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

[1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2007RG000228

A review on Hilbert‐Huang transform: Method and its applications to geophysical studies

Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field

The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non‐stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre‐processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full‐frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non‐stationary processes by these new techniques. Data from length‐of‐day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.

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A confidence limit for the empirical mode decomposition and Hilbert spectral analysis

Welding Metallurgy of

A new method of spectral analysis, using an approach we call the empirical mode decomposition (EMD) and the Hilbert spectrum analysis (HSA), is presented. The EMD method decomposes any data into a finite number of intrinsic mode function (IMF) components with time-variable amplitudes and frequencies. This decomposition is nearly orthogonal and totally adaptive. With the decomposition, a Hilbert, rather than Fourier, transform is applied to each IMF component, which gives each component instantaneous frequency and energy density. This approach is totally new, and it is different from any of the existing methods: it uses differentiation to define the frequency rather than the traditional convolution computation; thus, it gives the instantaneous frequency and energy density. The greatest advantage of the new approach is that it is the only spectral analysis method applicable to nonstationary and nonlinear data. To illustrate the capability of his new method, we have applied it to the earthquake record from station TCU129, at Chi-Chi, Taiwan, collected during the 21 September 1999 earthquake. The same record is also analyzed with Fourier analysis, wavelet transform, and response spectrum analysis. Comparisons among the different analysis methods indicate that the Hilbert spectral analysis gives the most detailed information in a time-frequency-energy presentation. It also emphasizes the potentially damage-causing low-frequency energy in the earthquake signal missed by all the other methods.

Manuscript received 19 December 2000.

A New Spectral Representation of Earthquake Data: Hilbert Spectral Analysis of Station TCU129, Chi-Chi, Taiwan, 21 September 1999

Structural health monitoring using empirical mode decomposition and the Hilbert phase

A wave approach to estimating frequency-dependent damping under transient loading

Continuity on an embedded phase space is enough to imply determinism in time series. Also, it is possible to define infinitely many arbitrary vector fields over an attractor. We exploit this arbitrariness to generate a detector of smoothness and therefore of determinism in time series. We report results of numerical studies of both flow and map examples and of a chaotic experimental system.

Smoothness Implies Determinism: A Method to Detect It in Time Series

There is increasing interest by the naval engineering community in permanent monitoring systems that can monitor the structural behaviour of ships during their operation at sea. This study seeks to reduce the cost and installation complexity of hull monitoring systems by introducing wireless sensors into their architectural designs. Wireless sensor networks also provide other advantages over their cable-based counterparts such as adaptability, redundancy, and weight savings. While wireless sensors can enhance functionality and reduce cost, the compartmentalised layout of most ships requires some wired networking to communicate data globally throughout the ship. In this study, 20 wireless sensing nodes are connected to a ship-wide fibre-optic data network to serve as a hybrid wireless hull monitoring system on a high-speed littoral combat vessel (FSF-1 Sea Fighter). The wireless hull monitoring system is used to collect acceleration and strain data during unattended operation during a one-month period at s...

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Liming W. Salvino

Papers

A New Spectral Representation of Earthquake Data: Hilbert Spectral Analysis of Station TCU129, Chi-Chi, Taiwan, 21 September 1999

Structural health monitoring using empirical mode decomposition and the Hilbert phase

A wave approach to estimating frequency-dependent damping under transient loading

Smoothness Implies Determinism: A Method to Detect It in Time Series

Hybrid wireless hull monitoring system for naval combat vessels