Optimal Variational Mode Decomposition Research Articles

Identification of Sub-Synchronous Oscillation Mode Based on HO-VMD and SVD-Regularized TLS-Prony Methods

To reduce errors in sub-synchronous oscillation (SSO) modal identification and improve the accuracy and noise resistance of the traditional Prony algorithm, this paper focuses on SSOs caused by the integration of doubly fed induction generators (DFIGs) with series compensation into the grid. A novel SSO modal identification method based on the hippopotamus optimization–variational mode decomposition (HO-VMD) and singular value decomposition–regularized total least squares–Prony (SVD-RTLS-Prony) algorithms is proposed. First, the energy ratio function is used for real-time monitoring of the system to identify oscillation signals. Then, to address the limitations of the VMD algorithm, the HO algorithm’s excellent optimization capabilities were utilized to improve the VMD algorithm, leading to preliminary denoising. Finally, the SVD-RTLS-improved Prony algorithm was employed to further suppress noise interference and extract oscillation characteristics, allowing for the accurate identification of SSO modes. The performance of the proposed method was evaluated using theoretical and practical models on the Matlab and PSCAD simulation platforms. The results indicate that the algorithms effectively perform denoising and accurately identify the characteristics of SSO signals, confirming its effectiveness, accuracy, superiority, and robustness against interference.

In-depth research on fault diagnosis of turbine rotor utilizing NGSABO-optimized VMD and CNN-BiLSTM

Abstract To solve the problem of difficulty in extracting and identifying fault types during turbine rotor operation, a fault diagnosis method based on improved subtraction mean optimizer (NGSABO) algorithm to optimize variational mode decomposition (VMD) and CNN-BiLSTM neural network is proposed. Firstly, three improvements are made to the subtraction average optimizer algorithm. Secondly, the optimal VMD parameter combination of NGSABO adaptive selection mode decomposition number K and penalty factor is used to decompose the rotor fault signal, and the minimum sample entropy is used as the fitness function for feature extraction. Combining convolutional neural network and bidirectional long short-term memory network to identify and classify features. Compared with other methods, this method has outstanding performance in the diagnosis of single and coupled rotor faults. The accuracy of fault diagnosis reaches 98.5714%, which has good practical application value.

Operating modal parameter identification of railway vehicle bogie based on k-value optimization variational mode decomposition and second-order blind identification method

Due to the variable operating conditions and strong background noise, the accuracy of modal parameter identification of the railway vehicle bogie is low. This paper proposes a method for identifying operational modal parameters by combining the K-value optimization variational mode decomposition (KVMD) and second-order blind identification (SOBI) method (KVMD–SOBI method). Firstly, the variational mode decomposition (VMD) algorithm is used to adaptively decompose a single-channel vibration signal into intrinsic mode function (IMF) components with different scale characteristics. The feature IMF components are selected through the K-value optimization method based on energy ratio and stability graph. Then, the SOBI algorithm is used to separate the matrix composed of the feature IMF components. And the mode shape and single-mode signal are obtained. Finally, the natural frequency and damping ratio of each order mode are extracted by the single-mode parameter recognition method. Through simulation and experimental verification, it is shown that the proposed method has good noise robustness and can effectively identify the first three modal parameters of railway vehicle bogies in variable-speed operation. At the same time, the feature IMF components extracted by KVMD algorithm eliminate the sensitivity of sensor installation positions and operating conditions to detection results. Therefore, this method is an excellent operational mode identification method based on a single-channel signal with good noise and working condition robustness.

Parametric noise reduction and construction of performance degradation indexes for low-voltage switchgear appliances

Aiming at the problem that there is a lot of noise in the feature parameter data of low-voltage switchgear, which makes it difficult to extract useful information about the feature parameters and unable to construct the performance degradation index reasonably. This paper proposes a noise reduction method through Relative Entropy (KL) optimized Variational Mode Decomposition (VMD) combined with Non-Local Mean (NLM) and a method of constructing performance degradation indexes for low-voltage switching appliances through Convolutional Autoencoder (CAE). Firstly, the voltage and current signals are collected based on the full-life test platform of low-voltage switchgear, and the subset of feature parameters is extracted. Then, the feature parameters are decomposed into different components by relative entropy optimization VMD and the noise-dominant and effective components are selected based on the correlation. Secondly, NLM denoising is performed on the noise-dominated signal, and the noise-reduced signals are obtained by signal reconstruction. Finally, the construction of performance degradation indexes for multi-type switchgear is completed based on CAE. The final results show that the two noise reduction evaluation indicators including Noise Rejection Ratio (NRR) and trendiness (T), and the three performance degradation evaluation indexes including Goodness of Fit (R), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) all show optimal results, indicating that this paper’s method can better complete the construction of noise reduction and performance degradation indicators for the feature parameters of low-voltage switchgear.

