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Journal of Vibration and Acoustics | Volume 138 | Issue 5 | research-article
Research Papers

Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform

[+] Author and Article Information
Y. Deng

State Key Laboratory of Mechanical
System and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China;
School of Mechanical Engineering
and Automation,
Beijing University of Aeronautics
and Astronautics,
Beijing 100191, China

C. M. Cheng, Y. Yang, W. M. Zhang

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Z. K. Peng

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: z.peng@sjtu.edu.cn

W. X. Yang

School of Marine Science and Technology,
Newcastle University,
Newcastle upon Tyne NE1 7RU, UK

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 6, 2015; final manuscript received May 12, 2016; published online June 23, 2016. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 138(5), 051014 (Jun 23, 2016) (18 pages) Paper No: VIB-15-1251; doi: 10.1115/1.4033717 History: Received July 06, 2015; Revised May 12, 2016
Article
References
Figures
Tables

The response of a nonlinear oscillator is characterized by its instantaneous amplitude (IA) and instantaneous frequency (IF) features, which can be significantly affected by the physical properties of the system. Accordingly, the system properties could be inferred from the IA and IF of its response if both instantaneous features can be identified accurately. To fulfill such an idea, a nonlinear system parameter identification method is proposed in this paper with the aid of polynomial chirplet transform (PCT), which has been proved a powerful tool for processing nonstationary signals. First, the PCT is used to extract the instantaneous characteristics, i.e., IA and IF, from nonlinear system responses. Second, instantaneous modal parameters estimation was adopted to extract backbone and damping curves, which characterize the inherent nonlinearities of the system. Third, the physical property parameters of the system were estimated through fitting the identified average nonlinear characteristic curves. Finally, the proposed nonlinear identification method is experimentally validated through comparing with two Hilbert transform (HT) based methods.
Copyright © 2016 by ASME
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References

Figures

Grahic Jump Location
Fig. 1

Extracted (a) IF and (b) IA

+Extracted (a) IF and (b) IA
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Extracted (a) IF and (b) IA
Grahic Jump Location
Fig. 2

IF extracted using HT (a), CWT (b), and PCT (c) under  SNR=2dB

+IF extracted using HT (a), CWT (b), and PCT (c) under  SNR=2dB
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IF extracted using HT (a), CWT (b), and PCT (c) under  SNR=2dB
Grahic Jump Location
Fig. 3

IA extracted using HT and PCT under  SNR=2dB

+IA extracted using HT and PCT under  SNR=2dB
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IA extracted using HT and PCT under  SNR=2dB
Grahic Jump Location
Fig. 4

The noise-contaminated response (a) and its fast Fourier transform (FFT) spectrum (b) for case 1

+The noise-contaminated response (a) and its fast Fourier transform (FFT) spectrum (b) for case 1
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The noise-contaminated response (a) and its fast Fourier transform (FFT) spectrum (b) for case 1
Grahic Jump Location
Fig. 5

The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 1

+The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 1
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The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 1
Grahic Jump Location
Fig. 6

The identified backbone and the damping curve for case 1

+The identified backbone and the damping curve for case 1
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The identified backbone and the damping curve for case 1
Grahic Jump Location
Fig. 7

The identified average nonlinear characteristic forces for case 1

+The identified average nonlinear characteristic forces for case 1
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The identified average nonlinear characteristic forces for case 1
Grahic Jump Location
Fig. 8

The estimated IF (a) and IA (b) of the primary component for case 2

+The estimated IF (a) and IA (b) of the primary component for case 2
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The estimated IF (a) and IA (b) of the primary component for case 2
Grahic Jump Location
Fig. 9

The identified backbone and the damping curve for case 2

+The identified backbone and the damping curve for case 2
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The identified backbone and the damping curve for case 2
Grahic Jump Location
Fig. 10

The identified average nonlinear characteristic forces for case 2

+The identified average nonlinear characteristic forces for case 2
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The identified average nonlinear characteristic forces for case 2
Grahic Jump Location
Fig. 11

The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 3

+The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 3
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The TFD (a), the estimated IF (b), and the IA (c) of the primary component for case 3
Grahic Jump Location
Fig. 12

The identified backbone and the damping curve for case 3

+The identified backbone and the damping curve for case 3
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The identified backbone and the damping curve for case 3
Grahic Jump Location
Fig. 13

The identified average nonlinear characteristic forces for case 3

+The identified average nonlinear characteristic forces for case 3
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The identified average nonlinear characteristic forces for case 3
Grahic Jump Location
Fig. 14

The estimated IF (a) and the IA (b) of the primary component for case 4

+The estimated IF (a) and the IA (b) of the primary component for case 4
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The estimated IF (a) and the IA (b) of the primary component for case 4
Grahic Jump Location
Fig. 15

The identified backbone and the damping curve for case 4

+The identified backbone and the damping curve for case 4
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The identified backbone and the damping curve for case 4
Grahic Jump Location
Fig. 16

The identified average nonlinear characteristic forces for case 4

+The identified average nonlinear characteristic forces for case 4
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The identified average nonlinear characteristic forces for case 4
Grahic Jump Location
Fig. 17

The test rig: mass (1), tension mechanism (2), rigid foundation (3), and ruler springs (4)

+The test rig: mass (1), tension mechanism (2), rigid foundation (3), and ruler springs (4)
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The test rig: mass (1), tension mechanism (2), rigid foundation (3), and ruler springs (4)
Grahic Jump Location
Fig. 18

Setting up of the experiment: (a) test rig and hammer and (b) data acquisition device

+Setting up of the experiment: (a) test rig and hammer and (b) data acquisition device
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Setting up of the experiment: (a) test rig and hammer and (b) data acquisition device
Grahic Jump Location
Fig. 19

Time-domain impulse force (a) and response signal (b)

+Time-domain impulse force (a) and response signal (b)
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Time-domain impulse force (a) and response signal (b)
Grahic Jump Location
Fig. 20

The analysis of response signal: the spectrum (a), the TFD (b), the IF (c), and the IA (d)

+The analysis of response signal: the spectrum (a), the TFD (b), the IF (c), and the IA (d)
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The analysis of response signal: the spectrum (a), the TFD (b), the IF (c), and the IA (d)
Grahic Jump Location
Fig. 21

Identified backbone (a), the damping curve (b), and the hysteresis loop of cubic nonlinearity model (c)

+Identified backbone (a), the damping curve (b), and the hysteresis loop of cubic nonlinearity model (c)
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Identified backbone (a), the damping curve (b), and the hysteresis loop of cubic nonlinearity model (c)
Grahic Jump Location
Fig. 22

Identified equivalent nonlinear characteristic forces

+Identified equivalent nonlinear characteristic forces
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Identified equivalent nonlinear characteristic forces
Grahic Jump Location
Fig. 23

Comparison between the artificial response and the real response: the time-domain signal (a) and the absolute error (b)

+Comparison between the artificial response and the real response: the time-domain signal (a) and the absolute error (b)
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Comparison between the artificial response and the real response: the time-domain signal (a) and the absolute error (b)

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