Real-time fatigue curve extraction algorithm for wearable sEMG devices based on fast variational mode decomposition

The decomposition number $K$ and penalty factor $\alpha $ in the variational mode decomposition (VMD) algorithm have a great influence on the decomposition effect and the accuracy of subsequent fault diagnosis. Therefore, a gear fault diagnosis method based on genetic mutation particle swarm optimization VMD and probabilistic neural network (GMPSO-VMD-PNN) algorithm is proposed in this paper. Firstly, the GMPSO algorithm is used to optimize the $[K,\alpha]$ parameter combination in the VMD algorithm, and the optimal $[K,\alpha]$ parameter combination of each gear fault vibration signal to be decomposed is selected. Then, the gear fault vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, and the sample entropy value of each IMFs is extracted to form the feature vector of subsequent fault diagnosis. Finally, the characteristic vector of gear fault vibration signal is input into PNN model, and gear fault is accurately classified. By comparing with fixed parameter VMD algorithm, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm, the superiority of this method in gear fault diagnosis is verified. Therefore, the GMPSO-VMD-PNN algorithm proposed in this paper has certain application value for gear fault diagnosis.

A new denoising algorithm and feature extraction algorithm that combine a new kind of permutation entropy (NPE) and variational mode decomposition (VMD) are put forward in this paper. VMD is a new self-adaptive signal processing algorithm, which is more robust to sampling and noise, and also can overcome the problem of mode mixing in empirical mode decomposition (EMD) and ensemble EMD (EEMD). Permutation entropy (PE), as a nonlinear dynamics parameter, is a powerful tool that can describe the complexity of a time series. NPE, a new version of PE, is interpreted as distance to white noise, which shows a reverse trend to PE and has better stability than PE. In this paper, three kinds of ship-radiated noise (SN) signal are decomposed by VMD algorithm, and a series of intrinsic mode functions (IMF) are obtained. The NPEs of all the IMFs are calculated, the noise IMFs are screened out according to the value of NPE, and the process of denoising can be realized by reconstructing the rest of IMFs. Then the reconstructed SN signal is decomposed by VMD algorithm again, and one IMF containing the most dominant information is chosen to represent the original SN signal. Finally, NPE of the chosen IMF is calculated as a new complexity feature, which constitutes the input of the support vector machine (SVM) for pattern recognition of SN. Compared with the existing denoising algorithms and feature extraction algorithms, the effectiveness of proposed algorithms is validated using the numerical simulation signal and the different kinds of SN signal.

With the ubiquitous deployment of mobile and sensor technologies in modes of transportation, taxis have become a significant component of public transportation. However, vacant taxis represent an important waste of transportation resources. Forecasting taxi demand within a short time achieves a supply–demand balance and reduces oil emissions. Although earlier studies have forwarded highly developed machine learning- and deep learning-based models to forecast taxicab demands, these models often face significant computational expenses and cannot effectively utilize large-scale trajectory sensor data. To address these challenges, in this paper, we propose a hybrid deep learning-based model for taxi demand prediction. In particular, the Variational Mode Decomposition (VMD) algorithm is integrated along with a Bidirectional Long Short-Term Memory (BiLSTM) model to perform the prediction process. The VMD algorithm is applied to decompose time series-aware traffic features into multiple sub-modes of different frequencies. After that, the BiLSTM method is utilized to predict time series data fed with the relevant demand features. To overcome the limitation of high computational expenses, the designed model is performed on the Spark distributed platform. The performance of the proposed model is tested using a real-world dataset, and it surpasses existing state-of-the-art predictive models in terms of accuracy, efficiency, and distributed performance. These findings provide insights for enhancing the efficiency of passenger search and increasing the profit of taxicabs.

