zhonglai Wang ◽  
Zhihua Wang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Dynamic Properties ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Multi Objective Optimization ◽  
Engineering Structures ◽  
Integrated Framework ◽  
Multi Objective

Due to the uncertain and dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. During the product design and development stages, designers often encounter reliability and robustness measures of dynamic uncertain structures. Time-varying and high nonlinear performance brings a new challenge for the 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 integrated framework is first established by minimizing the mean value and coefficient of variation of the objective performance at the same time subject to time-dependent probabilistic constraints. The time-dependent probabilistic constraints are then converted into deterministic constraints using the dimension reduction 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.

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.

Multi-objective approach for robust design optimization problems

2007 ◽  
Vol 15 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Igor N. Egorov ◽  
Gennadiy V. Kretinin ◽  
Igor A. Leshchenko ◽  
Sergey V. Kuptzov
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optimization Problems ◽  
Robust Design Optimization ◽  
Multi Objective

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 Robust Design Optimization and Emerging Technologies for Electrical Machines: Challenges and Open Problems

2020 ◽  
Vol 10 (19) ◽  
pp. 6653 ◽  
Author(s):  
Tamás Orosz ◽  
Anton Rassõlkin ◽  
Ants Kallaste ◽  
Pedro Arsénio ◽  
David Pánek ◽  
...  
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Emerging Technologies ◽  
Optimization Problems ◽  
Parameter Tuning ◽  
Optimization Techniques ◽  
Electrical Machines ◽  
Robust Design Optimization ◽  
Open Problems ◽  
Electrical Machinery

The bio-inspired algorithms are novel, modern, and efficient tools for the design of electrical machines. However, from the mathematical point of view, these problems belong to the most general branch of non-linear optimization problems, where these tools cannot guarantee that a global minimum is found. The numerical cost and the accuracy of these algorithms depend on the initialization of their internal parameters, which may themselves be the subject of parameter tuning according to the application. In practice, these optimization problems are even more challenging, because engineers are looking for robust designs, which are not sensitive to the tolerances and the manufacturing uncertainties. These criteria further increase these computationally expensive problems due to the additional evaluations of the goal function. The goal of this paper is to give an overview of the widely used optimization techniques in electrical machinery and to summarize the challenges and open problems in the applications of the robust design optimization and the prospects in the case of the newly emerging technologies.

An Effective Approach to Solve Design Optimization Problems With Arbitrarily Distributed Uncertainties in the Original Design Space Using Ensemble of Gaussian Reliability Analyses

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Po Ting Lin ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Design Space ◽  
Optimization Problems ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Original Design ◽  
Design Point ◽  
Standard Normal

Reliability-based design optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the modified reliability index approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the performance measure approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. To this end, a new algorithm, ensemble of Gaussian reliability analyses (EoGRA), was developed to estimate the failure probability using Gaussian-based kernel density estimation (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations (FEs). Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The results showed that EoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods. Furthermore, experiments of image processing with arbitrarily distributed photo pixels are performed. The lighting of image pixels is maximized subject to the acceptable limit. Our implementation showed that the accuracy of the estimation of normal distribution is poor while the proposed method is capable of finding the optimal solution with acceptable accuracy.

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.

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