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Research Papers

Study on the Identification of Experimental Chaotic Vibration Signal for Nonlinear Vibration Isolation System

[+] Author and Article Information
Shuyong Liu, Zhu Shijian, Yang Qingchao, He Qiwei

College of Naval Architecture and Power, Naval University of Engineering, 430033 Wuhan, P.R. China

J. Comput. Nonlinear Dynam 6(4), 041006 (Apr 12, 2011) (11 pages) doi:10.1115/1.4003805 History: Received September 07, 2009; Revised March 01, 2011; Published April 12, 2011; Online April 12, 2011

In order to identify experimental chaotic vibration signals correctly, the measured data were analyzed by applying the methods of Poincaré section, return map, and phase space reconstruction. However, the nonlinear time series analysis based on phase space reconstruction is complex and time-consuming for large quantities of experimental signals. Besides, especially when the signal identification process should be completed online, the conventional method is unable to meet the requirements. The energy distribution features of signals in different frequency bands were extracted with the wavelet package analysis method, and the important characteristic vectors for chaos identification were provided. These methods were verified with numerical simulation first in this paper. Then, the nonlinear vibration system based on an air spring isolator was designed, which exhibits different responses with different parameters. In the experiment, the wavelet package technology and neural network were applied to identify the system behavior; results showed that the vibration system exhibited chaotic responses under special parameter ranges, and the parameter variation law was concluded, which is the foundation of linear spectra isolation for chaotic vibration control technology.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Period-3 response of system: (a) phase plane attractor of response and (b) Poincaré map of response

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Figure 2

Chaotic response of system: (a) strange attractor of chaos and (b) Poincaré map of chaos

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Figure 3

Quasi-periodic response of system: (a) phase plane attractor of response and (b) Poincaré section of the response

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Figure 4

Return map of different signals: (a) return map of chaotic response and (b) return map of random

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Figure 5

Return map of quasi-periodic and periodic responses: (a) return map of quasi-periodic signal and (b) return map of periodic-1 response

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Figure 6

Wavelet packet energy curves of different signals: (a) wavelet package node number i and (b) wavelet package node number i

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Figure 7

Training and checking curves of neural network: (a) training curve of neural network and (b) identification results of neural network

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Figure 8

Performance of neural network affected by learning mode: (a) training curve of neural network and (b) identification results of neural network

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Figure 9

Training and checking curves with the variation in system parameters: (a) training curve of neural network and (b) identification results of neural network

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Figure 10

The designed air spring vibration system

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Figure 11

Vibration acceleration response of experimental system: (a) time series of system response, (b) power spectra of response, (c) reconstructed attractor of phase plane, and (d) Poincaré section of attractor

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Figure 12

Recurrence map of experimental signal

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Figure 13

Multi-ahead prediction of experimental signal

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Figure 14

Different responses with the variation in excitation force: (a) TEST2081 experimental data reconstructed attractor, (b) TEST2082 experimental data reconstructed attractor, (c) TEST3081 experimental data reconstructed attractor, (d) TEST3082 experimental data reconstructed attractor, (e) TEST4081 experimental data reconstructed attractor, and (f) TEST4082 experimental data reconstructed attractor

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Figure 15

Reconstructed attractor under different excitation frequencies: (a) attractor of TEST5071 experimental data, (b) attractor of TEST5072 experimental data, (c) attractor of TEST5091experimental data, (d) attractor of TEST5092 experimental data, (e) attractor of TEST50151 experimental data, (f) power spectrum of TEST50151 experimental data, (g) attractor of TEST50152 experimental data, (h) power spectrum of TEST50152 experimental data, (i) attractor of TEST50181 experimental data, and (j) attractor of TEST50182 experimental data

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Figure 16

Reconstructed attractor with the variation in excitation frequency: (a) attractor of TEST0820101 experimental data, (b) attractor of TEST0820102 experimental data, (c) attractor of TEST0820151experimental data, and (d) attractor of TEST0820152 experimental data

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Figure 17

Reconstructed attractor under external excitation at 30 N: (a) attractor of TEST083051 experimental data, (b) attractor of TEST083052 experimental data, (c) attractor of TEST0830101 experimental data, (d) attractor of TEST0830102 experimental data, (e) attractor of TEST0830151 experimental data, and (f) attractor of TEST0830152 experimental data

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Figure 18

Reconstructed attractor under external excitation at 20 N: (a) attractor of TEST122051 experimental data, (b) attractor of TEST122052 experimental data, (c) attractor of TEST1220101 experimental data, and (d) attractor of TEST1220102 experimental data

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Figure 19

Reconstructed attractor under external excitation at 30 N: (a) attractor of TEST123051 experimental data, (b) attractor of TEST123052 experimental data, (c) attractor of TEST1230151 experimental data, and (d) attractor of TEST1230152 experimental data

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Figure 20

Reconstructed attractor under external excitation at 40 N: (a) attractor of TEST124051 experimental data, (b) attractor of TEST124052 experimental data, (c) attractor of TEST1240101 experimental data, and (d) attractor of TEST1240102 experimental data

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Figure 21

Reconstructed attractor under external excitation at 50 N: (a) attractor of TEST125051 experimental data, (b) attractor of TEST125052 experimental data, (c) attractor of TEST1250101 experimental data, and (d) attractor of TEST1250102 experimental data

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Figure 22

Test results of neural network

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