Empirical mode decomposition and correlation properties of long daily ozone records

Quantifying Uniform Droplet Formation in Microfluidics Using Variational Mode Decomposition

Using variational mode decomposition, we analyze the signal from velocities at the center of the channel of a microfluidics drop-maker. We simulate the formation of water in oil droplets in a microfluidic device. To compare signals from different drop-makers, we choose the length of the water inlet in one drop-maker to be slightly shorter than the other. This small difference in length leads to the formation of satellite droplets and uncertainty in droplet uniformity in one of the drop-makers. By decomposing the velocity signal into only five intrinsic modes, we can fully separate the oscillatory and noisy parts of the velocity from an underlying average flow at the center of the channel. We show that the fifth intrinsic mode is solely sufficient to identify the uniform droplet formation while the other modes encompass the oscillations and noise. Mono-disperse droplets are formed consistently and as long as the fifth mode is a plateau with a local standard deviation of less than 0.02 for a normalized signal at the channel inlet. Spikes in the fifth mode appear, coinciding with fluctuations in the sizes of droplets. Interestingly, the spikes in the fifth mode indicate non-uniform droplet formation even for the velocities measured upstream in the water inlet in a region far before where droplets form. These results are not sensitive to the spatial resolution of the signal, as we decompose a velocity signal averaged over an area as wide as 40% of the channel width.

Statistical Analysis of Field-Aligned Alfvénic Turbulence and Intermittency in Fast Solar Wind

The statistical properties of fast Alfvénic solar wind turbulence have been analyzed by means of empirical mode decomposition and the associated Hilbert spectral analysis. The stringent criteria employed for the data selection in the Wind spacecraft database, has made possible to sample multiple k‖ field-aligned intervals of the three magnetic field components. The results suggest that the spectral anisotropy predicted by the critical balance theory is not observed in the selected database, whereas a Kolmogorov-like scaling (E(k‖)∼k−5/3) and a weak or absent level of intermittency are robust characteristics of the Alfvénic slab component of solar wind turbulence.

Long-Range Correlations and Characterization of Financial and Volcanic Time Series

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

Scaling Properties of Atmospheric Wind Speed in Mesoscale Range

The scaling properties of turbulent flows are well established in the inertial sub-range. However, those of the synoptic-scale motions are less known, also because of the difficult analysis of data presenting nonstationary and periodic features. Extensive analysis of experimental wind speed data, collected at the Mauna Loa Observatory of Hawaii, is performed using different methods. Empirical Mode Decomposition, interoccurrence times statistics, and arbitrary-order Hilbert spectral analysis allow to eliminate effects of large-scale modulations, and provide scaling properties of the field fluctuations (Hurst exponent, interoccurrence distribution, and intermittency correction). The obtained results suggest that the mesoscale wind dynamics owns features which are typical of the inertial sub-range turbulence, thus extending the validity of the turbulent cascade phenomenology to scales larger than observed before.

Wearable Sensor-Based Human Activity Recognition Method with Multi-Features Extracted from Hilbert-Huang Transform

Wearable sensors-based human activity recognition introduces many useful applications and services in health care, rehabilitation training, elderly monitoring and many other areas of human interaction. Existing works in this field mainly focus on recognizing activities by using traditional features extracted from Fourier transform (FT) or wavelet transform (WT). However, these signal processing approaches are suitable for a linear signal but not for a nonlinear signal. In this paper, we investigate the characteristics of the Hilbert-Huang transform (HHT) for dealing with activity data with properties such as nonlinearity and non-stationarity. A multi-features extraction method based on HHT is then proposed to improve the effect of activity recognition. The extracted multi-features include instantaneous amplitude (IA) and instantaneous frequency (IF) by means of empirical mode decomposition (EMD), as well as instantaneous energy density (IE) and marginal spectrum (MS) derived from Hilbert spectral analysis. Experimental studies are performed to verify the proposed approach by using the PAMAP2 dataset from the University of California, Irvine for wearable sensors-based activity recognition. Moreover, the effect of combining multi-features vs. a single-feature are investigated and discussed in the scenario of a dependent subject. The experimental results show that multi-features combination can further improve the performance measures. Finally, we test the effect of multi-features combination in the scenario of an independent subject. Our experimental results show that we achieve four performance indexes: recall, precision, F-measure, and accuracy to 0.9337, 0.9417, 0.9353, and 0.9377 respectively, which are all better than the achievements of related works.

