Sliding Empirical Mode Decomposition-Brain Status Data Analysis and Modeling

Biomedical signals are in general non-linear and non-stationary which renders them difficult to analyze with classical time series analysis techniques. Empirical Mode Decomposition (EMD) in conjunction with a Hilbert spectral transform, together called Hilbert-Huang Transform, is ideally suited to extract informative components which are characteristic of underlying biological or physiological processes. The method is fully adaptive and generates a complete set of orthogonal basis functions, called Intrinsic Mode Functions (IMFs), in a purely data-driven manner. Amplitude and frequency of IMFs may vary over time which renders them different from conventional basis systems and ideally suited to study non-linear and non-stationary time series. However, biomedical time series are often recorded over long time periods. This generates the need for efficient EMD algorithms which can analyze the data in real time. No such algorithms yet exist which are robust, efficient and easy to implement. The contribution shortly reviews the technique of EMD and related algorithms and develops an on-line variant, called slidingEMD, which is shown to perform well on large scale biomedical time series recorded during neuromonitoring.

In the marine environment, the recorded time series are often nonlinear and nonstationary and interact with each other. Their analysis faces new challenges and thus requires the implementation of adequate and specific methods. We use the Hilbert-Huang Transform (HHT) for the spectral analysis of high frequency sampled time series in near shore waters of Cambridge Bay, located in the Canadian Arctic. We focus particularly on automatic measurements of temperature records, salinity, turbidity and chlorophyll data sets from deployments on an Ocean Networks Canada cabled platform. We look at the contribution of different Intrinsic Mode Functions (IMFs) obtained by the Empirical Mode Decomposition (EMD). The inertial wave and several low-frequency tidal waves are identified by the application of EMD. Furthermore, the correlation between two nonstationary time series is investigated. By Time Dependent Intrinsic Correlation (TDIC) analysis, it was concluded that the high-frequency modes have small correlation; whereas the trends are perfectly correlated. The methodologies presented in this paper are general. They can be applied for identification of main properties of other time series from the environmental and oceanic sciences, where the records are complex with fluctuations over a large range of different spatial and temporal scales.

The theory and practice of the Hilbert-Huang transform (HHT) provide another way of analyzing nonlinear and nonstationary time series. The central idea of HHT is the empirical mode decomposition (EMD), which is then decomposed into a set of intrinsic mode functions (IMFs) and analyzed by using the Hilbert spectrum. This chapter is primarily a summary of current applications of HHT and suggests areas for future research based on my personal views. 13.

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach.

The electric power load is inherently nonlinear and nonstationary time series, which has periodicity and randomicity. It is difficult to accurately forecast with a single method. So a hybrid method based on empirical mode decomposition (EMD) and support vector machines (SVMs) was presented in this paper. First, load time series was adaptively decomposed into a series of smooth intrinsic mode functions (IMFs) with different scales via EMD; second, tendency of each IMF was forecasted with different SVM respectively according to its change and weather factors were taken account in forecasting; finally, final results were obtained by summing up these forecasting results of each IMF together. The simulation results show that the hybrid method has higher precision and greater generalization ability.

A Hilbert–Huang transform (HHT) is a time–frequency technique and has been widely applied to analyzing vibration signals in the field of fault diagnosis of rotating machinery. It analyzes the vibration signals using intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). However, EMD sometimes cannot reveal the signal characteristics accurately because of the problem of mode mixing. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate this problem. The IMFs generated by EEMD have different sensitivity to faults. Some IMFs are sensitive and closely related to the faults but others are irrelevant. To enhance the accuracy of the HHT in fault diagnosis of rotating machinery, an improved HHT based on EEMD and sensitive IMFs is proposed in this paper. Simulated signals demonstrate the effectiveness of the improved HHT in diagnosing the faults of rotating machinery. Finally, the improved HHT is applied to diagnosing an early rub-impact fault of a heavy oil catalytic cracking machine set, and the application results prove that the improved HHT is superior to the HHT based on all IMFs of EMD.

Spatiotemporal Characteristics of Precipitation and Drought Variability in Taiwan Using Multi-dimensional Complementary Ensemble Empirical Mode Decomposition AbstractMost time series observed in natural systems are nonlinear and nonstationary, particularly under the influence of climate change. Taiwan has experienced increasingly frequent drought events in recent decades. Droughts are characterized by their gradual development, cumulative impacts, and lack of clear early warning signals, which makes their detection and analysis challenging. To address these issues, this study applies Multi-dimensional Complementary Ensemble Empirical Mode Decomposition (MCEEMD) to analyze long-term temperature and precipitation data in Taiwan from 1960 to 2023. MCEEMD is an effective time–frequency analysis method designed for nonlinear and nonstationary time series. It enables the decomposition of multi-dimensional signals into a set of Intrinsic Mode Functions (IMFs), allowing both spatial and temporal characteristics of climate variables to be examined. Through these IMFs, meaningful instantaneous frequencies and long-term trends in the signals can be identified. This study considers both stochastic and deterministic influences by reconstructing the IMFs into two components based on their autocorrelation coefficients. The relationships between temperature, precipitation variability, and drought-related characteristics are then examined, providing insights into the spatiotemporal behavior of drought events in Taiwan. Key word: Multi-dimensional Complementary Ensemble Empirical Mode Decomposition(MCEEMD ),Intrinsic Mode Functions (IMFs)

