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Hilbert-Huang transform - A new method of analyzing unsteady, nonlinear turbulent flow data

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The Hilbert-Huang transform (HHT) is a new and powerful signal-processing technique developed in the late 1990’s by Dr Norden E. Huang and his colleagues. The HHT can analyse any nonlinear and non-stationary signals without mathematical requirements. It has been applied successfully for the past ten years in various domains: biomedical applications, chemistry and chemical engineering, digital image analysis, financial applications, fluid mechanics, meteorological and atmospheric applications, ocean engineering, seismic studies, structural applications, health monitoring, and system identification. It proceeds in two steps: first an ingenious method called the empirical mode decomposition (EMD) decomposes a discrete time-series into intrinsic mode functions (IMFs). These IMFs reveal the different mechanisms mingled in the original signal. Second, the Hilbert transform is applied to each IMF to compute the instantaneous frequency and amplitude. It eventually yields a physically meaningful time-frequency-amplitude spectrum, which gives very useful insights about the underlying mechanisms of the phenomenon studied.

The basics of the HHT algorithm are introduced. Then, key points, such as the stopping criterion for the sifting process, the end-effect, and the problem of mode mixing, are described. Some solutions addressing these problems are then presented. Finally, results obtained with two signals, the length-of-day data (LOD data) and vortex-shedding data are discussed. The analysis of the LOD data, initially studied by Dr Huang and colleagues., is a good example showing the efficiency of the EMD . The results obtained with the second signal have revealed a nonlinear phenomenon of intra-wave frequency modulation.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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