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Article
Publication date: 8 January 2020

Hailiang Su, Fengchong Lan, Yuyan He and Jiqing Chen

Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit…

Abstract

Purpose

Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

Design/methodology/approach

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

Findings

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

Originality/value

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

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Article
Publication date: 5 December 2019

Liang Li, Xuesong Chu and Guangming Yu

The paper aims to construct a method to simulate the relationship between the parameters of soil properties and the area of sliding mass of the true slip surface of a landslide.

Abstract

Purpose

The paper aims to construct a method to simulate the relationship between the parameters of soil properties and the area of sliding mass of the true slip surface of a landslide.

Design/methodology/approach

The smoothed particle hydrodynamics (SPH) algorithm is used to calibrate a response surface function which is adopted to quantify the area of sliding mass of the true slip surface for each failure sample in Monte Carlo simulation. The proposed method is illustrated through a homogeneous and a heterogeneous cohesive soil slope.

Findings

The comparison of the results between the proposed method and the traditional method using the slip surface with minimum factor of safety (FSmin) to quantify the failure consequence has shown that the landslide risk tends to be attributed to a variety of risk sources, and that the use of a slip surface with FSmin to quantify the consequence of a landslide underestimates the landslide risk value. The difference of the risk value between the proposed method and the traditional method increases dramatically as the uncertainty of soil properties becomes significant.

Practical implications

A geotechnical engineer could use the proposed method to perform slope failure analysis.

Originality/value

The failure consequence of a landslide can be rationally predicted using the proposed method.

Details

Engineering Computations, vol. 37 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 8 February 2019

Pengpeng Zhi, Yonghua Li, Bingzhi Chen, Meng Li and Guannan Liu

In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment…

Abstract

Purpose

In a structural optimization design-based single-level response surface, the number of optimal variables is too much, which not only increases the number of experiment times, but also reduces the fitting accuracy of the response surface. In addition, the uncertainty of the optimal variables and their boundary conditions makes the optimal solution difficult to obtain. The purpose of this paper is to propose a method of fuzzy optimization design-based multi-level response surface to deal with the problem.

Design/methodology/approach

The main optimal variables are determined by Monte Carlo simulation, and are classified into four levels according to their sensitivity. The linear membership function and the optimal level cut set method are applied to deal with the uncertainties of optimal variables and their boundary conditions, as well as the non-fuzzy processing is carried out. Based on this, the response surface function of the first-level design variables is established based on the design of experiments. A combinatorial optimization algorithm is developed to compute the optimal solution of the response surface function and bring the optimal solution into the calculation of the next level response surface, and so on. The objective value of the fourth-level response surface is an optimal solution under the optimal design variables combination.

Findings

The results show that the proposed method is superior to the traditional method in computational efficiency and accuracy, and improves 50.7 and 5.3 percent, respectively.

Originality/value

Most of the previous work on optimization was based on single-level response surface and single optimization algorithm, without considering the uncertainty of design variables. There are very few studies which discuss the optimization efficiency and accuracy of multiple design variables. This research illustrates the importance of uncertainty factors and hierarchical surrogate models for multi-variable optimization design.

Details

International Journal of Structural Integrity, vol. 10 no. 2
Type: Research Article
ISSN: 1757-9864

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Article
Publication date: 5 May 2020

Amir Moslemi and Mahmood Shafiee

In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but is also dependent on the quality of…

Abstract

Purpose

In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but is also dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case.

Design/methodology/approach

In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem.

Findings

The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also GC index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method.

Originality/value

To the best of the authors’ knowledge, there are few papers focusing on quality-oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches.

Details

International Journal of Quality & Reliability Management, vol. 38 no. 1
Type: Research Article
ISSN: 0265-671X

Keywords

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Article
Publication date: 28 April 2020

Wenliang Fan, Wentong Zhang, Min Li, Alfredo H.-S. Ang and Zhengliang Li

Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to…

Abstract

Purpose

Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM).

Design/methodology/approach

First, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed.

Findings

The criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency.

Originality/value

The constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.

Details

Engineering Computations, vol. 37 no. 9
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 17 May 2021

Wenliang Fan, Wei Shen, Qingbin Zhang and Alfredo H.-S. Ang

The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.

Abstract

Purpose

The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.

Design/methodology/approach

By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.

Findings

The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.

