Improved Variational Mode Decomposition Research Articles

A Novel Improved Variational Mode Decomposition-Temporal Convolutional Network-Gated Recurrent Unit with Multi-Head Attention Mechanism for Enhanced Photovoltaic Power Forecasting

Photovoltaic (PV) power forecasting plays a crucial role in optimizing renewable energy integration into the grid, necessitating accurate predictions to mitigate the inherent variability of solar energy generation. We propose a novel forecasting model that combines improved variational mode decomposition (IVMD) with the temporal convolutional network-gated recurrent unit (TCN-GRU) architecture, enriched with a multi-head attention mechanism. By focusing on four key environmental factors influencing PV output, the proposed IVMD-TCN-GRU framework targets a significant research gap in renewable energy forecasting methodologies. Initially, leveraging the sparrow search algorithm (SSA), we optimize the parameters of VMD, including the mode component K-value and penalty factor, based on the minimum envelope entropy principle. The optimized VMD then decomposes PV power, while the TCN-GRU model harnesses TCN’s proficiency in learning local temporal features and GRU’s capability in rapidly modeling sequence data, while leveraging multi-head attention to better utilize the global correlation information within sequence data. Through this design, the model adeptly captures the correlations within time series data, demonstrating superior performance in prediction tasks. Subsequently, the SSA is employed to optimize GRU parameters, and the decomposed PV power mode components and environmental feature attributes are inputted into the TCN-GRU neural network. This facilitates dynamic temporal modeling of multivariate feature sequences. Finally, the predicted values of each component are summed to realize PV power forecasting. Validation using real data from a PV station corroborates that the novel model demonstrates a substantial reduction in RMSE and MAE of up to 55.1% and 54.5%, respectively, particularly evident in instances of pronounced photovoltaic power fluctuations during inclement weather conditions. The proposed method exhibits marked improvements in accuracy compared to traditional PV power prediction methods, underscoring its significance in enhancing forecasting precision and ensuring the secure scheduling and stable operation of power systems.

Remaining useful life prediction method of lithium-ion battery Based on KPCA-IVMD-SE-DNN

In this paper, aiming at the problems of feature processing and capacity regeneration in the prediction of remaining useful life (RUL) of lithium-ion batteries, an RUL prediction method based on kernel principal component analysis (KPCA), improved variational mode decomposition (IVMD), sample entropy (SE), and deep neural network (DNN) are proposed. Firstly, six health indicators (HI) are extracted by analyzing the character of batteries charging and discharging process, and their correlation with capacity is calculated. Secondly, the KPCA is used to denoise and simplify the dimension of the HI set and ensure that they fully contain the degradation information. Thirdly, the battery capacity is decomposed into trend and interference components by using the improved VMD of the central frequency method (CFM), and the reconstruction is carried out according to the SE of each component to increase the efficiency and accuracy of prediction. Finally, the prediction model is constructed based on DNN. The experimental analysis of NASA battery data sets shows that the proposed method has the best prediction accuracy, efficiency, and robustness than DNN, KPCA-DNN, KPCA-EMD-DNN, KPCA-VMD-SE-DNN, and so on.

Laser ultrasonic spatially resolved acoustic spectroscopy for grain size study based on Improved Variational Mode Decomposition (IVMD)

Laser Ultrasonic Spatially Resolved Acoustic Spectroscopy (SRAS) is a technique used for detecting the grain size of metal surfaces. It involves exciting Surface Acoustic Waves (SAW) using a grated light source and employs optical deflection techniques to detect ultrasound. The differences in sound velocity between different grains are utilized for grain size characterization. However, this technique is susceptible to the influence of sample surface roughness, resulting in issues like low signal-to-noise ratio and waveform distortion. To address these challenges, a study was conducted on grain size characterization using Laser Ultrasonic SRAS based on Improved Variational Mode Decomposition (IVMD). This involved optimizing Variational Mode Decomposition (VMD) by introducing Permutation Entropy (PE), Weighted Spectral Kurtosis (WSK), and Dynamic Time Warping (DTW). Adaptive decomposition and selection of simulated surface wave signals were employed to achieve signal recovery. A comparison with Empirical Mode Decomposition (EMD) demonstrated that the proposed algorithm had higher noise robustness. The Laser Ultrasonic SRAS detection system was used to characterize the grain size of Ti-6Al-4V casting alloys, and the data were processed using the proposed algorithm. The results were consistent with optical microscopy images, further confirming the reliability and effectiveness of the improved algorithm. The research findings indicate that Laser Ultrasonic Spatially Resolved Acoustic Spectroscopy based on IVMD can effectively reduce the impact of noise on detection signals, thereby enhancing the detectability of grain size measurement.

