Variational Mode Decomposition Research Articles

Degradation Evaluation of Hydropower Equipment Based on Variational Modal Decomposition

Degradation Evaluation of Hydropower Equipment Based on Variational Modal Decomposition

Using enhanced Variational Modal Decomposition and Dung Beetle Optimization Algorithm optimization-kernel Extreme Learning Machine model to forecast short-term wind power

With the widespread use of clean energy, the forecasting of wind power has become increasingly significant. Extracting time series from sophisticated wind power data and thus improving the prediction accuracy of wind power generation has become the key to short-term forecasting. This paper proposes a Kernel Extreme Learning Machine (KELM) prediction model based on Crested Porcupine Optimizer (CPO), Variational Modal Decomposition (VMD) with Improved Dung Beetle Optimization Algorithm (QHDBO). Firstly, by analyzing the correlation between the variables in the wind power data, the CPO algorithm is used to optimize the modal decomposition number and the penalty parameter of the VMD and extract the time-series information of the wind power series, and smooth it to obtain a number of sub-sequences with strong regularity. Then, the KELM prediction model is constructed for different subsequences, and the kernel parameters and regularization coefficients of KELM are optimized using the QHDBO algorithm. Finally, the predicted values of different subsequences are reconstructed to obtain the final prediction results. The simulation results show that the CVMD-QHDBO-KELM model can effectively improve the wind power prediction performance, and the MAPE values are all below 9 %, and most of the RE values are below 10 %.

State of Health Estimation of Lithium-Ion Battery for Electric Vehicle Based on VMD-DBO-SVR Model

State-of-health (SOH) of lithium-ion batteries is an important indicator for measuring performance and remaining life. We propose an innovative prediction model that integrates variational mode decomposition (VMD), Dung Beetle optimizer (DBO), and support vector regression (SVR) algorithms. We extracted relevant features from the discharge characteristic curve and incremental capacity curve. We used Pearson and Spearman correlation coefficient methods for correlation analysis on the extracted health factors (HFs), selecting those that significantly impact SOH as input features. A DBO-SVR model was constructed to establish a nonlinear correlation between HFs and SOH, and the DBO algorithm was used to globally search and optimize the hyperparameters of the SVR model to improve its prediction accuracy. To reduce the impact of noise in battery signals on model performance, VMD technology was introduced to decompose battery signals into multiple intrinsic mode components, to extract useful features and remove noise to further improve prediction accuracy. The proposed method was validated using the NASA battery dataset and compared with other algorithm models. Results showed that the prediction model was significantly better than other models, with a maximum RMSE value of 0.84%, a maximum MAE value of 0.71%, and a stable prediction error value within 1%.

Prediction of packing performance of pneumatic control valve based on stem mechanism model and VMD-SSA-LSTM

Abstract Packing performance is one of the most important parts affecting the control operation of pneumatic control valves. In order to avoid the failure caused by packing wear and aging of pneumatic control valves after long-term use, this paper constructs a valve stem mechanism model and combines the advantage of deep learning to predict the packing performance of pneumatic control valves based on Long Short-term Memory (LSTM) and Variable Mode Decomposition (VMD) and Sparrow Search Algorithm (SSA). Firstly, the historical data of the actuator is calculated based on the mechanism model of the valve stem. The time-friction force obtained by the calculation is the parameter set. After the parameter set is subject to the variational mode decomposition, the parameter set is imported into the SSA-LSTM prediction model for prediction, and the prediction data is obtained.

Chaos Analysis and Prediction of Monthly Runoff Using a Two-Stage Variational Mode Decomposition Framework

Chaos Analysis and Prediction of Monthly Runoff Using a Two-Stage Variational Mode Decomposition Framework

Power quality disturbance signal classification in microgrid based on kernel extreme learning machine

AbstractThis paper presents a kernel extreme learning machine (KELM) integrated with the improved whale optimization algorithm (IWOA) to address the power quality disturbance (PQD) issue in microgrids. First, an adaptive variational mode decomposition method is employed to extract PQD signals in microgrids. Then, the IWOA is utilized to optimize the penalty factor and kernel function parameters for the KELM classifier model, thereby enhancing the performance of the classifier. Furthermore, the test results indicate that the proposed IWOA–KELM achieves high classification accuracy and rapid convergence for complex PQD signals.

