Bivariate Empirical Mode Decomposition Research Articles

An enhanced interval PM2.5 concentration forecasting model based on BEMD and MLPI with influencing factors

In order to protect public health by providing an early warning of harmful air pollutants, various forecasting models are proposed to forecast the average values of daily pollutant concentrations. In fact, even on the same day, the concentration of pollutants will fluctuate greatly during different time periods, point-based models can not reflect the variability well. Thus, an enhanced interval PM2.5 concentration forecasting model is developed in this paper, which is based on interval decomposition ensemble and considering influencing factors. For the purpose of obtaining main influencing factors, interval grey incidence analysis (IGIA) is used to select input variables for model. The interval-valued time series (ITS) of PM2.5 concentration and its influencing factors are decomposed into a finite number of complex-valued intrinsic mode functions (IMFs) and one complex-valued residual by bivariate empirical mode decomposition (BEMD) algorithm. Considering the different amounts of various IMFs, the complex-valued IMFs and residual are clustered into fewer classes by reconstruction technique. Then, interval multilayer perceptron (MLPI) is employed to fit the lower and upper bound simultaneously of all classes to obtain the corresponding forecasting results, which are combined to generate the aggregated interval-valued output by a simple addition approach. The model is tested by the dataset collected from three environmental monitoring stations in Beijing, China. Experimental results show that the enhanced model outperforms other considered models by means of forecasting accuracy and stability.

Spillover effect and Granger causality investigation between China’s stock market and international oil market: A dynamic multiscale approach

With the rapid development of China’s economy and the increasing dependence of crude oil on foreign countries, the relationship between China’s stock market and the international oil market is becoming closer and closer. Aiming to explore the interrelation of the two markets theoretically and empirically, the linear and nonlinear Granger causality tests combined with the bivariate empirical mode decomposition model are used to evaluate the dynamic multiscale interaction and the volatility effect between China’s stock market and the international oil market. With the Shanghai stock index and Brent Spot Price (FOB price) as empirical study samples, some interesting conclusions emerged. There is a bi-directional nonlinearity between the two markets, but the relationship between international crude oil price and China’s stock market shows a gradual strengthening trend. The Granger causality between China’s stock market and the international oil market is relatively diverse and is varying with different timescales. And when analyzing the inner factors either in the Brent oil market or the stock market, we need to consider the spillover effect between the two markets.

Medición de desplazamientos nanométricos en polímeros piezoeléctricos usando método de descomposición en modos empíricos bivariados en patrones de speckle

En este trabajo se presenta un método óptico para la determinación directa del coeficiente piezoeléctrico de películas delgadas de material polimérico. Esto se logra a través de la medición de desplazamientos mecánicos nanométricos generados en el film cuando es excitado con señales eléctricas armónicas de baja frecuencia (0.5 Hz). El sistema está basado en la inteferometría temporal de patrones de speckle y en la recuperación de fase por descomposición en modos empíricos bivariada. El esquema experimental fue usado sobre una muestra de polifluoruro de vinilideno depositada sobre un substrato de vidrio que presenta condiciones de contorno similares a las que se encuentran en experiencias de caracterización de fluídos complejos por técnicas fotoacústicas. El valor medido concuerda con aquellos obtenidos por otros métodos y con el reportado por el fabricante.

Augmented EMD for complex‐valued univariate signals

In this study, the authors propose an efficient extension of the standard empirical mode decomposition (EMD) for complex-valued univariate signal decomposition. The key idea of the extension is to convert a complex-valued univariate signal into a longer real-valued signal by augmenting the real part with the flipped imaginary part, and then to decompose it into intrinsic mode functions (IMFs) using the EMD once only. The bivariate IMFs are then retrieved from the obtained IMFs. Their empirical results on synthetic data show that the proposed method significantly outperforms the traditional bivariate EMD (BEMD) method in terms of computational efficiency while producing a comparable extraction error. Moreover, the proposed method shows better micro-Doppler signature analysis performance on physically measured continuous-wave radar data than that of the BEMD.

