Variational Mode Decomposition Research Articles

Rolling bearing fault diagnosis based on acoustic-vibration data fusion and mode decomposition combined with the crested porcupine optimization algorithm

Variational Mode Decomposition (VMD) is extensively utilized in the domain of rotating machinery fault diagnosis. Nevertheless, the reliance on empirical parameter tuning and the limitations inherent in traditional single-signal (either vibration signals or acoustic signals) fault diagnosis methods present substantial challenges. These include incomplete information and high sensitivity to noise. To address these shortcomings, a new method is introduced that integrates multi-modal sensor data and implements an adaptive VMD approach, enhanced through the Crested Porcupine Optimization Algorithm (CPO) to automatically optimize the key parameter. Then, uses optimized VMD to decompose the time series into intrinsic mode functions of different frequencies to capture the multi-scale characteristics of data. Finally, the decomposed acoustic-vibro signal components are fed into the CNN-BiGRU-AT network, which learns the spatio-temporal dependencies to enhance the accuracy of fault classification. The experimental results conducted across diverse high-noise environments demonstrate that this method’s superior noise robustness compared to single-modality sensor approaches， highlighting the method's potential for machinery fault detection in noisy conditions.

Diagnosis of faults using a new VMD-WMRA approach, optimized by a new criterion: Industrial application

This paper proposes a new criterion for selecting the optimum number of Intrinsic Mode Functions (IMFs) from vibration signals measured on rotating machines. The criterion is based on calculating the variation of normalized Shannon entropy ([Formula: see text]) between two successive IMFs, enabling the optimization of the number of processed IMFs. The method combines Variational Mode Decomposition (VMD) with Wavelet Multi-Resolution Analysis (WMRA) using the newly introduced criterion. The key steps involve determining the optimal number of IMFs, decomposing the vibration signals using VMD, and applying WMRA to the selected IMFs. Numerical simulations and experimental results demonstrate its effectiveness in identifying various faults, including gear defects, shaft misalignment, insufficient backlash, and belt defects. These latter flaws are the primary cause of the elevated noise levels in the measured signals. Finally, to validate our approach in an industrial setting, we diagnosed a turbofan, which revealed the presence of several typical faults for this type of installation. The proposed approach addresses a critical industry need by increasing fault diagnosis accuracy in noisy environments. Its practical impact stems from its ability to improve early fault detection, which is critical for predictive maintenance strategies aimed at reducing equipment downtime and extending its lifespan.

Probabilistic oil price forecasting with a variational mode decomposition-gated recurrent unit model incorporating pinball loss

Prediction methods have garnered significant attention in intelligent decision-making. Most existing approaches to predicting crude oil prices prioritize accuracy and stability while providing precise prediction intervals (PIs) that can offer valuable insights. Thus far, we introduce a novel hybrid model to forecast future crude oil prices. Our approach leverages the variational mode decomposition (VMD) to simplify the complexity of the original time series, yielding a set of subseries. These subseries are then modeled using a deep neural network architecture called a gated recurrent unit (GRU). To address the prediction uncertainty, we employed the pinball loss function rather than the mean square error (MSE) to guide the proposed VMD-GRU. This adaptation extends the traditional GRU-based point forecasting to probabilistic forecasting by estimating quantiles. We evaluated our proposed model on a well-established crude oil price series by conducting both single- and multi-step-ahead forecasting analyses. Our findings underscore the efficacy of the combined model, demonstrating its superior predictive performance compared to benchmark models.

Hybrid deep learning model with VMD-BiLSTM-GRU networks for short-term traffic flow prediction

Accelerating urbanization and the rapid development of intelligent transportation systems have rendered short-term traffic flow prediction an important research field. Accurate prediction of traffic flow is beneficial for the optimization of traffic planning, improvement of road utilization, reduction of traffic congestion, and reduction in the incidence of traffic accidents. However, data pertaining to traffic flow are typically influenced by a multitude of factors, resulting in data that exhibit a considerable degree of nonlinearity and complexity. To address the issue of noise in raw traffic flow data, this study proposes a hybrid model that combines variational modal decomposition (VMD), a bidirectional long short-term memory network (BiLSTM), and a gated recurrent unit (GRU) for short-term traffic flow prediction. To validate the effectiveness of the model, an experimental validation was conducted based on traffic flow data from UK highways, and the performance of the model was compared with common benchmark models. The experimental results demonstrate that the proposed method yields superior prediction results in terms of mean absolute error, coefficient of determination, and root-mean-square error compared to existing prediction techniques, thereby substantiating its efficacy in short-term traffic flow prediction.

