群延迟加权的非凸稀疏时频分析方法及其应用  

Weighted Group-delay and Non-convex Sparse Time-frequency Analysis Method and Its Application in Fault Diagnosis

作　　者：赵文强 王正伟 周军 石生超 马海峰 李富才[3] ZHAO Wenqiang;WANG Zhengwei;ZHOU Jun;SHI Shengchao;MA Haifeng;LI Fucai(Electric Power Research Institute,State Grid Qinghai Elecctric Power Company,Xining 810008,China;Ultra High Voltage Company,State Grid Qinghai Eletric Power Company,Xining 810021,China;State Key Laboratory of Mechanical System and Vibration,Shanghai Jiaotong University,Shanghai 200240,China)

机构地区：[1]国网青海省电力公司电力科学研究院,西宁810008 [2]国网青海省电力公司超高压公司,西宁810021 [3]上海交通大学机械系统与振动全国重点实验室,上海200240

出　　处：《噪声与振动控制》2025年第1期152-157,286,共7页Noise and Vibration Control

基　　金：国网青海省电力公司科技资助项目(522807220005)。

摘　　要：时频分析方法被广泛应用于机械系统故障诊断,如何有效提高非平稳信号的时频分布可读性成为时频分析的难点。将稀疏理论与时频分析方法相结合,可实现高分辨率的时频表示。在理想脉冲信号模型的基础上,将群延迟算子引入广义极大极小凹正则稀疏时频表示模型,提出基于群延迟加权的非凸稀疏时频表示。首先,建立基于广义极大极小凹正则的非凸稀疏时频模型,并给出保证目标函数凸性的参数条件。其次,推导群延迟算子并建立加权策略,提出前向后向分裂算法以求解加权非凸稀疏时频表示模型。再次,利用仿真信号对所提方法在时频聚集性和重构性等方面的性能进行分析。最后,根据滚动轴承的模拟信号和实验信号进行故障分析,验证了所提出的方法在滚动轴承故障诊断中的有效性。Time-frequency analysis is widely used in mechanical system fault diagnosis,but improving the readability of time-frequency representation of non-stationary signals is difficult.To address this problem,this study combines sparse theory with time-frequency analysis to achieve high-resolution time-frequency representation.According to the model of ideal impulse signal,a non-convex sparse time-frequency representation model based on group delay weighting was proposed.First of all,the sparse time-frequency model based on generalized maximum-minimum concave normalization was established,and the parameter condition which guarantees the convex of the objective function was given,Then,the group-delay operator was formulated and the weighting strategy was established,and the forward-backward splitting algorithm was proposed to solve the weighted non-covex sparse representative model.And the proposed method was evaluated and analyzed in the aspects of time-frequency aggregation and reconstruction feature using the simulated signals.Finally,the proposed method was applied to rolling bearing fault diagnosis according to the simulated and experimental signals,which demonstrated the effectiveness of this method in rolling bearing fault diagnosis.

关 键 词：故障诊断 稀疏理论 时频分析 群延迟 非平稳信号 

分 类 号：TH133.2[机械工程—机械制造及自动化]