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Research Papers

A Frequency-Shift Synchrosqueezing Method for Instantaneous Speed Estimation of Rotating Machinery

[+] Author and Article Information
Songtao Xi

State Key Laboratory for
Manufacturing Systems Engineering,
Xi’an Jiaotong University,
Xi’an 710049, China
e-mail: xst121@stu.xjtu.edu.cn

Hongrui Cao

Associate Professor
State Key Laboratory for
Manufacturing Systems Engineering,
Xi’an Jiaotong University,
Xi’an 710049, China
e-mail: chr@mail.xjtu.edu.cn

Xuefeng Chen

Professor
State Key Laboratory for
Manufacturing Systems Engineering,
Xi’an Jiaotong University,
Xi’an 710049, China
e-mail: chenxf@mail.xjtu.edu.cn

Xingwu Zhang

Assistant Professor
State Key Laboratory for
Manufacturing Systems Engineering,
Xi’an Jiaotong University,
Xi’an 710049, China
e-mail: xwzhang@mail.xjtu.edu.cn

Xiaoliang Jin

Assistant Professor
Mem. ASME
School of Mechanical and
Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74078-5016
e-mail: xiaoliang.jin@okstate.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 15, 2014; final manuscript received February 5, 2015; published online March 2, 2015. Assoc. Editor: Robert Gao.

J. Manuf. Sci. Eng 137(3), 031012 (Jun 01, 2015) (11 pages) Paper No: MANU-14-1539; doi: 10.1115/1.4029824 History: Received October 15, 2014; Revised February 05, 2015; Online March 02, 2015

Instantaneous speed (IS) measurement is crucial in condition monitoring and real-time control of rotating machinery. Since the direct measurement of instantaneous rotating speed is not always available, the vibration measurement has been used for indirect estimation methods. In this paper, a novel indirect method is proposed to estimate the IS of rotating machinery. First, a frequency-shift synchrosqueezing transform is proposed to process the vibration signal to obtain the time–frequency (TF) representation. Second, the Viterbi algorithm is employed to extract the shifted instantaneous frequency (IF) from the TF representation. Finally, the extracted IF is used to recover the IF of the measured vibration signal. The IS of rotating machinery can be calculated from the estimated IF. The proposed method is validated with both numerical simulations and experiments. The results show that the proposed method could provide much higher frequency resolution, better TF concentration results, and more accurate IF estimation of the considered signal compared with the synchrosqueezing method. Furthermore, the proposed method was confirmed to be less sensitive to noise, especially for high-frequency components.

