Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

Majewski, M. W.; Magalas, Leszek B.

doi:10.1515/amm-2015-0267

Cited by 1 publication

(6 citation statements)

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“…The zero-point drift (non-harmonic distortion), is neglected here [10]. The additive white noise, ε w (t), is described by the signal-to-noise ratio S/N [8][9][10][11][12][13][14].…”

Section: Methodsmentioning

confidence: 99%

“…Dispersion in internal friction values around Q −1 = 0.014 is reported in Refs. [25,26] and assessed in [14]. The relationship between the internal friction, Q −1 , and the logarithmic decrement, δ, is well known [4,10,27].…”

Section: The True Envelope Of Exponentially Damped Time-invariant Harmentioning

confidence: 99%

“…This paper describes an endeavor to use the Hilbert transform [6,7] to compute the logarithmic decrement [2,[10][11][12][13], δ, from exponentially damped time-invariant harmonic oscillations embedded in the experimental noise, ε w (t), [10][11][12][13][14] and recorded in a low-frequency mechanical spectrometer (inverted torsion pendulum [1,2,4,5,[8][9][10][11][12][13]). In this paper, damped harmonic oscillations containing noise are referred to as the 'free-elastic decay'.…”

Section: Introductionmentioning

confidence: 99%

“…The H-twin method provides the 'true envelope', and thus shows excellent performance in the computation of the logarithmic decrement, δ. In the present study the δ values are computed according to the following methods: (1) the OMI (Optimization in Multiple Intervals) [8,9], (2) the YM (Yoshida-Magalas) [12][13][14] and (3) the Y (Yoshida) based on interpolated discrete Fourier transform, IpDFT [12][13][14]19], (4) the H-twin (Hilbert-twin), and (5) the HT (the Hilbert transform) [6,7]. The estimated values of δ are compared.…”

Section: Introductionmentioning

confidence: 99%

“…The estimated values of δ are compared. To ensure meaningful comparison of the results, all computations are performed with (1) the same experimental conditions, (2) the same parameters used in signal processing, such as the length of the analyzed signal, the number of oscillations N osc (the number of periods), the sampling frequency f s , (3) the signal-to-noise ratio, S/N, (4) the maximal strain amplitude, A 0 , and the same signal processing technique [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Hilbert-Twin – A Novel Hilbert Transform-Based Method To Compute Envelope Of Free Decaying Oscillations Embedded In Noise, And The Logarithmic Decrement In High-Resolution Mechanical Spectroscopy HRMS

Magalas¹,

Majewski²

2015

Archives of Metallurgy and Materials

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In this work, we present a novel Hilbert-twin method to compute an envelope and the logarithmic decrement, δ, from exponentially damped time-invariant harmonic strain signals embedded in noise. The results obtained from five computing methods: (1) the parametric OMI (Optimization in Multiple Intervals) method, two interpolated discrete Fourier transform-based (IpDFT) methods: (2) the Yoshida-Magalas (YM) method and (3) the classic Yoshida (Y) method, (4) the novel Hilbert-twin (H-twin) method based on the Hilbert transform, and (5) the conventional Hilbert transform (HT) method are analyzed and compared. The fundamental feature of the Hilbert-twin method is the efficient elimination of intrinsic asymmetrical oscillations of the envelope, a HT (t), obtained from the discrete Hilbert transform of analyzed signals. Excellent performance in estimation of the logarithmic decrement from the Hilbert-twin method is comparable to that of the OMI and YM for the low-and high-damping levels. The Hilbert-twin method proved to be robust and effective in computing the logarithmic decrement and the resonant frequency of exponentially damped free decaying signals embedded in experimental noise. The Hilbert-twin method is also appropriate to detect nonlinearities in mechanical loss measurements of metals and alloys.Keywords: Logarithmic decrement, mechanical spectroscopy, Hilbert transform, envelope, interpolated discrete Fourier transform W pracy przedstawiono nową metodę Hilbert-twin, opartą na dyskretnej transformacie Hilberta, do obliczeń obwiedni wykładniczo tłumionych sygnałów odkształceń sprężystych zawierających w sobie szum oraz do estymacji logarytmicznego dekrementu tłumienia. Przeanalizowano i porównano wyniki obliczeń uzyskane z pięciu różnych metod: (1) metoda parametryczna OMI (Optimization in Multiple Intervals), dwie metody bazujące na interpolowanej dyskretnej transformacie Fouriera (IpDFT): (2) metoda Yoshida-Magalas (YM) i (3) klasyczna metoda Yoshidy (Y), (4) nowa metoda Hilbert-twin (H-twin), którą po raz pierwszy przedstawiono w niniejszej pracy oraz (5) klasyczna metoda obliczeń obwiedni z transformaty Hilberta (HT).Zaletą i fundamentalną cechą charakterystyczną metody H-twin jest skuteczne usunięcie typowych dla dyskretnej transformaty Hilberta asymetrycznych oscylacji obwiedni. Z tego właśnie względu metoda H-twin zapewnia bardzo dobrą estymację logarytmicznego dekrementu tłumienia, która jest porównywalna z metodami OMI i YM zarówno dla niskich, jak i wysokich poziomów tłumienia. Metoda H-twin jest niewrażliwa na szum i jest wyjątkowo skuteczna w precyzyjnym wyznaczaniu logarytmicznego dekrementu tłumienia oraz częstotliwości rezonansowej wykładniczo tłumionych drgań swobodnie tłumionych zawierających szum eksperymentalny.Metoda H-twin może również służyć do detekcji i analizy efektów nieliniowych występujących w trakcie pomiarów rozpraszania energii mechanicznej w metalach i stopach metali badanych metodą spektroskopii mechanicznej.

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“…The zero-point drift (non-harmonic distortion), is neglected here [10]. The additive white noise, ε w (t), is described by the signal-to-noise ratio S/N [8][9][10][11][12][13][14].…”

Section: Methodsmentioning

confidence: 99%