A wind power forecasting model based on data decomposition and cross-attention mechanism with cosine similarity

In the context of societal advancement, escalating energy demands underscore the critical significance of exploring renewable resources. The accurate prediction of wind power is crucial for maximizing the utilization of wind energy and ensuring the smooth operation of wind farms. Currently, the majority of models are built upon architectures such as Transformer and Long-Short Term Memory (LSTM). However, Transformer-type models are not well-suited for time series forecasting, and LSTM often focuses on historical sequence information, exhibiting limited capability in capturing the relevant information between weather factors and power. Recognizing this inadequacy, this study proposes a novel model—a linear network architecture featuring a cosine-related cross-attention mechanism. The signal decomposition is carried out utilizing variational mode decomposition, with the determination of the optimal decomposition count guided by sample entropy analysis, named Improved Variational Mode Decomposition (IVMD). Subsequently, the conventional self-attention mechanism is replaced with a cross-attention mechanism. Contemporary mainstream models are primarily based on improved versions of core algorithms such as LSTM, Transformer, and Extreme Learning Machines. Experimental results show significant performance enhancements compared to these models across different timescales. In short-term, medium-term, and long-term forecasts, accuracy improves by more than 40 %, 20 %, and 5 %, respectively.

A design of new wind power forecasting approach based on IVMD-WSA-IC-LSTM model

The wind power forecasting (WPF) technology can reduce the adverse impact of wind power grid connection. Based on the characteristics of wind power data, an algorithm based on improved variational mode decomposition (IVMD) and long short-term memory (LSTM) Network is proposed to predict the wind power, and hyper parameter optimization search of LSTM using Whale Swarm Algorithm with Iterative Counter (WSA-IC). Firstly, through correlation analysis, the characteristics of 10 different wind power data are screened, and two kinds of data with large correlation with wind power are determined as input of the mode. Secondly, IVMD is used to calculate the maximum envelope kurtosis, determine the best decomposition parameters of the variational mode decomposition (VMD), and the original wind power and wind speed sequences are decomposed to obtain the IMF with different time scales. Finally, to address the problems of difficult optimization of hyper parameter and difficulty in obtaining optimal solutions for LSTM neural network modes, the WSA-IC algorithm is proposed to optimize its key hyper parameter, and the IVMD-WSA-IC-LSTM forecasting mode is established to obtain the short-term forecasting results of wind power. The algorithm is tested with the data of China Longyuan Power Group Corporation Limited. Compared with other common forecasting approaches using same data, the mean absolute error (MAE) of the forecasting approach is reduced to 0.007859, the mean square error (MSE) is reduced to 0.00011, and the determination coefficient is improved to 0.998828, which has higher forecasting accuracy.

Data-driven structural dynamic characteristics investigation by combining RDT and IVMD method

Data-driven structural monitoring results are often mixed with noise, resulting in the inability to identify the dynamic characteristics. In order to develop an efficient approach to correctly estimate the dynamic modal parameters of structures, a method combining random decrement technology (RDT) and improved variational mode decomposition (IVMD) was proposed. The approach focuses on obtaining the free decay response (FDR) with noise directly by RDT from the original monitoring signal rather than pre-denoising for the raw signal and then derives the noiseless FDR using IVMD to get the dynamic parameters with fewer data. First, the steps of the IVMD principle were established based on traditional VMD. Next, the performance of IVMD was verified. The simulated signal test shows that the IVMD addresses the shortcoming of the VMD algorithm and has better advantages in signal decomposition and reconstruction than complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Finally, the frequencies and damping ratios of two large-scale civil structures (a super-high-rise building and a suspension bridge) in the field experiments were captured from the signal response data via RDT-IVMD, proving the reliability of the presented method. The results can provide a basis for structural preventive maintenance.

