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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.

Keywords rotary machines      condition monitoring      fault diagnosis      GPTFT      SCI     
Corresponding Author(s): 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
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
Parameter typef1/Hzα1α2
Estimated29.898−6.4460.492
Exact30.000−6.5000.500
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
kParameter typefk/Hza1a2
First one (k = 1)Estimated9.9971.001−1.159×10−4
Exact10.0001.0000.000
Second one (k = 2)Estimated20.0013.998−0.199
Exact20.0004.000−0.200
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
kParameter typefk/Hza1a2
First one (k = 1)Estimated39.995−2.332−6.384×10−5
Real40.000−7/30
Second one (k = 2)Estimated19.998−1.3310.133
Real20.000−4/32/15
Third one (k = 3)Estimated4.9960.6635.150×10−4
Real5.0002/30
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
Componentsfk/Hza1a2a3
Fundamental frequency1.6045−0.06180.0011−7.8561×10−6
3.1383−0.12150.0023−1.6728×10−5
4.7132−0.18400.0036−2.5872×10−5
6.2118−0.23670.0045−3.2075×10−5
Tab.4  Estimated parameters of the four IFs of the vibration signal
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