The Denoising Method With Variational Mode Decomposition for Signal-Dependent Counting Noise in Molecular Communications

The Denoising Method With Variational Mode Decomposition for Signal-Dependent Counting Noise in Molecular Communications

Multi-step ozone concentration prediction model based on improved secondary decomposition and adaptive kernel density estimation

Accurately predicting ozone concentration is crucial for human pollution prevention and health protection. In recent years, decomposition ensemble frameworks have been widely applied to ozone concentration forecasting. However, due to the inefficiencies of secondary decomposition and insufficient emphasis on interval predictions, developing a stable and efficient model for ozone concentration prediction remains a challenging task. Therefore, this study proposes a hybrid model based on an improved secondary decomposition algorithm (ISD) and adaptive kernel density estimation (AKDE). The original sequences are initially decomposed and reconstructed using Complex Empirical Mode Decomposition (CEEMD) and K-means clustering based on sample entropy. Subsequently, Optimal Variational Mode Decomposition (OVMD) is employed to address the strong fluctuations in high-frequency components, followed by establishing individual Long Short-Term Memory (LSTM) prediction models for each component. The error correction model is then constructed by combining ISD and Gated circulation unit (GRU), culminating in uncertainty quantification using AKDE. Empirical analysis of the Beijing and Shanghai, China datasets shows that the average R2 of their multi-step forecasts are 0.9966 and 0.9938, respectively, which are significantly better than the baseline model.

Dynamic time warping based instantaneous frequency estimation for rotating machineries under non-stationary operating conditions

Abstract For tacho-less order tracking, it is crucial to achieve an accurate estimation of instantaneous phase and frequency under non-stationary conditions for fault diagnosis of mechanical systems. Therefore, an instantaneous frequency estimation method based on dynamic time warping for rotating machinery was proposed. Firstly, a mono-component signal is obtained by variational mode decomposition of multi-harmonic vibration signal generated in practical engineering. Then, a stationary reference signal is constructed by the mean frequency of the vibration signal, which is obtained by the signal spectrum. Aligning the vibration signal with the reference signal to obtain the rough phase estimation and warping path. Finally, a polynomial model is constructed to calculate the analytic expression of the smooth warping path to obtain the instantaneous frequency result. The simulation and experiment present that the dynamic time warping-based method can estimate the instantaneous frequency of the signal under non-stationary conditions. Compared with the classical Hilbert transform method, the proposed dynamic time-warping algorithm has stronger noise resistance.

Characterization of Contactor Degradation States Based on Improved Variational Modal Decomposition and Optimized Similarity Metrics With Combined Weights

Characterization of Contactor Degradation States Based on Improved Variational Modal Decomposition and Optimized Similarity Metrics With Combined Weights

A wavelet packet deep learning model for Energy-Based structural collapse assessment under Earthquake-Fire Scenarios: Framework and hybrid simulation

An energy-based framework is proposed for the dynamic stability assessment of structures subjected to earthquake-fire scenarios and verified through earthquake-fire hybrid simulation. In this framework, the wavelet packet Long Short-Term Memory (LSTM) model is used to separate the noise and residue caused by earthquake and fire within the structural response signals, guided by wavelet packet energy and power spectral density of signals. Moreover, a comparative analysis is performed with 4 previous signal processing models (empirical mode decomposition, variational mode decomposition, wavelet packet transform, and LSTM). Additionally, Latin hypercube sampling is employed to account for uncertainties in structural characteristics and hazards for dataset establishment and fragility analysis. The experimental findings suggest a decline in the structural dominant frequency with the emergence of high-frequency noise and residuals in structural responses due to the multi-hazard effect. The wavelet packet transform eliminates the high-frequency noise in the signal and avoids the oscillation of the LSTM prediction results. Post-earthquake fire increases the structural collapse possibility even under a moderate earthquake excitation. The proposed framework proves to be rational and has the potential to be further applied to other multi-hazard scenarios.

