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Article
Publication date: 16 April 2018

Qi Zhou, Xinyu Shao, Ping Jiang, Tingli Xie, Jiexiang Hu, Leshi Shu, Longchao Cao and Zhongmei Gao

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly…

Abstract

Purpose

Engineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.

Design/methodology/approach

In K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.

Findings

Five numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.

Practical implications

The proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.

Originality/value

A K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 16 April 2018

Jie Liu, Guilin Wen, Qixiang Qing, Fangyi Li and Yi Min Xie

This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.

Abstract

Purpose

This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.

Design/methodology/approach

An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.

Findings

The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.

Originality/value

A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Details

Engineering Computations, vol. 35 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 20 October 2023

Duo Zhang, Yonghua Li, Gaping Wang, Qing Xia and Hang Zhang

This study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of…

Abstract

Purpose

This study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of uncertainty analysis.

Design/methodology/approach

The method first introduces a dual adaptive chaotic flower pollination algorithm (DACFPA) to overcome the shortcomings of the original flower pollination algorithm (FPA), such as its susceptibility to poor accuracy and convergence efficiency when dealing with complex optimization problems. Furthermore, a DACFPA-Kriging model is developed by optimizing the relevant parameter of Kriging model via DACFPA. Finally, the dual Kriging model is constructed to improve the efficiency of uncertainty analysis, and a robust design optimization method based on DACFPA-Dual-Kriging is proposed.

Findings

The DACFPA outperforms the FPA, particle swarm optimization and gray wolf optimization algorithms in terms of solution accuracy, convergence speed and capacity to avoid local optimal solutions. Additionally, the DACFPA-Kriging model exhibits superior prediction accuracy and robustness contrasted with the original Kriging and FPA-Kriging. The proposed method for robust design optimization based on DACFPA-Dual-Kriging is applied to the motor hanger of the electric multiple units as an engineering case study, and the results confirm a significant reduction in the fluctuation of the maximum equivalent stress.

Originality/value

This study represents the initial attempt to enhance the prediction accuracy of the Kriging model using the improved FPA and to combine the dual Kriging model for uncertainty analysis, providing an idea for the robust optimization design of mechanical structure with black-box problem.

Details

Multidiscipline Modeling in Materials and Structures, vol. 19 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 18 January 2023

Zhao Dong, Ziqiang Sheng, Yadong Zhao and Pengpeng Zhi

Mechanical products usually require deterministic finite element analysis in the design phase to determine whether their structures meet the requirements. However, deterministic…

Abstract

Purpose

Mechanical products usually require deterministic finite element analysis in the design phase to determine whether their structures meet the requirements. However, deterministic design ignores the influence of uncertainties in the design and manufacturing process of mechanical products, leading to the problem of a lack of design safety or excessive redundancy in the design. In order to improve the accuracy and rationality of the design results, a robust design method for structural reliability based on an active-learning marine predator algorithm (MPA)–backpropagation (BP) neural network is proposed.

Design/methodology/approach

The MPA was used to obtain the optimal weights and thresholds of a BP neural network, and an active-learning function applicable to neural networks was proposed to efficiently improve the prediction performance of the BP neural network. On this basis, a robust optimization design method for mechanical product reliability based on the active-learning MPA-BP model was proposed. Random moving quadrilateral sampling was used to obtain the sample points required for training and testing of the neural network, and the reliability sensitivity corresponding to each sample point was calculated by subset simulated significant sampling (SSIS). The total mass of the mechanical product and the structural reliability sensitivity of the trained active-learning MPA-BP model output were taken as the optimization objectives, and a multi-objective reliability-robust optimization design model was constructed, which was solved by the second-generation non-dominated ranking genetic algorithm (NSGA-II). Then, the dominance function was used in the obtained Pareto solution set to make a dominance-seeking decision to obtain the final reliability-robust optimization design solution. The feasibility of the proposed method was verified by a reliability-robust optimization design example of the bogie frame.

Findings

The prediction error of the active-learning MPA-BP neural network was smaller than those of the particle swarm optimization (PSO)-BP, marine predator algorithm (MPA)-BP and genetic algorithm (GA)-BP neural networks under the same basic parameter settings of the algorithm, which indicated that the improvement strategy proposed in this paper improved the prediction accuracy of the BP neural network. To ensure the reliability of the bogie frame, the reliability sensitivity and total mass of the bogie frame were reduced, which not only realized the lightweight design of the bogie frame, but also improved the reliability and robustness of the bogie.

Originality/value

The MPA algorithm with a higher optimization efficiency was introduced to find the weights and thresholds of the BP neural network. A new active-learning function was proposed to improve the prediction accuracy of the MPA-BP neural network.

Details

International Journal of Structural Integrity, vol. 14 no. 2
Type: Research Article
ISSN: 1757-9864

Keywords

Article
Publication date: 5 October 2021

Yonghua Li, Hao Yin and Qing Xia

This study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the…

Abstract

Purpose

This study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.

Design/methodology/approach

A robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.

Findings

Compared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.

Originality/value

This study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

Details

Multidiscipline Modeling in Materials and Structures, vol. 17 no. 6
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 15 November 2011

Min Li and David A. Lowther

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of…

Abstract

Purpose

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of electromagnetic problems which may be sensitive to parameter variations. The purpose of this paper is to propose a robust objective function for topological design problems.

Design/methodology/approach

In this paper, a robust objective function for topology optimization is defined on an uncertainty set using the worst case analysis. The robustness of a topological design is defined as the worst response due to the variations of the location of the topology change. The approach is based on the definition of a topological gradient.

Findings

The robust topology optimization (RTO) was applied to eddy current crack reconstruction problems. The numerical applications showed that this method can provide more reliable results for the reconstruction in the presence of significant noise in the measured signal.

