A Gaussian process regression based on variable parameters fuzzy dominance genetic algorithm for B-TFPMM torque estimation

Abstract

Transverse Flux Permanent Magnet Motor (TFPMM) has received extensive attention in the field of electric vehicles. The magnetic circuit of TFPMM is three-dimensional and non-linear, which leads to the high nonlinearity of electromagnetic torque. Although the three-dimensional finite element method (3DFEM) could be used to estimate torque, it is very time-consuming. Instead of it, this study adopts a kind of machine learning method—Gaussian process regression (GPR). For the hyper-parameters optimization of GPR, most previous studies used single-objective algorithms for improving the regression accuracy. However, GPR is an algorithm of probability prediction and it could not guarantee to have the satisfactory confidence interval characteristic simultaneously while the regression precision achieves optimal. Therefore this paper proposes a variable parameters fuzzy dominance genetic algorithm (VPFDGA) which is suitable for the multi-objective optimization, including the optimization of regression precision, confidence interval reliability, confidence interval width and skill score. By combining GPR with VPFDGA, the electromagnetic torque of a building-block transverse flux permanent magnet motor (B-TFPMM) is estimated by VPFDGA-GPR (GPR based on variable parameters fuzzy dominance genetic algorithm). Besides, two other GPRs based multi-objective optimization, three GPRs based on single-objective optimization and a GPR based on weighted sum method that is the classic multi-objective optimization algorithm are all implemented to compare with VPFDGA-GPR. The results of comparison show that VPFDGA-GPR has the better performances including the higher regression precision, more powerful ability of probability prediction, higher stability, less convergence time and so on.