Noise-assisted Multivariate Empirical Mode Decomposition Research Articles

Forecasting interval carbon price through a multi-scale interval-valued decomposition ensemble approach

This paper proposes a novel Multi-scale Interval-valued Decomposition Ensemble (MIDE) framework for forecasting European Union Allowance (EUA) carbon futures prices, which integrates Noise-assisted Multivariate Empirical Mode Decomposition (NAMEMD), Interval-valued Vector Auto-Regressive (IVAR) model, Interval Event Analysis (IEA) method, and Interval Multi-Layer Perceptron (IMLP). First, the original interval-valued carbon prices with other interval-valued control variables are decomposed and integrated into high, medium, and low-frequency components by NAMEMD. Second, IVAR is used to investigate the dynamics of the interval-valued vector system in low-frequency components, while IMLP is employed to characterize the high-frequency components. Besides, the interval event analysis investigates typical events that significantly impact carbon prices in the medium-frequency component. Furthermore, empirical findings indicate that our proposed MIDE learning approach significantly outperforms some other benchmark models in out-of-sample forecasting.

A deep learning‐based multivariate decomposition and ensemble framework for container throughput forecasting

AbstractTraditional linear models struggle to capture the intricate relationship between dynamic container throughput and its complex interplay with economic fluctuations. This study introduces a novel, deep learning‐based multivariate framework for precision in demanding landscapes. The framework consistently outperforms eight established benchmark models by employing vital economic indicators like GDP and port tonnage, identified through rigorous predictor importance analysis of an initial set of four variables, including imports and exports. Statistical significance is demonstrably achieved through the Diebold–Mariano and Wilcoxon rank‐sum tests. Utilizing the Port of Singapore as a case study, the framework offers agile adaptability for the ever‐evolving global supply chain. Comprehensive analyses ensure robustness, decoding intricate throughput dynamics. Incorporating noise‐assisted multivariate empirical mode decomposition (NA‐MEMD) for nonlinear decomposition and bidirectional long short‐term memory (BiLSTM) for time series dependencies, this innovative approach holds promise for revolutionizing container throughput forecasting and enhancing competitiveness in the global market through optimized resource allocation and streamlined operations.

Research on rotor fault diagnosis technology of three-phase asynchronous motor based on NA-MEMD mutual information and SVM

Aiming at the problem of mode aliasing in the adaptive decomposition of nonlinear and non-stationary current signals generated by three-phase asynchronous motor faults, and the fault features contained in signals collected by a single sensor can not be accurately and comprehensively extracted and characterized when early rotor bar breakage and air gap eccentricity faults occur, A fault diagnosis method for three-phase asynchronous motor based on noise assisted multivariate empirical mode decomposition (NA-MEMD) and mutual information is proposed. Firstly, the NA-MEMD algorithm is used to decompose the three-phase stator current signal of the asynchronous motor to obtain multi-scale intrinsic mode functions (IMFs). Then, the correlation algorithm is used to screen the IMFs containing useful information. Then, the filtered IMF components are reconstructed into new signals and their features are extracted, Finally, support vector machines (SVM) are used to identify the rotor broken bars and air gap eccentric faults of the three-phase asynchronous motor. The experimental results show that the NA-MEMD method has a higher recognition rate than the traditional empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) methods.

A statistical analysis of causal decomposition methods applied to Earth system time series

Causal Decomposition (CD) constitutes a novel and widely accepted method for discovering and quantifying the internal causal relationships inherent to complex systems. This new causality bases not on time nor state. Instead, it relies on instantaneous phase coherence between the corresponding Intrinsic Mode Functions (IMFs) of the signals, obtained via Empirical Mode Decomposition (EMD). In this paper we compare the results obtained with two noise-assisted methods: Ensemble EMD (EEMD) and Noise Assisted Multivariate EMD (NA-MEMD). Given the inherent stochastic nature of noise-assisted methods, CD was treated as a randomized experiment. Hence, we repeated procedures to perform a robust statistical analysis. Confidence intervals, adequate normality conditions and differential causality hypothesis testing were then evaluated. The methodology was adjusted through the paradigmatic case of a forced mechanical oscillator, since the causal implications are known in advance. CD was then applied to a couple of series from the Earth system: insolation and oxygen isotope rate. Differential causality was established in favor of insolation at the frequency corresponding to the obliquity cycle. The apparent causality detected with EEMD on other time scales was discarded and attributed to a mode mixing problem. Therefore, NA-MEMD outperformed EEMD with less mode mixing and sharper mode alignment.

