基于频率成比例重分配线性Chirplet变换的时频分析方法  

Time-frequency analysis method of frequency proportional reassignment linear Chirplet transform

作　　者：岳子毫 裴帮 王征兵 李志远 雷欢欢 YUE Zihao;PEI Bang;WANG Zhengbing;LI Zhiyuan;LEI Huanhuan(Zhengzhou Research Institute of Mechanical Engineering Co.,Ltd.,Zhengzhou 450001,China)

机构地区：[1]郑州机械研究所有限公司,河南郑州450001

出　　处：《机电工程》2023年第12期1823-1834,共12页Journal of Mechanical & Electrical Engineering

基　　金：河南省中央引导地方科技发展资金项目(113ZP20220165)。

摘　　要：齿轮故障信号具有典型的调制特征,其各个频率分量的瞬时频率轨迹具有成比例特征;同时,传统的时频方法存在时频能量集中度低、弱分量信号被淹没的问题。为此,提出了一种频率成比例重分配线性Chirplet变换(PFSRLCT)的时频分析方法。首先,修改了线性Chirplet变换,利用新的核函数来匹配信号的瞬时频率轨迹,以获得时频域表示,利用脊线搜索方法提取了时频脊线;然后,利用时频脊线和狄拉克函数构造了同步重分配算子,对所得到的时频结果进行了重分配,进一步提高了时频能量集中度;最后,利用模拟信号验证了PFSRLCT方法的有效性,并将其与其他方法进行了比较;此外又将该方法应用于实际齿轮箱故障信号的诊断,从所得到的时频结果中可以清楚地分辨出啮合频率fm及其谐波和边频带,所诊断出的故障类型与预设故障类型符合,验证了该方法的适用性。研究结果表明:PFSRLCT在处理具有瞬时频率轨迹成比例特征的信号时,显示出了良好的性能,在信噪比为-2 dB~10 dB时,所得的频率估计误差均小于0.01,在信噪比为-1 dB时,所得Rényi熵仅为4.7451,均明显小于其他方法,证明该方法的噪声鲁棒性相较于其他方法更强,能量集中度更高;同时,该方法应用于实际齿轮故障信号时,所得Rényi熵仅为3.0698,明显低于其他方法,说明其可以获得更高的时频能量集中度,具有更好的表现能力。The gear fault signal had typical modulation characteristics,and the instantaneous frequency trajectories of its individual frequency components had proportional characteristics.Meanwhile,the traditional time-frequency method had the problems of low concentration of time-frequency energy and drowning of weak component signals.To address this problem,a time-frequency analysis method of proportional frequency reassignment linear Chirplet transform(PFSRLCT)was proposed.First,the linear Chirplet transform was modified to match the instantaneous frequency trajectory of the signal to obtain the time-frequency domain representation using the new kernel function,and the time-frequency spine was extracted using the spine search method.Then,the synchro-reassign operator was constructed using the time-frequency spine and the Dirac function to redistribute the obtained time-frequency results to further improve the time-frequency energy concentration.Finally,the effectiveness of the PFSRLCT method was verified by simulated signals,and it was compared with other methods.In addition,the method was applied to the diagnosis of actual gearbox fault signals,and the meshing frequency fm and its harmonics and side frequency bands were clearly distinguished from the obtained time-frequency results,and the diagnosed fault types were consistent with the preset fault types,which verified the applicability of the method.The research results show that PFSRLCT has good performance in processing signals with proportional characteristics of instantaneous frequency trajectories,and the obtained frequency estimation errors are less than 0.01 at signal-to-noise ratios of-2 dB to 10 dB.The obtained Rényi entropy is only 4.7451 at signal-to-noise ratios of-1 dB,which is significantly smaller than other methods.It is proved that the noise robustness of this method is stronger and the energy concentration is higher than other methods.Meanwhile,when this method is applied to the actual gear fault signal,the Rényi entropy obtained is only 3.0698,whi

关 键 词：地铁齿轮故障诊断 频率成比例重分配线性Chirplet变换 时频分析方法 故障信号调制 脊提取 时频重分配 

分 类 号：TH132.41[机械工程—机械制造及自动化]