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LED (light-emitting diode)-lidar (light detection and ranging) has gradually been focused on by researchers because of its characteristics of low power, high stability, and safety to human eyes. However, LED-lidar systems are easily disturbed by background light noise. Echo signal denoising is an essential work that directly affects the measurement accuracy of the LED-lidar system. The traditional variational modal decomposition (VMD) method in lidar signal denoising relies on practical experience to optimize the critical parameters of quadratic penalty factor α and the number of intrinsic mode function (IMF) components K globally, which is hard to denoise effectively. For this problem, a denoising method based on VMD with the adaptive weighted particle swarm optimization (PSO) is proposed in this work. The PSO-VMD method adaptively adjusts the weight value ω for different lidar echo signals and optimizes of the parameters α and K globally. The LED-lidar echo signals are denoised by moving average, VMD, and PSO-VMD. Using the denoised echo signals, the range compensation waveforms and the extinction coefficients are derived. The results show that the PSO-VMD denoised echo signal has the highest R-square value of 0.9972 and the minimum standard deviation value of 5.7369, while the values of r-square and standard deviation of the echo signal denoised by moving average and VMD method are 0.9902, 9.7450, 0.9945, and 7.3588, respectively. The derived distance compensation waveforms and extinction coefficients based on the PSO-VMD denoising have better stability than those based on the moving average and VMD denoising.

The goal of the paper is to present a solution to improve the fault detection accuracy of rolling bearings. The method is based on variational mode decomposition (VMD), multiscale permutation entropy (MPE) and the particle swarm optimization-based support vector machine (PSO-SVM). Firstly, the original bearing vibration signal is decomposed into several intrinsic mode functions (IMF) by using the VMD method, and the feature energy ratio (FER) criterion is introduced to reconstruct the bearing vibration signal. Secondly, the multiscale permutation entropy of the reconstructed signal is calculated to construct multidimensional feature vectors. Finally, the constructed multidimensional feature vector is fed into the PSO-SVM classification model for automatic identification of different fault patterns of the rolling bearing. Two experimental cases are adopted to validate the effectiveness of the proposed method. Experimental results show that the proposed method can achieve a higher identification accuracy compared with some similar available methods (e.g., variational mode decomposition-based multiscale sample entropy (VMD-MSE), variational mode decomposition-based multiscale fuzzy entropy (VMD-MFE), empirical mode decomposition-based multiscale permutation entropy (EMD-MPE) and wavelet transform-based multiscale permutation entropy (WT-MPE)).

In order to realize the economic dispatch and safety stability of offshore wind farms, and to address the problems of strong randomness and strong time correlation in offshore wind power forecasting, this paper proposes a combined model of principal component analysis (PCA), sparrow algorithm (SSA), variational modal decomposition (VMD), and bidirectional long- and short-term memory neural network (BiLSTM). Firstly, the multivariate time series data were screened using the principal component analysis algorithm (PCA) to reduce the data dimensionality. Secondly, the variable modal decomposition (VMD) optimized by the SSA algorithm was applied to adaptively decompose the wind power time series data into a collection of different frequency components to eliminate the noise signals in the original data; on this basis, the hyperparameters of the BiLSTM model were optimized by integrating SSA algorithm, and the final power prediction value was obtained. Ultimately, the verification was conducted through simulation experiments; the results show that the model proposed in this paper effectively improves the prediction accuracy and verifies the effectiveness of the prediction model.

The quantitative diagnosis of rolling bearings is essential to automating maintenance decisions. Over recent years, Lempel–Ziv complexity (LZC) has been widely used for the quantitative assessment of mechanical failures as one of the most valuable indicators for detecting dynamic changes in nonlinear signals. However, LZC focuses on the binary conversion of 0–1 code, which can easily lose some effective information about the time series and cannot fully mine the fault characteristics. Additionally, the immunity of LZC to noise cannot be insured, and it is difficult to quantitatively characterize the fault signal under strong background noise. To overcome these limitations, a quantitative bearing fault diagnosis method based on the optimized Variational Modal Decomposition Lempel–Ziv complexity (VMD-LZC) was developed to fully extract the vibration characteristics and to quantitatively characterize the bearing faults under variable operating conditions. First, to compensate for the deficiency that the main parameters of the variational modal decomposition (VMD) have to be selected by human experience, a genetic algorithm (GA) is used to optimize the parameters of the VMD and adaptively determine the optimal parameters [k, α] of the bearing fault signal. Furthermore, the IMF components that contain the maximum fault information are selected for signal reconstruction based on the Kurtosis theory. The Lempel–Ziv index of the reconstructed signal is calculated and then weighted and summed to obtain the Lempel–Ziv composite index. The experimental results show that the proposed method is of high application value for the quantitative assessment and classification of bearing faults in turbine rolling bearings under various operating conditions such as mild and severe crack faults and variable loads.