Disentangling slope‐scale spatial variability of saturated hydraulic conductivity in the black soil region of northeast China using noise‐assisted multivariate empirical mode decomposition

AbstractReliable estimates of saturated hydraulic conductivity (Ks) are usually difficult to obtain, as Ks is regulated by a variety of soil processes acting at different spatial scales that may obscure each other's impacts. We hypothesized that these scale‐specific relationships could be well characterized with the aid of the noise‐assisted multivariate empirical mode decomposition (NA‐MEMD), thereby serving as a solid foundation for an accurate Ks prediction. The objective was to evaluate whether the incorporation of NA‐MEMD could improve the estimation of Ks based on the multiscale associations it unraveled. On a typical slope transect of 860 m in the black soil region of northeast China, Ks, mollic epipedon thickness, bulk density, soil organic carbon content, total (ϕ) and effective porosities (ϕe), and particle size distribution were investigated at every 20 m. Prior to NA‐MEMD, Ks was most strongly correlated with ϕe, and the linear regression models based on ϕe solely were satisfactory for Ks estimation at the scale of investigation. Adding other predictors significantly improved Ks prediction in calibration, but impaired it in validation. Upon decomposition by NA‐MEMD, Ks was found to be significantly associated with each attribute at two scales of oscillation at least. Summing up the estimates of each Ks component derived from the properties at the equivalent oscillation scales, the results outperformed the traditional multiple linear regressions made at the investigation scale, when the same sets of predictors were used. The application of NA‐MEMD, moreover, could save the tedious measurements of ϕe and ϕ. Excluding these two porosity‐related properties, Ks estimates obtained by incorporating NA‐MEMD were statistically similar or even better than those involving them before NA‐MEMD. These findings demonstrate the great potential of NA‐MEMD in untangling scale‐dependent relationships of Ks with various processes and hold important implications for future estimations of Ks and other hydraulic properties in the black soil region of northeast China and similar regions.

Series Arc Fault Detection under Vibration Condition Based on N-M-M-B

Under the conditions of a mechanical fault in a motor, mechanical vibration of a specific frequency can be generated. The electrical contact points directly connected to the motor can vibrate at the same frequency. The electrical contact points with poor contact can easily produce a series arc fault under vibration conditions, which affects the reliability of the power supply. In order to detect the series arc fault under different vibration conditions, the arc fault generator is connected between the back end of the frequency converter and the motor. An arc fault experiment under different vibration conditions was carried out and the fault phase current and arc voltage signals were collected. In this paper, the noise-assisted multivariate empirical mode decomposition and the correlation coefficient between each intrinsic mode function are used to select the fault feature signals. Then, the reconstructed signal is input into the series arc fault model combining a multi-scale convolutional neural network and a bidirectional long short-term memory network for training. The research results show that the series arc fault detection method proposed in this paper can effectively detect the series arc fault and can preliminarily identify the type of motor fault causing the mechanical vibration of the motor; the model has good noise immunity and generalization.