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.

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.

Wear state identification of ball screw meta action unit based on parameter optimization VMD and improved Bilstm

In this paper, a novel neural network based on parameter optimization Variational Mode Decomposition (VMD) and improved bidirectional long short-term memory (BiLSTM) is proposed. Wear state recognition method of ball screw element action unit component based on Bilstm. Firstly, Tent chaotic map and adaptive sine cosine Algorithm were used to improve the improved Northern Goshawk Optimisation Algorithm (INGO) to verify the superiority of INGO algorithm and determine the optimal parameter combination of VMD. Secondly, INGO-VMD was used to decompose the collected vibration signals and calculate the correlation of IMF components, and the multi-feature information matrix that could characterize the wear state change of the lead screw was constructed after retaining the IMF components with large correlation. Finally, the divided feature information matrix and labels were input into the Bilstm network model of Bayesian optimization (BO) for training, and the Softmax classifier was used to classify and identify the wear state category.

FMM-VMD-Transformer: A hybrid deep learning model for predicting natural gas consumption

The rapid advancement of energy digitization and intelligence has engendered an escalating demand for accurate and timely prediction of natural gas consumption across diverse temporal scales. This exigency finds solutions in the swift development of intelligent algorithms. Most of the current short-term prediction algorithms are season-dependent and can achieve high prediction accuracy in temperate regions. However, in tropical and subtropical regions where seasonal patterns are not obvious, the prediction accuracy of related studies tends to decrease significantly. To address this challenge, we propose a natural gas hybrid prediction model that is applicable to temperate, subtropical, and tropical regions. This model integrates mode decomposition, feature selection and prediction. Specifically, the Feature Matching Maximization (FMM) optimization algorithm and Variational Mode Decomposition (VMD) are proposed to decompose the natural gas consumption into three sub-series: trend component, feature component, and residue component, thereby enhancing the feature representation capability for complex nonlinear characteristics. Furthermore, the Transformer model based on multi-head attention is enhanced to predict the temporal data of each sub-series. This augmentation capitalizes on the Transformer model’s robust long-term dependence modeling capability, enabling it to extract valuable information from historical data. The hybrid model is experimentally validated on the natural gas consumption dataset of Xiamen, a subtropical region. Compared to other decomposition-based prediction algorithms, our findings possess superior feature extraction capabilities and higher prediction accuracy, especially in the case of nonlinear and non-stationary data. Finally, the robustness of the model is validated using datasets from multiple cities and different time spans.

A novel underwater weak signal detection method based on parameter optimized VMD and 3D chaotic system

Based on chaos theory, combined with improved variational mode decomposition, a novel method for underwater weak signal detection and frequency extraction is proposed. The aim of this research is to address the challenge of detecting underwater signals and extracting their frequencies under ultra-low Signal-to-Noise Ratio (SNR). A novel three-dimensional (3D) chaotic system with infinitely shrinking attractors is proposed, which incorporates a cosine function to achieve chaos control and enhancement. The nonlinear characteristics of the system, such as Lyapunov exponent and bifurcation, are analyzed in detail. Then, we design a frequency array and perform scale transformation on the chaotic system to construct a detection model that covering all frequencies. The model can transition from critical chaos to large period or intermittent chaos in the presence of external periodic signals by adjusting the parameters of the cosine function. Considering the relationship between the generation of intermittent chaos and the frequency of target signal, a frequency extraction algorithm based on chaos sparrow search algorithm optimization variational mode decomposition (CSSA-VMD) and Hilbert transform is designed. The algorithm can estimate the real frequency of underwater signals by performing noise reduction and envelope analysis on intermittent chaotic signals. The experimental results demonstrate that the proposed system can detect weak signals in complex marine backgrounds and extract their frequency features, with a detection SNR of -48 dB and a frequency error of less than 0.01%. Importantly, the circuit of the detection system has been implemented, verifying its feasibility for detecting and tracking underwater signals.

