改进希尔伯特-黄变换含噪振动信号时频分析

Time-Frequency Analysis of Noisy Vibration Signal Based onImproved Hilbert-Huang Transform

针对希尔伯特-黄变换(Hilbert-Huang Transform, HHT)含噪振动信号时频分析产生的模态混淆和瞬时频率缺乏实际意义的现象,改进经验模态分解(EMD)得到自适应补充集合经验模态分解(CEEMDAN)后,结合多尺度排列熵(MPE)抑制EMD模态混淆,再改进Hilbert变换得到改进归一化Hilbert变换(INHT),最终形成CEEMDAN·MPE-INHT.为验证CEEMDAN·MPE-INHT含噪振动信号时频分析的准确性,进行EMD-HT、EEMD-NHT、CEEMDAN-INHT、CEEMDAN·MPE-INHT含噪仿真振动信号时频分析对比研究.研究结果表明:CEEMDAN能够控制低频噪声;MPE能抑制高频噪声;INHT使Hilbert变换不受Bedrosian定理约束.最后将CEEMDAN·MPE-INHT算法用于实际工程含噪振动信号时频分析中,CEEMDAN·MPE分解得到的固有模态函数(IMF)经INHT处理得到的时频谱在时域和频域上都具有较高的分辨率,可提高时频特征参数提取精度,有助于振动信号危害控制.

Aimed at the phenomenon of modal confusion and lack of practical significance of instantaneous frequency caused by Hilbert-Huang transform(HHT)noisy vibration signal time-frequency analysis,complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)is obtained by improving empirical mode decomposition(EMD),and in combination with multiscale permutation entropy(MPE)to suppress EMD modal confusion.At the same time,improved normalized Hilbert transform(INHT)is obtained by improving Hilbert transform,and finally the CEEMDAN·MPE-INHT time-frequency analysis algorithm is formed.In order to verify the accuracy of time-frequency analysis of CEEMDAN·MPE-INHT noisy vibration signals,a comparative study of time-frequency analysis of EMD-HT,EEMD-NHT,CEEMDAN-INHT and CEEMDAN·MPE-INHT noisy simulation vibration signals is conducted.The results show that CEEMDAN can control low frequency noise;MPE can suppress high frequency noise;INHT can make Hilbert transform not constrained by Bedrosian theorem.Finally,CEEMDAN·MPE-INHT algorithm is applied to the time-frequency analysis of noisy vibration signals in practical engineering.The time spectrum of intrinsic mode function(IMF)decomposed by CEEMDAN·MPE after INHT processing has a high resolution in time domain and frequency domain,which can improve the extraction accuracy of time-frequency characteristic parameters and help control the harm of vibration signals.