Study on permanent magnetic drive forecasting by designing Takagi Sugeno Kang type interval type-2 fuzzy logic systems

Abstract

The process of permanent magnetic drive (PMD) presents high uncertainty under the complex operating conditions. In this paper, a type of Takagi Sugeno Kang (TSK) interval type-2 fuzzy logic systems (IT2 FLSs) under the Karnik-Mendel (KM) structure is designed for data-based PMD torque and revolutions per minute (rpm) forecasting. For designing the antecedent and input measurement of TSK IT2 FLSs, the primary membership functions (MFs) of interval type-2 fuzzy sets (IT2 FSs) are all selected as Gaussian type-2 MFs with uncertain derivation, while the consequent parameters are chosen as type-1 fuzzy numbers. According to matrix transformation, the complicated task of calculating derivatives in the TSK IT2 FLSs under the Karnik-Mendel structure can be managed subtly by some elementary vectors and partitioned matrices. And the parameters of the proposed systems are also tuned by the back propagation (BP) algorithms. Simulation examples based on the data of PMD torque and rpm are used to test the advanced fuzzy logic systems forecasting methods. The effective and feasibility of forecasting by the proposed type-2 systems compared with their type-1 counterparts is illustrated in the light of Monte Carlo simulations, convergence and stability analysis.