Abstract:  In order to solve the problem that support matrix machine (SMM) used parallel hyperplanes to classify different types of samples, which could not maximize the interval between any two types of samples. By analyzing the related theories of nonparallel hyperplane and SMM, a multi-class bounded support matrix machine (MBSMM) was proposed. It was applied to the fault diagnosis of rolling bearing. Firstly,in MBSMM, the multi classification objective function was established with the matrix as the modeling element, which made full use of the structured information between the rows and columns of the input matrix. Then, the nonparallel bounded hyperplane was used to isolate any two types of data, and the hyperplane could maximize the interval between any two types of samples. The successive overrelaxation (SOR) method was introduced to solve the dual problem. SOR could converge linearly to the optimal value, and could deal with large-scale data sets without too much calculation, which greatly improved the computational efficiency of the algorithm. Finally, it was applied to the fault diagnosis of rolling bearing. It was verified by rolling bearing data and different indexes. The experimental results show that MBSMM can accurately classify complex data samples by using nonparallel bounded hyperplane, which proves the MBSMM has superior classification performance in recognition rate, time, kappa, accuracy, recall rate, F1 score and statistical test.

Key words:  multi-class bounded support matrix machine（MBSMM）; rolling bearing; fault diagnosis; nonparallel bounded hyperplane

MA Wen-jing, LI Xin, ZHANG Yun. Multi-class bounded support matrix machine and its application in rolling bearing fault diagnosis［J］.Journal of Mechanical & Electrical Engineering, 2022,39(1):65-70.