TSK-type FLC using a combined LR and GA: Surface roughness prediction in ultraprecision turning

Due to non-linearity of the cutting parameters, tool–work combination and rigidity of machine tool, it has been proved that a fuzzy logic concept gives a better way to model a complex manufacturing process, such as grinding, ultraprecision turning, etc. In this paper, an Takagi–Sugeno–Kang (TSK)-type fuzzy logic controller (FLC) is designed to model the input–output relationship of ultraprecision turning. The performance of an FLC primarily depends on its knowledge base, which consists of rule base and the membership function distributions (fuzzy subsets) considered for the variables. In TSK-type fuzzy system, the output of a fuzzy rule is a linear combination of the input variables, which is characterized by function coefficients and the variableʹs exponential parameters. In the present work, two approaches are considered to design the TSK-type FLC: one is based on linear regression (LR) method with constant and same exponential parameters for all the rule, and the other is based on LR with simultaneous optimization of exponential parameter using genetic algorithm (GA). The results of the proposed approaches are compared with the empirical expression, which is not accurate, as well as real experimental data to predict surface roughness in ultraprecision turning.