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References

Attanasio, A., Ceretti, E., Giardini, C., and Cappellini, C., 2013, “Tool Wear in Cutting Operations: Experimental Analysis and Analytical Models,” ASME J. Manuf. Sci. Eng., 135(5), p. 051012. [CrossRef]
Hu, X., Choi, K. S., Sun, X., and Golovashchenko, S. F., 2014, “Edge Fracture Prediction of Traditional and Advanced Trimming Processes for AA6111-T4 Sheets,” ASME J. Manuf. Sci. Eng., 136(2), p. 021016. [CrossRef]
Ma, L., Melkote, S. N., and Castle, J. B., 2013, “A Model-Based Computationally Efficient Method for On-Line Detection of Chatter in Milling,” ASME J. Manuf. Sci. Eng., 135(3), p. 031007. [CrossRef]
Ding, Y., Zhu, L., Zhang, X., and Ding, H., 2013, “Stability Analysis of Milling Via the Differential Quadrature Method,” ASME J. Manuf. Sci. Eng., 135(4), p. 044502. [CrossRef]
Pawł, W., 2013, “Dynamic Model of Oscillation-Assisted Cylindrical Plunge Grinding With Chatter,” ASME J. Manuf. Sci. Eng., 135(5), p. 051010 [CrossRef].
Niu, L., Cao, H., He, Z., and Li, Y., 2014, “Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways,” ASME J. Manuf. Sci. Eng., 136(4), p. 041015. [CrossRef]
Li, Y., Cao, H., Niu, L., and Jin, X., 2014, “A General Method for the Dynamic Modeling of Ball Bearing-Rotor Systems,” ASME J. Manuf. Sci. Eng., 137(2), p. 021016 [CrossRef].
Lamraoui, M., Thomas, M., El Badaoui, M., and Girardin, F., 2014, “Indicators for Monitoring Chatter in Milling Based on Instantaneous Angular Speeds,” Mech. Syst. Signal Process., 44(1–2), pp. 72–85. [CrossRef]
Gubran, A. A., and Sinha, J. K., 2014, “Shaft Instantaneous Angular Speed for Blade Vibration in Rotating Machine,” Mech. Syst. Signal Process., 44(1–2), pp. 47–59. [CrossRef]
André, H., Rémond, D., and Bourdon, A., 2011, “On the Use of the Instantaneous Angular Speed Measurement in Non Stationary Mechanism Monitoring,” ASME Paper No. DETC2011-47470 [CrossRef].
Stander, C. J., and Heyns, P. S., 2005, “Instantaneous Angular Speed Monitoring of Gearboxes Under Non-Cyclic Stationary Load Conditions,” Mech. Syst. Signal Process., 19(4), pp. 817–835. [CrossRef]
Renaudin, L., Bonnardot, F., Musy, O., Doray, J., and Rémond, D., 2010, “Natural Roller Bearing Fault Detection by Angular Measurement of True Instantaneous Angular Speed,” Mech. Syst. Signal Process., 24(7), pp. 1998–2011. [CrossRef]
Rémond, D., Antoni, J., and Randall, R. B., 2014, “Editorial for the Special Issue on Instantaneous Angular Speed (IAS) Processing and Angular Applications,” Mech. Syst. Signal Process., 44(1–2), pp. 1–4. [CrossRef]
Urbanek, J., Barszcz, T., and Antoni, J., 2013, “A Two-Step Procedure for Estimation of Instantaneous Rotational Speed With Large Fluctuations,” Mech. Syst. Signal Process., 38(1), pp. 96–102. [CrossRef]
Rodopoulos, K., Yiakopoulos, C., and Antoniadis, I., 2014, “A Parametric Approach for the Estimation of the Instantaneous Speed of Rotating Machinery,” Mech. Syst. Signal Process., 44(1–2), pp. 31–46. [CrossRef]
Li, Y., Gu, F., Harris, G., Ball, A., Bennett, N., and Travis, K., 2005, “The Measurement of Instantaneous Angular Speed,” Mech. Syst. Signal Process., 19(4), pp. 786–805. [CrossRef]
André, H., Girardin, F., Bourdon, A., Antoni, J., and Rémond, D., 2014, “Precision of the IAS Monitoring System Based on the Elapsed Time Method in the Spectral Domain,” Mech. Syst. Signal Process., 44(1–2), pp. 14–30. [CrossRef]
Yu, S. D., and Zhang, X., 2010, “A Data Processing Method for Determining Instantaneous Angular Speed and Acceleration of Crankshaft in an Aircraft Engine–Propeller System Using a Magnetic Encoder,” Mech. Syst. Signal Process., 24(4), pp. 1032–1048. [CrossRef]
Gubran, A. A., and Sinha, J. K., 2014, “Comparison Between Long and Short Blade Vibration Using Shaft Instantaneous Angular Speed in Rotating Machine,” ASME Paper No. GT2014-25904. [CrossRef]
Zimroz, R., Urbanek, J., Barszcz, T., Bartelmus, W., Millioz, F., and Martin, N., 2011, “Measurement of Instantaneous Shaft Speed by Advanced Vibration Signal Processing-Application to Wind Turbine Gearbox,” Metrol. Meas. Syst., 18(4), pp. 701–712 [CrossRef].
Zimroz, R., Millioz, F., and Martin, N., 2010, “A Procedure of Vibration Analysis From Planetary Gearbox Under Non-Stationary Cyclic Operations by Instantaneous Frequency Estimation in Time–Frequency Domain,” Seventh International Conference on Condition Monitoring and Machinery Failure Prevention Technologies, CM 2010 and MFPT 2010, Stafford-upon-Avon, UK.
Combet, F., and Zimroz, R., 2009, “A New Method for the Estimation of the Instantaneous Speed Relative Fluctuation in a Vibration Signal Based on the Short Time Scale Transform,” Mech. Syst. Signal Process., 23(4), pp. 1382–1397. [CrossRef]
