自适应学习字典的信号稀疏表示方法及其在轴承故障诊断中的应用  

Signal sparse representation method of adaptive learning dictionary and its application in bearing fault diagnosis

作　　者：张成 黄伟国 马玉强 阙红波 江星星 朱忠奎 ZHANG Cheng;HUANG Wei-guo;MA Yu-qiang;QUE Hong-bo;JIANG Xing-xing;ZHU Zhong-kui(School of Rail Transportation,Soochow University,Suzhou 215131,China;CRRC Qishuyan Institute Co.,Ltd.,Changzhou 213011,China)

机构地区：[1]苏州大学轨道交通学院,江苏苏州215131 [2]中车戚墅堰机车车辆工艺研究所有限公司,江苏常州213011

出　　处：《振动工程学报》2022年第5期1278-1288,共11页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(52075353,51875376)。

摘　　要：信号稀疏表示的过完备字典根据构造方式分为解析字典和学习字典两大类。解析字典结构固定,自适应性差。构建解析字典需要充分分析振动信号的振荡特性,获取充足的先验知识。学习字典摆脱了先验知识的桎梏,可以直接从信号中自适应地训练学习出来,自适应性强。结合信号保真能力较好的广义极小极大凹罚函数,提出了基于自适应学习字典的信号稀疏表示方法,改进了K‐SVD算法中样本训练矩阵的构造方式,减少了运算时间,并且利用软阈值算法弥补了学习字典对噪声抵抗性较差的缺点。最后在缺乏先验知识的条件下,分别在轴承的仿真信号和实验信号的分析过程中,运用所提出方法实现故障诊断。The over-complete dictionaries of signal sparse representation can be divided into analytical dictionary and learning dictionary according to the construction method.The analytical dictionary has a fixed structure and poor adaptability.The construction of the analyti‐cal dictionary needs to fully analyze the oscillation characteristics of the vibration signal and obtain sufficient prior knowledge.The learn‐ing dictionary gets rid of the shackles of prior knowledge and can be trained directly from the signal,with strong adaptability.Combined with the generalized minimum maximum concave penalty function,which has strong signal fidelity ability,this paper proposes a signal sparse representation method based on an adaptive learning dictionary.The proposed method improves the construction of the sampletraining matrix in the K-SVD algorithm,reduces the computing time,and makes up for the shortcomings of the learning dictionary's poor resistance to noise with the soft threshold algorithm.Without any prior knowledge,the method proposed in this paper is used to realize the fault diagnosis,in the process of analyzing the simulation signal and experimental signal of the bearing.

关 键 词：故障诊断 轴承 稀疏表示 K‐SVD算法 字典学习 GMC罚函数 

分 类 号：TH165.3[机械工程—机械制造及自动化] TH133.3