Internal defect detection model based on laser ultrasonic signal decomposition and deep learning

It is essential to accurately detect the internal defects of metal equipment. The accuracy of traditional detection methods is affected by noise. This paper proposes an innovative genetic algorithm-weighted permutation entropy (GA-WPE) optimized Variational mode Decomposition (VMD), continuous wavelet Transform (CWT) and deep learning fusion model, which aims to achieve efficient automatic defect detection. Firstly, the laser ultrasonic experimental system was built, and the hole defects with different diameters and depths were prepared. The GA-WPE-VMD was used to decompose and reconstruct the ultrasound signal, and CWT converted the reconstructed signal into a time–frequency scalogram. Three deep learning models were used for defect detection. ViT model achieved 99.88%, 97.01%, and 91.7% accuracy on the training, validation, and test set, respectively, significantly better than DenseNet121 and ResNet50. The AUC of ViT on the test set was close to 100%. The results verify the feasibility and effectiveness of the proposed method.

The risk spillover between geopolitical risk and China’s 5G, semiconductor and rare earth industries

Spillover effect refers to the phenomenon that when an economic entity, industry or market encounters a change or shock, its impact is transmitted to other entities, industries or markets. In recent years, 5G, semiconductors and rare earths have successively become geopolitical battlegrounds. In this paper, sparrow search algorithm was used to optimize the parameters of variational mode decomposition (VMD), then use the optimized VMD to decompose the geopolitical risk (GPR), 5G, semiconductor and rare earth time series data, and exploit fuzzy c-means clustering algorithm to obtain low-frequency and high-frequency time series. Finally we investigates the connectedness between GPR and China's 5G, semiconductor, and rare earth industries based on TVP-VAR model in different cycles, as well as between these industries. The findings reveal that there exists risk spillover between GPR and the three industries, which is significantly enhanced under the impact of geopolitical events. In addition, there is heterogeneity in the risk spillover between GPR and these three industries in different cycles. Notably, in the short term, the GPR is the main source of risk, and in the long term, the semiconductor industry has the great impact on GPR, 5G and rare earth industries, indicating that the semiconductor industry has very important geopolitical significance.

A day-ahead wind speed correction method: Enhancing wind speed forecasting accuracy using a strategy combining dynamic feature weighting with multi-source information and dynamic matching with improved similarity function

Forecasting error of day-ahead wind speed (WS) seriously affects wind power integration and power system security and stability. In this regard, this paper fully considers the spatiotemporal correlation of wind farms (WFs) in different geographical locations, and proposes a day-ahead WS combined correction method that integrates multi-source station dynamic information weighting. Different from the previous WS correction methods, this paper fully considers the dynamic correlation of WS between the WFs, introduces an improved weighted similarity function to screen and dynamically weight the information of WFs with dynamic correlation, and introduces the dynamic weighting feature into the WS correction process. A combined decomposition mechanism is proposed, which combines sequential variational mode decomposition (SVMD) and feature mode decomposition (FMD) models to extract the most relevant trend components and non-stationary components of forecasted and measured WS. A combined correction model is introduced, and a combined architecture of Non-stationary Transformer combined with bidirectional long short-term memory network (Ns-Transformer-BILSTM) is used to correct the stationary WS component. A dynamic matching mechanism of fluctuation components considering improved similarity is proposed for the correction of non-stationary components. The proposed method is applied to several regional WFs in China. The experimental results show that the average correction of NRMSE, NMAE and R can reach 2.4 % ∼ 3.7 %, 2.0 % ∼ 3.0 % and 3.3 % ∼ 9.7 %, respectively. The NRMSE and NMAE corresponding to the corrected WS of certain individual WFs can be reduced by 10 % and 9 %, respectively, and R can be increased by 33 %.

