Bivariate Empirical Mode Decomposition Research Articles

A time-frequency-based interval decomposition ensemble method for forecasting gasoil prices under the trend of low-carbon development

Given that gasoil plays a crucial role in carbon emission reduction, in this paper we propose a time-frequency-based interval decomposition ensemble (TFIDE) learning approach to forecast gasoil prices and capture the nonlinear impact of the global trend of low-carbon development on gasoil prices. The proposed method integrates bivariate empirical mode decomposition (BEMD), an interval multilayer perceptron (IMLP) network and a threshold autoregressive interval (TARI) model. First, we use BEMD to decompose interval-valued weekly gasoil prices into a finite number of complex-valued intrinsic mode function (IMF) components and a residual component. Second, we apply the IMLP model to forecast the IMFs and the TARI model to predict the residual part with predictors of carbon reduction technology and carbon emission concerns. After that, we combine all the forecasting results to generate the final gasoil price interval forecasting results. Our empirical results show that our carbon reduction technology variable improves middle-frequency IMF forecasting and that carbon emission concerns have a nonlinear impact on long-term gasoil price intervals. Furthermore, the proposed TFIDE approach outperforms other competing methods under different accuracy measurements.

Ultra-short-term wind power prediction based on copula function and bivariate EMD decomposition algorithm

Ultra-short-term wind power prediction based on copula function and bivariate EMD decomposition algorithm

A novel secondary decomposition method for forecasting crude oil price with twitter sentiment

With the ubiquity of the Internet, valuable social media data have been generated, and a promising idea for using sentiment from social media has emerged in oil price forecasting. To address the complexity of oil price, this study proposed a novel secondary decomposition framework with Twitter sentiment, in which Twitter sentiment provides new information and secondary decomposition technique reduces the difficulty of oil price forecasting. This methodology involves three major steps: (1) sentiment extraction, to collect and extract Twitter sentiment via the state-of-the-art sentiment analysis technique—Bidirectional Encoder Representations from Transformers (BERT); (2) secondary decomposition, to extract scale-aligned components from crude oil price and Twitter sentiment using bivariate empirical mode decomposition (BEMD) first and then decomposing the residual terms through GA-VMD; and (3) oil price prediction, including individual prediction at each intrinsic mode function (IMF) and ensemble prediction across different IMFs. With WTI oil price as a sample, the empirical study results indicate that the proposed novel learning paradigms statistically outperform their corresponding original techniques (without Twitter sentiment and secondary decomposition), semi-improved variants (with either Twitter sentiment or secondary decomposition), and similar counterparts (with one-time decomposition analysis) in terms of prediction accuracy.

Influence of neuromuscular electrical stimulation pulse waveform on corticomuscular coupling and the brain functional connectivity network

ObjectiveNeuromuscular electrical stimulation (NMES) has been shown to promote functional corticomuscular coupling (FCMC), but its effect on brain functional connectivity network (BFCN) remains uncertain. This study aims to propose a new method to analyze the influence of NMES with different stimulation waveforms on the motor system from two perspectives of FCMC and BFCN. ApproachThe bivariate empirical mode decomposition time-delay maximal information coefficient (BTDMIC) method was used to assess the local frequency band characteristics of the cortex and muscle. Main resultThe experimental results showed that the FCMC increment after NMES was prominent in the β1 (15–25 Hz), β2 (25–35 Hz), and γ1 (35–45 Hz) bands. Additionally, the coupling values of C3 after sine-NMES were highest in the β1 band, while the coupling values after square-NMES were highest in the β2 and γ1 bands. For BFCN, the cortical-cortical coupling of the C3 after square-NMES was high in the C3 → others direction. Moreover, in the α (8–14 Hz) and β1 bands, the clustering coefficient, density, and efficiency after square-NMES were significantly higher than those of the three other frequency bands. ConclusionNMES effectively promoted information exchange between the motor cortices of the brain, and the facilitating effect is particularly pronounced in the case of square-NMES. SignificanceThis study offers a novel perspective for evaluating rehabilitation therapies based on NMES.