Multi-Step-Ahead Wind Speed Forecast Method Based on Outlier Correction, Optimized Decomposition, and DLinear Model

Precise and dependable wind speed forecasting (WSF) enables operators of wind turbines to make informed decisions and maximize the use of available wind energy. This study proposes a hybrid WSF model based on outlier correction, heuristic algorithms, signal decomposition methods, and DLinear. Specifically, the hybrid model (HI-IVMD-DLinear) comprises the Hampel identifier (HI), the improved variational mode decomposition (IVMD) optimized by grey wolf optimization (GWO), and DLinear. Firstly, outliers in the wind speed sequence are detected and replaced with the HI to mitigate their impact on prediction accuracy. Next, the HI-processed sequence is decomposed into multiple sub-sequences with the IVMD to mitigate the non-stationarity and fluctuations. Finally, each sub-sequence is predicted by the novel DLinear algorithm individually. The predictions are reconstructed to obtain the final wind speed forecast. The HI-IVMD-DLinear is utilized to predict the real historical wind speed sequences from three regions so as to assess its performance. The experimental results reveal the following findings: (a) HI could enhance prediction accuracy and mitigate the adverse effects of outliers; (b) IVMD demonstrates superior decomposition performance; (c) DLinear has great prediction performance and is suited to WSF; and (d) overall, the HI-IVMD-DLinear exhibits superior precision and stability in one-to-four-step-ahead forecasting, highlighting its vast potential for application.

Short-Term Subway Passenger Flow Prediction Based on Time Series Adaptive Decomposition and Multi-Model Combination (IVMD-SE-MSSA)

The accurate forecasting of short-term subway passenger flow is beneficial for promoting operational efficiency and passenger satisfaction. However, the nonlinearity and nonstationarity of passenger flow time series bring challenges to short-term passenger flow prediction. To solve this challenge, a prediction model based on improved variational mode decomposition (IVMD) and multi-model combination is proposed. Firstly, the mixed-strategy improved sparrow search algorithm (MSSA) is used to adaptively determine the parameters of the VMD with envelope entropy as the fitness value. Then, IVMD is applied to decompose the original passenger flow time series into several sub-series adaptively. Meanwhile, the sample entropy is utilized to divide the sub-series into high-frequency and low-frequency components, and different models are established to predict the sub-series with different frequencies. Finally, the MSSA is employed to determine the weight coefficients of each sub-series to combine the prediction results of the sub-series and get the final passenger flow prediction results. To verify the prediction performance of the established model, passenger flow datasets from four different types of Nanning Metro stations were taken as examples for carrying out experiments. The experimental results showed that: (a) The proposed hybrid model for short-term passenger flow prediction is superior to several baseline models in terms of both prediction accuracy and versatility. (b) The proposed hybrid model is excellent in multi-step prediction. Taking station 1 as an example, the MAEs of the proposed model are 3.677, 5.7697, and 8.1881, respectively, which can provide technical support for subway operations management.

An Adaptive Hybrid Model for Wind Power Prediction Based on the IVMD-FE-Ad-Informer.

Accurate wind power prediction can increase the utilization rate of wind power generation and maintain the stability of the power system. At present, a large number of wind power prediction studies are based on the mean square error (MSE) loss function, which generates many errors when predicting original data with random fluctuation and non-stationarity. Therefore, a hybrid model for wind power prediction named IVMD-FE-Ad-Informer, which is based on Informer with an adaptive loss function and combines improved variational mode decomposition (IVMD) and fuzzy entropy (FE), is proposed. Firstly, the original data are decomposed into K subsequences by IVMD, which possess distinct frequency domain characteristics. Secondly, the sub-series are reconstructed into new elements using FE. Then, the adaptive and robust Ad-Informer model predicts new elements and the predicted values of each element are superimposed to obtain the final results of wind power. Finally, the model is analyzed and evaluated on two real datasets collected from wind farms in China and Spain. The results demonstrate that the proposed model is superior to other models in the performance and accuracy on different datasets, and this model can effectively meet the demand for actual wind power prediction.

