On the Application of a Design of Experiments along with an ANFIS and a Desirability Function to Model Response Variables

Carmelo J Luis Pérez

doi:10.3390/sym13050897

Abstract

In manufacturing engineering, it is common to use both symmetrical and asymmetrical factorial designs along with regression techniques to model technological response variables, since the in-advance prediction of their behavior is of great importance to determine the levels of variation that lead to optimal response values to be obtained. For this purpose, regression techniques based on the response surface method combined with a desirability function for multi-objective optimization are commonly employed, since it is usual to find manufacturing processes that require simultaneous optimization of several variables, which exhibit in many cases an opposite behavior. However, these regression models are sometimes not accurate enough to predict the behavior of these response variables, especially when they have significant non-linearities. To deal with this drawback, soft computing techniques are very effective in overcoming the limitations of conventional regression models. This present study is focused on the employment of a symmetrical design of experiments along with a new desirability function, which is proposed in this study, and with soft computing techniques based on fuzzy logic. It will be shown that more accurate results than those obtained from regression techniques are obtained. Moreover, this new desirability function is analyzed in this study.

Highlights

In manufacturing engineering, it is necessary to model the behavior of response variables as a function of several input variables in order to be able to select the most suitable operating conditions in advance
The use of models based on response surfaces, together with a desirability function, is commonly used to model response variables in manufacturing engineering and to solve a multiple optimization problem because it is possible to find a solution using optimization methods
In the event that the regression does not provide high values of the coefficient of determination, it is very likely that these regression models will not provide accurate results and it would be better to employ other models for the output responses for example based on soft computing, because, in this way, more accurate results can be obtained

Summary

Introduction

It is necessary to model the behavior of response variables as a function of several input variables in order to be able to select the most suitable operating conditions in advance. The optimal selection of operating conditions is not an easy task and it is necessary to use statistical tools for modeling of the response variables versus variations in the process parameters This can sometimes lead to a high number of experiments being carried out, and it is common practice to employ design of experiments techniques that allow, with a relatively small number of experiments, some very useful information on the behavior of the variables under study to be obtained. In this way, response surface method (RSM), artificial neuronal networks (ANN), fuzzy inference systems (FIS) [1,2], and adaptive neural fuzzy inference system (ANFIS) [3] have been widely employed. Several studies can be found in the literature dealing with the application of these aforementioned techniques [4,5,6]

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Conclusion