Abstract: Condition monitoring and fault diagnosis of gearboxes play an important role in the maintenance of mechanical systems. The vibration signal of gearboxes is characterized by complex spectral structure and strong time variability, which brings challenges to fault feature extraction. To address this issue, a new demodulation technique, based on the Fourier decomposition method and resonance demodulation, is proposed to extract fault-related information. First, the Fourier decomposition method decomposes the vibration signal into Fourier intrinsic band functions (FIBFs) adaptively in the frequency domain. Then, the original signal is segmented into short-time vectors to construct double-row matrices and the maximum singular value ratio method is employed to estimate the resonance frequency. Then, the resonance frequency is used as a criterion to guide the selection of the most relevant FIBF for demodulation analysis. Finally, for the optimal FIBF, envelope demodulation is conducted to identify the fault characteristic frequency. The main contributions are that the proposed method describes how to obtain the resonance frequency effectively and how to select the optimal FIBF after decomposition in order to extract the fault characteristic frequency. Both numerical and experimental studies are conducted to investigate the performance of the proposed method. It is demonstrated that the proposed method can effectively demodulate the fault information from the original signal.

基于傅里叶分解和共振解调的齿轮箱故障诊断

[1]AntoniJ, 2006. The spectral kurtosis: a useful tool for characterising non-stationary signals. Mechanical Systems and Signal Processing, 20(2):282-307.

[2]AntoniJ, 2007. Fast computation of the kurtogram for the detection of transient faults. Mechanical Systems and Signal Processing, 21(1):108-124.

[3]AntoniJ, RandallRB, 2006. The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines. Mechanical Systems and Signal Processing, 20(2):308-331.

[4]CongFY, ChenJ, DongGM, et al., 2013. Short-time matrix series based singular value decomposition for rolling bearing fault diagnosis. Mechanical Systems and Signal Processing, 34(1-2):218-230.

[5]DengMQ, DengAD, ZhuJ, et al., 2019. Adaptive bandwidth Fourier decomposition method for multi-component signal processing. IEEE Access, 7:109776-109791.

[6]DengMQ, DengAD, ZhuJ, et al., 2020. Bandwidth Fourier decomposition and its application in incipient fault identification of rolling bearings. Measurement Science and Technology, 31(1):015012.

[7]DragomiretskiyK, ZossoD, 2014. Variational mode decomposition. IEEE Transactions on Signal Processing, 62(3):531-544.

[8]FengZP, ZhangD, ZuoMJ, 2017. Adaptive mode decomposition methods and their applications in signal analysis for machinery fault diagnosis: a review with examples. IEEE Access, 5:24301-24331.

[9]HuangNE, ShenZ, LongSR, et al., 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454(1971):903-995.

[10]LeiYG, LinJ, HeZJ, et al., 2013. A review on empirical mode decomposition in fault diagnosis of rotating machinery. Mechanical Systems and Signal Processing, 35(1-2):‍108-126.

[11]LeiYG, LinJ, ZuoMJ, et al., 2014. Condition monitoring and fault diagnosis of planetary gearboxes: a review. Measurement, 48:292-305.

[12]LiH, LiZ, MoW, 2017. A time varying filter approach for empirical mode decomposition. Signal Processing, 138:146-158.

[13]LiZ, LiWG, ZhaoXZ, 2019. Feature frequency extraction based on singular value decomposition and its application on rotor faults diagnosis. Journal of Vibration and Control, 25(6):1246-1262.

[14]LiuYY, YangGL, LiM, et al., 2016. Variational mode decomposition denoising combined the detrended fluctuation analysis. Signal Processing, 125:349-364.

[15]ManZH, WangWY, KhooS, et al., 2012. Optimal sinusoidal modelling of gear mesh vibration signals for gear diagnosis and prognosis. Mechanical Systems and Signal Processing, 33:256-274.

[16]MoshrefzadehA, FasanaA, 2018. The autogram: an effective approach for selecting the optimal demodulation band in rolling element bearings diagnosis. Mechanical Systems and Signal Processing, 105:294-318.

[17]RatoRT, OrtigueiraMD, BatistaAG, 2008. On the HHT, its problems, and some solutions. Mechanical Systems and Signal Processing, 22(6):1374-1394.

[18]ShiJC, RenY, TangHS, et al., 2022. Hydraulic directional valve fault diagnosis using a weighted adaptive fusion of multi-dimensional features of a multi-sensor. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 23(4):257-271.