Dynamic Modeling of Flue Gas Desulfurization Process via Bivariate EMD-Based Temporal Convolutional Network

Sulfur dioxide (SO2) can cause detrimental impacts on the ecosystem. It is well known that coal-fired power plants play a dominant role in SO2 emissions, and consequently industrial flue gas desulfurization (IFGD) systems are widely used in coal-fired power plants. To remove SO2 effectively such that ultra-low emission standard can be satisfied, IFGD modeling has become urgently necessary. IFGD is a chemical process with long-term dependencies between time steps, and it typically exhibits strong non-linear behavior. Furthermore, the process is rendered non-stationary due to frequent changes in boiler loads. The above-mentioned properties make IFGD process modeling a truly formidable problem, since the chosen model should have the capability of learning long-term dependencies, non-linear dynamics and non-stationary processes simultaneously. Previous research in this area fails to take all the above points into account at a time, and this calls for a novel modeling approach so that satisfactory modeling performance can be achieved. In this work, a novel bivariate empirical mode decomposition (BEMD)-based temporal convolutional network (TCN) approach is proposed. In our approach, BEMD is employed to generate relatively stationary processes, while TCN, which possesses long-term memory ability and uses dilated causal convolutions, serves to model each subprocess. Our method was validated using the operating data from the desulfurization system of a coal-fired power station in China. Simulation results show that our approach yields desirable performance, which demonstrates its effectiveness in the IFGD dynamic modeling problem.

A two-stage interval-valued carbon price forecasting model based on bivariate empirical mode decomposition and error correction.

Economic development has brought about global greenhouse gas emissions and, thus, global climate change, a common challenge worldwide and urgently needs to be addressed. Accurate carbon price forecasting plays a pivotal role in providing a reasonable basis for carbon pricing and ensuring the healthy development of carbon markets. Therefore, this paper proposes a two-stage interval-valued carbon price combination forecasting model based on bivariate empirical mode decomposition (BEMD) and error correction. In Stage I, the raw carbon price and multiple influencing factors are decomposed into several interval sub-modes by BEMD. Then, we select artificial intelligence-based multiple neural network methods such as IMLP, LSTM, GRU, and CNN to conduct combination forecasting for interval sub-modes. In Stage II, the error generated in Stage I is calculated, and LSTM is used to predict the error; then, the error forecasting result is added to the first stage result to obtain the error-corrected forecasting result. Taking the carbon trading prices of Hubei, Guangdong, and the national carbon market, China, as the research object, the empirical analysis proves that the combination forecasting of interval sub-modes of Stage I outperforms the single forecasting method. In addition, the error correction technique in Stage II can further improve the forecasting accuracy and stability, which is an effective model for interval-valued carbon price forecasting. This study can help policymakers formulate regulatory policies to reduce carbon emissions and help investors avoid risks.

A hybrid deep learning model for predicting the Kuroshio path south of Japan

At present, many prediction models based on deep learning methods have been widely used in ocean prediction with satisfactory results. However, few deep learning models are used to predict the Kuroshio path south of Japan. In this study, a hybrid deep learning prediction model is constructed based on the long short-term memory (LSTM) neural network, combined with the complex empirical orthogonal function (CEOF) and bivariate empirical mode decomposition (BEMD), called CEOF-BEMD-LSTM. We train the model by using a 50-year (1958-2007) long time series of daily mean positions of the Kuroshio path south of Japan extracted from a regional ocean reanalysis dataset. During the test period of 15 years (2008-2022) by using daily altimetry dataset, our model shows a good performance for the Kuroshio path prediction with the lead time of 120 days, with 0.44° root-mean-square error (RMSE) and 0.75 anomaly correlation coefficient (ACC). This model also has good prediction skill score (SS). Moreover, the CEOF-BEMD-LSTM model successfully hindcasts the formation of the latest Kuroshio large meander since the summer of 2017. Predictions of the Kuroshio path for the coming 120 days (from January1 to April 30, 2023) indicate that the Kuroshio will continue to remain in the state of the large meander. Besides, predictor(s) of the Kuroshio path south of Japan need to be sought and added in future research.