Comparative analysis of profits from Bitcoin and its derivatives using artificial intelligence for hedge

Because there is a discrepancy between how individual investors and investment institutions choose Bitcoin and its new derivatives and Exchange-Traded Funds (ETFs), this paper used Bitcoin and ProShares Bitcoin Strategy ETF (BITO) data and a mixed variational mode decomposition and bidirectional gated cycle unit model to examine the interconnections between Bitcoin and its new derivative ETFs, from which actionable recommendations were developed. As well as conducting financial simulation trading using Bitcoin and BITO, the study expanded to examine other major ETFs. It was found that: (1) Bitcoin data could be employed to forecast and describe BITO; (2) under T+0 trading, Bitcoin was more volatile, profitable, and risky than BITO; and (3) under T+1 trading, Bitcoin was less volatile, profitable, and risky than BITO; however, the T+1 trading was found to have higher volatility, profits, and risk than T+0 trading. This study, therefore, builds a bridge from theory to practice for the prediction and description of new ETFs. Different from previous studies, this study explored the relationships between Bitcoin and BITO using Artificial Intelligence and quantitative financial simulations, which extends the practical and theoretical understanding of the Bitcoin market.

Development of a Hybrid AI Model for Fault Prediction in Rod Pumping System for Petroleum Well Production

Rod pumping systems are widely used in oil wells. Accurate fault prediction could reduce equipment fault rate and has practical significance in improving oilfield production efficiency. This paper analyzed the production journal of rod pumping wells in block X of Xinjiang Oilfield. According to the production journal, oil well maintenance operations are primarily caused by five types of faults: scale, wax, corrosion, fatigue, and wear. These faults make up approximately 90% of all faults. 1354 oil wells in the block that experienced workover operations as a result of the aforementioned factors were chosen as the research objects for this paper. To lower the percentage of data noise, wavelet threshold denoising and variational mode decomposition were used. Based on the bidirectional long short-term memory network, an intelligent model for fault prediction was built. It was trained and verified with the help of the sparrow search algorithm. Its efficacy was demonstrated by testing various deep learning models in the same setting and with identical parameters. The results show that the prediction accuracy of the model is the highest compared with other 11 models, reaching 98.61%. It is suggested that the model using artificial intelligence can provide an accurate fault warning for the oilfield and offer guidance for the maintenance of the rod pumping system, which is meant to reduce the occurrence of production stagnation and resource waste.

Multisource Data-Driven Carbon Price Composite Forecasting Model: Based on Feature Selection and Multiscale Prediction Strategy

Accurate prediction of carbon trading prices is crucial for guiding investors to make informed decisions and assisting governments in formulating scientific carbon trading policies. This paper introduces a multisource data-driven carbon price composite forecasting model, aimed at enhancing prediction accuracy through advanced data processing and analysis methods. The model initially employs a secondary decomposition strategy, including Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variational Mode Decomposition (VMD) methods, to decompose the original data series into three sub-sequences of different frequencies. Subsequently, it utilizes the Partial Autocorrelation Function (PACF) and Random Forest algorithm for feature selection to determine the input variables for different frequency sequences and conducts in-depth analysis and selection of influencing factors, including unstructured data. Furthermore, the model employs a multiscale forecasting strategy, combining Particle Swarm Optimization (PSO) enhanced Bidirectional Long Short-Term Memory (BiLSTM) and Extreme Gradient Boosting (XGBoost) models, along with the Autoregressive Integrated Moving Average (ARIMA) method, to predict based on the characteristics of different frequency components. Finally, the forecasts are integrated using PSO-BiLSTM to form a comprehensive forecast. Notably, given the high correlation between the trend series and influencing factor variables, the model jointly predicts them. A case study based on the Guangdong carbon market in China demonstrates that the proposed composite forecasting model outperforms other benchmark models, with Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) values of 0.4009, 0.2699, and 0.5183%, respectively. This forecasting model provides an effective tool for predicting and analyzing carbon price fluctuations, offering new insights for precise carbon market price predictions.

