Multivariate Empirical Mode Decomposition Algorithm Research Articles

Efficient GPU implementation of the multivariate empirical mode decomposition algorithm

An efficient GPU implementation of the Multivariate Empirical Mode Decomposition (MEMD) method is presented for speeding up the process of decomposing non-stationary multi-channel bioelectric signals into different oscillation modes. Each step of the MEMD algorithm is designed with performance in mind and implemented to remove all unnecessary overheads caused by CPU-GPU communication, data transfer operations and synchronisation. The implementation is validated with synthetic and real EEG signals of different lengths and channels (up to 128 channels) on different GPU cards, and compared to existing serial MEMD implementations. The final implementation achieved between 180x-430x speedup compared to MATLAB and a 10x improvement over the only known existing GPU implementation. The average decomposition error of our implementation is below 1.2 %. Our GPU program is the fastest known GPU implementation of the MEMD algorithm that reduces execution time from hours to seconds and as such makes it possible to perform MEMD time-frequency analysis of high-density EEG (MEG) or similar multi-channel signals in a fraction of time and opens the road towards its practical applicability.

Beyond Frequency Band Constraints in EEG Analysis: The Role of the Mode Decomposition in Pushing the Boundaries

This study investigates the use of empirical mode decomposition (EMD) to extract intrinsic mode functions (IMFs) for the spectral analysis of EEG signals in healthy individuals and its possible biological interpretations. Unlike traditional EEG analysis, this approach does not require the establishment of arbitrary band limits. The study uses a multivariate EMD algorithm (APIT-MEMD) to extract IMFs from the EEG signals of 34 healthy volunteers. The first six IMFs are analyzed using two different methods, based on FFT and HHT, and the results compared using the ANOVA test and the Bland–Altman method for agreement test. The outcomes show that the frequency values of the first six IMFs fall within the range of classic EEG bands (1.72–52.4 Hz). Although there was a lack of agreement in the mean weighted frequency values of the first three IMFs between the two methods (>3 Hz), both methods showed similar results for power spectral density (<5% normalized units, %, of power spectral density). The HHT method is found to have better frequency resolution than APIT-MEMD associated with FTT that produce less overlapping between IMF3 and 4 (p = 0.0046) and it is recommended for analyzing the spectral properties of IMFs. The study concludes that the HHT method could help to avoid the assumption of strict frequency band limits, and that the potential impact of EEG physiological phenomenon on mode-mixing interpretation, particularly for the alpha and theta ranges, must be considered in future research.

A multivariate EMD-LSTM model aided with Time Dependent Intrinsic Cross-Correlation for monthly rainfall prediction

Accurate prediction of rainfall is a complex problem because of the large number of controlling factors, complex interrelationships between them and the multiscaling behaviour of the process. Because of the multiscaling behaviour of the problem, the use of hybrid modelling involving decomposition techniques is preferable over strenuous physical models and standalone driven techniques for accurate rainfall predictions. This study proposes a novel hybrid modelling framework integrating Long Short Term Memory (LSTM) and Multivariate Empirical Mode Decomposition (MEMD) aided with Time Dependent Intrinsic Cross-Correlation (TDICC) analysis algorithm for monthly rainfall predictions. The application of the proposed model is demonstrated for monthly rainfall prediction of 2005–2015 period at All India spatial domain considering El-Niño Southern Oscillation(ENSO), Indian Ocean Dipole(IOD) and five antecedent values of rainfall are the input variables. The proposed framework first uses MEMD to obtain a set of orthogonal components namely Intrinsic Mode Functions (IMFs) identifying and aligning the common scales embedded in the multiple input variables considered. Subsequently, scale specific rainfall information are predicted by incorporating them on relevant IMFs and their significant lags identified through TDIC and TDICC analyses. Final aggregation of predicted rainfall components from different scales gives the monthly rainfall of a generic time step ahead. The efficacy of the proposed MEMD-TDICC-LSTM framework is compared with five other hybrid models such as MEMD-TDIC-ANN, MEMD-TDICC-ANN, MEMD-ACO-ANN, MEMD-ACO-LSTM and MEMD-TDIC-LSTM, which used Time Dependent Intrinsic Correlation (TDIC) and Ant Colony Optimization (ACO) for predictor selection and Artificial Neural Network (ANN) as modelling tool. The study has used different graphical representations and ten different statistical performance evaluation measures for the prediction of validation period, it is observed that the proposed model could achieve a predictive skill of 0.98, Nash-SutcliffeEfficiency (NSE) of 0.95 and Index of Agreement (IA) of 0.91 which is better than all the five remaining models. The capability of MEMD-TDICC-LSTM model to predict the extremes is also confirmed by using the bar graph for the drought year rainfall of 2009 and is observed that the model is successful in capturing the extremes with an annual rainfall 975.16 mm closer to observed value 927.3 mm. MEMD algorithm facilitates the inclusion of multiple large scale climatic oscillations as inputs and their multi time scale decomposition, TDICC helps to fix the relevant inputs at different time scales and the LSTM functions as the robust modelling tool. Further, the framework using this specific combination resulted in substantial reduction in modelling complexity and faster execution, as the approach considers only the most relevant and significant inputs in the process.

