A parametric frequency response method for non-linear time-varying systems

Guo, Yuzhu; Guo, Lingzhong; Billings, S.A.; Coca, Daniel; Lang, Zi–Qiang

doi:10.1080/00207721.2012.762563

Cited by 10 publications

(3 citation statements)

References 32 publications

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“…Once the TV-ARMA structure and the associated timevarying coefficients are determined using the LROFR algorithm, the time-frequency spectrum can then be estimated using the following rational spectral estimation formula [34]: Formula (7) represents the frequency response function (FRF) of a time-varying ARMA process, which is a frequency domain description of the original time series. This description is sufficiently accurate when the time-varying coefficients change at a relatively slow rate [35]. It can be observed that poles and zeros of the FRF (7) correspond to peaks and valleys in the TFS respectively.…”

Section: Time-frequency Spectral Estimationmentioning

confidence: 93%

The Detection of Freezing of Gait in Parkinson’s Disease Using Asymmetric Basis Function TV-ARMA Time–Frequency Spectral Estimation Method

Guo

Wang

et al. 2019

IEEE Trans. Neural Syst. Rehabil. Eng.

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Section: Time-frequency Spectral Estimationmentioning

confidence: 93%

The Detection of Freezing of Gait in Parkinson’s Disease Using Asymmetric Basis Function TV-ARMA Time–Frequency Spectral Estimation Method

Guo

Wang

et al. 2019

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…Volterra series has been presented in recent years for modeling, solving and analyzing the nonlinear system. [7][8][9][10][11][12][13][14][15][16] Some new concepts have been presented based on Volterra series, 17,18 such as generalized frequency response functions (GFRFs) which can also be called as higher-order frequency response functions (HFRFs) or Volterra frequency-domain kernels (VFKs), nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response functions (AFRF). GFRF is defined as the multi-dimensional Fourier transform of Volterra kernel function by Lang et al 19 Lee 20 used a lot of sinusoidal excitation tests with several different excitation amplitudes at various frequencies to measure GFRFs, and estimated the system parameters accurately.…”

Section: Introductionmentioning

confidence: 99%

Axial stiffness identification of a ball screw feed system using generalized frequency response functions

Zhou

Long

Meng

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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Contact of balls in screw nuts and bearings causes the nonlinearity of a ball screw feed system. The identification of nonlinear stiffness helps to understand and control the feed system. The axial vibration of the ball screw feed system can be descripted by a single-degree-of-freedom (SDOF) system with polynomial nonlinear terms. Since generalized frequency response functions (GFRFs) can be expressed in terms of linear and nonlinear system parameters, one can estimate these parameters based on the measured GFRFs. In this effort, both single-tone and multitone harmonic inputs are employed to measure GFRFs, and a simple search algorithm is proposed to find the suitable frequency set of the multitone input. Parameter identification based on these two methods has been compared by numerical simulation and experiment. Since the response spectrum measured from vibration experiment of a ball screw system has even and odd harmonics, it is suitable to simplify the restoring force with square and cubic nonlinearity form. Static experiment is also conducted to verify the identified parameters, and the results show that the method based on single-tone inputs performs effectively in identifying axial stiffness of a ball screw feed system, but the method based on multitone inputs gets the incorrect results in practical application

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“…Identification of non-linear systems is, therefore, of great theoretical and practical interest. Recently, non-linear system identification has received more attention [1,2,7,[14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Support vector machine and higher‐order cumulants based blind identification for non‐linear Wiener models

Wang

Qian

2018

IET signal process.

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A blind identification method for non-linear Wiener models is investigated. When the input signal of the system does not adopt a Gaussian random signal, the identification process with the input signal is changed into the one without input signal by using the first-order statistical properties of the cyclostationary input signal and the inverse mapping of the non-linear part of the model initially, moreover, all internal variables are recovered only based on the output signal. Then, the estimates of the order and parameters of the model are obtained by using the support vector machine regression theory and the higher-order cumulants principle. Finally, compared with other methods, the simulation results show the effectiveness of the proposed method for identifying non-linear Wiener models.

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A parametric frequency response method for non-linear time-varying systems

Cited by 10 publications

References 32 publications

The Detection of Freezing of Gait in Parkinson’s Disease Using Asymmetric Basis Function TV-ARMA Time–Frequency Spectral Estimation Method

The Detection of Freezing of Gait in Parkinson’s Disease Using Asymmetric Basis Function TV-ARMA Time–Frequency Spectral Estimation Method

Axial stiffness identification of a ball screw feed system using generalized frequency response functions

Support vector machine and higher‐order cumulants based blind identification for non‐linear Wiener models

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