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

We have proposed a new denoising method for the simultaneous noise reduction and preservation of seismic signals based on variational mode decomposition (VMD). VMD is a recently developed adaptive signal decomposition method and an advance in non-stationary signal analysis. It solves the mode-mixing and non-optimal reconstruction performance problems of empirical mode decomposition that have existed for a long time. By using VMD, a multi-component signal can be non-recursively decomposed into a series of quasi-orthogonal intrinsic mode functions (IMFs), each of which has a relatively local frequency range. Meanwhile, the signal will focus on a smaller number of obtained IMFs after decomposition, and thus the denoised result is able to be obtained by reconstructing these signal-dominant IMFs. Synthetic examples are given to demonstrate the effectiveness of the proposed approach and comparison is made with the complete ensemble empirical mode decomposition, which demonstrates that the VMD algorithm has lower computational cost and better random noise elimination performance. The application of on field seismic data further illustrates the superior performance of our method in both random noise attenuation and the recovery of seismic events.

Due to the application of power electronics and wind power generation equipment in power systems, broadband oscillation events constantly appear, which makes broadband oscillation difficult to detect due to the limitations of communication bandwidth and the sampling theorem. To ensure the safety and stability of the system, and to detect and recognize the broadband oscillation information timely and accurately, this paper presents a multi-mode recognition method of broadband oscillation based on compressed sensing (CS) and the adaptive Variational Mode Decomposition (VMD) algorithm. Firstly, the high-dimensional oscillation signal data collected by the Phasor Measurement Unit (PMU) is compressed and sampled by a Gaussian random matrix, and the obtained low-dimensional data are uploaded to the main station. Secondly, the orthogonal matching pursuit (OMP) algorithm of the master station is used to reconstruct the low-dimension signal, and the original high-dimension signal data are recovered without losing the main features of the signal. Finally, an adaptive VMD algorithm with energy loss minimization as a threshold is used to decompose the reconstructed signal, and the Intrinsic Mode Function (IMF) components with broadband oscillation information are obtained. By constructing oscillating signals with different frequencies, Gaussian white noise with a signal-to-noise ratio of 10 dB to 30 dB is added successively. After the signal is compressed and reconstructed by the proposed method, the signal-to-noise ratio can reach 18.8221 dB to 40.0794 dB, etc., and the oscillation frequency and amplitude under each signal-to-noise ratio can be accurately identified. The results show that the proposed method not only has good robustness to noise, but also has good denoising effect to noise. By using the simulation measurement model, the original oscillation signal is compressed and reconstructed, and the reconstruction error is 0.1263. The basic characteristics of the signal are restored, and the frequency and amplitude of the oscillation mode are accurately identified, which proves that the method is feasible and accurate.

The power quality signals are always mixed with noise, which will influence the accurate measurement and characteristic extraction. Therefore, it’s important to denoise for the signal processing. This paper puts forward a novel denoising algorithm for power quality disturbances (PQDs) based on variational mode decomposition (VMD) and the truth that the energy density times the average period of each intrinsic mode function (IMF) is a constant. Firstly, the VMD algorithm is used to decompose the white noise into several IMF components. Then, the average period energy product of each IMF component is calculated, and some of the IMF components are selected for reconstruction according to the judgment criterion to obtain the denoised signal. The simulation results show that the proposed algorithm can greatly improve the signal-to-noise ratio (SNR), and the denoising effect is better than that of wavelet threshold and ensemble empirical mode decomposition (EEMD) algorithm.

Inner Mongolia is one of the most sensitive regions to global change with vegetation significantly affected by global warming and human activities. Therefore, exploring the dynamic change of vegetation and its impact mechanism is of great significance for guiding the protection ecosystem and policy formulation. Based on the 1982–2015 growing season and the interannual normalized difference vegetation index (NDVI), simultaneous temperature and precipitation data sets, we extracted the characteristic components of the NDVI and climatic factors by the Variational Mode Decomposition (VMD) methods. And the periodic characteristics of the NDVI in Inner Mongolia and its relationship with climate over a period of 34 years were analyzed. The results show that: 1) The VMD algorithm overcomes the “mode aliasing” problem of Empirical Mode Decomposition (EMD) and can more accurately extract the periodic information of long time series vegetation NDVI dataset containing complex frequencies.; 2) the NDVI in the growing season of Inner Mongolia has main change cycles of one growing season (7 months) and half a growing season, and temperature and NDVI have the same double-cycle relationship, whereas precipitation has a periodic change of one growing season; 3) the NDVI cycle change of Inner Mongolia vegetation from 1982 to 2015 shows multiple time scales, showing 16.95a, 6.8a, 4.85a, 4.25a, 3.4a and 2.83a change cycles; 4) vegetation NDVI in Inner Mongolia from 1982 to 2015 has a good correlation with climate factors, and the partial correlation coefficients are different in Inner Mongolia and three sampling areas. NDVI and precipitation have relatively good periodic consistency, and there is a significant positive correlation between vegetation NDVI and temperature and precipitation before and after removing the interference of periodic variables. In general, temperature and precipitation jointly affect the NDVI cyclical changes of Inner Mongolia. The VMD algorithm has significant effects on determining the cyclic dynamic changes of NDVI and climatic factors.

