Non-stationary signal analysis based on general parameterized time--frequency transform and its application in the feature extraction of a rotary machine

doi:10.1007/s11465-017-0443-0

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

Download: PDF(442 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-017-0443-0
https://academic.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 type	$f 1$ /Hz	$α 1$	$α 2$
Estimated	29.898	−6.446	0.492
Exact	30.000	−6.500	0.500

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

k	Parameter type	$f k$ /Hz	$a 1$	$a 2$
First one (k = 1)	Estimated	9.997	1.001	−1.159×10⁻⁴
First one (k = 1)	Exact	10.000	1.000	0.000
Second one (k = 2)	Estimated	20.001	3.998	−0.199
Second one (k = 2)	Exact	20.000	4.000	−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

k	Parameter type	$f k$ /Hz	$a 1$	$a 2$
First one (k = 1)	Estimated	39.995	−2.332	−6.384×10⁻⁵
First one (k = 1)	Real	40.000	−7/3	0
Second one (k = 2)	Estimated	19.998	−1.331	0.133
Second one (k = 2)	Real	20.000	−4/3	2/15
Third one (k = 3)	Estimated	4.996	0.663	5.150×10⁻⁴
Third one (k = 3)	Real	5.000	2/3	0

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

Components	$f k$ /Hz	$a 1$	$a 2$	$a 3$
Fundamental frequency	1.6045	−0.0618	0.0011	−7.8561×10⁻⁶
2×	3.1383	−0.1215	0.0023	−1.6728×10⁻⁵
3×	4.7132	−0.1840	0.0036	−2.5872×10⁻⁵
4×	6.2118	−0.2367	0.0045	−3.2075×10⁻⁵

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

[1]	Huijun ZOU, Qinghua LIANG. Establishing distinctive theories and methods of design science rooted in Chinese traditional culture[J]. Front. Mech. Eng., 2020, 15(3): 430-437.
[2]	Xuefeng CHEN, Shibin WANG, Baijie QIAO, Qiang CHEN. Basic research on machinery fault diagnostics: Past, present, and future trends[J]. Front. Mech. Eng., 2018, 13(2): 264-291.
[3]	Zhaohui DU, Xuefeng CHEN, Han ZHANG, Yanyang ZI, Ruqiang YAN. Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes[J]. Front. Mech. Eng., 2017, 12(3): 333-347.
[4]	Shoudao HUANG, Xuan WU, Xiao LIU, Jian GAO, Yunze HE. Overview of condition monitoring and operation control of electric power conversion systems in direct-drive wind turbines under faults[J]. Front. Mech. Eng., 2017, 12(3): 281-302.
[5]	Zongxia JIAO,Tianyi WANG,Liang YAN. Design and analysis of linear oscillating motor for linear pump application-magnetic field, dynamics and thermotics[J]. Front. Mech. Eng., 2016, 11(4): 351-362.
[6]	Olga EGOROVA,Dmitry SHCHERBININ. Creating technical heritage object replicas in a virtual environment[J]. Front. Mech. Eng., 2016, 11(1): 108-115.
[7]	Diego CABRERA,Fernando SANCHO,René-Vinicio SÁNCHEZ,Grover ZURITA,Mariela CERRADA,Chuan LI,Rafael E. VÁSQUEZ. Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition[J]. Front. Mech. Eng., 2015, 10(3): 277-286.
[8]	M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method[J]. Front. Mech. Eng., 2014, 9(1): 58-70.
[9]	Walha LASSAAD, Tounsi MOHAMED, Driss YASSINE, Chaari FAKHER, Fakhfakh TAHER, Haddar MOHAMED. Nonlinear dynamic behaviour of a cam mechanism with oscillating roller follower in presence of profile error[J]. Front Mech Eng, 2013, 8(2): 127-136.
[10]	H. BABAZADEH, G. DOMAIRRY, A. BARARI, R. AZAMI, A. G. DAVODI. Numerical analysis of strongly nonlinear oscillation systems using He’s max-min method[J]. Front Mech Eng, 2011, 6(4): 435-441.
[11]	Houjun SU, Tielin SHI, Fei CHEN, Shuhong HUANG. New method of fault diagnosis of rotating machinery based on distance of information entropy[J]. Front Mech Eng, 2011, 6(2): 249-253.
[12]	Lixin GAO, Lijuan WU, Yan WANG, Houpei WEI, Hui YE. Intelligent fault diagnostic system based on RBR for the gearbox of rolling mills[J]. Front Mech Eng Chin, 2010, 5(4): 483-490.
[13]	Shaohong WANG, Tao CHEN, Jianghong SUN. Design and realization of a remote monitoring and diagnosis and prediction system for large rotating machinery[J]. Front Mech Eng Chin, 2010, 5(2): 165-170.
[14]	Xiaohu CHEN, Wenfeng WU, Hangong WANG, Yongtao ZHOU, . Distributed monitoring and diagnosis system for hydraulic system of construction machinery[J]. Front. Mech. Eng., 2010, 5(1): 106-110.
[15]	Jun WANG. Depth of cut models for multipass abrasive waterjet cutting of alumina ceramics with nozzle oscillation[J]. Front. Mech. Eng., 2010, 5(1): 19-32.

Viewed

Full text

Abstract

Cited

Shared

Discussed