Multi-GNSS Combination Multipath Reflectometry Based on IVMD Method for Sea Level Retrieval

Sea level monitoring is particularly important in coastal areas that are vulnerable to marine disasters. It was recently demonstrated that the global navigation satellite system multipath reflectometry (GNSS-MR) technique, which uses multipath signals reflected from the sea, can be applied to determine the sea level. However, this approach does not provide sufficient accuracy or equally spaced sampling to meet the actual sea level monitoring requirements for certain stations. To solve the deficiency of the traditional GNSS-MR technique, the least squares method, which is based on sliding time windows, was applied. Using the sliding windows to combine the quad-constellation multi-GNSS retrieval can effectively improve the accuracy and time resolution of sea level retrieval, but insufficient data or a lack of data in some time ranges and missing overflights in some timeframes can lead to the calculation of faults in these time windows, causing the estimated loss of corresponding sampling points. In this study, we used a robust regression solution strategy based on multi-GNSS sea level retrieval and an improved variational mode decomposition (IVMD) algorithm to process sea level retrieval after robust regression. BRST and HKQT stations are located on the western coast of France and the northern coast of Hong Kong. The two stations can both receive satellite observation data from the four satellite systems. Through the experiment, using data retrieved from the BRST and HKQT stations, the results of this study demonstrate that the IVMD method based on multi-GNSS sea level retrieval can further improve the accuracy to <10 cm and can achieve 10 min equal interval sampling. This is significant for using GNSS-MR technology to detect sea level height and monitor sea level change and could be applied to other sites.

A mechanical part fault diagnosis method based on improved multiscale weighted permutation entropy and multiclass LSTSVM

Multi-scale permutation entropy (MPE) has poor stability, accuracy and noise immunity, recognition accuracy of twin SVM is low, so a diagnosis method based on improved multi-scale weighted permutation entropy (IMWPE) and least squares TSVM (LSTSVM) is proposed. The innovations include that the improved variational mode decomposition (IVMD) based on energy and mutual information is used to suppress noise, and novel composite coarse-grained and permutation pattern weighting methods are introduced to construct IMWPE, after which the noise immunity, stability and accuracy of features have been improved. LSTSVM is extended to a multi-class LSTSVM through one vs one (OVO) and binary tree (BT) strategies, the performance of the proposed methodology is significantly improved. The results show that signal-to-noise ratio of signal is enhanced, the stability of IMWPE is improved, the diagnosis accuracies for bearing and check valve are increased by 17.084 % and 12.498 %, which provides a reference for fault diagnosis under noise.

Single-Sensor Engine Multi-Type Fault Detection.

Engine fault detection is conducive to improving equipment reliability and reducing maintenance costs. In practical scenarios, high-quality data is difficult to obtain. Usually, only single-sensor data is available. This paper proposes a fault detection method combining Variational Mode Decomposition (VMD) and Random Forest (RF). At first, the spectral energy distribution is obtained by decomposing and statistic the engine data of multiple working conditions. Based on the spectral energy distribution, the overall optimal mode number was identified, and the quadratic penalty term was optimized using SNR. The improved VMD (IVMD) improves mode aliasing and iterative efficiency and unifies feature dimensions. Decomposition of real signals demonstrates the effectiveness. The paper designs a feature vector composed of seven types of attributes, including unit bandwidth energy, center frequency, maximum singular value and so on. The feature vector is then fed to RF for classification. Features are selected in order of importance to classification to improve the training efficiency. By comparing with various algorithms, the proposed method has higher accuracy and faster training efficiency in single-speed, multi-speed and cross-speed single-sensor data diagnosis. The results show that the method has application prospects with little training data and low hardware requirements.