Mode decomposition-based time-varying phase synchronization for fMRI

Recently, there has been significant interest in measuring time-varying functional connectivity (TVC) between different brain regions using resting-state functional magnetic resonance imaging (rs-fMRI) data. One way to assess the relationship between signals from different brain regions is to measure their phase synchronization (PS) across time. However, this requires the a priori choice of type and cut-off frequencies for the bandpass filter needed to perform the analysis. Here we explore alternative approaches based on the use of various mode decomposition (MD) techniques that provide a more data driven solution to this issue. These techniques allow for the data driven decomposition of signals jointly into narrow-band components at different frequencies, thus fulfilling the requirements needed to measure PS. We explore several variants of MD, including empirical mode decomposition (EMD), bivariate EMD (BEMD), noise-assisted multivariate EMD (na-MEMD), and introduce the use of multivariate variational mode decomposition (MVMD) in the context of estimating time-varying PS. We contrast the approaches using a series of simulations and application to rs-fMRI data. Our results show that MVMD outperforms other evaluated MD approaches, and further suggests that this approach can be used as a tool to reliably investigate time-varying PS in rs-fMRI data.

Linear and nonlinear framework for interval-valued PM2.5 concentration forecasting based on multi-factor interval division strategy and bivariate empirical mode decomposition

To forecast possible air pollution risks, a large number of models have been built to predict the daily average or hourly value of PM2.5 concentrations. In fact, due to the complexity of PM2.5 formation and the diversity of its influencing factors, PM2.5 concentrations may fluctuate greatly during a certain period, single-valued methods cannot present this uncertainty and variability. Therefore, this paper develops a hybrid modeling framework that combines the elastic net (EN) and multivariate relevance vector machine (MVRVM) for interval-valued PM2.5 time series (IPMTS) forecasting. Following the philosophy of the “linear and nonlinear” modeling framework, the EN and MVRVM are applied to capture the linear and nonlinear patterns hidden in the IPMTS. Different from existing studies that directly model linear and nonlinear patterns of time series, we introduce the multi-factor interval division (MFID) strategy and bivariate empirical mode decomposition (BEMD) algorithm into linear and nonlinear pattern modeling, respectively. This enhanced linear and nonlinear framework (termed MFID-EN-BEMD-MVRVM) can consider the possible linear relationship between PM2.5 and its related factors within the intervals and model the nonlinear pattern of IPMTS at multiple scales. The IPMTS extracted from four municipalities in China are used to validate the efficiency of the proposed model. Experimental results show that the MFID-EN-BEMD-MVRVM model achieves better forecasting performance than some benchmarks and state-of-the-art models in terms of comprehensive evaluation criteria. In addition, from the application analysis, the proposed interval-valued PM2.5 modeling architecture has the possibility of real-time forecasting.

A Hybrid Statistical Downscaling Framework Based on Nonstationary Time Series Decomposition and Machine Learning

AbstractDownscaling techniques are effective to bridge the scale gap between global circulation models and regional studies. Statistical downscaling methods are prevalent due to their advantages in high computational efficiency and accuracy. However, an implicit assumption of most statistical techniques is that time series should be relatively stationary after certain function transformations. Otherwise, statistics of nonstationary time series may be meaningless for describing future behavior. In this study, a hybrid statistical downscaling framework was developed through integrating bivariate empirical mode decomposition (BEMD) and a machine learning method to extract multi‐timescale features from nonstationary data to enhance downscaling performance. The proposed framework can reduce the effects of non‐stationarity in data‐driven models by using the BEMD method, which can decompose time series into independent and stationary components at multiple time‐frequency resolutions. It was applied to downscale monthly precipitation and temperature of Canadian Earth System Model in multiple stations with different climate types in the Central Valley of California, USA, to verify its accuracy and generalization ability. The performance of downscaling maximum and minimum temperatures (R2 > 0.9) was more accurate than that of precipitation. The potential reason is that precipitation is more sensitive to transient weather phenomena, which can only be extracted from data with higher temporal resolution. The proposed model was further compared with models based on discrete wavelet transform and models without time series decomposition. The results showed that a decomposition strategy of the proposed framework can improve the downscaling accuracy, potentially providing a viable option to deal with the nonstationary of data in statistical downscaling models.