The spillover effects between natural gas and crude oil markets: The correlation network analysis based on multi-scale approach

This paper proposes a new compound model to investigate the dynamic linkage mechanism between the natural gas and crude oil markets from the multi-scale perspective. In the proposed model, two main steps are involved: multi-scale analysis and network research. Based on the bivariate empirical mode decomposition (BEMD) and Fine-to-Coarse algorithm, the multi-scale analysis ensures the relationship between price fluctuations can be studied under three different time-scales, which corresponding to market disequilibrium, significant events, and long term trend. By integrating the grey correlation degree and Coarse-Gaining algorithm, the network research reveals the dynamic spillover effects of the two markets at different time-scales. To capture the different linked characteristic in different periods, the sample data of Henry Hub and WTI spot prices from 1997 to 2017 is divided into three periods. We transfer the daily correlations between the price fluctuations with specific time-scale into the correlation patterns and establish the network based on their transmission relations. The crucial correlation patterns and the significant transmission relations are revealed by some network indicators. And the proposed approach in this paper can be applied to other field of research.

A Strategy for Classification of "Vaginal vs. Cesarean Section" Delivery: Bivariate Empirical Mode Decomposition of Cardiotocographic Recordings.

We propose objective and robust measures for the purpose of classification of “vaginal vs. cesarean section” delivery by investigating temporal dynamics and complex interactions between fetal heart rate (FHR) and maternal uterine contraction (UC) recordings from cardiotocographic (CTG) traces. Multivariate extension of empirical mode decomposition (EMD) yields intrinsic scales embedded in UC-FHR recordings while also retaining inter-channel (UC-FHR) coupling at multiple scales. The mode alignment property of EMD results in the matched signal decomposition, in terms of frequency content, which paves the way for the selection of robust and objective time-frequency features for the problem at hand. Specifically, instantaneous amplitude and instantaneous frequency of multivariate intrinsic mode functions are utilized to construct a class of features which capture nonlinear and nonstationary interactions from UC-FHR recordings. The proposed features are fed to a variety of modern machine learning classifiers (decision tree, support vector machine, AdaBoost) to delineate vaginal and cesarean dynamics. We evaluate the performance of different classifiers on a real world dataset by investigating the following classifying measures: sensitivity, specificity, area under the ROC curve (AUC) and mean squared error (MSE). It is observed that under the application of all proposed 40 features AdaBoost classifier provides the best accuracy of 91.8% sensitivity, 95.5% specificity, 98% AUC, and 5% MSE. To conclude, the utilization of all proposed time-frequency features as input to machine learning classifiers can benefit clinical obstetric practitioners through a robust and automatic approach for the classification of fetus dynamics.

Instantaneous Amplitude‐Frequency Feature Extraction for Rotor Fault Based on BEMD and Hilbert Transform

The vibration signals propagating in different directions from rotating machines can contain a variety of characteristic information. A novel feature extraction method based on bivariate empirical mode decomposition (BEMD) for rotor is proposed to comprehensively extract the fault features. In this work, the number of signal projection directions is determined through simulation, and the energy end condition based on the energy threshold is increased using BEMD to enhance the decomposition quality. Mixed vibration signals are generated along two orthogonal directions. Then, the acquired vibration signal can be decomposed into several intrinsic mode functions (IMFs) at the rotational speed using the BEMD method. Furthermore, the instantaneous frequency and instantaneous amplitude of the real signals and the imaginary part of the IMF signals are obtained using the Hilbert transform. The fault features along two and three dimensions can be investigated, providing more comprehensive information to aid in the fault diagnosis of rotor. Experimental results on oil film oscillation, the oil whirl, the bistability of the rotor, and looseness and rotor rubbing composite fault indicate the effectiveness of the proposed method.

Interval decomposition ensemble approach for crude oil price forecasting

Crude oil is one of the most important energy sources in the world, and it is very important for policymakers, enterprises and investors to forecast the price of crude oil accurately. This paper proposes an interval decomposition ensemble (IDE) learning approach to forecast interval-valued crude oil price by integrating bivariate empirical mode decomposition (BEMD), interval MLP (MLPI) and interval exponential smoothing method (HoltI). Firstly, the original interval-valued crude oil price is transformed into a complex-valued signal. Secondly, BEMD is used to decompose the constructed complex-valued signal into a finite number of complex-valued intrinsic mode functions (IMFs) components and one complex-valued residual component. Thirdly, MLPI is used to simultaneously forecast the lower and the upper bounds of each IMF (non-linear patterns), and HoltI is used for modeling the residual component (linear pattern). Finally, the forecasting results of the lower and upper bounds of all the components are combined to generate the aggregated interval-valued output by employing another MLPI as the ensemble tool. The empirical results show that our proposed IDE learning approach with different forecasting horizons and different data frequencies significantly outperforms some other benchmark models by means of forecasting accuracy and hypothesis tests.