[19]SinghP, 2018. Novel Fourier quadrature transforms and analy

[20]tic signal representations for nonlinear and non-stationary time-series analysis. Royal Society Open Science, 5(11):181131.

[21]SinghP, JoshiSD, PatneyRK, et al., 2017. The Fourier decomposition method for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2199):20160871.

[22]SinghalA, SinghP, FatimahB, et al., 2020. An efficient removal of power-line interference and baseline wander from ECG signals by employing Fourier decomposition technique. Biomedical Signal Processing and Control, 57:101741.

[23]TongSG, HuangYY, JiangYQ, et al., 2019. The identification of gearbox vibration using the meshing impacts based demodulation technique. Journal of Sound and Vibration, 461:114879.

[24]TongSG, HuangYY, TongZM, et al., 2020. A novel short-frequency slip fault energy distribution-based demodulation technique for gear diagnosis and prognosis. International Journal of Advanced Robotic Systems, 17(2).

[25]TorresME, ColominasMA, SchlotthauerG, et al., 2011. A complete ensemble empirical mode decomposition with adaptive noise. IEEE International Conference on Acoustics, Speech and Signal Processing, p.4144-4147.

[26]WangD, 2018. Some further thoughts about spectral kurtosis, spectral L2/L1 norm, spectral smoothness index and spectral Gini index for characterizing repetitive transients. Mechanical Systems and Signal Processing, 108:360-368.

[27]WangJ, DuGF, ZhuZK, et al., 2020. Fault diagnosis of rotating machines based on the EMD manifold. Mechanical Systems and Signal Processing, 135:106443.

[28]WangTY, ChuFL, HanQK, et al., 2017. Compound faults detection in gearbox via meshing resonance and spectral kurtosis methods. Journal of Sound and Vibration, 392:367-381.

[29]WangTY, HanQK, ChuFL, et al., 2019. Vibration based condition monitoring and fault diagnosis of wind turbine planetary gearbox: a review. Mechanical Systems and Signal Processing, 126:662-685.

[30]WangWY, 2001. Early detection of gear tooth cracking using the resonance demodulation technique. Mechanical Systems and Signal Processing, 15(5):887-903.

[31]WuZH, HuangNE, 2009. Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1(1):1-41.

[32]YangXK, ZuoMJ, TianZG, 2022. Development of crack induced impulse-based condition indicators for early tooth crack severity assessment. Mechanical Systems and Signal Processing, 165:108327.

[33]YangXK, WeiDD, ZuoMJ, et al., 2023. Analysis of vibration signals and detection for multiple tooth cracks in spur gearboxes. Mechanical Systems and Signal Processing, 185:109780.

[34]YehJR, ShiehJS, HuangNE, 2010. Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method. Advances in Adaptive Data Analysis, 2(2):135-156.

[35]YiCC, LvY, DangZ, 2016. A fault diagnosis scheme for rolling bearing based on particle swarm optimization in variational mode decomposition. Shock and Vibration, 2016:9372691.

[36]ZhangD, LiuYY, FengZP, 2020. Demodulation analysis based on Fourier decomposition method and its application for gearbox fault diagnosis. International Conference on Sensing, Diagnostics, Prognostics, and Control, p.329-334.

[37]ZhangX, MiaoQ, ZhangH, et al., 2018. A parameter-adaptive VMD method based on grasshopper optimization algorithm to analyze vibration signals from rotating machinery. Mechanical Systems and Signal Processing, 108:58-72.

[38]ZhaoM, JiaXD, 2017. A novel strategy for signal denoising using reweighted SVD and its applications to weak fault feature enhancement of rotating machinery. Mechanical Systems and Signal Processing, 94:129-147.

[39]ZhaoXZ, YeBY, 2009. Similarity of signal processing effect between hankel matrix-based SVD and wavelet transform and its mechanism analysis. Mechanical Systems and Signal Processing, 23(4):1062-1075.

[40]ZhaoXZ, YeBY, 2011. Selection of effective singular values using difference spectrum and its application to fault diagnosis of headstock. Mechanical Systems and Signal Processing, 25(5):1617-1631.

[41]ZhouW, FengZR, XuYF, et al., 2022. Empirical Fourier decomposition: an accurate signal decomposition method for nonlinear and non-stationary time series analysis. Mechanical Systems and Signal Processing, 163:108155.