High resolution ADCP, CTD and Fluorometer time series analysis

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.

Biomedical signals are in general non-linear and non-stationary. Empirical Mode Decomposition in conjunction with Hilbert-Huang Transform provides a fully adaptive and data-driven technique to extract Intrinsic Mode Functions (IMFs). The latter represent a complete set of locally orthogonal basis functions to represent non-linear and non-stationary time series. Large scale biomedical time series necessitate an online analysis which is presented in this contribution. It shortly reviews the technique of EMD and related algorithms, discusses the newly proposed SEMD algorithm and presents some applications to biomedical time series recorded during neuromonitoring.

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 original signal of rolling bearing fault contains a large number of phase coupling components and is easily submerged in the background noise, which make the fault information difficult to be extracted accurately. Aiming at the above problems, a method of fault feature extraction for rolling bearing is proposed, which combines empirical mode decomposition (EMD) with a 1.5-dimensional spectrum. The original signal is decomposed by EMD to obtain the intrinsic modal function (IMF) of different scales. The IMF is selected by the size of a correlation coefficient and a kurtosis value to eliminate the high-frequency components, which is reconstructed to achieve the purpose of noise reduction. The reconstructed Hilbert envelope signal is analysed by the 1.5-dimensional spectrum to extract the nonlinear characteristic of two phase couplings, so that the fault characteristic frequency of the bearing is obtained. By analysing the signal of actual rolling bearings, the fault characteristic frequency of bearing inner and outer rings can be effectively extracted, and the validity and feasibility of the method are proved.

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.

In ultrasonic testing of coarse-grained materials, signal to noise ratio (SNR) of testing signals is reduced seriously for the structure noise, and echoes from defects are difficult to be identified. In order to improve the SNR and the reliability of ultrasonic testing of coarse-grained materials, empirical mode decomposition (EMD) is introduced to process the testing signal here. Signal envelope can be formed by using cubic spline interpolation, and nonlinear and non-stationary signal can be decomposed self-adaptive into the sum of several intrinsic mode functions (IMF) by using characteristic time scale of the signals, and then higher order and tendency of the original signals can be obtained. The denoising experiment with low SNR simulated signal are achieved according to the feature of EMD, and SNR is enhanced more by comparison with the wavelet analysis method. And testing signal collected from coarse-grained materials is used to finish denoising experiment, and it is shown from the experiment result that the EMD has better adaptive ability in decomposing noise-polluted signals and less empirical information is required in the denoising process. DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.3286

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.

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.

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.

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.

Financial time series forecasting has been a challenge for time series analysts and researchers because it is noisy, nonstationary and chaotic. To overcome this limitation, this study uses empirical mode decomposition (EMD) and phase space reconstruction (PSR) to assist in the task of financial time series forecasting. In addition, we propose an approach that combines these two data preprocessing methods with extreme learning machine (ELM). The approach contains four steps as follows. (1) EMD is used to decompose the dynamics of the exchange rate time series into several components of intrinsic mode function (IMF) and one residual component. (2) The IMF and residual time series phase space is reconstructed to reveal its unseen dynamics according to the optimum time delay $$\tau $$ź and embedding dimension m. (3) The reconstructed time series datasets are divided into two datasets: training and testing, in which the training datasets are used to build ELM models. (4) A regression forecast model is set up for each IMF as well as the residual component by using ELM. The final prediction results are obtained by compositing the prediction values. To verify the effectiveness of the proposed approach, four exchange rates are chosen as the forecasting targets. Compared with some existing state-of-the-art models, the proposed approach yields superior results. Academically, we demonstrated the validity and superiority of the proposed approach that integrates EMD, PSR, and ELM. Corporations or individuals can apply the results of this study to acquire accurate exchange rate information and reduce exchange rate expenses.

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.

Air pollution is a high-profile issue that causes precipitation acidification, water pollution, and building corrosion, negatively affecting human respiratory health. As technology gradually digitalizes, the rise in electricity demand may exacerbate pollution, further impacting the environment and public health. The process of electricity generation emits significant amounts of air pollutants like SO₂, NOₓ, O₃, CO, PM₁₀, and PM₂.₅, which cause acid precipitation and smog that can potentially threaten public health. Among various methods of generating electricity, the thermal power-based method has the most significant impact on air pollution, accounting for 70% of the total, primarily through gas-fired and coal-fired power. To comprehend the environmental impact of electricity generation by the government-operated Taiwan Power Company, this study concentrates on identifying the relationship between electricity consumption, air pollutants, and hydro-meteorological factors. To achieve this aim, two data-driven methods are employed: (1) Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), an improved version of Empirical Mode Decomposition (EMD), to extract long-term trends from non-stationary, non-linear data (2) Time-dependent Intrinsic Correlation (TDIC) to visualize and quantify the correlation, illustrating the degree of relationship between two time-series data sets. The CEEMDAN algorithm will decompose data into several Intrinsic Mode Functions (IMF) and one long-term trend of data. Those IMFs represent the changing data in different time scales. Subsequently, this research utilizes each IMF to reconstruct signals and generate wind rose diagrams. With the wind rose diagram, this research can analyze multi-scale distribution properties of wind direction and wind speed that can explore the changing trends of the wind field. By decoding these relationships, this research can better examine the degree of thermal power generation impacts on air pollution and how wind direction disperses air pollutants, providing a high-risk mapping to avoid human activities. Based on Taiwan's geographical address surrounded by the sea, this study can encompass the impacts of anthropogenic factors and natural factors, like monsoons, on air pollution, achieving a more comprehensive analysis. Moreover, integrating these findings and policy implementation enables more sustainable resource management and decision-making.

A robust time series prediction method based on empirical mode decomposition and high-order fuzzy cognitive maps

Novel and efficient computation of Hilbert–Huang transform on surfaces