Causal coupling between European and UK markets triggered by announcements of monetary policy decisions.

We investigate high-frequency reactions in the Eurozone stock market and the UK stock market during the time period surrounding European Central Bank (ECB) and the Bank of England (BoE)’s interest rate decisions, assessing how these two markets react and co-move influencing each other. The effects are quantified by measuring linear and nonlinear transfer entropy combined with a bivariate empirical mode decomposition from a dataset of 1 min prices for the Euro Stoxx 50 and the FTSE 100 stock indices. We uncover that central banks’ interest rate decisions induce an upsurge in intraday volatility that is more pronounced on ECB announcement days and there is a significant information flow between the markets with prevalent direction going from the market where the announcement is made towards the other.

Automatic Sleep Scoring Using Intrinsic Mode Based on Interpretable Deep Neural Networks

Sleep experts manually label sleep stages via polysomnography (PSG) to diagnose sleep disorders. However, this process is time-consuming, requires a lot of labor from sleep experts, and makes the participants uncomfortable with the attachment of multiple sensors. Thus, automatic sleep scoring methods are essential for practical sleep monitoring in our daily lives. In this study, we propose an automatic sleep scoring model based on intrinsic oscillations in a single channel electroencephalogram (EEG) signal. We applied noise assisted bivariate empirical mode decomposition (NA-BEMD) to extract the intrinsic mode components and an attention mechanism in deep neural networks to provide weights to the components depending on their significance to sleep scoring. In particular, through the attention mechanism, we found an interpretable model by examining the oscillations that correspond to specific sleep stages. Therefore, we analyzed which frequency components are more weighted to a sleep stage than the others, when the model classifies sleep stages, and, as a result, confirmed that the model assigns convincing weights to the frequency components for each sleep stage. Additionally, the model consists of a one-dimensional convolutional neural network (1D-CNN) to extract features of an epoch and bidirectional long short-term memory (Bi-LSTM) to learn the sequential information of the consecutive epochs. We evaluated proposed model using Fpz-Cz, Pz-Oz, and F3-M2 channel EEG from three different public datasets (Sleep-EDF-2013, Sleep-EDF-2018, WSC) and demonstrated that our model yielded the best overall accuracy (Fpz-Cz: 86.22%-82.67%, Pz-Oz: 83.63%-80.15%, F3-M2: 84.20%) and macro F1-score (Fpz-Cz: 80.79%-76.90%, Pz-Oz: 76.89%-72.98%, F3-M2: 74.88%) compared with the state-of-the-art sleep scoring algorithms using single channel EEG. As a benchmark test, FIR bandpass filters were compared, and it was confirmed that NA-BEMD was superior to the traditional filters in all experiments, demonstrating that the proposed model is interpretable and a state-of-the-art sleep scoring algorithm.

An interval decomposition-ensemble approach with data-characteristic-driven reconstruction for short-term load forecasting

Short-term load forecasting is crucial for power demand-side management and the planning of the power system. Considering the necessity of interval-valued time series modeling and forecasting for the power system, this study proposes an interval decomposition-reconstruction-ensemble learning approach to forecast interval-valued load, in terms of the concept of “divide and conquer”. First, bivariate empirical mode decomposition is applied to decompose the original interval-valued data into a finite number of bivariate modal components for extracting and identifying the fluctuation characteristics of data. Second, based on the complexity analysis of each bivariate modal component by multivariate multiscale permutation entropy, the components were reconstructed for capturing inner factors and reduce the accumulation of estimation errors. Third, long short-term memory is utilized to synchronously forecast the upper and the lower bounds of each bivariate component and optimized by the Bayesian optimization algorithm. Finally, generating the aggregated interval-valued output by ensemble the forecasting results of the upper and lower bounds of each component severally. The electric load of five states in Australia is used for verification, and the empirical results show that the forecasting accuracy of our proposed learning approach is significantly superior to single models and the decomposition-ensemble models without reconstruction. This indicates that our proposed learning approach appears to be a promising alternative for interval load forecasting.