A novel hybrid prediction model for PM2.5 concentration based on decomposition ensemble and error correction.

PM2.5 concentration is an important index to measure the degree of air pollution. It is necessary to establish an accurate PM2.5 concentration prediction system for urban air monitoring and control. Due to the nonlinear characteristics of PM2.5 concentration, it is difficult to predict it directly. Therefore, a novel hybrid model for PM2.5 concentration based on improved variational mode decomposition (IVMD), outlier-robust extreme learning machine (ORELM) optimized by hybrid cuckoo search (CS), and chimp optimization algorithm (ChOA), error correction (EC) is proposed named IVMD-ChOACS-ORELM-EC. First of all, an improved VMD based on energy loss coefficient, named IVMD, is proposed. IVMD decomposes the original data to obtain K IMF components. Then, a hybrid optimization algorithm based on ChOA improved by CS is proposed, named ChOACS. The hybrid optimization algorithm is used to optimize ORELM. On this basis, the prediction model ChOACS-ORELM is proposed, and the K IMF components are predicted by ChOACS-ORELM. Finally, the EC model based on decomposition ensemble is established to further improve the prediction accuracy. The PM2.5 concentration data collected at hourly intervals in Beijing, Shanghai, Shenyang, and Qingdao in China are used as experimental data. The experimental results show that the correlation coefficients between the prediction results and the actual values of the four cities are 0.9999, and the prediction performance of the proposed model is better than that of all comparison models.

Application of IPSO-MCKD-IVMD-CAF in the compound fault diagnosis of rolling bearing

The vibration signals of rolling bearings are mixed with a variety of noises and a variety of faults which are coupled to each other, and which make the fault frequencies interfere with each other. This in turn leads to difficulty of accurate extraction of the features of composite faults. Therefore, it is necessary not only to suppress the noise of vibration signals but also to separate and extract the features of compound faults. A compound fault feature extraction method based on improved particle swarm optimization (IPSO) algorithm optimized maximum correlation kurtosis deconvolution (MCKD), improved variational mode decomposition (IVMD) and cyclic autocorrelation function (CAF), named IPSO-MCKD-IVMD-CAF is proposed. Firstly, the parameters of MCKD are selected adaptively by the IPSO, and the original signal is pre-processed by the parameterized MCKD. Secondly, the IVMD is utilized to decompose the signal, several intrinsic mode functions (IMFs) are obtained, the kurtosis and correlation coefficients of each IMF component are calculated. Finally, appropriate IMF components are selected by kurtosis and correlation coefficient to be superimposed into the reconstructed signals, and the reconstructed signals are analyzed by CAF. The proposed method has been successfully applied in simulation and measured vibration signal analysis, and the features of compound faults can be separated and extracted with high accuracy. The IPSO algorithm shortens the optimization time, and the IVMD solves the parameter selection problem. The analysis results of simulation case and measured data show the advantages of the proposed method IPSO-MCKD-IVMD-CAF. Compared to existing methods, the proposed method not only increases the accuracy of compound fault feature extraction, but also has a very good performance on the separation and extraction of compound fault features. More importantly, the improved algorithm reduces the computational complexity.

Short-term Wind Power Forecasting Using the Hybrid Model of Improved Variational Mode Decomposition and Maximum Mixture Correntropy Long Short-term Memory Neural Network