Zhao, M., Lin, J., Wang, X., Lei, Y., and Cao, J., 2013, “A Tacho-Less Order Tracking Technique for Large Speed Variations,” Mech. Syst. Signal Process., 40(1), pp. 76–90. [CrossRef]
Qin, S., and Guo, Y., 2003, “Order Tracking Filtering Based on Instantaneous Frequency Estimation and Zero-Phase Distortion Digital Filtering,” ASME Paper No. DETC2003/VIB-48483 [CrossRef].
Bonnardot, F., El Badaoui, M., Randall, R. B., Danière, J., and Guillet, F., 2005, “Use of the Acceleration Signal of a Gearbox in Order to Perform Angular Resampling (With Limited Speed Fluctuation),” Mech. Syst. Signal Process., 19(4), pp. 766–785. [CrossRef]
Borghesani, P., Pennacchi, P., Chatterton, S., and Ricci, R., 2014, “The Velocity Synchronous Discrete Fourier Transform for Order Tracking in the Field of Rotating Machinery,” Mech. Syst. Signal Process., 44(1–2), pp. 118–133. [CrossRef]
Combet, F., and Gelman, L., 2007, “An Automated Methodology for Performing Time Synchronous Averaging of a Gearbox Signal Without Speed Sensor,” Mech. Syst. Signal Process., 21(6), pp. 2590–2606. [CrossRef]
Coats, M. D., Sawalhi, N., and Randall, R., 2009, “Extraction of Tach Information From a Vibration Signal for Improved Synchronous Averaging,” Proceedings of Acoustics.
Urbanek, J., Barszcz, T., Sawalhi, N., and Randall, R., 2011, “Comparison of Amplitude-Based and Phase-Based Methods for Speed Tracking in Application to Wind Turbines,” Metrol. Meas. Syst., 18(2), pp. 295–304 [CrossRef].
Yiakopoulos, C., Gryllias, K., and Antoniadis, I., 2009, “Instantaneous Frequency Estimation in Rotating Machinery Using a Harmonic Signal Decomposition (HARD) Parametric Method,” ASME Paper No. DETC2009-87348 [CrossRef].
Daubechies, I., Lu, J., and Wu, H.-T., 2011, “Synchrosqueezed Wavelet Transforms: An Empirical Mode Decomposition-Like Tool,” Appl. Comput. Harmonic Anal., 30(2), pp. 243–261. [CrossRef]
Zhang, A., Hu, F., He, Q., Shen, C., Liu, F., and Kong, F., 2014, “Doppler Shift Removal Based on Instantaneous Frequency Estimation for Wayside Fault Diagnosis of Train Bearings,” ASME J. Vib. Acoust., 136(2), p. 021019 [CrossRef].
Chandra Sekhar, S., and Sreenivas, T. V., 2004, “Effect of Interpolation on PWVD Computation and Instantaneous Frequency Estimation,” Signal Process., 84(1), pp. 107–116. [CrossRef]
Djurović, I., and Stanković, L., 2004, “An Algorithm for the Wigner Distribution Based Instantaneous Frequency Estimation in a High Noise Environment,” Signal Process., 84(3), pp. 631–643. [CrossRef]
Peng-Lang, S., Zheng, B., and Hong-Tao, S., 2008, “Nonparametric Detection of FM Signals Using Time–Frequency Ridge Energy,” IEEE Trans. Signal Process., 56(5), pp. 1749–1760. [CrossRef]
Peng, Z. K., Meng, G., Chu, F. L., Lang, Z. Q., Zhang, W. M., and Yang, Y., 2011, “Polynomial Chirplet Transform With Application to Instantaneous Frequency Estimation,” IEEE Trans. Instrum. Meas., 60(9), pp. 3222–3229. [CrossRef]
Kwok, H. K., and Jones, D. L., 2000, “Improved Instantaneous Frequency Estimation Using an Adaptive Short-Time Fourier Transform,” IEEE Trans. Signal Process., 48(10), pp. 2964–2972. [CrossRef]
Thakur, G., Brevdo, E., Fučkar, N. S., and Wu, H.-T., 2013, “The Synchrosqueezing Algorithm for Time-Varying Spectral Analysis: Robustness Properties and New Paleoclimate Applications,” Signal Process., 93(5), pp. 1079–1094. [CrossRef]
Li, C., and Liang, M., 2012, “A Generalized Synchrosqueezing Transform for Enhancing Signal Time–Frequency Representation,” Signal Process., 92(9), pp. 2264–2274. [CrossRef]
Li, C., and Liang, M., 2012, “Time–Frequency Signal Analysis for Gearbox Fault Diagnosis Using a Generalized Synchrosqueezing Transform,” Mech. Syst. Signal Process., 26, pp. 205–217. [CrossRef]
Feng, Z., Chen, X., and Liang, M., 2015, “Iterative Generalized Synchrosqueezing Transform for Fault Diagnosis of Wind Turbine Planetary Gearbox Under Nonstationary Conditions,” Mech. Syst. Signal Process., 52–53, pp. 360–375 [CrossRef].
Wang, S., Chen, X., Cai, G., Chen, B., Li, X., and He, Z., 2014, Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis, Institute of Electrical and Electronics Engineers, New York.
Djurović, I., 2011, “Viterbi Algorithm for Chirp-Rate and Instantaneous Frequency Estimation,” Signal Process., 91(5), pp. 1308–1314. [CrossRef]
Olhede, S., and Walden, A., 2005, “A Generalized Demodulation Approach to Time-Frequency Projections for Multicomponent Signals,” Proc. R. Soc. A, 461(2059), pp. 2159–2179. [CrossRef]
Brevdo, E., and Wu, H.-T., 2011, The Synchrosqueezing Toolbox, https://web.math.princeton.edu/∼ebrevdo/Synsq/