Strategy of Flywheel–Battery Hybrid Energy Storage Based on Optimized Variational Mode Decomposition for Wind Power Suppression

The fluctuation and intermittency of wind power generation seriously affect the stability and security of power grids. Aiming at smoothing wind power fluctuations, this paper proposes a flywheel–battery hybrid energy storage system (HESS) based on optimal variational mode decomposition (VMD). Firstly, the grid-connected power and charging–discharging power of the HESS are determined based on the sliding average algorithm. Secondly, the VMD algorithm, optimized using long short-term memory (LSTM), is used to decompose the hybrid energy storage power (HESP) into a series of sub-modes with frequencies from low to high. Then, the state of charge of the battery energy storage system and the speed of the flywheel energy storage system are monitored in real time, and the primary power of the HESS is modified according to the rules formulated by fuzzy control. Finally, through a simulation example, it is concluded that the method meets the requirements of smoothing wind power fluctuations and gives full play to the characteristics of energy storage battery and flywheel energy storage to ensure the stable operation of the energy storage system. The method presented in this paper can provide a reference for HESP configuration and control operation strategy formulation.

Carbon trading price forecasting based on parameter optimization VMD and deep network CNN–LSTM model

To meet carbon peak and neutrality targets, accurate carbon trading price forecasting is very important for enterprises making emission reduction decisions. By fusing convolutional neural network (CNN) and long short-term memory network (LSTM), the CNN–LSTM model is constructed. After variational mode decomposition (VMD), several intrinsic mode functions (IMFs) components are obtained and input into the CNN–LSTM model, thus constructing the combined sooty tern optimization algorithm (STOA)–VMD–CNN–LSTM forecasting model. To test this model, the carbon trading prices of the carbon emission trading markets of Hubei, Guangdong and Shenzhen were forecast. The prediction performance of the STOA–VMD–CNN–LSTM model is compared with ARIMA, BP, CNN and LSTM benchmark models and models combining different decomposition technologies. The international carbon trading price (EUR and CER) is used for prediction. Compared with other methods, the developed model makes fewer errors and achieves superior performance. Several important implications are provided for investors and risk managers involved in carbon financial products.

Short-term power grid load forecasting based on optimized VMD and GA-BP

Abstract The present article proposes an enhanced hybrid neural network model that combines variational mode decomposition (VMD) and genetic algorithm-backpropagation (GA-BP) to tackle the accurate prediction task of nonstationary and nonlinear power demand data. In comparison to existing methods, this study employs the North Gallic Hawk Optimization (NGO) algorithm to preliminarily ensure the optimization of the number of VMD modes, K and the penalty factor, α. Furthermore, it utilizes the envelope entropy criterion to determine the minimum optimal VMD components for predicting low-order spectral features vectors. Building upon this, the GA-BP optimization method establishes prediction models for the NGO-VMD model’s individual components. When compared with traditional methods, the GA-BP model exhibits significant advantages in terms of rapid convergence, fewer iterations and high prediction accuracy. Empirical results demonstrate that this approach holds promising prospects for practical application in power demand prediction. In comparison to traditional model predictive performance, the root mean square error is reduced by 60.36% and the mean absolute percentage error by 44.34%, providing robust support to enhance prediction accuracy and promote sustainable development of power systems.

NOx formation model for utility boilers using robust two-step steady-state detection and multimodal residual convolutional auto-encoder

BackgroundTo achieve carbon neutrality, thermal power plants will take on greater peak-shaving responsibilities, resulting in utility boilers running at more frequently-changing states. This variation inevitably contributes to dirtier measurement data, and the data will follow new distributions that represent asynchronous operational characteristics. MethodTo predict the NOx formation concentration in this new context, a novel modelling framework is proposed. First, a two-step steady-state detection algorithm, including a basic and a precise identification procedure, is proposed to select steady-state samples from operational data. This algorithm also combines with a bayesian optimization–variational mode decomposition (BO–VMD) approach to enhance its robustness by eliminating high-frequency noise, and with an empirical cumulative distribution based outlier detection (ECOD) to remove outliers. Therefore, a high-quality steady-state dataset is acquired. Based on these data, a multimodal residual convolutional auto-encoder is developed to extract the latent variables that vary with the operation modes. These variables are then used to construct the multimodal NOx prediction model. Significant findingsThe findings on a 660 MW utility boiler reveal that, the proposed modelling framework has a lower misdiagnosis rate in steady-state identification compared to the one-step detection technique, and achieves higher fitting and generalization accuracy than the global modelling method.

