基于辛几何迁移矩阵机的滚动轴承故障诊断方法

Fault Diagnosis Method for Rolling Bearings Based on SymplecticGeometry Transfer Matrix Machines

针对工程实践中获得的滚动轴承故障数据较少且包含大量噪声的问题,提出一种辛几何迁移矩阵机(SGTMM)的滚动轴承故障诊断方法。首先,利用辛几何相似变换重构辛几何系数矩阵,在保护信息结构的同时完成信号的降噪,有效提取信号的特征信息;然后,在SGTMM的目标函数中添加域权重差异项,通过最小化该项寻找不同域之间的相似特征以平衡模型间的差异,使得预测模型具有小样本分析能力;最后,利用交替方向乘子法求解模型,解决目标函数凸优化问题。2种滚动轴承故障试验结果表明,SGTMM利用辛几何相似变换和域权重差异项不仅可以保护原始信号结构化信息不变,而且能够充分利用小样本的状态信息,与支持向量机、支持矩阵机和鲁棒支持矩阵机相比,SGTMM具有优越的分类性能,平均识别率提高5%~10%。

In order to solve the problems of obtaining less fault data and containing a large amount of noise for rolling bearings in engineering practice,a bearing fault diagnosis method is proposed based on symplectic geometry transfer matrix machines(SGTMM).Firstly,SGTMM uses symplectic geometry similarity transformation to reconstruct the symplectic geometry coefficient matrix,which is able to denoise the signal while preserve the information structure,and extract the feature information of signal effectively.Then,a domain weight difference term is added to objective function of SGTMM,the similar features between different domains is found to balance the differences between models by minimizing the term,so that the prediction model has the ability to analyze small samples.Finally,the alternating direction multiplier method is used to solve the model,and the convex optimization problem of objective function is solved.The test results of two types of rolling bearing faults show that SGTMM can not only preserve the structured information of original signal by using symplectic geometry similarity transformation and domain weight difference term,but also fully utilize the state information of small samples.Compared with support vector machine(SVM),support matrix machine(SMM)and robust support matrix machine(RSMM),the proposed SGTMM method has superior classification performance,and the average recognition rate is increased by 5%~10%.