PERFORMANCE EVALUATION OF ENSEMBLE EMPIRICAL MODE DECOMPOSITION

Empirical mode decomposition (EMD) is an adaptive, data-driven algorithm that decomposes any time series into its intrinsic modes of oscillation, which can then be used in the calculation of the instantaneous phase and frequency. Ensemble EMD (EEMD), where the final EMD is estimated by averaging numerous EMD runs with the addition of noise, was an advancement introduced by Wu and Huang (2008) to try increasing the robustness of EMD and alleviate some of the common problems of EMD such as mode mixing. In this work, we test the performance of EEMD as opposed to normal EMD, with emphasis on the effect of selecting different stopping criteria and noise levels. Our results indicate that EEMD, in addition to slightly increasing the accuracy of the EMD output, substantially increases the robustness of the results and the confidence in the decomposition.

Long-range persistence of temperature records induced by long-term climatic phenomena

The occurrence of persistence in climatic systems has been investigated by analyzing 1167 surface temperature records, covering 110 years, in the whole United States. Due to the nonlinear and nonstationary character of temperature time series, the seasonal cycle suffers from both phase and amplitude modulations, which are not properly removed by the classical definition of the temperature anomaly. In order to properly filter out the seasonal component and the monotonic trends, we define the temperature anomaly in a different way by using the empirical mode decomposition (EMD). The essence of this method is to empirically identify the intrinsic oscillatory modes from the temperature records according to their characteristic time scale. The original signal is thus decomposed into a collection of a finite small number of intrinsic mode functions (IMFs), having its own time scale and representing oscillations experiencing amplitude and phase modulations, and a residue, describing the mean trend. The sum of all the IMF components as well as the residue reconstructs the original signal. Partial reconstruction can be achieved by selectively choosing IMFs in order to remove trivial trends and noise. The EMD description in terms of time-dependent amplitude and phase functions overcomes one of the major limitation of the Fourier analysis, namely, a correct description of nonlinearities and nonstationarities. By using the EMD definition of temperature anomalies we found persistence of fluctuations with a different degree according to the geographical location, on time scales in the range 3-15 years. The spatial distribution of the detrended fluctuation analysis exponent, used to quantify the degree of memory, indicates that the long-term persistence could be related to to the presence of climatic regions, which are more sensitive to climatic phenomena such as the El Niño southern oscillation.

Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: comparison study with detrended fluctuation analysis and wavelet leaders

In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Re(λ)≃250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξ(θ)(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before.

Amplitude-frequency fluctuations of the seasonal cycle, temperature anomalies, and long-range persistence of climate records

The presence of long-term persistence of climate records on scales from 2 to 15 yr has been reported in the literature, even if the universality of this result is controversial. In the present paper results from monthly temperature records measured for about 250 yr in Prague and Milan are reported. Because of the nonlinear and nonstationary character of temperature time series the seasonal contribution has been identified through the empirical mode decomposition. We find that the seasonal component of the climate records is characterized by some time scales showing both amplitude and phase fluctuations. By using a more suitable definition of temperature anomalies, and thus excluding persistence effects due to seasonal oscillations and trends, the occurrence of long-term persistence has been investigated through the detrended fluctuation analysis. Our results indicate persistence on scales from 3 to 10 yr with similar values for the detrended fluctuation analysis indices.