Originality/value

This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

Details

Engineering Computations, vol. 38 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 14 June 2019

Wentong Zhang and Yiqing Xiao

Balancing accuracy and efficiency is an important evaluation index of response surface method. The purpose of this paper is to propose an adaptive order response surface

Abstract

Purpose

Balancing accuracy and efficiency is an important evaluation index of response surface method. The purpose of this paper is to propose an adaptive order response surface method (AORSM) based on univariate decomposition model (UDM).

Design/methodology/approach

First, the nonlinearity of the univariate function can be judged by evaluating the goodness of fit and the error of curve fit rationally. Second, combining UDM with the order analysis of separate component polynomial, an easy-to-implement AORSM is proposed. Finally, several examples involving mathematical functions and structural engineering problems are studied in detail.

Findings

With the proposed AORSM, the orders of component functions in the original response surface can be determined adaptively and the results of those cases in this paper indicate that the proposed method performs good accuracy, efficiency and robustness.

Research limitations/implications

Because just the cases with single failure mode and single MPP are studied in this paper, the application in multi-failure mode and multi-MPP cases need to be investigated in the coming work.

Originality/value

The nonlinearity of the univariate in the response surface can be determined adaptively and the undetermined coefficients of each component function are obtained separately, which reduces the computation dramatically.

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Article
Publication date: 14 March 2019

Hailiang Su, Fengchong Lan, Yuyan He and Jiqing Chen

Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error…

Abstract

Purpose

Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model.

Design/methodology/approach

The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated.

Findings

The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations.

Originality/value

This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.

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Article
Publication date: 3 December 2018

Priyabrata Sahoo, Mantra Prasad Satpathy, Vishnu Kumar Singh and Asish Bandyopadhyay

Surface roughness and vibration during machining are inevitable which critically affect the product quality characteristics. This paper aims to suggest the implementation…

Abstract

Purpose

Surface roughness and vibration during machining are inevitable which critically affect the product quality characteristics. This paper aims to suggest the implementation of a multi-objective optimization technique to obtain the favorable parametric conditions which lead to minimum tool vibration and surface roughness of 6063-T6 aluminum alloy in computer numerically controlled (CNC) turning.

Design/methodology/approach

The case study has been accomplished according to response surface methodology RSM’s Box–Behnken design (BBD) matrix using Titanium Nitride-coated Tungsten Carbide insert in a dry environment. As the experimental results are quite nonlinear, a second-order regression model has been developed for the responses (surface roughness and tool vibration) in terms of input cutting parameters (spindle speed, feed rate and depth of cut). The goodness of fit of the models has also been verified with analysis of variance (ANOVA) results.

Findings

The significance efficacy of input parameters on surface roughness and tool vibrations has been illustrated through multi-objective overlaid 3D surface plots and contour plots. Finally, parametric optimization has been performed to get the desired response values under the umbrella of weighted aggregate sum product assessment (WASPAS) method and verified confidently with confirmatory test results.

Originality/value

The results of this study reveals that hybrid RSM with WASPAS method can be readily applicable to optimize multi-response problems in the manufacturing field with higher confidence.

Details

World Journal of Engineering, vol. 15 no. 6
Type: Research Article
ISSN: 1708-5284

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Article
Publication date: 16 November 2010

Wu‐Lin Chen, Chin‐Yin Huang and Chi‐Wei Hung

The purpose of this paper is to find the optimal values of process parameters in injection molding when both warpage and shrinkage are minimized.

Abstract

Purpose

The purpose of this paper is to find the optimal values of process parameters in injection molding when both warpage and shrinkage are minimized.

Design/methodology/approach

In finding the optimal values, advantages of finite element software, Moldflow, and dual response surface method (dual RSM) combined with the nonlinear programming technique by Lingo are exploited. Considering the nine process parameters, injection time, injection pressure, packing pressure, packing time, cooling time, coolant temperature, mold‐open time, melting temperature and mold surface temperature, a series of mold analyses are performed to exploit the warpage and shrinkage data. In the analyses, warpage is considered the primary response, whereas shrinkage is the secondary response.

Findings

The results indicate that dual RSM combined with the nonlinear programming technique can outperform the Taguchi's optimization method. The optimal process values are also confirmed by re‐running experiments on Moldflow. Additionally, an auxiliary dual RSM model is proposed to search for a better result based on the given findings by dual RSM at the cost of running extra experiments. Based on dual RSM, a multiple objective optimization for the whole plastic product is finally suggested to integrate the dual RSM models that are developed for the individual nodes or edges.

Originality/value

This paper proposes a new method to find the optimal process for plastic injection molding.

Details

Engineering Computations, vol. 27 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

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