A novel robust multivariate regression approach to optimize multiple surfaces

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1233-1243
Author(s):  
Amir Moslemi ◽  
Mirmehdi Seyyed-Esfahani
Keyword(s):  
Response Surface ◽  
Multivariate Regression ◽  
Ordinary Least Squares ◽  
Response Surfaces ◽  
Response Models ◽  
New Approach ◽  
Global Criterion ◽  
Global Criterion Method ◽  
Controllable Factors ◽  
Criterion Method

Response surface methodology involves relationships between different variables, specifically experimental inputs as controllable factors, and a response or responses by incorporating uncontrollable factors named nuisance. In order to optimize these response surfaces, we should have accurate response models. A common approach to estimate a response surface is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Most problems face with more than one response which are mostly correlated, that are called multi-response problem. This paper presents a new approach which takes the benefits of robust multivariate regression to cope with the mentioned difficulties. After estimating accurate response surfaces, optimization phase should be applied in order to have proper combination of variables and optimum solutions. Global criterion method of multi-objective optimization has also been used to reach a compromise solution which improves all response variables simultaneously. Finally, the proposed approach is described analytically by a numerical example.

Robust optimization of multistage process: response surface and multi-response optimization approaches

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amir Moslemi ◽  
Mirmehdi Seyyed-Esfahani
Keyword(s):  
Response Surface ◽  
Model Building ◽  
Optimization Methods ◽  
Ordinary Least Squares ◽  
Response Surfaces ◽  
Estimation Methods ◽  
Multistage System ◽  
Multiple Components ◽  
Global Criterion ◽  
Response Optimization

Abstract A multistage system refers to a system contains multiple components or stages which are necessary to finish the final product or service. To analyze these problems, the first step is model building and the other is optimization. Response surfaces are used to model multistage problem as an efficient procedure. One regular approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. OLS method is very sensitive to outliers, so some multivariate robust estimation methods have been discussed in the literature in order to estimate the response surfaces accurately such as multivariate M-estimators. In optimization phase, multi-response optimization methods such as global criterion (GC) method and ε-constraints approaches are different methods to optimize the multi-objective-multistage problems. An example of the multistage problem had been estimated considering multivariate robust approaches, besides applying multi-response optimization approaches. The results show the efficiency of the proposed approaches.

scholarly journals Optimization of the Resistance Spot Welding Process of 22MnB5-Galvannealed Steel Using Response Surface Methodology and Global Criterion Method Based on Principal Components Analysis

Metals ◽  
2020 ◽  
Vol 10 (10) ◽  
pp. 1338
Author(s):  
Robson Ribeiro ◽  
Estevão Luiz Romão ◽  
Eduardo Luz ◽  
José Henrique Gomes ◽  
Sebastião Costa
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Principal Components ◽  
Resistance Spot Welding ◽  
Spot Welding ◽  
Resistance Spot ◽  
Global Criterion ◽  
Global Criterion Method ◽  
Criterion Method ◽  
Galvannealed Steel

The 22MnB5-galvannealed steel is extensively used in the hot stamping process to produce car anti-collision structure parts. Furthermore, the resistance spot welding (RSW) is an important process in the automobile industry, especially in body construction, and the 22MnB5-galvannealed steels are a big challenge for the joining methods because their microstructure and mechanical properties are different from those of the conventional steels. In view of this, the present paper aims to optimize the parameters of the RSW process of the 22MnB5-galvannealed steel. Initially, the goal was to remove the galvannealed coating and in the next stage, the following responses were maximized: the nugget width, the nugget cross-sectional area, the penetration, the strength, the joint efficiency, and the energy absorption, whereas the indentation, heat affected zone and separation were used as constraints. The process parameters selected were the effective welding time, the effective welding current, the quenching time, and the upslope time. Response surface methodology (RSM) was applied jointly with the global criterion method based on principal components. The results of the multiobjective optimization are close to the individual targets for each response, highlighting the importance of considering the correlation structure presented in the responses.

scholarly journals A robust multi response surface approach for optimization of multistage processes

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amir Moslemi ◽  
Mahmood Shafiee
Keyword(s):  
Robust Optimization ◽  
Response Surface ◽  
Numerical Study ◽  
Ordinary Least Squares ◽  
Response Surfaces ◽  
Estimation Methods ◽  
Design Parameters ◽  
Optimization Approach ◽  
Content Type

PurposeIn 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/approachIn 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.FindingsThe 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/valueTo 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.

scholarly journals Global criterion formation in producer’s decisions

2014 ◽  
Vol 6 (1) ◽  
pp. 102-114
Author(s):  
Yury Vasilyevich Krivolutskiy ◽  
Elena Yuryevna Zakharova
Keyword(s):  
Decision Making ◽  
Human Resources ◽  
Weight Coefficient ◽  
Mathematical Methods ◽  
Main Attention ◽  
Optimum Range ◽  
Global Criterion ◽  
Global Criterion Method ◽  
Pros And Cons ◽  
Criterion Method

This article delves into decision making in producers activity under shortage of financials, materials and human resources. Every decision to be made is generally a multicriterial task. At the same time these criteria are controversial: amelioration of one criterion leads to degradation of another. That is why solution finding with the use of mathematical methods is worth to consider. Hereafter theoretical stuff and practical exemplification of decision making under multicriterial conditions are presented. In many mathematical methods of decision making multicriterial task is simplified to one criterion. Therefore the main attention is paid to global criterion method, providing a means to define optimum out of several criteria. The point of the method assumes to weigh up the initial criteria and create a single global criterion, serving as a key to decision making. The weight coefficient of each criterion is defined by experts. There are several methods of combining criteria. Nevertheless in practice three methods are used: criteria relation, criteria multiplication and criteria summing up. The methods are analyzed and practical examples are shown in the article. Other approaches to combining criteria are also examined. It is generally agreed that every method of decision making has its own pros and cons, which in turn define the optimum range of its application.

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