Frequency Response Function Measurements via Local Rational Modeling, Revisited

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leak...

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Veröffentlicht in:IEEE transactions on instrumentation and measurement Jg. 70; S. 1 - 16
Hauptverfasser: Pintelon, Rik, Peumans, Dries, Vandersteen, Gerd, Lataire, John
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Approximation
Bias
Estimation
Frequency measurement
Frequency response
Frequency response function (FRF)
Frequency response functions
Leakage
local polynomial (LP) modeling
local rational modeling
Low noise
Mathematical analysis
Measurement uncertainty
Modelling
Noise measurement
Noise reduction
Noise sensitivity
nonparametric estimation
Nonparametric statistics
Polynomials
Rational functions
Time measurement
transient
Transient analysis
Variance analysis
ISSN:0018-9456, 1557-9662
Online-Zugang:Volltext
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Zusammenfassung:A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. This article presents an overview of the existing methods and gives an in-depth bias and variance analysis of the FRF and disturbing noise variance estimates. In addition, a new local modeling approach is described, which combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model-order selection procedure applied to a specific subclass of rational functions.
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ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2020.3020601