Multivariate empirical mode decomposition

Despite empirical mode decomposition (EMD) becoming a de facto standard for time-frequency analysis of nonlinear and non-stationary signals, its multivariate extensions are only emerging; yet, they are a prerequisite for direct multichannel data analysis. An important step in this direction is the computation of the local mean, as the concept of local extrema is not well defined for multivariate signals. To this end, we propose to use real-valued projections along multiple directions on hyperspheres ( n -spheres) in order to calculate the envelopes and the local mean of multivariate signals, leading to multivariate extension of EMD. To generate a suitable set of direction vectors, unit hyperspheres ( n -spheres) are sampled based on both uniform angular sampling methods and quasi-Monte Carlo-based low-discrepancy sequences. The potential of the proposed algorithm to find common oscillatory modes within multivariate data is demonstrated by simulations performed on both hexavariate synthetic and real-world human motion signals.

Does cosmic-ray-induced heterogeneous chemistry influence stratospheric polar ozone loss?

Cosmic-ray (CR) -induced heterogeneous reactions of halogenated species have been suggested to play the dominant role in causing the Antarctic ozone hole. However, measurements of total ozone in Antarctica do not show a compact and significant correlation with CR activity. Further, a substantial CR-induced heterogeneous loss of chlorofluorocarbons is incompatible with multiyear satellite observations of N2O and CFC-12. Thus, CR-induced heterogeneous reactions cannot be considered as an alternative mechanism causing the Antarctic ozone hole.

Data analysis using a combination of independent component analysis and empirical mode decomposition

A combination of independent component analysis and empirical mode decomposition (ICA-EMD) is proposed in this paper to analyze low signal-to-noise ratio data. The advantages of ICA-EMD combination are these: ICA needs few sensory clues to separate the original source from unwanted noise and EMD can effectively separate the data into its constituting parts. The case studies reported here involve original sources contaminated by white Gaussian noise. The simulation results show that the ICA-EMD combination is an effective data analysis tool.

Advantages of the Hilbert Huang transform for marine mammals signals analysis

While marine mammals emit variant signals (in time and frequency), the Fourier spectrogram appears to be the most widely used spectral estimator. In certain cases, this approach is suboptimal, particularly for odontocete click analysis and when the signal-to-noise ratio varies during the continuous recordings. We introduce the Hilbert Huang transform (HHT) as an efficient means for analysis of bioacoustical signals. To evaluate this method, we compare results obtained from three time-frequency representations: the Fourier spectrogram, the wavelet transform, and the Hilbert Huang transform. The results show that HHT is a viable alternative to the wavelet transform. The chosen examples illustrate certain advantages. (1) This method requires the calculation of the Hilbert transform; the time-frequency resolution is not restricted by the uncertainty principle; the frequency resolution is finer than with the Fourier spectrogram. (2) The original signal decomposition into successive modes is complete. If we were to multiply some of these modes, this would contribute to attenuate the presence of noise in the original signal and to being able to select pertinent information. (3) Frequency evolution for each mode can be analyzed as one-dimensional (1D) signal. We not need a complex 2D post-treatment as is usually required for feature extraction.

Analysis of phase synchronization of coupled chaotic oscillators with empirical mode decomposition

Empirical mode decomposition is investigated as a tool to determine the phase and frequency and to study phase synchronization between complex chaotic oscillators. Within this approach, the oscillator is characterized by a spectrum of frequencies corresponding to the empirical modes. First, the phase and frequency of the oscillators resulting from two well-known methods, based on modified variables and the Poincaré surface of section, are compared with those obtained using empirical mode decomposition. Next, for both parametrically and essentially different chaotic oscillators coupled as a drive-response system, transition to phase synchronization between corresponding empirical modes is investigated, defined as an adjustment of the mode frequencies of the response oscillator to those of the drive oscillator as the coupling is increased. In particular, anomalous and imperfect phase synchronization between modes is observed.