High load data dimension and insufficient sample characteristics challenge the load clustering accuracy. For this challenge, this paper proposes a load analysis method based on variational mode decomposition (VMD) and the energy difference spectrum of singular value (EDSSV). Firstly, the load data is decomposed by VMD algorithm. Simultaneously, the lowest frequency intrinsic function in the decomposition results is selected for EDSSV. The decomposition manifests load sample characteristics and reduces the load data dimension. Furthermore, the singular value is used to obtain an energy difference spectrum curve by EDSSV, which converts curve features to energy features and reduces the amount of data. The k-means clustering result of the original sample and the result of the energy difference spectrum curve are compared through compactness index. Compared with the k-means method, the result of clustering index CP with the proposed method is reduced by 0.0627, which shows that the clustering accuracy is improved. Also, the load data dimension is reduced by about 80%.

In-car vital sign monitoring is of great importance for ensuring safe driving. Impulse Radio Ultra-WideBand (IRUWB) radar with low power consumption and high resolution, is widely used for vital sign monitoring. However, existing researches focus on monitoring the single target in the car, especially for the driver. This paper proposes a location-based Variational Mode Decomposition (VMD) algorithm for in-car vital sign monitoring on multiple targets, including the driver and passengers, with only one radar. Firstly, the prior knowledge of seat locations is obtained after determining the position of the radar, based on which the received radar signals are divided into several intervals. Secondly, VMD is performed on each signal interval to extract vital signals in the corresponding location. Finally, in order to alleviate the severely superposed signals caused by the multipath environment in the car, the correlation coefficients between extracted vital signals in different locations are compared to select the corresponding vital signs. The Heart Rate (HR) and Respiration Rate (RR) of the driver and passengers are obtained. In addition, this paper analyzes the impact of passengers' locations when monitoring multiple targets vital signs. To the best of our knowledge, this is the first attempt to monitor multiple targets in the car. Experiments are conducted in an off-the-shelf car with five seats, and two scenarios, including only the driver and two targets (the driver and the passenger), are considered. Then real time monitoring is implemented. Experimental results demonstrate the effectiveness of the proposed algorithm. The accuracies of vital sign monitoring on only the driver and two targets reach 92.66% and 88.44% respectively.

Ground roll is a common coherent noise in land seismic acquisition, which is usually characterized by high amplitudes, low frequencies, and low propagation velocities. Removing ground roll is a key procedure in seismic data processing. In this letter, we develop a novel ground roll suppression approach termed f-x variational mode decomposition (VMD), which has the characteristic of a frequency-dependent, high-wavenumber filter. This new algorithm first applies VMD on constant frequency slices in the frequency-offset domain within the frequency range of ground roll in order to extract the ground roll, and then the denoised data can be obtained by subtracting them adaptively from the original data. A synthetic example is given to demonstrate that the proposed method is able to suppress ground roll well and preserve seismic reflections effectively compared with other conventional techniques such as frequency filtering and f-k filtering. Application of the method on field data further demonstrates the potential of the f-x VMD algorithm in industrial applications.