Bivariate empirical mode decomposition of the spatial variation in the soil organic matter content: A case study from NW China

Soil organic matter (SOM) significantly affects soil quality, food security, and the global carbon cycle. Variations in the SOM content are controlled by many environmental factors and differ depending on the scale and region. The Mountain–Oasis–Desert System (MODS) in arid areas is limited by climate conditions and water and soil resources. Therefore, the effects of environmental factors on the SOM content may differ. This study aimed to characterize spatial patterns of the SOM content in a MODS in northwestern China and reveal the SOM variations at different scales and regions. First, we employed the random forest model to predict the SOM content and the uncertainty at the nodes of a 90 m grid. We then extracted scale- and region-dependent variations in the SOM content using bivariate empirical mode decomposition (BEMD). Data analysis, geostatistics, and a two-dimensional fast Fourier transform were applied to analyze the SOM pattern and its correlations with environmental covariates at different scales. The results suggest that the variations in the SOM content were mainly concentrated at the large scale. The correlations between environmental factors and the SOM were scale- and region-specific, indicating complex interrelationships among topography, land use, salinization, soil erosion, and fertilization. At the intermediate-large spatial scale, topography characteristics and surface features were the major factors controlling the SOM content, whereas the climate had a larger effect on SOM than other factors at the large scale. Based on our results, BEMD has great potential to reveal SOM variations in the scale–region domain. BEMD can be used in environmental modeling in the future to gain insights into the variations in soil properties depending on environmental factors and anthropogenic activities.

Causal coupling between European and UK markets triggered by announcements of monetary policy decisions

We investigate high-frequency reactions in the Eurozone stock market and the UK stock market during the time period surrounding the European Central Bank (ECB) and the Bank of England (BoE)'s interest rate decisions assessing how these two markets react and co-move influencing each other. The dynamic multiscale interaction between these markets and the spillover effect on monetary policy announcement days are quantified by measuring linear and non-linear transfer entropy combined with a Bivariate Empirical Mode Decomposition (BEMD) from a dataset of 1-minute prices for the Euro Stoxx 50 and the FTSE 100 stock indices. We draw the following conclusions. First, central banks' interest rate decisions induce an upsurge in intraday volatility that is more pronounced on ECB announcement days. Second, there is a clear and significant information flow between the markets surrounding the time interest rates are released with prevalent direction going from the market where the announcement is made towards the other. Third, the coupling between the two markets describing the spillover effects is sufficiently well modeled with the linear approach to transfer entropy. %appears to be sufficient in detecting the spillover.

Double decomposition and optimal combination ensemble learning approach for interval-valued AQI forecasting using streaming data.

To forecast possible future environmental risks, numerous models are developed to predict the hourly values or daily averages of air pollutant concentrations using streaming data (a kind of big data collected from the Internet). On the one hand, real-time hourly data is massive and redundant, making it difficult to process. On the other hand, daily averages cannot reflect the fluctuations of air pollutant concentrations throughout the day. Therefore, a double decomposition and optimal combination ensemble learning approach is proposed for interval-valued AQI (air quality index) forecasting in this paper. In the first decomposition, considering the strong seasonal representation of AQI, the original data of each year is decomposed into four seasonal subseries on the basis of the Chinese calendar. Subsequently, we reconstruct the data of the same season in different years to get a new seasonal series to reduce the interference of seasonal changes on AQI forecasting. In the second decomposition, due to the nonlinearity and irregularity of interval-valued AQI time series, BEMD (bivariate empirical mode decomposition) is employed to decompose the interval-valued signals into a finite number of complex-valued IMF (intrinsic mode function) components and one complex-valued residue component with different frequencies to reduce the complexity of interval times series. Interval multilayer perceptron (iMLP) is utilized to model the lower bound and the upper bound simultaneously of the total components to obtain the corresponding forecasting results, which are merged to produce the final interval-valued output by an optimal combination ensemble method. Empirical study results show that the proposed model with different datasets and different forecasting horizons is significantly better than other considered models for its superior forecasting performances.

