Modeling and Analysis of a Tempering process using a Fuzzy Inference System and Fuzzy Least Squares

Nowadays, there has been an increased interest in advance materials having high hardness, temperature resistance, and high strength to weight ratio and used in mold and die making industries, aerospace component, medical appliance, and automotive industries. Thus, the heat treatment is a very important task on manufacturing industry, processes like tempering on D2 and H13 steels are essential at the present industry. Therefore, is necessary to have tools that help us to understand the behavior of the process and at the same time made accurate predictions. The regression models are used to complete this task, however due to the complexity of the tempering process are necessary other type of models. Fuzzy models are widely used to model manufacturing processes. In most of the cases those processes have high variability, uncertainty, ambiguity, and nonlinearity. Further, fuzzy models incorporate the experience and knowledge of the expert of the process. Nevertheless, fuzzy models do not have the structure to be analyzed through statistical metrics, one of them is the statistic metric R
²
. This work demonstrates that the fuzzy models do not have the statistical basis to apply a statistical analysis like R
²
and ANOVA, so it is proposing a methodology to transform a fuzzy model to a fuzzy least squares model. The above, using the membership functions and the if-then rules to transform the fuzzy model into a fuzzy least squares model. This methodology was applied on a tempering process which has as an input variables time of tempering, supplier, steel, and temperature, as output variable the hardness of the steel. Fuzzy least squares model shows an improve of 40% over the fuzzy model on the statistic metric R
²
, which means a better prediction to the process.