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Application of Integral Transforms in Flood Studies
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
Vahid Nourani, Mehran Dadashzadeh, Saeid Eslamian
Despite the capabilities of the Hilbert transform, the application of this transform by itself is associated with restrictions in the field of hydrology. For example, it is not usable for general random data and its applications have been limited to narrow-band data in the past (Long et al., 1993). Especially problems arise when the signal is in fact a superposition of oscillating components with different time scales – a common situation in the real world – oscillations (Lam et al., 2005). In order to overcome the limitations of the method, Huang and coworkers combined the Hilbert spectral analysis with empirical mode decomposition. A number of Hilbert-Huang transform applications in hydrology are given below.
Hilbert-Huang transformation (HHT) based texture profile analysis for continuous friction characterisation of pavements
Published in International Journal of Pavement Engineering, 2022
Wenying Yu, Joshua Qiang Li, Guangwei Yang, Kelvin C. P. Wang, Nii Attoh-Okine
After the EMD process, the Hilbert spectral analysis is performed on each IMF component to compute the instantaneous frequency as the derivative of the phase function and then extract the localised texture information. The results of Hilbert spectral analysis can subsequently yield a full energy-frequency–time distribution of the signal in the Hilbert spectrum (Ayenu-Prah and Attoh-Okine 2009). Thereby, the original data can be expressed as the real part, Re, in the following form (Gagarin 2004): where and represent the amplitude and instantaneous frequency as a function of distance (or time) variable x.
Identifying corrosion forms on synthetic electrochemical noise signals by the Hilbert–Huang transform method
Published in Corrosion Engineering, Science and Technology, 2018
Luigi Calabrese, Massimiliano Galeano, Edoardo Proverbio
This method operates in the time domain, and it is very adaptive: it is highly efficient and furnishes a holomorphic function that is suitable to be used with the well-known Hilbert Transform to obtain a Hilbert Spectral analysis (HSA), in such a way to perform an accurate description of the signal [25]. It was successfully applied in several fields, such as biomedical [26], atmospheric observation [27], oscillating systems [28], human–computer interfaces [29] and many others.