Resolving Nonstationary Spectral Information in Wind Speed Time Series Using the Hilbert–Huang Transform

Abstract

This work is motivated by the observation that large-amplitude wind fluctuations on temporal scales of 1–10 h present challenges for the power management of large offshore wind farms. Wind fluctuations on these scales are analyzed at a meteorological measurement mast in the Danish North Sea using a 4-yr time series of 10-min wind speed observations. An adaptive spectral analysis method called the Hilbert–Huang transform is chosen for the analysis, because the nonstationarity of time series of wind speed observations means that they are not well described by a global spectral analysis method such as the Fourier transform. The Hilbert–Huang transform is a local method based on a nonparametric and empirical decomposition of the data followed by calculation of instantaneous amplitudes and frequencies using the Hilbert transform. The Hilbert–Huang transformed 4-yr time series is averaged and summarized to show climatological patterns in the relationship between wind variability and time of day. First, by integrating the Hilbert spectrum along the frequency axis, a scalar time series representing the total variability within a given frequency range is calculated. Second, by calculating average spectra conditional to time of day, the time axis of the Hilbert spectrum is “remapped” to show climatological patterns. Third, the daily patterns in wind variability and wind speed are compared for the four seasons of the year. It is found that the most intense wind variability occurs in autumn even though the strongest observed wind speeds occur in winter.

Wind fluctuations over the North Sea

“…As argued by Vincent et al (2010), wind speed time series should be treated as non-stationary, even though the classification of such complex time series is difficult because it depends on the time scale under consideration.…”

Continuous Wavelet and Hilbert-Huang Transforms Applied for Analysis of Active and Reactive Power Consumption

“…On the other hand, HHT approach is composed of two parts: empirical mode decomposition (EMD) and Hilbert spectral analysis. Based on [9][10][11][12][13][14][15][16][17], this approach is described in short as follows: Using the EMD method, signal or time series is decomposed into IMFs. The signal can be composed of several IMF components, where each one has the following properties: (i) in the whole data set the number of extrema (minima and maxima) and the number of zero crossings must be equal or differ by at most one, (ii) at any point, the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero.…”

“…On the other hand, Hilbert-Huang transform (HHT) is a somewhat younger technique and today one of the most popular approaches for analysing non-stationary and nonlinear signals and time series [9][10][11][12]. HHT is being applied in almost all fields of science [12][13][14][15][16][17]. HHT is composed of two parts: (i) Empirical Mode Decomposition (EMD) and (ii) Hilbert spectral analysis.…”

Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation

“…Figure 1(a) depicts a time series of mean hourly wind speed at the Horns Rev wind farm in Denmark over a period of almost 1000 h. † This offshore wind farm has been the first large-scale offshore wind farm worldwide, and has hence motivated a number of studies for e.g. the characterization of local wind characteristics (Vincent, et al, 2009) or the (probabilistic) forecasting of its power output (Pinson and Madsen, 2009a). The time series of wind speed is normalized by the maximum wind speed observed over the period, consequently taking values in [0, 1].…”

“…Intuitively, since it is expected that time series of hourly wind-speed averages will exhibit a significant autocorrelation pattern (see discussion in Vincent, et al, 2009), and since such time series are transformed through a monotonic (strictly) increasing function, an autocorrelation pattern is also expected to be present in the time series {z t,k } of probability integral transforms. This argument also applies to the corresponding time series {z t,k }.…”