A novel combination prediction model of ultra-short-term wind speed

The accurate prediction of ultra-short-term wind speed has important theoretical significance and practical application value. In this paper, a combination prediction model of ultra-short-term wind speed based on variational mode decomposition is proposed. Firstly, the variational mode decomposition algorithm is introduced to decompose the ultra-short-term wind speed and obtain the components of different frequency. The approximate entropy algorithm is used to calculate the complexity of each component. According to the calculation results, echo state network is selected to predict high complexity components, support vector machine is used to predict medium complexity components, and autoregressive integrated moving average model is used to predict low complexity components. Then, the predicted values of each component are added to get the final prediction result. Gray wolf algorithm is used to optimize the model parameters of support vector machine and echo state network. In addition, the approximate entropy calculation results show that compared with the original ultra-short-term wind speed, the complexity of the components obtained by the variational mode decomposition algorithm is reduced, which makes the modeling of the ultra-short-term wind speed system simpler. Finally, the validity of the model is verified by taking the ultra-short-term wind speed data of 5 minutes and 10 minutes sampling period actually collected as the research object. The results show that the prediction model proposed in this paper has better performance than other single or combination prediction models.

Novel optimized coupled rainfall model simulation based on stepwise decomposition technique.

Precipitation forecasting plays a pivotal role in guiding the effective management of regional water resources and providing crucial warnings for regional droughts and floods. Finding a monthly precipitation simulation model with robust fitting performance is a significant research endeavor in practical precipitation prediction. This paper introduces two modified African vulture optimization algorithms (MAVOA1 and MAVOA2). It provides hyperparameter optimization techniques for the least squares support vector machine (LSSVM), long short-term memory neural network (LSTM), and random forest (RF) models. These techniques are used to construct a monthly precipitation simulation model based on algorithmic optimization coupled with variational mode decomposition for full decomposition. The test results at five typical stations in the North China Plain reveal the following: (1) the LSSVM model demonstrates significantly better performance than the LSTM and RF models. (2) the MAVOA2-LSSVM model has the best-integrated effect: the average test fitting error is RMSE = 17.50 mm/month, MRE = 117.25%, NSE = 0.90, which shows its superiority in practical application and can significantly improve the accuracy of precipitation prediction; MAVOA2 is more suitable for machine learning models with more hyperparameters of its own, which provides a reference for hyperparameter optimization algorithms in the other fields.

A Research on Emotion Recognition of the Elderly Based on Transformer and Physiological Signals

Aiming at problems such as the difficulty of recognizing emotions in the elderly and the inability of traditional machine-learning models to effectively capture the nonlinear relationship between physiological signal data, a Recursive Map (RM) combined with a Vision Transformer (ViT) is proposed to recognize the emotions of the elderly based on Electroencephalogram (EEG), Electrodermal Activity (EDA), and Heart Rate Variability (HRV) signals. The Dung Beetle Optimizer (DBO) is used to optimize the variational modal decomposition of EEG, EDA, and HRV signals. The optimized decomposed time series signals are converted into two-dimensional images using RM, and then the converted image signals are applied to the ViT for the study of emotion recognition of the elderly. The pre-trained weights of ViT on the ImageNet-22k dataset are loaded into the model and retrained with the two-dimensional image data. The model is validated and compared using the test set. The research results show that the recognition accuracy of the proposed method on EEG, EDA, and HRV signals is 99.35%, 86.96%, and 97.20%, respectively. This indicates that EEG signals can better reflect the emotional problems of the elderly, followed by HRV signals, while EDA signals have poorer effects. Compared with Support Vector Machine (SVM), Naive Bayes (NB), and K-Nearest Neighbors (KNN), the recognition accuracy of the proposed method is increased by at least 9.4%, 11.13%, and 12.61%, respectively. Compared with ResNet34, EfficientNet-B0, and VGG16, it is increased by at least 1.14%, 0.54%, and 3.34%, respectively. This proves the superiority of the proposed method in emotion recognition for the elderly.