With the development of emerging technology, wind power forecasting hybrid with artificial intelligence methods has become a research hotspot. Most of these methods are based on Mean Square Error (MSE) loss. However, when conducting the forecasting studies, the forecasting models built based on the traditional MSE loss have a poor effect, and the wind power data also lack the sensitivity to the nuclear parameters, make it difficult to achieve satisfactory results. Therefore, a wind power forecasting method based on Mixture Correntropy (MC) Long Short-term Memory (LSTM) neural network and Improved Variational Mode Decomposition (IVMD) is proposed in this paper. Aiming at the fact that the mixing coefficient and kernel parameters in Maximum Mixture Correntropy Criterion (MMCC) loss have an impact on its performance, Particle Swarm Optimization (PSO) algorithm is used to optimize the parameters, and PMC(PSO-MC)-LSTM model is constructed. Meanwhile, an IVMD-SE data preprocessing strategy combining Sample Entropy (SE) and IVMD is proposed. The IVMD-SE-PMC-LSTM hybrid forecasting model is constructed. Finally, four groups original data from a wind farm are simulated to verify the forecasting performance of the proposed method. The results show that the hybrid forecasting method proposed in this paper can be better applied to the forecasting with higher data complexity.

Channel identification with Improved Variational Mode Decomposition

The identification of the type of wireless propagation channel (e.g., Line of Sight (LOS) or Non Line of Sight (NLOS)) is an important function in the wireless communication design and deployment especially in rich propagation environments. The wireless channel characteristics can be quite specific not only between Line of Sight (LOS) and Non Line of Sight (NLOS) wireless propagation conditions but also in different NLOS environments.In recent times, machine learning approaches have been increasingly used to differentiate and classify channel characteristics and this paper is part of this trend. In particular, this paper proposes the combination of machine learning with a recently proposed signal processing tool called Variational Mode Decomposition (VMD), which is a decomposition algorithm that decomposes a time series into several modes which have specific sparsity properties. VMD itself is a refinement of the Empirical Mode Decomposition (EMD) and demonstrated a superior performance to EMD for classification problems. One issue for the practical deployment of VMD in channel identification problems is the presence of hyper-parameters, which must be tuned for the applied context. The main contribution of this paper is to propose a novel approach for channel identification based on an improvement of VMD called Improved Variational Mode Decomposition (IVMD), where the optimal values of the hyper-parameters of VMD are automatically identified on the basis of the Shannon entropy of the signal output from the channel. Then, various features are extracted from the modes generated by IVMD and a sequential feature selection algorithm is applied to select the optimal features. This paper applies the proposed approach with IVMD to a data set generated by the authors with a wireless channel emulator, where 6 different propagation scenarios (including no fading conditions) are created for WiFi 802.11g signals, where only the preamble is used for channel identification. Even if channel identification based on the normalized preamble is a challenging classification problem, the proposed IVMD is able to outperform significantly the application of basic VMD, EMD and the time and frequency domain representations (as commonly done in literature) of the WiFi signals.

Mid-term electricity demand forecasting using improved variational mode decomposition and extreme learning machine optimized by sparrow search algorithm

Mid-term electricity demand forecasting plays an important role in ensuring the operational safety of the power system and the economic efficiency of grid companies. Most studies have focused on deterministic forecasting of electricity demand, while ignoring uncertainty analysis of electricity demand. To bridge this research gap, a point-interval mid-term electricity demand forecasting model is proposed. Firstly, based on Pearson correlation coefficient, feature dimensionality reduction is carried out to filter out key features that greatly affect electricity demand, such as socio-economic factors and meteorological factors, to enhance forecasting efficiency. Secondly, improved variational mode decomposition (IVMD) optimized by sparrow search algorithm (SSA) is proposed to decompose electricity demand series into several subsequences. By combining SSA, extreme learning machine (ELM) and adaptive boosting algorithm (Adaboost), IELM-Adaboost is constructed to forecast each subsequence, and the point forecasting results are obtained by superimposing each subsequence forecasting result. Finally, electricity demand forecasting intervals will be obtained by the application of the kernel density estimation (KDE) of point forecasting error. Three Chinese provinces are applied for empirical analysis in this paper. Compared with ELM, the MAPE of the proposed model in the three datasets are reduced by 87.90%, 66.05% and 75.97% respectively, showing promising point forecasting performance. The empirical results prove that IVMD-IELM-Adaboost performs well in both point forecasting and interval forecasting.