Chaotic time series wind power interval prediction based on quadratic decomposition and intelligent optimization algorithm

Wind power prediction plays a critical role in the economic deployment of power systems including wind farm. To improve the prediction accuracy of wind power, a chaotic wind power interval prediction method, which relies on quadratic decomposition and improved state transition algorithm, is proposed in this study. Firstly, the data are decomposed twice through the optimal variational mode decomposition, improved complete ensemble empirical mode decomposition and permutation entropy (OVMD-ICEEMDAN-PE) in combination, so as to deal with the volatility and complexity of wind power time series. Then, the decomposed data are used to build the prediction model for each component. In addition, the improved state transition algorithm is introduced to optimize the hyperparameters of the convolutional neural network and bidirectional long short-term memory (CNN-BiLSTM), time convolutional network (TCN) and gated recurrent unit (GRU) of the prediction models. With the optimal hyperparameters solved for each model, the linear weights are combined to achieve accurate prediction. Finally, through the combined prediction model, interval prediction is achieved. The results show that the proposed method outperforms other models in the accuracy of prediction.

Research on vessel noise signal compression sensing algorithm based on Particle Swarm Optimization and Variational Mode Decomposition

Due to the complexity of marine environmental factors and strong background noise, the collected vessel signal becomes intricate and challenging to transmit and reconstruct using conventional parameter estimation methods. Additionally, identifying vessel targets becomes difficult. In order to detect the vessel target and obtain the corresponding orientation information, it is necessary to eliminate the interference of noise as much as possible and reconstruct the original signal more accurately. In this work, we propose an optimized signal denoising method PSO-VMD (Particle Swarm Optimization–Variational Mode Decomposition). By conducting simulations using experimental data and evaluating the model, we demonstrate the superior denoising capabilities of this method. Then we apply this method to denoise the real vessel sound signal and then compress and reconstruct the signal using compressed sensing. The experimental results show that the signal processed by PSO + VMD method has the maximum SNR and the minimum RMSE and MAE. What’s more, the selected suitable denoising method can effectively suppress the environmental noise in the signal and improve the reconstruction efficiency of compressed sensing.

Multi-Scale Response Analysis and Displacement Prediction of Landslides Using Deep Learning with JTFA: A Case Study in the Three Gorges Reservoir, China

Reservoir water and rainfall, leading to fluctuations groundwater levels, are the main triggering factors that induce landslides in the Three Gorges Reservoir area. This study investigates the response mechanism of landslide deformation under reservoir water and rainfall variations through long-time on-site observations. To address the non-stationary characteristics of the time-series records, joint time-frequency analysis (JTFA) is first introduced into our landslide prediction model. This model employs optimal variational mode decomposition (VMD) to obtain specific signal components with clear physical meaning, such as trend component and periodic components. Then, multi-scale response analysis between the displacement and external factors three wavelet methods was conducted. The analysis results show a 1 year primary cycle of the time series associated with the landslide evolution. The reservoir water level and rainfall show anti-phase fluctuations. The periodic displacement correlates significantly with rainfall, lagging by about two months. The reservoir water is anti-phase with the landslide displacement, preceding it by approximately three months (−51 ± 8° phase difference). For landslide displacement prediction, the gated recurrent units (GRU) neural network model is integrated into the deep learning forecasting architecture. The model takes into account the correlation and hysteresis effect of input variables. Through six experiments, we investigate the effect of data volume on model predictions to determine the optimal model. The results demonstrate that our proposed model ensures high performance in landslide prediction. Moreover, a comparison with six other intelligent algorithms shows the advantages of our model in terms of time-effectiveness and long-sequence forecasting.

Coal-rock drilling states recognition of drilling robot for rockburst prevention based on multi-sensor information fusion

Accurate recognition of coal-rock drilling sates is a prerequisite for achieving intelligent drilling pressure relief. In this paper, a novel coal-rock drilling states recognition method of drilling robot for rockburst prevention is proposed. Firstly, different coal-rock drilling signals are collected and processed by using improved antlion optimization (ALO) algorithm and variational mode decomposition (VMD). Meanwhile, the elite opposition-based learning (EOL) strategy is used to improve the global search ability and optimization performance of ALO, and the EOL-ALO is developed and employed to automatically search the optimal key parameters of VMD. Subsequently, the root mean square of frequency and kurtosis are used to extract the feature information from the decomposed signals and the singular value decomposition method is employed to reduce the dimensionality of high-dimensional feature vectors. Furthermore, an improved D-S evidence theory is developed to fuse the recognition results of support vector machine through a single sensor information and the fusion recognition framework of coal-rock drilling states is designed. Finally, a coal-rock drilling experimental platform is established and some experimental analysis is carried out. The experimental results indicate the feasibility and superiority of proposed coal-rock drilling states recognition method.