Figures

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Fig. 1

(a) The theoretical IF of the chirp signal f(t) = 2 sin (20πt+25πt2), (b) the continuous WT of f(t), and (c) the synchrosqueezed TF representation of f(t)

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Fig. 2

Schematic diagram of the central frequency sequence and the frequency interval sequence

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Fig. 3

Central frequency sequence and frequency interval sequence change rule along the frequency direction

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Fig. 4

Schematic diagram of the proposed method

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Fig. 5

Comparison of the frequency-shift synchrosqueezing method and the synchrosqueezing method, using a signal without noise: (a) the signal f(t), (b) comparison of the theoretical IF and the IFs obtained by the frequency-shift synchrosqueezing method and the synchrosqueezing method, (c) the synchrosqueezed TF representation, (d) extracted IF of the synchrosqueezed TF representation, (e) the frequency-shift synchrosqueezed TF representation, and (f) extracted IF of the frequency-shift synchrosqueezed TF representation

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Fig. 6

Comparison of the frequency-shift synchrosqueezing method and the synchrosqueezing method, using a signal imbedded in a white noise with SNR of −3 dB: (a) The signal g(t), (b) comparison of the theoretical IF and IFs obtained by the frequency-shift synchrosqueezing method and the synchrosqueezing method, (c) the synchrosqueezed TF representation, (d) extracted IF of the synchrosqueezed TF representation, (e) the frequency-shift synchrosqueezed TF representation, and (f) extracted IF of the frequency-shift synchrosqueezed TF representation

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Fig. 7

Frequency-shift synchrosqueezed representation of the signal f(t) sampled by 400 HZ

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Fig. 8

Experimental setup of the Bentley rotor test rig

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Fig. 9

The displacement signal: (a) the time waveform and (b) the spectrum

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Fig. 10

The IF detected by the tachometer

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Fig. 11

Experimental comparison of the synchrosqueezing method and the frequency-shift synchrosqueezing method: (a) The synchrosqueezed TF representation, (b) extracted IF of the synchrosqueezed TF representation, (c) the frequency-shift synchrosqueezed TF representation, and (d) extracted IF of the frequency-shift synchrosqueezed TF representation

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Fig. 12

The displacement signal: (a) the time waveform and (b) the zoomed spectrum

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Fig. 13

Experimental comparison of the synchrosqueezing method and the frequency-shift synchrosqueezing method: (a)Synchrosqueezed TF representation and (b) frequency-shift synchrosqueezed TF representation

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Fig. 14

Comparison of IF detected by the tachometer and obtained by the proposed method

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