This paper presents a variational mode decomposition (VMD)-based heart rate extraction algorithm to extract heart rate of the target under intermittent interference of non-stationary clutters caused by another person. When nonstationary clutters exist around the interested target, the heart rate detection becomes difficult for FMCW radars. In regard to the situation, VMD is utilized to extract the heartbeat signal and suppress the effect of non-stationary clutters after applying filter preprocessing. This approach is compared to other methods based on ensemble empirical mode decomposition (EEMD) and traditional fast Fourier transform (FFT). As a result, the proposed algorithm can achieve low computational load and high accuracy of heart rate extraction with relative error of 1.7%. The heartbeat signal extracted by the proposed algorithm has signal-to-noise ratio (SNR) improvement of 2.4 dB compared with EEMD algorithm.

The variational mode decomposition (VMD) method for signal decomposition is severely affected by the number of components of the VMD method. In order to determine the decomposition modal number, K, in the VMD method, a new center frequency method of the multi-threshold is proposed in this paper. Then, an improved VMD (MTCFVMD) algorithm based on the center frequency method of the multi-threshold is obtained to decompose the vibration signal into a series of intrinsic modal functions (IMFs). The Hilbert transformation is used to calculate the envelope signal of each IMF component, and the maximum frequency value of the power spectral density is obtained in order to effectively and accurately extract the fault characteristic frequency and realize the fault diagnosis. The rolling element vibration data of the motor bearing is used to test the effectiveness of proposed methods. The experiment results show that the center frequency method of the multi-threshold can effectively determine the number, K, of decomposed modes. The proposed fault diagnosis method based on MTCFVMD and Hilbert transformation can effectively and accurately extract the fault characteristic frequency, rotation frequency, and frequency doubling, and can obtain higher diagnostic accuracy.

This paper proposes a study on gearbox fault feature extraction of wind turbine under variable speed condition using improved adaptive variational mode decomposition (VMD). Frequent changes in wind speed and critical noise interference make the vibration signal exhibit non-stationary characteristics. Although computational order tracking can transform non-stationary signals in the time domain into stationary angular signals, and then extract fault features from order spectrum obtained by FFT, the obtained order spectrum is liable to be polluted by noise or to appear order aliasing. To avoid order aliasing and eliminate noise interference, the original non-stationary signal is firstly processed using the improved adaptive VMD method called adaptive differential evolution – VMD (ADE-VMD). ADE-VMD can not only utilise the advantages of traditional VMD but also adaptively select narrow-band intrinsic mode function (NBIMF) to construct the reconstructed signal with less noise and without order aliasing. In the experiment, we compared the ADE-VMD method with other VMD methods such as GA-VMD, PSO-VMD and DE-VMD, and the results showed that ADE-VMD has excellent adaptive processing ability, and its convergence and optimisation speed are more remarkable. ADE-VMD can effectively filter the noise inference and avoid the order aliasing, so it is well suitable for fault feature extraction under variable speed.

In order to improve the recognition accuracy of partial discharge (PD) by making full use of the time-frequency characteristics of PD signals and employing deep learning theory, a kind of PD pattern recognition method based on variational mode decomposition (VMD)-Choi-Williams distribution (CWD) spectrum and optimized convolutional neural network (CNN) with cross-layer feature fusion is proposed in this paper. Firstly, a PD signal is decomposed into several components by VMD algorithm, and the CWD analysis of the obtained components is carried out to obtain the VMD-CWD time-frequency spectrum. Secondly, the cross-layer feature fusion and optimization CNN (CFFO-CNN) is constructed by introducing cross-layer connection and optimization algorithm. Thirdly, the VMD-CWD is regarded as the input vector to train CFFO-CNN to learn and extract the intrinsic features of the spectrum. Finally, the trained network is used to recognize the PD types of the testing samples. The proposed method is compared with traditional recognition methods such as BP neural network (BPNN) and support vector machine (SVM), as well as some commonly used deep learning algorithms. The experimental results indicate that the recognition performance of the proposed method is significantly better than that of existing recognition methods with accuracy up to 99.5%. It is proved that CFFO-CNN has superior feature extraction ability, which can extract the internal features of the VMD-CWD spectrum independently with higher recognition accuracy and wider application prospect.