Variance analysis of frequency response function measurements using periodic excitations

Dhaene, Tom; Pintelon, R.; Schoukens, Johan; Gheem, Els Van

doi:10.1109/imtc.2004.1351387

Cited by 13 publications

(12 citation statements)

References 6 publications

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“…The weighting function WL(k) is chosen as the inverse of the total variance of GBLA(jω k ), hence encompassing the variability caused by nonlinear and noise distortions. This choice comes down to setting [41] WL…”

Section: Identification Resultsmentioning

confidence: 99%

Hysteresis Identification Using Nonlinear State-Space Models

Noël

Esfahani

Kerschen

et al. 2016

Nonlinear Dynamics, Volume 1

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Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.

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Section: Identification Resultsmentioning

confidence: 99%

Hysteresis Identification Using Nonlinear State-Space Models

Noël

Esfahani

Kerschen

et al. 2016

Nonlinear Dynamics, Volume 1

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“…This effect allows the level of the nonlinearity to be detected. By suppressing certain harmonics in the input spectrum, the resulting amplitude levels in the output spectrum at those suppressed harmonics indicates the presence and level of the nonlinear distortions (Evans et al, 1994;D'haene et al, 2005). Further if all even harmonics (including the d.c) are suppressed, the distortions at the even harmonics are due to even order nonlinearities and if some odd harmonics are suppressed, the distortions at the suppressed odd harmonics are due to odd order nonlinearities (Schoukens 6 et al, 2009).…”

Section: Input Signal Considerationmentioning

confidence: 99%

Nonlinear system-identification of the filling phase of a wet-clutch system

Widanage

Stoev²,

Mulders

et al. 2011

Control Engineering Practice

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“…Multisine signals allow for leakage free measurements as opposed to (standard) noise excited measurements, where windowing is required to counteract the leakage. Furthermore, when the multisine is correctly selected [1], [8], [9], it is possible to identify the variances on the measured linearized dynamics due to stochastic distortions and nonlinear effects separately. Finally, it is possible to detect the type of nonlinearity in this way as well.…”

Section: Broadband Excitationmentioning

confidence: 99%

“…Furthermore, this method does not provide a distinction between the variance of the output spectrum due to noise and the variance due to nonlinearities. To accomplish this, multiple experiments are required with different realizations of the multisine signal [1]. In this paper these detection methods are combined to both quantify the extend of nonlinear effects and classify them.…”

Section: Signal Processing and Analysismentioning

confidence: 99%

Nonlinearities in Industrial motion stages - detection and classification

Rijlaarsdam

Loon

Nuij

et al. 2010

Proceedings of the 2010 American Control Conference

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Abstract-Detection and classification of nonlinearities in motion systems becomes of increasing importance with high demands on (closed loop) performance. In this paper two methods are compared that aim to measure both the linearized dynamics and the influence of nonlinearities. First, a broadband signal is used to measure a linear approximation of the systems dynamics. This method uses multisine signals with identical amplitude spectrum, but randomly distributed phases. Averaging over multiple periodic responses to the same signal and over multiple realizations of the random phase multisine allows the computation of the level of nonlinearities and external disturbances separately. This yields both a linear approximation of the systems dynamics and the amount of nonlinear 'disturbance' as a function of frequency. Second, single sine based measurements are used to measure the Higher Order Sinusoidal Input Describing Functions (HOSIDF) of the system under test. HOSIDFs describe the response of the system by describing not only the 'direct' response (gain and phase shift) of the system at the input frequency, but by describing the response at higher harmonics of the input frequency as well. This yields a quantitative measure of the power generated by nonlinearities at harmonics of the input frequency as a function of this frequency and the signal amplitude. In the paper these methods are utilized to acquire a non-parametric model for an industrial high precision stage. The effects of and sources for nonlinear influences are discussed for this particular case as well.

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Variance analysis of frequency response function measurements using periodic excitations

Cited by 13 publications

References 6 publications

Hysteresis Identification Using Nonlinear State-Space Models

Hysteresis Identification Using Nonlinear State-Space Models

Nonlinear system-identification of the filling phase of a wet-clutch system

Nonlinearities in Industrial motion stages - detection and classification

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