Wind power forecasting based on variational mode decomposition and high-order fuzzy cognitive maps

Accurate wind power forecasting can effectively reduce the adverse effects of wind power forecasting errors on wind power grid integration and power dispatch. However, current wind power forecasting technology, such as the method based on machine learning, belongs to the black box model and is not solvable. Variational mode decomposition (VMD) is a decomposition technique based on the time–frequency characteristics of the original time series, which has a mathematical theoretical foundation. Besides, fuzzy cognitive map (FCMs) is a kind of soft computing method with strong knowledge representation and reasoning ability. Therefore, to enhance the forecasting accuracy of wind power, in this paper, a novel time series forecasting method based on improved VMD (IVMD) and high-order FCM (HFCM), namely IVMDHFCM is proposed. IVMD can effectively extract the features in the raw time series depending on the time–frequency characteristics of the time series. Then, the subseries obtained by IVMD are modeled and forecasted by HFCM, and the Bayesian ridge regression method is adopted to learn the weight of HFCM. Finally, the differential evolution (DE) algorithm is used to get the optimal hyperparameters of IVMDHFCM. The performance of IVMDHFCM is verified by comparing it with that of state-of-the-art methods on ten publicly available datasets. Moreover, the proposed IVMDHFCM is compared with the existing HFCM based method on ten actual wind power datasets. The results show that the IVMDHFCM can effectively improve the accuracy of wind power forecasting and reduce the forecasting error. Besides, the IVMDHFCM can also effectively explore the fluctuations of wind power.

Short-Term Traffic Flow Prediction via Improved Mode Decomposition and Self-Attention Mechanism Based Deep Learning Approach

Short-term traffic flow prediction (STFP) is one of the key technologies in Intelligence Transportation System (ITS). With the development of artificial intelligence technology, deep learning has been employed to STFP and certain achievements have been obtained. However, further improvement of STFP accuracy is constrained by the presence of noise, modal aliasing in the modal components and insufficient feature extraction of neural networks. Therefore, to more accurately capture the changing trend of traffic flow in different time periods, and increase the reliability and interpretability of the prediction models, improved variational mode decomposition (IVMD) and self-attention mechanism (SAM) based hybrid convolutional neural network (CNN) and long short term memory network (LSTM) are proposed for STFP in this study, benefited from the modal decomposition of IVMD and redistribution of the neural weights in CNN-LSTM networks by SAM, the proposed IVMD-CNN-LSTM-SAM effectively suppresses the influence of randomness and volatility of traffic flow, and accurately predict the short-term lane occupancy in the designated area. Furthermore, this study analyses the mechanism of SAM and IVMD in STFP, and proves the superiority of IVMD and SAM in signal decomposition with physical significance and weight allocation respectively. Therefore, the interpretability of the proposed neural network model is significantly improved. Eleven competitive neural networks forecasting methods are used as benchmarks and numerical studies based on actual traffic flow validate the accuracy and stability of the proposed IVMD-CNN-LSTM-SAM. Mean absolute percentage error and goodness of fit of the proposed model are 0.81% and 0.9968, respectively.

Improved Variational Mode Decomposition and CNN for Intelligent Rotating Machinery Fault Diagnosis.

This paper proposes an intelligent diagnosis method for rotating machinery faults based on improved variational mode decomposition (IVMD) and CNN to process the rotating machinery non-stationary signal. Firstly, to solve the problem of time-domain feature extraction for fault diagnosis, this paper proposes an improved variational mode decomposition method with automatic optimization of the number of modes. This method overcomes the problems of the traditional VMD method, in that each parameter is set by experience and is greatly influenced by subjective experience. Secondly, the decomposed signal components are analyzed by correlation, and then high correlated components with the original signal are selected to reconstruct the original signal. The continuous wavelet transform (CWT) is employed to extract the two-dimensional time–frequency domain feature map of the fault signal. Finally, the deep learning method is used to construct a convolutional neural network. After feature extraction, the two-dimensional time-frequency image is applied to the neural network to identify fault features. Experiments verify that the proposed method can adapt to rotating machinery faults in complex environments and has a high recognition rate.