Dynamic mode decomposition-based technique for cross-term suppression in the Wigner-Ville distribution

This paper presents a new method for time-frequency representation (TFR) using dynamic mode decomposition (DMD) and Wigner-Ville distribution (WVD), which is termed as DMD-WVD. The proposed method helps in removing cross-term in WVD-based TFR. In the suggested method, the DMD decomposes the multi-component signal into a set of modes where each mode is considered as mono-component signal. The analytic modes of these obtained mono-component signals are computed using the Hilbert transform. The WVD is computed for each analytic mode and added together to obtain cross-term free TFR based on the WVD. The effectiveness of the proposed method for TFR is evaluated using Rényi entropy (RE). Experimental results for synthetic signals namely, multi-component amplitude modulated signal, multi-component linear frequency modulated (LFM) signal, multi-component nonlinear frequency modulated (NLFM) signal, multi-component signal consisting of LFM and NLFM mono-component signal, multi-component signal consisting of sinusoidal and quadratic frequency modulated mono-component signals, and synthetic mechanical bearing fault signal and natural signals namely, electroencephalogram (EEG) and bat echolocation signals are presented in order to show the effectiveness of the proposed method for TFR. It is clear from the results that the proposed method suppresses cross-term effectively as compared to the other existing methods namely, smoothed pseudo WVD (SPWVD), empirical mode decomposition (EMD)-WVD, EMD-SPWVD, variational mode decomposition (VMD)-WVD, VMD-SPWVD, and DMD-SPWVD.

A Deep Learning PM2.5 Hybrid Prediction Model Based on Clustering–Secondary Decomposition Strategy

Accurate prediction of PM2.5 concentration is important for pollution control, public health, and ecological protection. However, due to the nonlinear nature of PM2.5 data, the accuracy of existing methods suffers and performs poorly in both short-term and long-term predictions. In this study, a deep learning hybrid prediction model based on clustering and quadratic decomposition is proposed. The model utilizes the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to decompose the PM2.5 sequences into multiple intrinsic modal function components (IMFs), and clusters and re-fuses the subsequences with similar complexity by permutation entropy (PE) and K-means clustering. For the fused high-frequency sequences, a secondary decomposition is performed using the whale optimization algorithm (WOA) optimized variational modal decomposition (VMD). Finally, the nonlinear and temporal features are captured for prediction using the long- and short-term memory neural network (LSTM). Experiments show that this proposed model exhibits good stability and generalization ability. It does not only make accurate predictions in the short term, but also captures the trends in the long-term prediction. There is a significant performance improvement over the baseline models. Further comparisons with existing models outperform the current state-of-the-art models.

A River Water Quality Prediction Method Based on Dual Signal Decomposition and Deep Learning

Traditional single prediction models struggle to address the complexity and nonlinear changes in water quality forecasting. To address this challenge, this study proposed a coupled prediction model (RF-TVSV-SCL). The model includes Random Forest (RF) feature selection, dual signal decomposition (Time-Varying Filtered Empirical Mode Decomposition, TVF-EMD, and Sparrow Search Algorithm-Optimized Variational Mode Decomposition, SSA-VMD), and a deep learning predictive model (Sparrow Search Algorithm-Convolutional Neural Network-Long Short-Term Memory, SSA-CNN-LSTM). Firstly, the RF method was used for feature selection to extract important features relevant to water quality prediction. Then, TVF-EMD was employed for preliminary decomposition of the water quality data, followed by a secondary decomposition of complex Intrinsic Mode Function (IMF) components using SSA-VMD. Finally, the SSA-CNN-LSTM model was utilized to predict the processed data. This model was evaluated for predicting total phosphorus (TP), total nitrogen (TN), ammonia nitrogen (NH3-N), dissolved oxygen (DO), permanganate index (CODMn), conductivity (EC), and turbidity (TB), across 1, 3, 5, and 7-d forecast periods. The model performed exceptionally well in short-term predictions, particularly within the 1–3 d range. For 1-, 3-, 5-, and 7-d forecasts, R2 ranged from 0.93–0.96, 0.79–0.87, 0.63–0.72, and 0.56–0.64, respectively, significantly outperforming other comparison models. The RF-TVSV-SCL model demonstrates excellent predictive capability and generalization ability, providing robust technical support for water quality forecasting and pollution prevention.

