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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).

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.

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.

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.

This paper aims to develop an efficient algorithm combining straightforward response surface functions with Monte Carlo simulation to conduct seismic reliability analysis in a systematical way.

The representative slip surfaces are identified and based on to calibrate multiple response surface functions with acceptable accuracy. The calibrated response surfaces are used to determine the yield acceleration in Newmark sliding displacement analysis. Then, the displacement-based limit state function is adopted to conduct seismic reliability analysis.

The calibrated response surface functions have fairly good accuracy in predicting the yield acceleration in Newmark sliding displacement analysis. The seismic reliability is influenced by such factors as PGA, spatial variability and threshold value. The proposed methodology serves as an effective tool for geotechnical practitioners.

The multiple sources of a seismic slope response can be effectively determined using the multiple response surface functions, which are easily implemented within geotechnical engineering.

There is growing evidence of a knowledge gap in the association of maintenance with production activities in bottling plants. Indeed, insights into how to jointly optimise these activities are not clear. In this paper, two optimisation models, Taguchi schemes and response surface methodology are proposed.

Borrowing from the “hard” total quality management elements in optimisation and prioritisation literature, two new models were developed based on factor, level and orthogonal array selection, signal-to-noise ratio, analysis of variance and optimal parametric settings as Taguchi–ABC and Taguchi–Pareto. An additional model of response surface methodology was created with analysis on regression, main effects, residual plots and surface plots.

The Taguchi S/N ratio table ranked planned maintenance as the highest. The Taguchi–Pareto shows the optimal parametric setting as A4B4C1 (28 h of production, 30.56 shifts and 37 h of planned maintenance). Taguchi ABC reveals that the planned maintenance and number of shifts will influence the outcome of production greatly. The surface regression table reveals that the production hours worked decrease at a value of planned maintenance with a decrease in the number of shifts.

This is the first time that joint optimisation for bottling plant will be approached using Taguchi–ABC and Taguchi–Pareto. It is also the first time that response surface will be applied to optimise a unique platform of the bottling process plant.

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).

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.

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.

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.

This paper aims to develop a mathematical model for analysing surface roughness during end milling by using response surface methodology (RSM) and to determine how the input parameters (cutting speed, depth of cut and feed rate) influence the output parameter (surface roughness) in the machining of hybrid glass fibre reinforced plastic (GFRP; Abaca and Glass) composite by using solid carbide end mill cutter.

Three factors and a three-level Box–Behnken design in RSM were used to carry out the experimental investigation. Handysurf E-35A was used to measure the surface roughness of the machined hybrid GFRP composites. The “Design Expert 8.0” was used to analyse the data collected graphically. Analysis of variance was carried out to validate the model and determine the most significant parameter.

The response surface model was used to predict the input factors influencing the surface roughness of the machined surfaces of hybrid GFRP composite at different cutting conditions with a chosen range of 95 per cent confidence intervals. Analysis of the influences of the entire individual input machining parameters on the surface roughness carried out using RSM.

The effect of the milling of hybrid GFRP composite on the surface roughness with solid carbide end mill by using RSM has not been analysed yet.

The purpose of this paper is to develop a mathematical model for the surface delamination through response surface methodology (RSM) and analyse the influences of the entire individual input machining parameters (cutting speed, feed rate and depth of cut) on the responses in milling of carbon fibre reinforced polymer (CFRP) composites with solid carbide end mill cutter coated with polycrystalline diamond.

Three factors, three level face-centered central composite design in RSM was employed to carry out the experimental investigation. The “Design Expert 8.0” software was used for regression and graphical analysis of the data collected. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots. Analysis of variance was used to check the validity of the model and for finding the significant parameters.

The developed second-order response surface model is used to calculate the delamination of the machined surfaces at different cutting conditions with the chosen range with 95 per cent confidence intervals. Using such model, one can obtain remarkable savings in time and cost.

The effect of machining parameters on surface delamination during milling of CFRP composites using RSM has not been previously analysed.

Most of the previous work on reliability analysis was based on the traditional reliability theory. The calculated results can only reflect the reliability of components at a specific time, which neglects the uncertainty of load and resistance over time. The purpose of this paper is to develop a time-dependent reliability analysis approach based on stochastic process to deal with the problem and apply it to the structural design of railway vehicle components.

First, the parametric model of motor hanger for electric multiple unit (EMU) is established by ANSYS parametric design language, and its structural stress is analyzed according to relevant standards. The Latin hypercube method is used to analyze the sensitivity of the structure, and the uncertainty parameters (sizes and loads) which have great influence on the structural strength are determined. The D-optimal experimental design is carried out to establish the polynomial response surface function, which characterizes the relationship between uncertainty parameters and structural stress. Second, the Poisson stochastic process is adopted to describe the number of loads acting, and the Monte Carlo method is used to obtain the load acting history according to its probability distribution characteristics. The load history is introduced into the response surface function and the uncertainty of other parameters is considered at the same time, and the stress history of the motor hanger is obtained. Finally, the degradation process of structural resistance is described by a Gamma stochastic process, and the time-dependent reliability of the motor hanger is calculated based on the reliability theory.

