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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

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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