Short-Term Multi-Step Wind Direction Prediction Based on OVMD Quadratic Decomposition and LSTM

Accurate and reliable wind direction prediction is important not only for enhancing the efficiency of wind power conversion and ensuring safe operation, but also for promoting sustainable development. Wind direction forecasting is a challenging task due to the random, intermittent and unstable nature of wind direction. This paper proposes a short-term wind direction prediction model based on quadratic decomposition and long short-term memory (LSTM) to improve the accuracy and efficiency of wind direction prediction. Firstly, the model adopts a seasonal-trend decomposition procedure based on the loess (STL) method to divide the wind direction series into three subsequences: trend, seasonality and the remainder, which reduces the impact of the original sequence’s complexity and non-stationarity on the prediction performance. Then, the remainder subsequence is decomposed by the optimal variational mode decomposition (OVMD) method to further explore the potential characteristics of the wind direction sequence. Next, all the subsequences are separately input into the LSTM model, and the prediction results of each subsequence from the model are superimposed to obtain the predicted value. The practical wind direction data from a wind farm were used to evaluate the model. The experimental results indicate that the proposed model has superior performance in the accuracy and stability of wind direction prediction, which also provides support for the efficient operation of wind turbines. By developing advanced wind prediction technologies and methods, we can not only enhance the efficiency of wind power conversion, but also ensure a sustainable and reliable supply of renewable energy.

Hybrid intelligent deep learning model for solar radiation forecasting using optimal variational mode decomposition and evolutionary deep belief network - Online sequential extreme learning machine

Accurate prediction of solar radiation is of great significance to improve the utilization of solar energy for photovoltaic power generation on the roofs of urban buildings. Therefore, a hybrid model, namely the OVMD-PACF-ISSA-DBN-OSELM model, is being proposed in this study for solar radiation prediction. Firstly, the data is decomposed by optimal variational mode decomposition (OVMD) technology. Secondly, the partial autocorrelation function (PACF) technology selected features for components decomposed by OVMD technology. Thirdly, a deep belief network-online sequential extreme learning machine (DBN-OSELM) prediction model is constructed, and sparrow search algorithm (SSA) is utilized to optimize the model hyperparameters. Aiming at the shortcomings of SSA algorithm, Tent map and differential evolution strategy are introduced to improve the SSA algorithm. Finally, the model is used to predict each component, and the prediction results of each component are summarized to obtain the prediction results of solar radiation. To verify that the proposed method can obtain accurate prediction results, experiments are conducted using solar radiation data for January, May and October 2022, and compared with other models. Taking January as an example, compared with shallow model BP, the RMSE, MAE and R of the proposed model are increased by 66.83%, 58.65% and 5.33%, respectively. Moreover, the experiments of the proposed model in other months have excellent results. The current findings demonstrate that the suggested model is a strong contender in the arena of solar radiation prediction, and can consequently provide valuable support in enhancing the efficiency of photovoltaic equipment installed on urban building roofs.

A novel rolling bearing fault diagnosis method based on parameter optimization variational mode decomposition with feature weighted reconstruction and multi-target attention convolutional neural networks under small samples.

To enhance the precision of rolling bearing fault diagnosis, an intelligent hybrid approach is proposed in this paper for signal processing and fault diagnosis in small samples. This approach is based on advanced techniques, combining parameter optimization variational mode decomposition weighted by multiscale permutation entropy (MPE) with maximal information coefficient and multi-target attention convolutional neural networks (MTACNN). First, an improved variational mode decomposition (VMD) is developed to denoise the raw signal. The whale optimization algorithm was used to optimize the penalty factor and mode component number in the VMD algorithm to obtain several intrinsic mode functions (IMFs). Second, separate MPE calculations are performed for both the raw signal and each of the IMF components obtained from the VMD decomposition; the results are used to calculate the maximum information coefficient (MIC). Subsequently, each MIC is normalized and converted to a weight coefficient for signal reconstruction. Ultimately, the reconstructed signals serve as input to the MTACNN for diagnosing rolling bearing faults. Results demonstrate that the signal processing approach exhibits superior noise reduction capability through simple processing. Furthermore, compared to several similar approaches, The method proposed for fault diagnosis achieves superior performance levels in the fault pattern recognition target and the fault severity recognition target.