Phase unwrapping error identification and suppression method in φ-OTDR systems based on PELT-VMD-ARIMA

In phase-sensitive optical time-domain reflectometer (φ-OTDR) systems, phase unwrapping errors can distort vibration information. To address this issue, a phase unwrapping error identification and suppression method combining pruned exact linear time (PELT) changepoint detection, variational mode decomposition (VMD), and autoregressive integrated moving average (ARIMA) models, termed PELT-VMD-ARIMA, is proposed. Firstly, the principle of the proposed method is introduced, and its effectiveness is verified through a series of numerical simulation experiments. Next, piezoelectric transducers (PZTs) are employed as seismic sources in experiments involving single-frequency and chirp signals. Compared to the mean-shift method, the proposed method reduces the average root mean square error (RMSE) by 70.36% within 2δ range around the changepoints. Finally, the proposed method was validated through an active source seismic application. The results demonstrate the efficacy of the proposed method in identifying and suppressing phase unwrapping errors, thereby enhancing signal quality. This method enhances the vibration recognition capability of φ-OTDR systems, which facilitates precise distributed acoustic sensing applications.

Prediction of Sea Level Using Double Data Decomposition and Hybrid Deep Learning Model for Northern Territory, Australia

Sea level rise (SLR) attributed to the melting of ice caps and thermal expansion of seawater is of great global significance to vast populations of people residing along the world’s coastlines. The extent of SLR’s impact on physical coastal areas is determined by multiple factors such as geographical location, coastal structure, wetland vegetation and related oceanic changes. For coastal communities at risk of inundation and coastal erosion due to SLR, the modelling and projection of future sea levels can provide the information necessary to prepare and adapt to gradual sea level rise over several years. In the following study, a new model for predicting future sea levels is presented, which focusses on two tide gauge locations (Darwin and Milner Bay) in the Northern Territory (NT), Australia. Historical data from the Australian Bureau of Meteorology (BOM) from 1990 to 2022 are used for data training and prediction using artificial intelligence models and computation of mean sea level (MSL) linear projection. The study employs a new double data decomposition approach using Multivariate Variational Mode Decomposition (MVMD) and Successive Variational Mode Decomposition (SVMD) with dimensionality reduction techniques of Principal Component Analysis (PCA) for data modelling using four artificial intelligence models (Support Vector Regression (SVR), Adaptive Boosting Regressor (AdaBoost), Multilayer Perceptron (MLP), and Convolutional Neural Network–Bidirectional Gated Recurrent Unit (CNN-BiGRU). It proposes a deep learning hybrid CNN-BiGRU model for sea level prediction, which is benchmarked by SVR, AdaBoost, and MLP. MVMD-SVMD-CNN-BiGRU hybrid models achieved the highest performance values of 0.9979 (d), 0.996 (NS), 0.9409 (L); and 0.998 (d), 0.9959 (NS), 0.9413 (L) for Milner Bay and Darwin, respectively. It also attained the lowest error values of 0.1016 (RMSE), 0.0782 (MABE), 2.3699 (RRMSE), and 2.4123 (MAPE) for Darwin and 0.0248 (RMSE), 0.0189 (MABE), 1.9901 (RRMSE), and 1.7486 (MAPE) for Milner Bay. The mean sea level (MSL) trend analysis showed a rise of 6.1 ± 1.1 mm and 5.6 ± 1.5 mm for Darwin and Milner Bay, respectively, from 1990 to 2022.

An Adaptive Noise Reduction Method for High Temperature and Low Voltage Electromagnetic Detection Signals Based on SVMD Combined with ICEEMDAN.

In view of the low signal-to-noise ratio (SNR) of shear wave electromagnetic acoustic transducers (EMAT) in the detection of high-temperature equipment, the use of low excitation voltage (LEV) further deteriorates the detection results, resulting in the echo signal containing defects being drowned in noise. For the extraction of the EMAT signal, an adaptive noise reduction method is proposed. Firstly, the minimum envelope entropy is taken as the fitness function for the Harris Hawks Optimizer (HHO), and the optimal successive variational mode decomposition (SVMD) balance parameter is searched by HHO adaptive iteration to decompose LEV EMAT signals at high temperatures. Then the filter is carried out according to the excitation center frequency and correlation coefficient threshold function. Then, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is used to decompose the filtered signal and combine the kurtosis factor to select the appropriate intrinsic mode functions. Finally, the signal is extracted by the Hilbert transform. In order to verify the effectiveness of the method, it is applied to the low-voltage detection of 40Cr from 25 °C to 700 °C. The results show that the method not only suppresses the background noise and clutter noise but also significantly improves the SNR of EMAT signals, and most importantly, it is able to detect and extract the 2 mm small defects from the echo signals. It has great application prospects and value in the LEV detection of high-temperature equipment.