Crude oil price forecasting based on internet concern using an extreme learning machine

The growing internet concern (IC) over the crude oil market and related events influences market trading, thus creating further instability within the oil market itself. We propose a modeling framework for analyzing the effects of IC on the oil market and for predicting the price volatility of crude oil’s futures market. This novel approach decomposes the original time series into intrinsic modes at different time scales using bivariate empirical mode decomposition (BEMD). The relationship between the oil price volatility and IC at an individual frequency is investigated. By utilizing decomposed intrinsic modes as specified characteristics, we also construct extreme learning machine (ELM) models with variant forecasting schemes. The experimental results illustrate that ELM models that incorporate intrinsic modes and IC outperform the baseline ELM and other benchmarks at distinct horizons. Having the power to improve the accuracy of baseline models, internet searching is a practical way of quantifying investor attention, which can help to predict short-run price fluctuations in the oil market.

FPGA-Based Real-Time Implementation of Bivariate Empirical Mode Decomposition

A field programmable gate array (FPGA)-based parallel architecture for the real-time and online implementation of the bivariate extension of the empirical mode decomposition (EMD) algorithm is presented. Multivariate extensions of EMD have attracted significant attention in recent years owing to their scope in applications involving multichannel and multidimensional data processing, e.g. biomedical engineering, condition monitoring, image fusion. However, these algorithms are computationally expensive due to the empirical and data-driven nature of these methods. That has hindered the utilisation of EMD, and particularly its bivariate and multivariate extensions, in real-time applications. The proposed parallel architecture is aimed at bridging this gap through real-time computation of the bivariate EMD algorithm. The crux of the architecture is the simultaneous computation of multiple signal projections, locating their local extrema and finally the calculation of their associated complex-valued envelopes for the estimation of local mean. The architecture is implemented on a Xilinx Kintex 7 FPGA and offers significant computational improvements over the existing software-based sequential implementations of bivariate EMD.

Application of Empirical Mode Decomposition to Mother and Infant Physical Activity.

The mutual dependencies between mother and infant circadian rhythms are important for examining disturbances of maternal circadian rhythms, which are considered substantial risk factors for the development of maternal depression during childrearing periods. We characterized the mutual dependencies of maternal-infant circadian rhythms by an index of synchronization properties and then tested the hypothesis that such an index, specifically the instantaneous phase differences between their rhythms, is associated with maternal mental health. We performed longitudinal recordings of maternal symptoms of fatigue, stress, and mood states by ecological momentary assessment, together with simultaneous measurements of mother and infant physical activity data in daily life, on 20 mother-infant pairs for a period of >1 week. The circadian components in their physical activity data were extracted by ensembled bivariate empirical mode decomposition, and the corresponding instantaneous phases were then obtained based on the Hilbert transformation. The associations between diurnal maternal symptoms and absolute phase differences between mother and infant circadian rhythms were tested by multilevel models. Diurnal fatigue and depressive mood scores showed positive and significant correlations (p < 0.05) with the increase in instantaneous mother-infant phase differences, indicating the significant role of synchronization of mother-infant circadian rhythms for maintaining maternal mental health. These findings suggest that modifications of maternal and/or infant circadian rhythms may lead to the improvement of maternal mental health during child-rearing periods.