Enhanced Hessian locally linear embedding method for rolling bearing fault diagnosis based upon novel variational mode decomposition

Due to the plenty of redundant information contained in the fault feature sets of the original vibration signals of rolling bearings, the diagnostic accuracy is reduced and computational complexity is increased, making it very difficult to achieve accurate and fast fault recognition. So as to address the hard issue, this article develops an Enhanced Hessian Locally Linear Embedding (EHLLE) method for rolling bearing fault diagnosis based upon Novel Variational Mode Decomposition (NVMD). Firstly, NVMD method is utilized to denoise sample vibration signals and the sensitive modes containing main fault information are obtained. Secondly, some time-domain and frequency-domain statistical features are used to construct sample high-dimensional features, the dimensionality of which is reduced by EHLLE. Ultimately, K-Means algorithm is employed to cluster the low-dimensional features, which are utilized to train Support Vector Machine (SVM), and then the trained SVM is applied to the recognition of testing sample low-dimensional features. Two experiments of rolling bearing fault diagnosis demonstrate the effectiveness of NVMD-EHLLE method. Additionally, the superiority of the developed method is verified by comparing with other three typical methods.

Enhancing streamflow prediction in the Wujiang River basin: a two-stage decomposition approach with deep learning integration

ABSTRACT Global climate change and human activities have profoundly impacted the geological and hydrological processes in watersheds, increasing the challenges in streamflow prediction. In this study, we propose a streamflow prediction model based on deep learning and dual-mode decomposition specifically tailored for the Wujiang River basin, a significant tributary on the southern bank of the upper Yangtze River. This model effectively addresses the prediction error issue caused by high-frequency components through dual-mode decomposition of time-series data. The results demonstrate that employing the coupled complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)–variational mode decomposition (VMD)–temporal convolutional network (TCN)–long short-term memory network (LSTM) model reduces prediction errors by at least 35% compared to single decomposition models. Furthermore, compared to individual TCN or LSTM models, the TCN–LSTM coupled model exhibits greater stability and higher prediction accuracy during training, with reductions in mean absolute error and root mean square error by 43.13 and 24.57%, respectively. This model holds promising prospects for application and can provide crucial insights for water resource management.

A robust multi-model framework for groundwater level prediction: The BFSA-MVMD-GRU-RVM model

Groundwater level prediction is critical for environmental protection and agricultural planning. Accurate predictions help manage risks associated with excessive groundwater extraction and land subsidence. This study introduces a novel model combining multivariate variational mode decomposition (MVMD), gated recurrent unit (GRU), and relevance vector machine (RVM), along with the Boruta feature selection algorithm (BFSA), for precise groundwater level forecasting. The model operates in several stages. First, BFSA selects the most informative features as input data. Next, the MVMD method decomposes the time series of these features. The GRU model then extracts crucial information from these decompositions. Finally, the extracted data is fed into the RVM model to predict groundwater levels one month ahead in Iran's Bastam Plain. To assess the model's accuracy, multiple error indices were employed. The MVMD-GRU-RVM model outperformed other models, improving the testing Nash–Sutcliffe Efficiency and mean absolute error by 24–31 % and 6–61 %, respectively. Additionally, it enhanced R2 values of the MVMD-CNN, MVMD-RNN, MVMD-MLP, and MVMD-RBFNN models by 1.0–3.33 %. These results demonstrate that the MVMD-GRU-RVM model significantly improves groundwater level prediction accuracy. The key points of the paper are the successful effectiveness of MVMD in processing non-stationary time series and improving the predictive performance of the models, as well as the high ability of the GRU model in data feature extraction. The study also shows that the novel model can provide outputs with lower uncertainty.