LDCT image denoising algorithm based on two-dimensional variational mode decomposition and dictionary learning

Low-dose X-CT scanning method effectively reduces radiation hazards, however, reducing the radiation dose will introduce noise and artifacts during the projection process, resulting in a decrease in the quality of the reconstructed image. To address this problem, we combined 2D variational modal decomposition and dictionary learning. We proposed a low-dose CT (LDCT) image denoising algorithm based on an improved K-SVD algorithm with image decomposition. The dictionary obtained by K-SVD training lacks consideration of image structure information. To address this problem, we employ the two-dimensional variational mode decomposition (2D-VMD) method to decompose the image into distinct modal components. Through the adaptive learning of dictionaries based on the characteristics of each modal component, independent denoising processing is applied to each component, avoiding the loss of structural and detailed information in the image. In addition, we introduce the regularized orthogonal matching pursuit algorithm (ROMP) and dictionary atom optimization method to improve the sparse representation ability of the dictionary and reduce the impact of noise atoms on denoising performance. The experiments show that the proposed method outperforms other denoising methods regarding peak signal-to-noise ratio and structural similarity. The proposed method maintains the denoised image details and structural information while removing LDCT image noise and artifacts. The image quality after denoising is significantly improved and facilitates more accurate detection and analysis of lesion areas.

MFTM-Informer: A multi-step prediction model based on multivariate fuzzy trend matching and Informer

Multi-step forecasting is a critical process in various fields, such as disaster warning and financial analysis. Nevertheless, achieving precise multi-step forecasting is challenging due to the intricate nature of the factors influencing the time series, most of which are highly nonlinear and nonstationary. In this paper, a multi-step forecasting model named MFTM-Informer, employing a multiple input multiple output strategy for multivariate trend matching is proposed. The dependent variable and the influencing factors are initially decomposed using multivariate variational modal decomposition to minimize noise. Afterwards, the decomposed data are reconstructed into multivariate trends and fluctuations using sample entropy, enabling the development of tailored forecasting strategies based on data characteristics. A multivariate trend is predicted using an enhanced pattern matching model, while the high-frequency fluctuation is modelled using Informer. Finally, the outcomes are combined to generate multi-step predictions. To validate the performance of the proposed model, we observed its performance on three real-world datasets, including Brent crude oil prices, European Union Allowance future prices, and Standard & Poor’s 500 index. Results indicate that the model surpasses all the benchmark models in terms of multiple evaluation metrics and forecast ranges, highlighting its effectiveness and robustness in multi-step forecasting.

Enhanced multi-step streamflow series forecasting using hybrid signal decomposition and optimized reservoir computing models

This study evaluates the use of different time series decomposition methods in association with echo state networks (ESNs), deep echo state networks (DeepESNs), and next generation reservoir computing (NGRC) models to predict the natural flow of water in two hydropower reservoirs with horizons of one, seven, fourteen, and twenty-one steps ahead. The Coyote optimization algorithm is used to adjust the hyperparameters of the ESNs. The use of reservoir computing (RC) methods with Coyote optimization algorithm, a swarm intelligence approach, is compared with the use of variational mode decomposition (VMD), empirical wavelet transform, and empirical mode decomposition. Analysis of the results shows that the use of signal decomposition methods in association with RC can improve the accuracy and performance of the prediction model. The results are compared using different statistical metrics, showing that, in most cases, decomposition methods can improve the forecasting performance of RC. Overall, NGRC outperformed ESN and DeepESN in most of evaluated cases. The best results were obtained using VMD for the forecast horizons of 7, 14, and 21 days ahead, with a decrease in mean absolute error in a range from 43.70% to 88.88% compared to all the other models. Using a Diebold–Mariano test, the results show that the use of VMD is statistically significant in all the cases, with a significant value of 1% in all tested cases of ESN forecasting.