Coupling Fault Feature Extraction Method Based on Bivariate Empirical Mode Decomposition and Full Spectrum for Rotating Machinery

To accurately extract the fault characteristics of vibration signals of rotating machinery is of great significance to the unit online monitoring and evaluation. However, because the current feature extraction methods are mainly for single channel, the results of feature extraction are often inaccurate. To this end, a coupling fault feature extraction method based on bivariate empirical mode decomposition (BEMD) and full spectrum is proposed for rotating machinery. Firstly, the two-dimensional orthogonal signal obtained by orthogonal sampling technique is decomposed by bivariate empirical mode decomposition to obtain the intrinsic mode function with phase information. In order to obtain the sensitive modal components, the sensitivity coefficients are constructed on the basis of mutual information. Then, the sensitivity coefficient of each intrinsic mode function is calculated, and the intrinsic mode function with the larger sensitive coefficient is selected as the sensitive component. Finally, the full spectrum of the sensitive component is obtained using the full vector envelope technique, so as to get a comprehensive and accurate characteristic component. The results of simulations experiment and an application example show that this method can extract the fault characteristic component of the rotating machinery comprehensively and accurately. It is of great significance to realize the accurate diagnosis of coupling faults of rotating machinery.

Features Of Sleep Apnea Recognition And Analysis

abstract Sleep apnea is a growing sleep disorder issue and estimate to affect 7% of the adult population in Malaysia. In this study, the electrical activity of the brain is studied using Electroencephalogram (EEG). The data obtained was then decomposed using three methods; Empirical Mode Decomposition (EMD), Bivariate EMD and finally Ensemble EMD. The Index of Orthogonatility (IO) was obtained which shows EMD performed the most poorly, EEMD the best and Bivariate in between. The performance of EMD greatly improves when the number of samples was greatly decreased and very high peaks and more complex parts of the signal were excluded in the analysis. Segmentation was also conducted and the segmentation error revealed when an Event Related Potential (ERP) has happened which is when apnea occurred.

Suppressing the discrete spectral interference of the partial discharge signal based on bivariate empirical mode decomposition

Summary In the present study, a discrete spectral interference (DSI) suppressing method based on bivariate empirical decomposition mode (BEMD) related to partial discharge measurements is presented. PD complex-valued signals are generated first, whose real part is DSI polluting PD signals and imaginary part is zero mean white Gaussian noise (WGN) signals. PD complex-valued signals are decomposed based on BEMD, and intrinsic mode functions (IMFs) can be sifted by this decomposition. The real part of IMFs (RIMFs) are decomposition results of DSI polluting signals and imaginary part of IMFs (IIMFs) are decomposition results of zero mean WGN signals. With the assistance of WGN signals, the mode mixing effect in RIMFs can be alleviated. Besides, RIMFs are free from the influence of WGN signals, which will avoid the disadvantage of long-time computing for ensemble empirical mode decomposition (EEMD) and satisfy the request of PD online monitoring. The goal for suppressing DSI of PD signals can be achieved by reconstructing RIMFs based on sine amplitude judgment method proposed in this study. The DSI suppressing method presented in this article was applied on the simulated and measured PD signals, and the obtained denoising results mainly based on EEMD, BEMD, and wavelet transform (WT) were compared and analyzed to verify the effectiveness of the proposed method. Besides, assessment indices including signal to noise ratio (SNR), amplitude relative error (ARE), root mean square error (RMSE), and normalized correlation coefficient (NCC) were used as objective evaluation criteria for denoising effect, and the results show that the presented method is superior to traditional EEMD methods and WT methods, which has less amplitude error as well as less waveform destination.

Energy Dissipation and Vibration Control: Modeling, Algorithm, and Devices

The topic of vibration control and energy dissipation is among the oldest and most relevant in the field of engineering [...]

Bivariate empirical mode decomposition for ECG-based biometric identification with emotional data.

Emotions modulate ECG signals such that they might affect ECG-based biometric identification in real life application. It motivated in finding good feature extraction methods where the emotional state of the subjects has minimum impacts. This paper evaluates feature extraction based on bivariate empirical mode decomposition (BEMD) for biometric identification when emotion is considered. Using the ECG signal from the Mahnob-HCI database for affect recognition, the features were statistical distributions of dominant frequency after applying BEMD analysis to ECG signals. The achieved accuracy was 99.5% with high consistency using kNN classifier in 10-fold cross validation to identify 26 subjects when the emotional states of the subjects were ignored. When the emotional states of the subject were considered, the proposed method also delivered high accuracy, around 99.4%. We concluded that the proposed method offers emotion-independent features for ECG-based biometric identification. The proposed method needs more evaluation related to testing with other classifier and variation in ECG signals, e.g. normal ECG vs. ECG with arrhythmias, ECG from various ages, and ECG from other affective databases.

