基于CPP与S变换的自适应时频滤波及其在滚动轴承故障诊断中的应用

针对变转速下滚动轴承故障调制信息的提取与分离,提出了基于线调频小波路径追踪(CPP)与S变换的自适应时频滤波方法。该方法先采用Hilbert解调对齿轮箱振动信号进行分析获取其包络信号,并对包络信号进行S变换,以获取其时频分布,同时,采用CPP算法从齿轮箱振动信号中估计出啮合频率曲线,进而获取转轴转速；然后,根据估计的转速信号分别设计各阶时频滤波器；再采用时频滤波器对包络信号的时频分布进行时频滤波,并将滤波结果进行S逆变换,以获取各阶故障调制信号；最后对各阶故障调制信号进行阶次谱分析,并根据阶次谱中的调制信息诊断滚动轴承故障。算法仿真和应用实例表明,自适应时频滤波方法可根据轴承故障调制信号的频率变化特点自适应地改变滤波器的中心频率与带宽,能有效提取并分离轴承的各阶调制信息,且分离效果优于基于集合经验模态分解（EEMD）的阶次谱方法。 

Adaptive time frequency filtering method based on CPP and S transform and its application in fault diagnosis of rolling bearing

Aiming at extracting and separating fault modulation message of rolling bearing under variable rotational speed, an adaptive time frequency filtering method based on chirplet path pursuit (CPP) and S transform was proposed. In this method, the envelope of vibration signal of a gearbox was obtained by Hilbert demodulation, and the S transform was carried out for the envelope signal so as to get its time frequency distribution, meanwhile, the CPP algorithm was used to estimate the gear mesh frequency from the vibration signal of a gearbox, then, the shaft rotational speed can be got. According to the shaft rotational speed, each adaptive time frequency filter was designed. Then the time frequency filtering was carried out for the time frequency distribution of envelope signal, and the S inverse transform was used for the filtered results so as to get each fault demodulation signal. Lastly, the order spectrum analysis was carried out for each fault demodulation signal, and the fault of rolling bearing was diagnosed according to the demodulation information in order spectrum. Simulation and application examples indicate that the adaptive time frequency filtering method can adaptively change the filters center frequency and bandwidth according to the frequency variation characteristics of the rolling bearings fault modulation signal, and also can effectively extract and separate each order demodulation message of rolling bearing, besides, it has better separation effect than the ensemble empirical mode decomposition(EEMD) based order spectrum method.