Research limitations/implications

The RTO may be applied to some more complicated design problems; however large computational costs may result.

Originality/value

This paper has defined a robustness metric for topology design and a robust design model is proposed for topology optimization problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 6
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 14 July 2020

Xiaojun Wang, Zhenxian Luo and Xinyu Geng

This paper is to present an experiment to verify that the motion errors of robust topology optimization results of compliant mechanisms are insensitive to load dispersion.

330

Abstract

Purpose

This paper is to present an experiment to verify that the motion errors of robust topology optimization results of compliant mechanisms are insensitive to load dispersion.

Design/methodology/approach

First, the test pieces of deterministic optimization and robust optimization results are manufactured by the combination of three-dimensional (3D) printing and casting techniques. To measure the displacement of the test piece of compliant mechanism, a displacement measurement method based on the image recognition technique is proposed in this paper.

Findings

According to the experimental data analysis, the robust topology optimization results of compliant mechanisms are less sensitive to uncertainties, comparing with the deterministic optimization results.

Originality/value

An experiment is presented to verify the effectiveness of robust topology optimization for compliant mechanisms. The test pieces of deterministic optimization and robust optimization results are manufactured by the combination of 3D printing and casting techniques. By comparing the experimental data, it is found that the motion errors of robust topology optimization results of compliant mechanisms are insensitive to load dispersion.

Details

Rapid Prototyping Journal, vol. 26 no. 9
Type: Research Article
ISSN: 1355-2546

Keywords

Article
Publication date: 2 May 2017

Yalin Pan, Jun Huang, Feng Li and Chuxiong Yan

The purpose of this paper is to propose a robust optimization strategy to deal with the aerodynamic optimization issue, which does not need a large sum of information on the…

Abstract

Purpose

The purpose of this paper is to propose a robust optimization strategy to deal with the aerodynamic optimization issue, which does not need a large sum of information on the uncertainty of input parameters.

Design/methodology/approach

Interval numbers were adopted to describe the uncertain input, which only requires bounds and does not necessarily need probability distributions. Based on the method, model outputs were also regarded as intervals. To identify a better solution, an order relation was used to rank interval numbers.

Findings

Based on intervals analysis method, the uncertain optimization problem was transformed into nested optimization. The outer optimization was used to optimize the design vector, and inner optimization was used to compute the interval of model outputs. A flying wing aircraft was used as a basis for uncertainty optimization through the suggested optimization strategy, and optimization results demonstrated the validity of the method.

Originality/value

In aircraft conceptual design, the uncertain information of design parameters are often insufficient. Interval number programming method used for uncertainty analysis is effective for aerodynamic robust optimization for aircraft conceptual design.

Details

Aircraft Engineering and Aerospace Technology, vol. 89 no. 3
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 18 April 2017

Qi Zhou, Ping Jiang, Xinyu Shao, Hui Zhou and Jiexiang Hu

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval…

Abstract

Purpose

Uncertainty is inevitable in real-world engineering optimization. With an outer-inner optimization structure, most previous robust optimization (RO) approaches under interval uncertainty can become computationally intractable because the inner level must perform robust evaluation for each design alternative delivered from the outer level. This paper aims to propose an on-line Kriging metamodel-assisted variable adjustment robust optimization (OLK-VARO) to ease the computational burden of previous VARO approach.

Design/methodology/approach

In OLK-VARO, Kriging metamodels are constructed for replacing robust evaluations of the design alternative delivered from the outer level, reducing the nested optimization structure of previous VARO approach into a single loop optimization structure. An on-line updating mechanism is introduced in OLK-VARO to exploit the obtained data from previous iterations.

Findings

One nonlinear numerical example and two engineering cases have been used to demonstrate the applicability and efficiency of the proposed OLK-VARO approach. Results illustrate that OLK-VARO is able to obtain comparable robust optimums as to that obtained by previous VARO, while at the same time significantly reducing computational cost.

Practical implications

The proposed approach exhibits great capability for practical engineering design optimization problems under interval uncertainty.

Originality/value

The main contribution of this paper lies in the following: an OLK-VARO approach under interval uncertainty is proposed, which can significantly ease the computational burden of previous VARO approach.

Details

Engineering Computations, vol. 34 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 17 April 2009

Jami Kovach, Byung Rae Cho and Jiju Antony

Robust design is a well‐known quality improvement method that focuses on building quality into the design of products and services. Yet, most well established robust design models…

Abstract

Purpose

Robust design is a well‐known quality improvement method that focuses on building quality into the design of products and services. Yet, most well established robust design models only consider a single performance measure and their prioritization schemes do not always address the inherent goal of robust design. This paper aims to propose a new robust design method for multiple quality characteristics where the goal is to first reduce the variability of the system under investigation and then attempt to locate the mean at the desired target value.

Design/methodology/approach

The paper investigates the use of a response surface approach and a sequential optimization strategy to create a flexible and structured method for modeling multiresponse problems in the context of robust design. Nonlinear programming is used as an optimization tool.

Findings

The proposed methodology is demonstrated through a numerical example. The results obtained from this example are compared to that of the traditional robust design method. For comparison purposes, the traditional robust design optimization models are reformulated within the nonlinear programming framework developed here. The proposed methodology provides enhanced optimal robust design solutions consistently.

Originality/value

This paper is perhaps the first study on the prioritized response robust design with the consideration of multiple quality characteristics. The findings and key observations of this paper will be of significant value to the quality and reliability engineering/management community.

Details

International Journal of Quality & Reliability Management, vol. 26 no. 4
Type: Research Article
ISSN: 0265-671X

Keywords

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