A New Algorithm for Predicting Dam Deformation Using Grey Wolf-Optimized Variational Mode Long Short-Term Neural Network

To solve the problems of difficult-to-model parameter selections, useful-signal extraction and improper-signal decomposition in nonlinear, non-stationary dam displacement time series prediction methods, we propose a new predictive model for grey wolf optimization and variational mode decomposition and long short-term memory (GVLSTM). Firstly, we used the grey wolf optimization (GWO) algorithm to optimize the parameters of variable mode decomposition (VMD), obtaining the optimal parameter combination. Secondly, we used multiscale permutation entropy (MPE) as a standard to select signal screening, determining and recon-structing the effective modal components. Finally, the long short-term memory neural network (LSTM) was used to learn the dam deformation characteristics. The result shows that the GVLSTM model can effectively reduce the estimation deviation of the prediction model. Compared with VMDGRU and VMDANN, the average RMSE and MAE value of each station is increased by 19.11%~28.58% and 27.66%~29.63%, respectively. We used determination (R2) coefficient to judge the performance of the prediction model, and the value of R2 was 0.95~0.97, indicating that our method has good performance in predicting dam deformation. The proposed method has outstanding advantages of high accuracy, reliability, and stability for dam deformation prediction.

Identification of ocular artifact in EEG signals using VMD and Hurst exponent.

Electroencephalographic (EEG) readings are usually infected with unavoidable artifacts, especially physiological ones. One such physiological artifact is the ocular artifacts (OAs) that are generally related to eyes and are characterized by high magnitude and a specific spike pattern in the prefrontal region of the brain. During the long-duration EEG acquisition, the retrieval of important information becomes quite complicated in prefrontal regions as ocular artifacts dominate the EEG recorded, making it difficult to discern underlying brain activity. With the progress and development in signal processing techniques, artifact handling has become a progressive field of investigation. This paper presents a framework for the detection and correction of ocular artifacts. This study emphasizes improving the quality and reducing the time complexity by using higher-order statistics (HOS) for artifact identification and variational mode decomposition (VMD) for OA correction. An overall SNR of 14 dB, MAE of 0.09, and PSNR of 33.59 dB has been attained by the proposed framework. It was observed that the proposed HOS-VMD surpassed the state-of-the-art mode decomposition techniques.

Short-Term Power Load Forecasting Method Based on Improved Sparrow Search Algorithm, Variational Mode Decomposition, and Bidirectional Long Short-Term Memory Neural Network

Short-Term Power Load Forecasting Method Based on Improved Sparrow Search Algorithm, Variational Mode Decomposition, and Bidirectional Long Short-Term Memory Neural Network

Heart Rate Estimation Considering Reconstructed Signal Features Based on Variational Mode Decomposition via Multiple-Input Multiple-Output Frequency Modulated Continuous Wave Radar.

Accurate heart rate estimation using Doppler radar and Frequency Modulated Continuous Wave (FMCW) radar is highly valued for privacy protection and the ability to measure through clothing. Conventional methods struggle to isolate the heartbeat from respiration and body motion. This paper introduces a novel heart rate estimation method using Variational Mode Decomposition (VMD) via Multiple-Input Multiple-Output (MIMO) FMCW radar. The proposed method first estimates human positions within the radar's coverage, reducing noise by focusing on signals from these positions. The signal is then decomposed into multiple Intrinsic Mode Function (IMF) signals using VMD, and the heartbeat-specific IMF is extracted based on its center frequency. The heart rate signal is reconstructed using weighted addition of IMF signals for each radar cell, with cells defined by specific angles and distances within the coverage area. Peak detection is used to estimate heart rate from these reconstructed signals. To ensure accuracy, the method selects the heart rate estimate with the highest energy and periodicity for the first four time windows. From the fifth time window onward, it selects the estimate closest to the average of the previous four, minimizing extraneous variations. Experiments conducted with one and two subjects showed promising results. In case 1, with one subject, the method achieved a Mean Absolute Error (MAE) of 2.54 BPM and an exclusion rate of 0.94% using MIMO FMCW radar, compared to 4.72% with Doppler radar. In case 2, with two subjects, the method achieved an MAE of 2.28 BPM, confirming accurate simultaneous heart rate estimation.