# Frontiers of Mechanical Engineering

 Front. Mech. Eng.    2018, Vol. 13 Issue (2) : 292-300     https://doi.org/10.1007/s11465-017-0443-0
 RESEARCH ARTICLE |
Non-stationary signal analysis based on general parameterized time--frequency transform and its application in the feature extraction of a rotary machine
Peng ZHOU, Zhike PENG(), Shiqian CHEN, Yang YANG, Wenming ZHANG
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 201100, China
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 Abstract With the development of large rotary machines for faster and more integrated performance, the condition monitoring and fault diagnosis for them are becoming more challenging. Since the time-frequency (TF) pattern of the vibration signal from the rotary machine often contains condition information and fault feature, the methods based on TF analysis have been widely-used to solve these two problems in the industrial community. This article introduces an effective non-stationary signal analysis method based on the general parameterized time–frequency transform (GPTFT). The GPTFT is achieved by inserting a rotation operator and a shift operator in the short-time Fourier transform. This method can produce a high-concentrated TF pattern with a general kernel. A multi-component instantaneous frequency (IF) extraction method is proposed based on it. The estimation for the IF of every component is accomplished by defining a spectrum concentration index (SCI). Moreover, such an IF estimation process is iteratively operated until all the components are extracted. The tests on three simulation examples and a real vibration signal demonstrate the effectiveness and superiority of our method. Corresponding Authors: Zhike PENG Just Accepted Date: 08 June 2017   Online First Date: 06 July 2017    Issue Date: 19 March 2018
 Cite this article: Peng ZHOU,Zhike PENG,Shiqian CHEN, et al. Non-stationary signal analysis based on general parameterized time--frequency transform and its application in the feature extraction of a rotary machine[J]. Front. Mech. Eng., 2018, 13(2): 292-300. URL: http://journal.hep.com.cn/fme/EN/10.1007/s11465-017-0443-0 http://journal.hep.com.cn/fme/EN/Y2018/V13/I2/292
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 Fig.1  Principle of the GPTFT (vector graph) Fig.2  TF patterns of the signal in Eq. (5). (a) STFT; (b) WT; (c) WVD; (d) PCT Tab.1  Estimated parameters based on the PCT for signal in Eq. (5) Fig.3  (a) TF pattern of the original signal; (b) frequency spectrum of the original signal; (c) TF pattern after rotation; (d) frequency spectrum after rotation Fig.4  Multi-component IF extraction process (vector graph) Fig.5  TF patterns in several steps of the proposed algorithm. (a) STFT of the original signal; (b) STFT after demodulating the first component; (c) filtering the first component; (d) PCT of the reconstructed component; (e) PCT of the second component; (f) assembled TF pattern Tab.2  Estimated parameters based on the SCI for signal in Eq. (13) Fig.6  TF patterns of signal in Eq. (14). (a) STFT; (b) WT; (c) WVD; (d) assembled PCT Tab.3  Estimated parameters based on SCI for signal in Eq. (14) Fig.7  TF patterns of the hydroturbine vibration signal. (a) STFT; (b) WT; (c) WVD; (d) assembled PCT Tab.4  Estimated parameters of the four IFs of the vibration signal
 1 Chu F, Peng Z, Feng Z, et al.. Modern Signal Processing Approach in Machine Fault Diagnosis. Beijing: Science Press, 2009 (in Chinese) 2 Yang P. Data mining diagnosis system based on rough set theory for boilers in thermal power plants. Frontiers of Mechanical Engineering, 2006, 1(2): 162–167 https://doi.org/10.1007/s11465-006-0017-z 3 Li W, Shi T, Yang S. An approach for mechanical fault classification based on generalized discriminant analysis. Frontiers of Mechanical Engineering, 2006, 1(3): 292–298 https://doi.org/10.1007/s11465-006-0022-2 4 Chen X, Wu W, Wang H, et al.. Distributed monitoring and diagnosis system for hydraulic system of construction machinery. Frontiers of Mechanical Engineering, 2010, 5(1): 106–110 https://doi.org/10.1007/s11465-009-0089-7 5 Wang S, Chen T, Sun J. Design and realization of a remote monitoring and diagnosis and