Estimation of the FRF Through the Improved Local Bandwidth Selection in the Local Polynomial Method

Thummala, Prasanth; Schoukens, Johan

doi:10.1109/tim.2012.2196393

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…These ideas can be transferred to the local parametric methods. A first attempt to do so is presented in [81]. At a cost of additional calculations, a lower RMS error can be obtained.…”

Section: General Remarksmentioning

confidence: 99%

Nonparametric Data-Driven Modeling of Linear Systems: Estimating the Frequency Response and Impulse Response Function

2018

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Intersample assumptionsAll the data processing in this article starts from discrete-time measurements u(kT s ), y(kT s ), sampled at a sampling frequency f s = 1/T s . No information is available how the continuous-time signals u(t), y(t) vary in between the measured samples. For that reason assumptions are needed, and the measurement setup should match the intersample assumption well. The two most popular intersample assumptions [16], [33] are shown in Figure 2: the zero-order-hold (ZOH) and the band-limited assumption (BL). A detailed discussion of both intersample assumptions (the facts and their appreciation) is given in Sections 13.2 and 13.3 of [16]. ZOH setupThe ZOH setup puts a condition on the excitation that is assumed to remain constant in between the samples. In this setup, the IR/FRF are estimated between the discrete-time reference signal in the memory of the generator, and the sampled output. The intersample behavior and the actuator characteristic are an intrinsic part of the model: if the intersample behavior changes, also the corresponding model will change. The ZOH-assumption is very popular in digital control. In that case the sampling frequency f s is commonly chosen 10 times larger than the frequency band of interest. A discrete-time model gives an exact description of the continuous-time system.

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“…These ideas can be transferred to the local parametric methods. A first attempt to do so is presented in [81]. At a cost of additional calculations, a lower RMS error can be obtained.…”

Section: General Remarksmentioning

confidence: 99%

Nonparametric Data-Driven Modeling of Linear Systems: Estimating the Frequency Response and Impulse Response Function

2018

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“…This will provide the reader with a better understanding of the underlying error mechanism, and will offer a simple rule of thumb to design the experiment. In [9], a heuristic procedure is proposed to tune one of the parameters of the LPM. Although this method provides good result, it does not give insight in the underlying structure of the problem.…”

Section: Introductionmentioning

confidence: 99%

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Schoukens

Vandersteen

Pintelon

et al. 2013

IEEE Trans. Instrum. Meas.

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Abstract-Frequency response function (FRF) measurements take a central place in the instrumentation and measurement field because many measurement problems boil down to the characterisation of a linear dynamic behaviour. The major problems to be faced are leakage-and noise errors. The local polynomial method (LPM) was recently presented as a superior method to reduce the leakage errors with several orders of magnitude while the noise sensitivity remained the same as that of the classical windowing methods. The kernel idea of the LPM is a local polynomial approximation of the FRF and the leakage errors in a small frequency band around the frequency where the FRF is estimated. Polynomial approximation of FRF's is also present in other measurement and design problems. For that reason it is important to have a good understanding of the factors that influence the polynomial approximation errors. This article presents a full analysis of this problem, and delivers a rule of thumb that can be easily applied in practice to deliver an upper bound on the approximation error of FRF's. It is shown that the approximation error for lowly damped systems is bounded by (BLP M /B 3dB ) R+2 with BLP M the local bandwidth of the LPM, R the degree of the local polynomial that is selected to be even (user choices), and B 3dB the 3 dB bandwidth of the resonance, which is a system property.

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Quantifying the Time-Variation in FRF Measurements Using Random Phase Multisines With Nonuniformly Spaced Harmonics

Pintelon

Louarroudi

Lataire

2014

IEEE Trans. Instrum. Meas.

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Estimation of the FRF Through the Improved Local Bandwidth Selection in the Local Polynomial Method

Cited by 6 publications

References 23 publications

Nonparametric Data-Driven Modeling of Linear Systems: Estimating the Frequency Response and Impulse Response Function

Nonparametric Data-Driven Modeling of Linear Systems: Estimating the Frequency Response and Impulse Response Function

Bounding the Polynomial Approximation Errors of Frequency Response Functions

Quantifying the Time-Variation in FRF Measurements Using Random Phase Multisines With Nonuniformly Spaced Harmonics

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