Hilbert-Huang Transform (HHT) is a kind of signal analysis method suitable for non-stationary signal, and the combination of HHT and vector signal processing is called vector HHT, by which the instantaneous azimuth of the target can be estimated. In vector HHT signal processing method, the existence of intermittent signal and noise leads to mode mixing in the results of empirical mode decomposition (EMD). Mode mixing influences exact extraction of vibration mode, which causes that the signal which should be in the same order of intrinsic mode function (IMF) distributes in different IMFs. In vector HHT signal processing method, the two vibration speed components need to be multiplied by sound pressure respectively, so mode mixing will lead to great error in the estimation of azimuth of the target. To overcome the influence of mode mixing on vector HHT, this paper proposes a kind of vector HHT signal processing method based on scale filtering. The new method can effectively eliminate mode mixing resulting from intermittent signal and noise, and exact decomposition results can be achieved. The improved vector HHT method is used in processing acoustic vector signal, and the data obtained from a certain sea experiment in Dalian city is analyzed by the new method. The waterfall plot accurately shows the azimuth of the target ship, which proves the validity of the method.

Accurate clustering of time series is a challenging problem for data arising from areas such as financial markets, biomedical studies, and environmental sciences, especially when some, or all, of the series exhibit nonlinearity and nonstationarity. When a subset of the series exhibits nonlinear characteristics, frequency domain clustering methods based on higher-order spectral properties, such as the bispectra or trispectra are useful. While these methods address nonlinearity, they rely on the assumption of series stationarity. We propose the Bispectral Smooth Localized Complex EXponential (BSLEX) approach for clustering nonlinear and nonstationary time series. BSLEX is an extension of the SLEX approach for linear, nonstationary series, and overcomes the challenges of both nonlinearity and nonstationarity through smooth partitions of the nonstationary time series into stationary subsets in a dyadic fashion. The performance of the BSLEX approach is illustrated via simulation where several nonstationary or nonlinear time series are clustered, as well as via accurate clustering of the records of 16 seismic events, eight of which are earthquakes and eight are explosions. We illustrate the utility of the approach by clustering S&P 100 financial returns.

Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT

The analysis and calculation are conducted in combination with a real example, the Lanzhou station in the upper reaches of the Yellow River and Lancun station in the Fenhe River, Hilbert-Huang Transform (HHT) and the empirical mode decomposition (EMD) method are used to analyze runoff time series in this paper. Firstly original series is step-by-step decomposed by means of EMD method, so the result is four intrinsic mode functions (IMF) and a residual component at the Lanzhou station, and is three intrinsic mode functions (IMF) and a residual component at the Lancun station. It is computed that natural annual runoff have the periodicity of 2.23 a, 5.57 a, 10.23a and 19.76a at the Lanzhou station, and 2.63 a, 6.67a and 25 a at the Lancun station. The physical cause is analyzed. The result provides scientific ground for planning and management water resource in the basin.

Novel and efficient computation of Hilbert–Huang transform on surfaces

Empirical mode decomposition (EMD) is particularly useful in analyzing nonstationary and nonlinear time series. However, only partial data within boundaries are available because of the bounded support of the underlying time series. Consequently, the application of EMD to finite time series data results in large biases at the edges by increasing the bias and creating artificial wiggles. This study introduces a new two-stage method to automatically decrease the boundary effects present in EMD. At the first stage, local polynomial quantile regression (LLQ) is applied to provide an efficient description of the corrupted and noisy data. The remaining series is assumed to be hidden in the residuals. Hence, EMD is applied to the residuals at the second stage. The final estimate is the summation of the fitting estimates from LLQ and EMD. Simulation was conducted to assess the practical performance of the proposed method. Results show that the proposed method is superior to classical EMD.

This paper presents an Empirical mode decomposition (EMD) approach for achieving high-speed frequency-tagged steady state visual evoked potential (SSVEP) brain computer interface (BCI) system. Empirical mode decomposition (EMD) has been demonstrated as a local and fully data-driven technique for the data processing of nonlinear and non-stationary time-series. It allows the frequency and amplitude of a time-series to be evaluated with excellent time resolution. The proposed system utilized flickering sources with high flickering rate acting as cursor system for the purpose of alternatively communication system. Induced EEG signal were decomposed into different scale of oscillation components namely intrinsic mode functions. In order to find out the SSVEP-related IMFs, instantaneous frequency were computed by generalized zero crossing (GZC). After identification of the frequency power by quadrature detection, the result shows the proposed system achieved 51.46 bits/min of average ITR. Compare with FFT approaches, EMD method provide better temporal and frequency sensitivity in detection of cognitive state of neuron activities.KeywordsBrain computer interface (BCI)Empirical mode decomposition (EMD)Steady-state visual evoked potential (SSVEP)

This paper presents an improved version of the Hilbert-Huang transform (HHT) for the modal evaluation of structural systems or signals. In this improved HHT, a well-designed bandpass filter is used as preprocessing to separate and determine each mode of the signal for solving the inherent modemixing problem in HHT (i.e., empirical mode decomposition, EMD, associated with the Hilbert transform). A screening process is then applied to remove undesired intrinsic mode functions (IMFs) derived from the EMD of the signal's mode. A "best" IMF is selected in each screening process that utilizes the orthogonalization coefficient between the signal's mode and its IMFs. Through mode-by-mode signal filtering, parameters such as the modal frequency can be evaluated accurately when compared to the theoretical value. Time history of the identified modal frequency is available. Numerical results prove the efficiency of the proposed approach, showing relative errors 1.40%, 2.06%, and 1.46%, respectively, for the test cases of a benchmark structure in the lab, a simulated time-varying structural system, and of a linear superimposed cosine waves.