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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: 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.

235

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: 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…

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: 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…

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: 19 May 2022

Yiying Li, Dun Sun and Shiyou Yang

The purpose of this paper is to develop a robust optimization methodology for metamaterial (MM) unit designs to minimize the effect of manufacturing and operational uncertainties.

Abstract

Purpose

The purpose of this paper is to develop a robust optimization methodology for metamaterial (MM) unit designs to minimize the effect of manufacturing and operational uncertainties.

Design/methodology/approach

A new robustness quantification function, applicable to both convex and nonconvex relationships between the mean and the standard deviation, is introduced. A distance-based local radial basis function network surrogate model is proposed to substitute the global radial basis function network to reduce the heavy computational cost without any scarification on the solution accuracy.

Findings

The optimized results of a prototype MM unit demonstrate the feasibility and merit of the proposed methodology. The proposed methodology outperforms the existing ones in both performance and robust parameters in the design of a prototype MM unit.

Originality/value

It provides a robust optimization methodology for MM units when considering the imperfections in fabrications and fluctuations in operation and environment conditions in engineering applications.

Details

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

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…

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: 12 October 2010

Nikos D. Lagaros, Vagelis Plevris and Manolis Papadrakakis

This paper, by taking randomness and uncertainty of structural systems into account aims to implement a combined reliability‐based robust design optimization (RRDO…

Abstract

Purpose

This paper, by taking randomness and uncertainty of structural systems into account aims to implement a combined reliability‐based robust design optimization (RRDO) formulation. The random variables to be considered include the cross section dimensions, modulus of elasticity, yield stress, and applied loading. The RRDO problem is to be formulated as a multi‐objective optimization problem where the construction cost and the standard deviation of the structural response are the objectives to be minimized.

Design/methodology/approach

The solution of the optimization problem is performed with the non‐dominant cascade evolutionary algorithm with the weighted Tchebycheff metric, while the probabilistic analysis required is carried out with the Monte Carlo simulation method. Despite the computational advances, the solution of a RRDO problem for real‐world structures is extremely computationally demanding and for this reason neurocomputing estimations are implemented.

Findings

The obtained estimates with the neural network predictions are shown to be very satisfactory in terms of accuracy for performing this type of computation. Furthermore, the present numerical results manage to achieve a reduction in computational time up to four orders of magnitude, for low probabilities of violation, compared to the conventional procedure making thus feasible the reliability‐robust design optimization of realistic structures under probabilistic constraints.

Originality/value

The novel parts of the present work include the implementation of neurocomputing strategies in RRDO problems for reducing the computational cost and the comparison of the results given by RRDO and robust design optimization formulations, where the significance of taking into account probabilistic constraints is emphasized.

Details

Engineering Computations, vol. 27 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 4 October 2019

Seyed Jafar Sadjadi, Zahra Ziaei and Mir Saman Pishvaee

This study aims to design a proper supply chain network for the vaccine industry in Iran, which considers several features such as uncertainties in demands and cost…

Abstract

Purpose

This study aims to design a proper supply chain network for the vaccine industry in Iran, which considers several features such as uncertainties in demands and cost, perishability of vaccines, wastages in storage, limited capacity and different priorities for demands.

Design/methodology/approach

This study presents a mixed-integer linear programming (MILP) model and using a robust counterpart approach for coping with uncertainties of model.

Findings

The presented robust model in comparison with the deterministic model has a better performance and is more reliable for network design of vaccine supply chain.

Originality/value

This study considers uncertainty in the network design of vaccine supply chain for the first time in the vaccine context It presents an MILP model where strategic decisions for each echelon and tactical decisions among different echelons of supply chain are determined. Further, it models the difference between high- and low-priority demands for vaccine.

Article
Publication date: 14 November 2016

Yelin Fu, Lianlian Song, Kin Keung Lai and Liang Liang

The purpose of this paper is to propose robust optimization models addressing the container slot allocation problem with minimum quantity commitment (MQC) under uncertain…

Abstract

Purpose

The purpose of this paper is to propose robust optimization models addressing the container slot allocation problem with minimum quantity commitment (MQC) under uncertain demand, which is faced by international companies export to USA.

Design/methodology/approach

A novel robust optimization approach handling linear programming (LP) with right-hand-side uncertainty is developed by incorporating new parameters: uncertainty level, infeasibility tolerance and reliability level. Two types of uncertainty, namely, bounded uncertainty and symmetric uncertainty are considered, respectively.

Findings

The present work finds that the expected revenue increases as the uncertainty level and the MQC decrease, as well as the infeasibility tolerance and the reliability level increase, no matter which type of uncertainty is considered.

Research limitations/implications

Typically, the capacity constraints in a container shipping model should include two major restrictions: (1) number of slots and (2) total weight of loaded and empty containers. However, this study only addresses the first restriction for simplicity. It is recommended that future research explore the optimal solutions with additional restriction (2).

Originality/value

This paper fills a theoretical and practical gap for the problem of slot allocation with MQC in container liner revenue management. Deterministic and tractable mixed integer LP is formulated to derive robust solutions which immunes to demand uncertainty. Illustrative examples are presented to test the proposed models. The present work provides practical and solid advice and examples which demonstrates the application of the proposed robust optimization approach for logistics managers.

Details

The International Journal of Logistics Management, vol. 27 no. 3
Type: Research Article
ISSN: 0957-4093

Keywords

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