Probability density prediction of peak load based on mixed frequency noise-assisted multivariate empirical mode decomposition

Probability density prediction of peak load based on mixed frequency noise-assisted multivariate empirical mode decomposition

Changes in Qinghai Lake Area and Their Interactions with Climatic Factors

Lakes play a crucial role in the global water cycle and significantly contribute to enhancing regional ecological environments and simulating economic growth. In this study, based on the data from the Landsat TM 4-5, Landsat 7 ETM SLC-off, and Landsat 8-9 OLI/TIRS C2 L2 satellites, the surface area of Qinghai Lake is obtained by using the Normalized Difference Water Index (NDWI) method. Additionally, leveraging the European Centre for Medium-Range Weather Forecasts (ECMWF) fifth-generation land surface reanalysis dataset (ERA5-Land), we analyzed the interplay between lake area and related climate factors by using the Noise Assisted–Multivariate Empirical Mode Decomposition (NA-MEMD) and wavelet coherence analysis method. The surface area of Qinghai Lake showed an overall expansion trend from 1986 to 2022, with an expansion rate of 2.89 km2/a. Precipitation, temperature, and evapotranspiration (ET) also showed an increasing trend, with the largest increasing trend in autumn, summer, and summer, respectively. The area of Qinghai Lake did not demonstrate distinct periodic patterns from 1986 to 2022, in contrast to the marked 8–16 month oscillations observed in precipitation, temperature, and ET. In the phase of lake area expansion between 2008 and 2016, changes in the lake’s surface area were observed to trail behind variations in precipitation and temperature by approximately three months. Furthermore, the shift in ET was found to lag behind alterations in the lake area, displaying a delay of 3–6 months.

Multiclass classification of imagined speech EEG using noise-assisted multivariate empirical mode decomposition and multireceptive field convolutional neural network.

In this study, we classified electroencephalography (EEG) data of imagined speech using signal decomposition and multireceptive convolutional neural network. The imagined speech EEG with five vowels /a/, /e/, /i/, /o/, and /u/, and mute (rest) sounds were obtained from ten study participants. First, two different signal decomposition methods were applied for comparison: noise-assisted multivariate empirical mode decomposition and wavelet packet decomposition. Six statistical features were calculated from the decomposed eight sub-frequency bands EEG. Next, all features obtained from each channel of the trial were vectorized and used as the input vector of classifiers. Lastly, EEG was classified using multireceptive field convolutional neural network and several other classifiers for comparison. We achieved an average classification rate of 73.09 and up to 80.41% in a multiclass (six classes) setup (Chance: 16.67%). In comparison with various other classifiers, significant improvements for other classifiers were achieved (p-value < 0.05). From the frequency sub-band analysis, high-frequency band regions and the lowest-frequency band region contain more information about imagined vowel EEG data. The misclassification and classification rate of each vowel imaginary EEG was analyzed through a confusion matrix. Imagined speech EEG can be classified successfully using the proposed signal decomposition method and a convolutional neural network. The proposed classification method for imagined speech EEG can contribute to developing a practical imagined speech-based brain-computer interfaces system.

Functional Connectivity Analysis in Multi-channel EEG for Emotion Detection with Phase Locking Value and 3D CNN.

The noise-assisted multivariate Empirical mode decomposition (NA-MEMD) is applied to multi-channel EEG signals to obtain narrow-band scale-aligned intrinsic mode functions (IMFs) upon which functional connectivity analysis is performed. The connectivity pattern in relation to inherent functional activity of brain is estimated with the phase locking value (PLV). Instantaneous phase difference among different EEG channels gives PLV that is used to build the functional connectivity map. The connectivity map yields spatial-temporal feature representation which is taken as input of the proposed emotion detection system. The spatial-temporal features can be learned with a 3D convolutional neural network for classifying emotion states. The proposed system is evaluated on two publicly available DEAP and SEED dataset for binary and multi-class emotion classification. On detecting low versus high level in the valence and arousal dimensions, the attained accuracy values are 97.37% and 96.26% respectively. Meanwhile, this system yields 94.78% and 99.54% accuracy on multi-class task on DEAP and SEED, which outperform previously reported systems with other deep learning models and conventional EEG features.