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.

Quantitative assessment for characterization of breast lesion tissues using adaptively decomposed ultrasound RF images

Quantitative ultrasound is of significant relevance to the clinical diagnosis of benign and malignant breast lesions. Owing to desmoplastic reactions in the tumor and malignant cells invading the surrounding tissues, the irregular boundary of the lesion is a significant indication of malignancy. Complexity measured using entropy based on ultrasound radio frequency (RF) data is investigated to characterize the disease; however, the performance is reduced due to the slowly varying components in the data. In the present study, adoption of small-window entropy (SWE) based on adaptively decomposed ultrasound RF images is proposed for the characterization of breast lesion tissues. First, down-sampled, dilated and cropped RF (DDC_RF) images are obtained from the original ultrasonic RF data. Subsequently, a fast multivariate empirical mode decomposition algorithm is employed to adaptively decompose the DDC_RF images into intrinsic mode functions (IMFs). The ring regions of interest that are the areas surrounding the tumors are determined from all individual IMF images and their different combinations to calculate the SWEs. The assessment is performed using the Open Access Series of Breast Ultrasonic Data (OASBUD), which includes original RF data and histological assessment results of 48 benign and 48 malignant lesions. The receiver operating curve (ROC) and the area under the ROC (AUC) values are calculated to assess the ability to diagnose breast lesions. The results show that the SWEs based on the combinations of IMFs 1–3, IMFs 1,2, IMFs 1–4, and IMFs 1,3 provided the AUC values of 0.88, 0.87, 0.86, and 0.85, respectively, which are greater than 0.84, obtained from the undecomposed RF images. It is concluded that the SWE based on the adaptively decomposed ultrasound RF images is an improved characteristic for distinguishing between benign and malignant breast lesions, and it is suggested that it may serve as a basis for computer-assisted breast cancer ultrasound diagnosis.

Channel Contributions of EEG in Emotion Modelling Based on Multivariate Adaptive Orthogonal Signal Decomposition

Empirical Mode Decomposition (EMD) provides an adaptive signal processing tool, and its multivariate extension is useful to model multichannel signals. Recently, EMD and multivariate EMD have successfully been applied to solve different signal processing problems. Electroencephalogram signals are often employed to explore the emotional concepts for human-machine interaction. In this paper, an emotion recognition model is presented via EEG signal decomposition by utilizing multivariate EMD. Intrinsic Mode Functions extracted by the multivariate EMD algorithm are quasi-orthogonal. Hence the Gram-Schmidt Orthogonalization method is applied to the extracted IMFs. The number of orthogonal components reveals the number of modes used in the second step of the proposed method, where the Empirical Wavelet Transform is used to explore different features of the IMFs. By applying Ensemble and Decision Tree classifiers on the calculated features, the emotional states are classified as high-low arousal, valence, and dominance with 72.7%, 62.0%, and 64.7% highest classification performances using the selected channels, respectively.

Comparison between traditional fast Fourier transform and marginal spectra using the Hilbert–Huang transform method for the broadband spectral analysis of the electroencephalogram in healthy humans

AbstractThe fast Fourier transform (FFT) has been the main tool for electroencephalographic (EEG) Spectral Analysis (SPA). However, as the EEG dynamics show nonlinear and non‐stationary behavior, results using the FFT approach may result meaningless. A novel method has been developed for the analysis of nonlinear and non‐stationary signals known as the Hilbert–Huang transform method. In this study we analyze the differences for the broadband (SPA) of the EEG using the traditional FFT approach with those calculated with the Hilbert Marginal Spectra (HMS) after decomposition of the EEG with a multivariate empirical mode decomposition algorithm. EEG segments recorded from 19 leads of 47 healthy volunteers were studied. Statistically significant differences between methods were found for almost all leads by variance analyses. The agreement assessment shows that mean weighted frequencies have a good agreement for almost all bands, with the exception of beta‐2 and gamma bands where values for the HMS where higher than 3 Hz. Also the HMS method received lower than 5% energy values for alpha activity with an increment in the adjacent bands. The HMS may be considered a good alternative for the SPA of the EEG when nonlinearity or non‐stationarity may be present.

Trivariate Empirical Mode Decomposition via Convex Optimization for Rolling Bearing Condition Identification.