A novel BEMD-based method for forecasting tourist volume with search engine data

As helpful big data, search engine data (SED) regarding tourism-related factors have currently been introduced to tourist volume prediction, but they have been shown to impact the tourism market on different timescales (or frequency band). This study develops a novel forecasting method using an emerging multiscale analysis—bivariate empirical mode decomposition (BEMD)—to investigate multiscale relationships. Three major steps are performed: (1) SED process to construct an informative index from sufficient SED using statistical analyses, (2) multiscale analysis to extract scale-aligned common factors from the bivariate data of tourist volumes and SED using BEMD, and (3) tourist volume prediction using an SED-based index. In the empirical study, the novel BEMD-based method with SED is used to forecast the tourist volume of Hainan in China, a global tourist attraction, and significantly outperforms both popular techniques (not considering SED or multiscales) and similar variants (considering SED or multiscales) in accuracy and robustness.

Google Index-Driven Oil Price Value-at-Risk Forecasting: A Decomposition Ensemble Approach

The oil price is influenced not only by the fundamentals of supply and demand but also by unpredictable political conflicts, climate emergencies, and investor intentions, which cause enormous short-term fluctuations in the oil price. The proposition of the Google index-driven decomposition ensemble model to forecast crude oil price risk uses big data technology and a time series decomposition method. First, by constructing an index of investor attention for the market and emergencies combined with a bivariate empirical mode decomposition, we analyze the impact of investor attention on oil price fluctuations. Second, we establish a vector autoregression model, and the impulse responses define the impact of emergencies on the crude oil price. Finally, with the help of machine learning and historical simulation methods, the risk of crude oil price shocks from unexpected events is predicted. Empirical research demonstrates that concerns related to the oil market and emergencies that appear in Google search data are closely related to changes in oil prices. Based on the Google index, our model’s prediction of crude oil prices is more accurate than other models, and the prediction of value-at-risk is closer to the theoretical value than the historical simulation with the ARMA forecasts method. Considering the impact of emergencies in the prediction of crude oil price risk can help provide technical guidance for investors and risk managers and avoid economic risks caused by climate disasters or political conflicts.

Phase-synchrony evaluation of EEG signals for Multiple Sclerosis diagnosis based on bivariate empirical mode decomposition during a visual task

Background and objectiveDespite the widespread prevalence of Multiple Sclerosis (MS), the study of brain interactions is still poorly understood. Moreover, there has always been a great need to automate the MS diagnosis procedure to eliminate the evaluation errors thereby improving its consistency and reliability. To address these issues, in this work, we proposed a robust pattern recognition algorithm as a computer-aided diagnosis system. This method is based on calculating the pairwise phase-synchrony of EEG recordings during a visual task. Initially, the bivariate empirical mode decomposition (BEMD) was applied to extract the intrinsic mode functions (IMFs). The phases of these IMFs were then obtained using the Hilbert transform to be utilized in the mean phase coherence (MPC), a measure for phase-synchrony calculation. After the construction of the feature space using MPC values, the ReliefF algorithm was applied for dimension reduction. Finally, the best distinguishing features were input to a k-nearest neighbor (KNN) classifier. The results revealed a higher level of network synchronization in the posterior regions of the brain and desynchronization in the anterior regions among the MS group as compared with the normal subjects. In the validation phase, the leave-one-subject-out cross-validation (LOOCV) method was used to assess the validity of the proposed algorithm. We achieved an accuracy, sensitivity, and specificity of 93.09%, 91.07%, and 95.24% for red-green, 90.44%, 88.39%, and 92.62% for luminance, and 87.44%, 87.05%, and 87.86% for blue-yellow tasks, respectively. The experimental results demonstrated the reliability of the presented method to be generalized in the field of automated MS diagnosis systems.

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.