Underwater Acoustic Intensity Analysis using Noise Assisted-MEMD with Varying Distances

With current developments, underwater communication using acoustic signals is widely used. Many things need to be prepared to support a reliable underwater communication system, such as taking measurements in a test tank to find out the correct measurement configuration. Underwater acoustic intensity measurements, which are detailed in this paper, are performed in the test tank using distance variation schemes. Measurements were made at various distances of 4, 10, 20, and 50 meters from the signal source. The hydrophone that was used has a sensitivity of -180 dB re 1V/µPa. The hydrophone was placed at a depth of 2 meters below the surface of the water in the test tank, which divided the test tank depth in half to ensure that reflections from the bottom and the surface were kept to a minimum. However, the problem is that there are noisy signals at different frequencies. This paper proposes a method using Noise Assisted - Multivariate Empirical Mode Decomposition (NA-MEMD) to decompose the signal and then calculate the sound intensity. The result shows that an increase in the distance between the transmitter and receiver, also causes a change in the intensity with an average change of 0.467 dB/meter. It is concluded that the NA-MEMD approach was shown to be successful in decomposing the intended signal from the noise to equalize the quality of the signal received at different distances, and the correlation between intensity value and change in distance is resilient, with a correlation value of 0.98, indicating a very strong correlation.

Deep learning seismic damage assessment with embedded signal denoising considering three-dimensional time–frequency feature correlation

Fast and accurate seismic damage assessment is crucial for timely post-earthquake evaluation and rescue. In seismic damage assessment, the correlation between ground motions in three directions during the time–frequency transform and the appropriate denoising thresholds during signal data preprocessing pose challenges for traditional methods. We propose a novel deep learning framework, DRSNet (deep residual shrinkage network), which incorporates the CNN structure of ResNet and a soft-threshold denoising module for simultaneous seismic signal denoising and damage assessment. To consider the feature correlation in time–frequency transform of seismic signals, they are first decomposed synchronously with noise-assisted multivariate empirical mode decomposition (NAMEMD) into multi-dimensional intrinsic mode functions (MIMF), and MIMFs are then transformed into seismic time–frequency maps using a non-parametric time–frequency analysis with scalable time windows and the Duhamel integral form. The subsidence and the subsidence rate of the dam are computed with finite element analysis and considered to assess seismic damage. The time–frequency maps and the finite element analysis results are used as input and output data to train DRSNet with no need for preprocessing seismic signal noise. The proposed model has been applied to a large-scale hydropower dam and achieved an average precision of 94.52% for predicting the seismic damage levels, which outperforms ResNet and ResNeSt by 3.09% and 2.62%, respectively. Thorough comparison and analysis of the model demonstrate its potential for accurate and efficient seismic damage assessment.

How spanwise travelling transversal surface waves change the near-wall flow

The alteration of the near-wall flow field of a turbulent boundary layer flow subjected to spanwise travelling transversal surface waves at a friction Reynolds number $Re_\tau \approx 1525$ is investigated. The results of a spatial noise-assisted multivariate empirical mode decomposition reveal that this flow control method periodically induces near-wall large-scale bursts while simultaneously lowering the energetic content of small-scale features. The increasing occurrence of intense large-scale ejections in the near-wall region is of particular importance for reducing the wall-shear stress since these ejections balance large-scale sweeps originating from the outer layer. Thus, they corrupt the outer-layer impact on the near-wall dynamics and, consequently, the overall fluctuation intensity at the wall is attenuated. This disturbed top-down momentum exchange is highlighted by an inner–outer interaction analysis, which further reveals an increased bottom-up communication provoked by the large-scale ejections. Moreover, it is shown that the periodic secondary flow field induced by the actuation interferes with the quasi-streamwise vortices in the near-wall region. The velocity gradients of the secondary flow field deform the vortices’ cross-section into an elliptic shape, which yields an unstable vortex state resulting in vortex disintegration. In combination with the effect of the large-scale ejections, the reduced number of quasi-streamwise vortices compared with the undisturbed boundary layer flow results in a decreased wall-normal momentum exchange and the widening and weakening of near-wall streaks. This yields a reduced fluctuation intensity in the near-wall region that lowers the overall wall-shear stress level.