As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly, the uniform projection scheme on a hypersphere is used to estimate the local mean. However, the unbalanced data distribution in high-dimensional space often conflicts with the uniform samples and its performance is sensitive to the noise components. Considering the common fact that the vibration signal is generated by three sensors located in different measuring positions in the domain of the structural health monitoring for the key equipment, thus a novel trivariate empirical mode decomposition via convex optimization was proposed for rolling bearing condition identification in this paper. For the trivariate data matrix, the low-rank matrix approximation via convex optimization was firstly conducted to achieve the denoising. It is worthy to note that the non-convex penalty function as a regularization term is introduced to enhance the performance. Moreover, the non-uniform sample scheme was determined by applying singular value decomposition (SVD) to the obtained low-rank trivariate data and then the approach used in conventional MEMD algorithm was employed to estimate the local mean. Numerical examples of synthetic defined by the fault model and real data generated by the fault rolling bearing on the experimental bench are provided to demonstrate the fruitful applications of the proposed method.

GPU-Accelerated Multivariate Empirical Mode Decomposition for Massive Neural Data Processing

This paper presents an efficient implementation of multivariate empirical mode decomposition (MEMD) algorithm, a multivariate extension of EMD algorithm. Analogous to EMD, MEMD decomposes a multivariate signal into its intrinsic mode functions using joint rotational mode. The algorithm is computationally intensive because of its recursive nature and any increase in input data size results in a non-linear increase in its execution time. Therefore, it is extremely time-consuming to obtain a decomposition of signal, such as EEG into its intrinsic modes using MEMD. As the interest in applying MEMD algorithm in various domains is increasing, there is a need to develop an optimized implementation of the algorithm, since it requires repeated execution of the same operations and computationally extensive interpolations on each projected vector. This can be done using GPGPU, because it has the power to process similar function on different blocks of data. We have compared the optimized implementation of MEMD, using GPU, with the MATLAB implementation for hexa-variate and hexa-deca-variate data sets, and observed that the GPU-based optimized implementation results in approximately $6\times \sim 16\times $ performance improvements in terms of time consumption.

Signal analysis of acoustic and flow-induced vibrations of BWR main steam line

The aim of this work is the signal analysis of acoustic waves due to phenomenon known as singing in Safety Relief Valves (SRV) of the main steam lines (MSL) in a typical BWR5. The acoustic resonance in SRV standpipes and fluctuating pressure is propagated from SRV to the dryer through the MSL. The signals are analyzed with a novel method based on the Multivariate Empirical Mode Decomposition (M-EMD). The M-EMD algorithm has the potential to find common oscillatory modes (IMF) within multivariate data. Based on this fact, we implement the M-EMD technique to find the oscillatory mode in BWR considering the measurements obtained collected by the strain gauges located around the MSL. These IMF, analyzed simultaneously in time, allow obtaining an estimation of the effects of the multiple-SRV in the MSL. Two scenarios are analyzed: the first is the signal obtained before the installation of the acoustic dampers (ASB), and the second, the signal obtained after installation. The results show the effectiveness of the ASB to damp the strong resonances when the steam flow increases, which represents an important reduction in the acoustic loads to the steam dryer.

Dynamically sampled multivariate empirical mode decomposition

A method for accurate multivariate local mean estimation in the multivariate empirical mode decomposition algorithm by using a statistical data-driven approach based on the Menger curvature measure and normal-to-anything variate-generation method is proposed. This is achieved by aligning the projection vectors in the direction of the maximum ‘activity’ of the input signal by considering the local curvature of the signal in multidimensional spaces, resulting in accurate mean estimation even for a very small number of projection vectors.

Multivariate Empirical Mode Decomposition applied to the estimation of the decay ratio and out-of-phase oscillations in BWRs

This work presents a novel method based on the Multivariate Empirical Mode Decomposition (MEMD) to estimate the Decay Ratio (DR) and the apparition of a possible out-of-phase oscillation in Boiling Water Reactors (BWRs). The MEMD algorithm, have the potential to find common oscillatory modes within multivariate data called Intrisic Mode Functions (IMF). Based on this fact, we implement the MEMD technique to find the common oscillatory mode (density wave) in BWRs considering the measurements obtained in each Local Power Range Monitor (LPRM) through the entire core. These IMFs, analyzed simultaneously in time, permit to obtain an estimation of the DR and; also give some considerations about an incipient out-of-phase oscillation through the phase measured between two specific LPRMs. Effectiveness of the proposed method is demonstrated on a specific challenging case from the Forsmark stability benchmark.

Summary of session 8

This work presents a novel method based on the Multivariate Empirical Mode Decomposition (MEMD) to estimate the Decay Ratio (DR) and the apparition of a possible out-of-phase oscillation in Boiling Water Reactors (BWRs). The MEMD algorithm, have the potential to find common oscillatory modes within multivariate data called Intrisic Mode Functions (IMF). Based on this fact, we implement the MEMD technique to find the common oscillatory mode (density wave) in BWRs considering the measurements obtained in each Local Power Range Monitor (LPRM) through the entire core. These IMFs, analyzed simultaneously in time, permit to obtain an estimation of the DR and; also give some considerations about an incipient out-of-phase oscillation through the phase measured between two specific LPRMs. Effectiveness of the proposed method is demonstrated on a specific challenging case from the Forsmark stability benchmark.