Magnetic Remanence Prediction of NdFeB Magnets Based on a Novel Machine Learning Intelligence Approach Using a Particle Swarm Optimization Support Vector Regression

1. Introduction

The rare earth permanent material NdFeB with low rare earth content, high magnetic remanence, relatively high coercivity and high maximum magnetic enegy product has become a research focus in recent years(Kneller, & Hawig, 1991; Skomski, & Coey,1993; Schrefl, Fidler, & Kronmuller,1994). The magnetic remanence of NdFeB is closely related to the alloying element content. Usually the magnetic remanence can be improved through optimization of alloying compositions(Jakubowicz, & Jurczyk, 2000; Jakubowicz, & Szlaferek,1999; Rieger, Seeger, Li, & Kronmuller,1995). But the common method is to change a kind of element content while keep the other alloying element unchanged, and then to find the change trend between this element and the magnetic remanence, and then by using the same method study how the other elements affect the magnetic remanence. But in this method the experimental work is heavy, and that the effect of interaction between various components on magnetic remanence cannot be considered at the same time. The relationship between the interaction of various components and the magnetic remanence is very complex and nonlinear. It is difficult to build an accurate theoretical method to predict the magnetic remanence. Support vector regression (SVR), proposed by Vapnik and coworker in 1995, is a new powerful machine learning theory based on structural risk minimization principle(Vapnik, 1995, 1999). Due to its excellent performance such as fast-learning, global optimization and excellent generalization ability for small-sample, SVR has been developed to solve nonlinear regression issues(Cai, Han, Ji, Chen, & Chen, 2003; Cai, Han, Ji, & Chen, 2004; Cai, Wang,, & Chen, 2003; Cai, Wang, Sun, & Chen, 2003; Cai, Xiao, Tang, & Huang, 2013; Cai, Zhu, Wen, Pei, Wang, & Zhuang, 2010; Firat, Ozay, Onal, Oztekin, & Yarman Vural, 2013; Kharrat, Gasmi, Ben Messaoud, Benamrane, & Abid, 2011; Lin, & Pai, 2001; Pei, Cai, Zhu, & Yan, 2013; Tang, Cai, & Zhao, 2012; Wen, Cai, Liu, Pei, Zhu, &Xiao, 2009; Xiao, Cai, Tang, & Huang, 2013; Yi, Peng, & Li, 2012). In this paper the SVR model integrating leave-one-out cross validation (LOOCV) was build to predict the magnetic remanence of the NdFeB magnet combined with particle swarm optimization algorithm for its parameter optimization.