An ensemble dynamic self-learning model for multiscale carbon price forecasting

Precise carbon price forecasting can provide decision support for policy-makers and investors. However, due to the high non-stationarity and nonlinearity of carbon price series, it is difficult to get accurate forecasting results under volatile situations. To accommodate different scenarios, this paper proposes a dynamic self-learning integrating forecasting model to forecast the carbon price by considering external impact factors. The multi-dimensional time series is initially decomposed into different intrinsic mode functions simultaneously by the noise-assisted multivariate empirical mode decomposition method. After reconstructing the decomposed series into high-frequency, low-frequency, and trend modules, the extreme learning machine optimized by the cosine-based whale optimization algorithm is proposed to predict the carbon price. The dynamic relationships between the carbon price and impact factors are simulated by the sliding window structure, which improves the adaptability of the proposed model. The high prediction accuracy under different situations including extreme scenarios demonstrates the stability of the proposed model. A self-learning algorithm, which can automatically learn the evolving model structure and update model parameters, is designed to alleviate the underfitting/overfitting problem. The comparison results with existing models indicate the superiority of the proposed model.

Multivariate Empirical Mode Decomposition and Recurrence Quantification for the Multiscale, Spatiotemporal Analysis of Electricity Demand—A Case Study of Japan

In the new energy systems’ modeling paradigm with high temporal and spatial resolutions, the complexity of renewable resources and demand dynamics is a major obstacle for the scenario analysis of future energy systems and the design of sustainable solutions. Most advanced models are indeed currently restricted by past temporal energy demand data, improper for the analysis of future systems and often insufficient in terms of quantity or spatial resolution. A deeper understanding on energy demand dynamics is thus necessary to improve energy system models and expand their possibilities. The present study introduces noise-assisted multivariate empirical mode decomposition and recurrence quantification analysis for the study of this problematic variable with a case study of Japan’s electricity demand data per region. These tools are adapted to nonlinear, complex systems’ data and are already applied in a wide range of scientific fields including climate studies. The decomposition of electricity demand as well as the detection of irregularities in its dynamics allow to identify relations with temperature variations, demand sector shares, life style and local culture at different temporal scales.

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.

Wearable In-Ear PPG: Detailed Respiratory Variations Enable Classification of COPD.

An ability to extract detailed spirometry-like breathing waveforms from wearable sensors promises to greatly improve respiratory health monitoring. Photoplethysmography (PPG) has been researched in depth for estimation of respiration rate, given that it varies with respiration through overall intensity, pulse amplitude and pulse interval. We compare and contrast the extraction of these three respiratory modes from both the ear canal and finger and show a marked improvement in the respiratory power for respiration induced intensity variations and pulse amplitude variations when recording from the ear canal. We next employ a data driven multi-scale method, noise assisted multivariate empirical mode decomposition (NA-MEMD), which allows for simultaneous analysis of all three respiratory modes to extract detailed respiratory waveforms from in-ear PPG. For rigour, we considered in-ear PPG recordings from healthy subjects, both older and young, patients with chronic obstructive pulmonary disease (COPD) and idiopathic pulmonary fibrosis (IPF) and healthy subjects with artificially obstructed breathing. Specific in-ear PPG waveform changes are observed for COPD, such as a decreased inspiratory duty cycle and an increased inspiratory magnitude, when compared with expiratory magnitude. These differences are used to classify COPD from healthy and IPF waveforms with a sensitivity of 87% and an overall accuracy of 92%. Our findings indicate the promise of in-ear PPG for COPD screening and unobtrusive respiratory monitoring in ambulatory scenarios and in consumer wearables.

Matlab Open Source Code: Noise-Assisted Multivariate Empirical Mode Decomposition Based Causal Decomposition for Causality Inference of Bivariate Time Series.

