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

Abstract

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, aHT (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