Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

Wang, Lili; Zhang, Jinghui; Wang, Chao; Hu, Songyan

doi:10.1115/1.1545768

Cited by 10 publications

(5 citation statements)

References 7 publications

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“…According to (21), it is known that the amplitude of the torsion pendulum is related to the damping coefficients 1 and 2 . According to (22), the period of the torsion pendulum is related to the stiffness coefficients of the torsion bars 1 and 3 .…”

Section: Analytic Solution Of Nonlinear Torsion Pendulum Modelmentioning

confidence: 99%

Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

Zhao

Zhang

Han

et al. 2018

Mathematical Problems in Engineering

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The nonlinear model of torsion pendulum is presented by considering the nonlinear damping force and nonlinear restoring force. The analytic solution of the nonlinear model is calculated to analyze the relationship between the characteristics of torsion pendulum and the nonlinear factors. The instantaneous characteristics of nonlinear torsion pendulum are analyzed by instantaneous undamped natural frequency and instantaneous damping coefficient. The instantaneous characteristics can be used for the parameter estimation of nonlinear torsion pendulum system. The nonlinear characteristics of the torsion pendulum are validated by the torsion pendulum based on the air-hovered turntable. The parameter estimation method based on the instantaneous characteristics is validated by the moment of inertia measurement system based on the torsion pendulum.

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Section: Analytic Solution Of Nonlinear Torsion Pendulum Modelmentioning

confidence: 99%

Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

Zhao

Zhang

Han

et al. 2018

Mathematical Problems in Engineering

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“…Decomposing the terms in Eq. (4) into a fast-varying part and a slowvarying part, an equation that contains only slow-varying part can be obtained by using the methods proposed in [42], i.e. ̈+ 2ℎ 0 ( )̇+ 0 2 ( ) = ( )/ .…”

Section: Model Of Nonlinear Systemmentioning

confidence: 99%

“…Assume operator "{ }" represents averaging procedure that is realized through low-pass filtering. If primary vibration is ( ) = ( ) ( ), the approximate backbone [42] can be expressed as,…”

Section: Nonlinear Identification and Parameter Estimationmentioning

confidence: 99%

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Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform

Deng

Cheng

Yang

et al. 2016

Journal of Vibration and Acoustics

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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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“…Practical application of this technique for damage diagnosis purpose of rotors was presented by Feldman and Seibold [11]. While Wang et al [12] proposed a relatively new approach similar to the skeleton curve, namely the skeleton linear model (SLM). They related the (slowly timevarying) modal parameters of a system by using quadratic timefrequency distribution of its instantaneous response.…”

Section: Detc2005-85013mentioning

confidence: 99%

A Case Study in Backlash Characterization in Mechanical Systems

Tjahjowidodo

Al‐Bender

Brussel

2005

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C

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The Frequency Response Function (FRF) method using an experimental analysis such as free vibration with shock excitation or forced vibration with step or chirp excitation has proven to be a most efficient way to identify the modal parameters of mechanical structures. However, there is a limitation that only linear dynamic systems can be tested through these methods. The problem becomes more complex when nonlinear systems have to be identified. If the nonlinear system is ‘well-behaved’, i.e. if it shows periodic response to a periodic excitation, ‘skeleton’ identification techniques may be used to estimate the modal parameters, in function of the amplitude and frequency of excitation. However, under certain excitation conditions, chaotic behaviour might occur so that the response is aperiodic. In that case, chaos quantification techniques, such as Lyapunov exponent, are proposed in the literature. This paper deals with the application of the aforementioned nonlinear identification techniques to an experimental mechanical system with backlash. It compares and contrasts Hilbert transforms with Wavelet analysis in case of skeleton identification showing their possibilities and limitations. Chaotic response, which appears under certain excitation conditions and could be used as backlash signature, is dealt with both by a simulation study and by experimental signal analysis after application of appropriate filtration techniques.

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Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

Abstract: The joint time-frequency analysis method is adopted to study the

Cited by 10 publications

References 7 publications

Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

Instantaneous Characteristics of Nonlinear Torsion Pendulum and Its Application in Parameter Estimation of Nonlinear System

Parametric Identification of Nonlinear Vibration Systems Via Polynomial Chirplet Transform

A Case Study in Backlash Characterization in Mechanical Systems

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