Time and the uncertainties of parameters have great impact on reliability. The results of reliability decrease with time fluctuation are more reasonable, stable and credible than traditional methods.

In this paper, the proposed method is applied to the structural design of the motor hanger for EMU, which has a good guiding significance for accurately evaluating whether if the design meets the reliability requirements.

The value of this paper is that the method takes both the randomness of load over time and the uncertainty of structural parameters in the design and manufactures process into consideration, and describes the monotonous degradation characteristics of structural resistance. At the same time, the time-dependent reliability of mechanical components is calculated by a response surface method. It not only improves the accuracy of reliability analysis, but also improves the analysis efficiency and solves the problem that the traditional reliability analysis method can only reflect the static reliability of components.

The purpose of this paper is to develop a mathematical model for delamination through response surface methodology (RSM) and analyse the influences of the entire individual input machining parameters (cutting speed, depth of cut and feed rate) on the responses in milling of glass fibre reinforced plastics (GFRP) composites with solid carbide end mill cutter coated with polycrystalline diamond (PCD).

Three factors, three levels face-centered central composite design matrix in RSM is employed to carry out the experimental investigation. Shop microscope is used to examine the delamination of GFRP composites. The “Design Expert 8.0” software was used for regression and graphical analysis of the data collected. Analysis of variance is used to check the validity of the model and for finding the significant parameters.

The developed second-order response surface model is used to calculate the delamination of the machined surfaces at different cutting conditions with the chosen range of 95 per cent confidence intervals. Analysis of the influences of the entire individual input machining parameters on the delamination has been carried out using RSM.

Influence of solid carbide end mill coated with PCD on delamination of bi-directional GFRP composite during milling has not been analysed yet using RSM.

This study aims to address a deep statistical analysis on transtibial prostheses made of composite isogrid carbon/epoxy structure.

For the methodological procedure, an experimental arrangement was created using design of experiments, and the response surface methodology (RSM) was used. The RSM was obtained from the decision variables of the isogrid model, which consists of angle, circular width and helical width. All modeling was performed numerically using the finite element method.

Results obtained through analysis of variance (ANOVA) indicated the sensitivity of each decision variable (manufacture) in the mechanical responses. The results obtained in this study provide a starting point in formulating optimization problems for researchers and engineers.

A noteworthy thing about structural analysis and structural optimization is that some parameters and decision variables are more significant than others in certain responses (Major et al., 2011). Knowing the sensitivity of these parameters is essential for the correct formulation of an optimization problem. To handle these obstacles, design of experiments and ANOVA are used to solve and obtain the main effects on the structural performance. Nevertheless, to the best of the authors’ knowledge, very few efforts have been devoted to the development to show the factors that influence the various responses of a lower limb prosthesis isogrid tube.

This paper aims to focus on an experimental study of surface roughness, dimensional accuracy and time of fabrication of parts produced by fused deposition modelling (FDM) technique of additive manufacturing. The fabricated parts of acrylonitrile butadiene styrene (ABS) material have pyramidal and conical features. Influence of five process parameters of FDM, namely, layer thickness, wall print speed, build orientation, wall thickness and extrusion temperature is studied on response characteristics. Furthermore, regression models for responses are developed and significant process parameters are optimized.

Comprehensive experimental study is performed using response surface methodology. Analysis of variance is used to investigate the influence of process parameters on surface roughness, dimensional accuracy and time of fabrication in both outer pyramidal and inner conical regions of part. Furthermore, a multi-response optimization using desirability function is performed to minimize surface roughness, improve dimensional accuracy and minimize time of fabrication of parts.

It is found that layer thickness and build orientation are significant process parameters for surface roughness of parts. Surface roughness increases with increase in layer thickness, while it decreases initially and then increases with increase in build orientation. Layer thickness, wall print speed and build orientation are significant process parameters for dimensional accuracy of FDM parts. For the time of fabrication, layer thickness and build orientation are found as significant process parameters. Based on the analysis, statistical non-linear quadratic models are developed to predict surface roughness, dimensional accuracy and time of fabrication. Optimization of process parameters is also performed using desirability function.

The present study is restricted to the parts of ABS material with pyramidal and conical features only fabricated on FDM machine with delta configuration.

From the critical review of literature it is found that some researchers have made to study the influence of few process parameters on surface roughness, dimensional accuracy and time of fabrication of simple geometrical parts. Also, regression models and optimization of process parameters has been performed for simple parts. The present work is focussed on studying all these aspects in complicated geometrical parts with pyramidal and conical features.