Causality inference has arrested much attention in academic studies. Currently, multiple methods such as Granger causality, Convergent Cross Mapping (CCM), and Noise-assisted Multivariate Empirical Mode Decomposition (NA-MEMD) are introduced to solve the problem. Motivated by the researchers who uploaded the open-source code for causality inference, we hereby present the Matlab code of NA-MEMD Causal Decomposition to help users implement the algorithm in multiple scenarios. The code is developed on Matlab2020 and is mainly divided into three subfunctions: na_memd, Plseries, and cd_na_memd. na_memd is called in the main function to generate the matrix of Intrinsic Mode Functions (IMFs) and Plseries can display the average frequency and phase difference of IMFs of the same order in a matrix which can be used for the selection of the main Intrinsic Causal Component (ICC) and ICCs set. cd_na_memd is called to perform causal redecomposition after removing the main ICC from the original time series and output the result of NA-MEMD Causal Decomposition. The performance of the code is evaluated from the perspective of executing time, robustness, and validity. With the data amount enlarging, the executing time increases linearly with it and the value of causal strength oscillates in an ideally small interval which represents the relatively high robustness of the code. The validity is verified based on the open-access predator-prey data (wolf-moose bivariate time series from Isle Royale National Park in Michigan, USA) and our result is aligned with that of Causal Decomposition.

Intelligent Monitoring System Based on Noise-Assisted Multivariate Empirical Mode Decomposition Feature Extraction and Neural Networks.

Because of the nonlinearity and nonstationarity in the vibration signals of some rotating machinery, the analysis of these signals using conventional time- or frequency-domain methods has some drawbacks, and the results can be misleading. In this paper, a couple of features derived from multivariate empirical mode decomposition (MEMD) are introduced, which overcomes the shortcomings of the traditional features. A wind turbine gearbox and its bearings are investigated as rotating machinery. In this method, two types of feature structures are extracted from the decomposed signals resulting from the MEMD algorithm, called intrinsic mode function (IMF). The first type of feature vector element is the energy moment of effective IMFs. The other type of vector elements is amplitudes of a signal spectrum at the characteristic frequencies. A correlation factor is used to detect effective IMFs and eliminate the redundant IMFs. Since the basic MEMD algorithm is sensitive to noise, a noise-assisted extension of MEMD, NA-MEMD, is exploited to reduce the effect of noise on the output results. The capability of the proposed feature vector in health condition monitoring of the system is evaluated and compared with traditional features by using a discrimination factor. The proposed feature vector is utilized in the input layer of the classical three-layer backpropagation neural network. The results confirm that these features are appropriate for intelligent fault detection of complex rotating machinery and can diagnose the occurrence of early faults.

Exploring the short-term and long-term linkages between carbon price and influence factors considering COVID-19 impact.

Because of global lock-downs caused by the unexpected COVID-19, the interactions between emission trading and related markets have changed significantly compared to the pre-COVID-19 period. Considering the pandemic effect, this paper established an integrated system to identify the relationship trajectories between carbon trading market and impact factors. A noise-assisted multivariate empirical mode decomposition (N-A MEMD) method was utilized to simultaneously decompose the original multi-dimensional time series into intrinsic mode functions (IMFs), after which the Lempel-Ziv (LZ) complexity algorithm was applied to reconstruct the IMFs into high-frequency (HF), low-frequency (LF), and trend modules. Vector autoregression (VAR) and vector error correction (VEC) models were then used to systematically simulate the correlations. The time span was split into pre-COVID-19 and post-COVID-19 periods for comparison, and the mobility trends data during the outbreak period released by the Apple company was chosen to reflect the pandemic effects. The empirical analysis results revealed the energy prices, macroeconomic index, and exchange rate are the main external impact factors of carbon price in the short term. Summarizing from the cointegration models over the long term, the market stability reserve (MSR) mechanism was found to have ability on stabilizing the carbon price under the epidemic shock. Furthermore, the COVID-19 was found to complicate the relationships between carbon price and influence factors, which resulted in fluctuating markets.