A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...

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Ensemble empirical mode decomposition: a noise-assisted data analysis method

During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

Variational Mode Decomposition

Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.

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Empirical mode decomposition as a filter bank

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

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A new view of nonlinear water waves: the Hilbert spectrum

Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.

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Neurophysiological and Computational Principles of Cortical Rhythms in Cognition

Application of hermite polynomial to wave and wave force statistics

Effects of random wave surface fluctuation on response of offshore structures

It is known that when an unanchored rigid body is placed on a horizontal base which oscillates horizontally, it may undergo one of four modes of motion: rest, slide, slide–rock and rock. Initiation of a rigid body into these modes depends on the slenderness ratio of the body, the coefficient of friction between the body and the base and the acceleration of the base. In this study, the coefficient of friction and the base acceleration are considered random. For specific probability distributions of the coefficient of friction and the peak base acceleration, and for various values of the mean and standard deviation of the two random variables, the probabilities of occurrence of these modes of motion are obtained for a body of given slenderness ratio. It is shown that randomness of the coefficient of friction and base peak acceleration should not be ignored. Copyright © 2005 John Wiley & Sons, Ltd.

Criteria for initiation of motion of rigid bodies to base excitation

Based on the improved statistics model of breaking waves, we have calculated the following statistical quantities: S_t, breaking area ratio generated per unit time; V_t, the volume of water mass thrown out from the wave surface due to breaking on a unit area per unit time; (?)_t, the breaking energy loss rate on a unit area per unit time. Under the high sea state, the phase change governed by wave breaking is mechanistic. Based on the physical and dimensional consideration we have also derived the statistical quantities of upper ocean dynamics such as whitecap coverage, exchange fluxes in the high sea state and turbulence degree in the subsurface layer. The theoretical results are consistent with the existing experimental data.

Statistics of breaking waves and its application to upper ocean dynamics

In coastal areas residential houses are often built on piles. The space below the first floor and the ground is sometimes enclosed. The enclosure walls are constructed to break away under severe wave-induced forces so that the forces transmitted through the breakaway walls to the building's foundation are not unduly large. Successful design of a breakaway wall therefore depends critically on knowledge of the ultimate strength of nailed fasteners and wall material and of the behavior of breakaway wall under wave-induced forces. In this research, laboratory tests were performed to determine the ultimate strength of nailed connections. Behavior and failure modes of breakaway walls from water waves were studied analytically and in a series of laboratory wave channel tests.

C. C. Tung

Papers

Application of hermite polynomial to wave and wave force statistics

Effects of random wave surface fluctuation on response of offshore structures

Criteria for initiation of motion of rigid bodies to base excitation

Statistics of breaking waves and its application to upper ocean dynamics

Behavior of Breakaway Walls under Wave Action