【摘要】 由于支持矩阵机(SMM)利用平行超平面实现对不同类别样本的分类,使其无法最大化任意两类样本之间间隔,为此,通过分析非平行超平面与支持矩阵机的相关理论,提出了一种多分类边界支持矩阵机(MBSMM),并将其应用于滚动轴承的故障诊断中。首先,在MBSMM中以矩阵为建模元素,建立了其多分类目标函数,充分利用输入矩阵行与列之间的结构化信息;然后,利用非平行边界超平面来隔离任意两种类型的数据,非平行边界超平面可以最大化任意两类样本之间的间隔;引入了逐次超松弛法(SOR)进行对偶问题求解,SOR可以线性收敛到最优值,不需要太多计算就可以处理大规模数据集,大大提高了算法的计算效率;最后,将其应用于滚动轴承的故障诊断中,通过滚动轴承数据及不同指标对其进行了实验验证。研究结果表明:MBSMM利用非平行边界超平面可以完成对复杂数据样本的准确分类,在识别率、时间、kappa、准确率、召回率、F1得分和统计检验等方面具有良好表现,证明了RSMM具有优越的分类性能。更多还原

【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.更多还原