Does investor sentiment dynamically impact stock returns from different investor horizons? Evidence from the US stock market using a multi-scale method

ABSTRACTThis article uses the investor sentiment index to investigate the Granger causality between investor sentiment and stock returns for the US economy using a multi-scale method. To focus on the local analysis of different investor horizons, bivariate empirical mode decomposition is used to decompose time series of investor sentiment and stock returns at different timescales. We employ the linear and nonlinear integrated Granger causality method to examine the causal relationship of decomposed series on similar timescales. The results indicate both strong bilateral linear and nonlinear causality between longer-term investor sentiment and stock returns. However, there is no strong evidence for correlation of stock returns and investor sentiment on shorter timescales.

Dynamic multiscale interactions between European carbon and electricity markets during 2005–2016

This study explores the dynamic multiscale interactions between carbon and electricity markets during phases I (2005–2007), II (2008–2012) and ongoing III (2013–2016) by introducing the bivariate empirical mode decomposition (BEMD), linear and nonlinear Granger causality tests. Firstly, BEMD is used to decompose the European carbon and electricity prices into several pairs of simple modes with different timescales. Secondly, causality tests are performed at each pair of modes with a similar timescale. Significant but asymmetric causalities can be found that: the bidirectional linear causality turns to a unidirectional one running from the electricity price to the carbon price from phase I to phase III, whereas the nonlinear interaction enhances from insignificance to significance during the three phases. The causality at short-timescale is consistent with that of the original data, while the causalities at mid- and long-timescales are more diversified. The findings obtained show that the effect of carbon market on the electricity market is weakening, which indicates that it is needed to increase its efficiency by raising the carbon price. Moreover, a dynamic adjusting mechanism of emission allowances will be called for as well as the guidance aimed at different timescales in the future.

Complex Blind Source Separation

Blind source separation (BSS) techniques aim at recovering the original source signals from observed mixtures without a priori information. The bivariate empirical mode decomposition (BEMD) algorithm combined with complex independent component analysis by entropy bound minimization (ICA-EBM) technique is proposed as an alternative to separate convolutive mixtures of speech signals. The empirical mode decomposition (EMD) is a local self-adaptive decomposition method that allows analyzing data from non-stationary and/or nonlinear processes. Its principle is based on the sequential extraction of different amplitude and frequency modulation single-component contributions called intrinsic mode functions (IMFs). The BEMD is an extension of the EMD to complex-valued signals. First, the convolutive mixtures in the frequency domain are decomposed into a set of IMFs using the BEMD algorithm, and then, the complex ICA-EBM method is applied to extract the independent sources. The performance of the proposed approach is tested on real speech sounds chosen from available databases and compared to the results obtained via conventional frequency ICA and BEMD-ICA-based separation for convolutive mixtures. Simulation results show that the proposed method of BSS outperforms the BEMD-ICA separation technique for convolutive mixtures and conventional frequency ICA.

The Bivariate Empirical Mode Decomposition and Its Contribution to Grinding Chatter Detection

Grinding chatter reduces the long-term reliability of grinding machines. Detecting the negative effects of chatter requires improved chatter detection techniques. The vibration signals collected from grinders are mainly nonstationary, nonlinear and multidimensional. Hence, bivariate empirical mode decomposition (BEMD) has been investigated as a multiple signal processing method. In this paper, a feature vector extraction method based on BEMD and Hilbert transform was applied to the problem of grinding chatter. The effectiveness of this method was tested and validated with a simulated chatter signal produced by a vibration signal generator. The extraction criterion of true intrinsic mode functions (IMFs) was also investigated, as well as a method for selecting the most ideal number of projection directions using the BEMD algorithm. Moreover, real-time variance and instantaneous energy were employed as chatter feature vectors for improving the prediction of chatter. Furthermore, the combination of BEMD and Hilbert transform was validated by experimental data collected from a computer numerical control (CNC) guideway grinder. The results reveal the good behavior of BEMD in terms of processing nonstationary and nonlinear signals, and indicating the synchronous characteristics of multiple signals. Extracted chatter feature vectors were demonstrated to be reliable predictors of early grinding chatter.