prediction system for large rotating machinery. Frontiers of Mechanical Engineering, 2010, 5(2): 165–170 https://doi.org/10.1007/s11465-009-0090-1 6 Su H, Shi T, Chen F, et al.. New method of fault diagnosis of rotating machinery based on distance of information entropy. Frontiers of Mechanical Engineering, 2011, 6(2): 249–253 7 Yang Y. Theory, methodology of parameterized time-frequency analysis and its application in engineering signal processing. Dissertation for the Doctoral Degree. Shanghai: Shanghai Jiao Tong University, 2013 (in Chinese) 8 Yang Y, Peng Z, Dong X, et al.. General parameterized time-frequency transform. IEEE Transactions on Signal Processing, 2014, 62(11): 2751–2764 https://doi.org/10.1109/TSP.2014.2314061 9 Mihovilovic D, Bracewell R. Adaptive chirplet representation of signals on time-frequency plane. Electronics Letters, 1991, 27(13): 1159–1161 https://doi.org/10.1049/el:19910723 10 Mann S, Haykin S. ‘Chirplets’ and ‘warblets’: Novel time-frequency methods. Electronics Letters, 1992, 28(2): 114–116 https://doi.org/10.1049/el:19920070 11 Angrisani L, D’Arco M, Schiano Lo Moriello R, et al.. On the use of the warblet transform for instantaneous frequency estimation. IEEE Transactions on Instrumentation and Measurement, 2005, 54(4): 1374–1380 https://doi.org/10.1109/TIM.2005.851060 12 Yang Y, Peng Z, Meng G, et al.. Characterize highly oscillating frequency modulation using generalized Warblet transform. Mechanical Systems and Signal Processing, 2012, 26: 128–140 https://doi.org/10.1016/j.ymssp.2011.06.020 13 Gribonval R. Fast matching pursuit with a multiscale dictionary of Gauss chirps. IEEE Transactions on Signal Processing, 2001, 49(5): 994–1001 https://doi.org/10.1109/78.917803 14 Angrisani L, D’Arco M. A measurement method based on modificed version of the chirplet transform for instantaneous frequenct estimation. IEEE Transactions on Instrumentation and Measurement, 2002, 51(4): 704–711 https://doi.org/10.1109/TIM.2002.803295 15 Candès E J, Charlton P R, Helgason H. Detecting highly oscillatory signals by chiplet path pursuit. Applied and Computational Harmonic Analysis, 2008, 24(1): 14–40 https://doi.org/10.1016/j.acha.2007.04.003 16 Zou H, Dai Q, Wang R, et al.. Parametric TFR via windowed exponential frequency modulated atoms. IEEE Signal Processing Letters, 2001, 8(5): 140–142 https://doi.org/10.1109/97.917696 17 Yang Y, Peng Z, Dong X, et al.. Application of parameterized time-frequency analysis on multicomponent frequency modulated signals. IEEE Transactions on Instrumentation and Measurement, 2014, 63(12): 3169–3180 https://doi.org/10.1109/TIM.2014.2313961 18 Huang N, Shen Z, Long S, et al.. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A, 1998, 454(1971): 903–995 https://doi.org/10.1098/rspa.1998.0193 19 Wu Z, Huang N E. Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 2009, 1(1): 1–41 https://doi.org/10.1142/S1793536909000047 20 Mallat S G, Zhang Z. Matching pursuit in a time-frequency dictionary. IEEE Transactions on Signal Processing, 1993, 41(12): 3397–3415 https://doi.org/10.1109/78.258082 21 Chen S S, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM Review, 2001, 43(1): 129–159 https://doi.org/10.1137/S003614450037906X 22 Dragomiretskiy K, Zosso D. Variational mode composition. IEEE Transactions on Signal Processing, 2014, 62(3): 531–544 https://doi.org/10.1109/TSP.2013.2288675 23 Chen S, Yang Y, Wei K, et al.. Time-varying frequency-modulated component extraction based on parameterized demodulation and singular value decomposition. IEEE Transactions on Instrumentation and Measurement, 2016, 65(2): 276–285 https://doi.org/10.1109/TIM.2015.2494632 24 Peng Z, Meng G, Chu F, et al.. Polynomial chirplet transform with application to instantaneous frequency estimation. IEEE Transactions on Instrumentation and Measurement, 2011, 60(9): 3222–3229 https://doi.org/10.1109/TIM.2011.2124770 25 Yang Y, Peng Z, Meng G, et al.. Spline-kernelled chirplet transform for the analysis of signals with time-varying frequency and its application. IEEE Transactions on Industrial Electronics, 2012, 59(3): 1612–1621 https://doi.org/10.1109/TIE.2011.2163376
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