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.

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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
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

e-mail: z.peng@sjtu.edu.cn
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

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October 2016

Research-Article

# Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform

Y. Deng,

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

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

Search for other works by this author on:

C. M. Cheng,

C. M. Cheng

State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Search for other works by this author on:

Y. Yang,
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Y. Yang

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Search for other works by this author on:

Z. K. Peng,

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

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

e-mail: z.peng@sjtu.edu.cn

Search for other works by this author on:

W. X. Yang,

W. X. Yang

School of Marine Science and Technology,

Newcastle University,

Newcastle upon Tyne NE1 7RU, UK

Newcastle University,

Newcastle upon Tyne NE1 7RU, UK

Search for other works by this author on:

W. M. Zhang
State Key Laboratory of Mechanical System

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

W. M. Zhang

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Search for other works by this author on:

Y. Deng

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

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Y. Yang

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

Z. K. Peng

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

Newcastle University,

Newcastle upon Tyne NE1 7RU, UK

W. M. Zhang

and Vibration,

Shanghai Jiao Tong University,

Shanghai 200240, China

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*. Oct 2016, 138(5): 051014 (18 pages)

**Published Online:**June 23, 2016

Article history

Received:

July 6, 2015

Revised:

May 12, 2016

Citation

Deng, Y., Cheng, C. M., Yang, Y., Peng, Z. K., Yang, W. X., and Zhang, W. M. (June 23, 2016). "Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform." ASME. *J. Vib. Acoust*. October 2016; 138(5): 051014. https://doi.org/10.1115/1.4033717

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