With the continuous increase in user-side flexible controllable resources connected into a distribution system, the components of electrical load become too diverse and difficult to be accuracy forecasted. A short-term load forecast method that integrates variational modal decomposition (VMD), gated recurrent unit (GRU) and time convolutional network (TCN) into a hybrid network is proposed in this paper. Firstly, original electrical load sequence data with noise are decomposed into intrinsic IMF components with different frequencies and amplitudes based on the VMD method. Secondly, a combined load forecasting method based on the GRU and TCN network is proposed for the high and low-frequency load subsequent signals, respectively. Finally, the high and low-frequency signals forecasting results of the GRU and TCN network are rebuilt for the final load forecasting. The experiment results based on actual operation data (data set 1) and simulation data (data set 2), which show that the proposed method can reduce the forecasting error by 36.20% and 10.8%, respectively, in comparison with VMD-GRU. The reliability and accuracy of the proposed method is verified through the comparison with other methods such as LSTM, Prophet and XG Boost.

Water quality predicted accuracy is beneficial to river ecological management and water pollution prevention. Owing to water quality data has the characteristics of nonlinearity and instability, it is difficult to predict the change of water quality. This paper proposes a hybrid water quality prediction model based on variational mode decomposition optimized by the sparrow search algorithm (SSA-VMD) and bidirectional gated recursive unit (BiGRU). First, the sparrow search algorithm selects fuzzy entropy (FE) as the fitness function to optimize the two parameters of VMD, which improves the adaptability of VMD. Second, SSA-VMD is used to decompose the original data into several components with different center frequencies. Finally, BiGRU is employed to predict each component separately, which significantly improves predicted accuracy. The proposed model is validated using data about dissolved oxygen (DO) and the potential of hydrogen (pH) from the Xiaojinshan Monitoring Station in Qiandao Lake, Hangzhou, China. The experimental results show that the proposed model has superior prediction accuracy and stability when compared with other models, such as EMD-based models and other CEEMDAN-based models. The prediction accuracy of DO can reach 97.8% and pH is 96.1%. Therefore, the proposed model can provide technical support for river water quality protection and pollution prevention.

The emergence of Deep Learning provides an opportunity for traffic flow prediction. However, uncertainty and volatility exhibited by nonlinearity and instability of traffic flow pose challenges to Deep Learning models. Therefore, a combined prediction model, VMD-GAT-MGTCN, based on variational modal decomposition (VMD), graph attention network (GAT), and multi-gated attention time convolutional network (MGTCN) is proposed to enhance short-term traffic flow prediction accuracy. In the VMD-GAT-MGTCN, VMD decomposes traffic flow data to obtain the modal components, the GAT and MGTCN are integrated to design the spatio-temporal feature model to obtain the temporal and spatial features of traffic flow. The predicted value of traffic flow modal components by spatio-temporal feature model are stacked to obtain the ultimate traffic flow prediction results. The simulation experiments with the compared models and the baseline models show that the VMD-GAT-MGTCN have superior prediction accuracy and effect. It also verifies the enhancement effect of the VMD algorithm on the prediction performance of the VMD-GAT-MGTCN and the good prediction results obtained by the VMD-GAT-MGTCN in the traffic flow mutation region.

Wind energy reserves are large worldwide, but their randomness and volatility hinder wind power development. To promote the utilization of wind energy and improve the accuracy of wind power prediction, we comprehensively consider the influence of wind farm environmental factors and historical power on wind power generation. This paper presents a short-term wind power prediction model based on time convolution neural network (TCN) and variational mode decomposition (VMD). First, due to the non-smooth characteristics of the wind farm environmental data, this paper uses VMD to decompose the data of each environmental variable to reduce the influence of the random noise of the data on the prediction model. Then, the modal components with rich feature information are extracted according to the Pearson correlation coefficient and Maximal information coefficient (MIC) between each modal component and the power. Thirdly, a prediction model based on TCN is trained according to the preferred modal components and historical power data to achieve accurate short-term wind power prediction. In this paper, the model is trained and tested with a public wind power dataset provided by the Spanish Power Company. The simulation results show that the model has higher prediction accuracy, with MAPE and R2 are 2.79% and 0.9985, respectively. Compared with the conventional long short-term neural network (LSTM) model, the model in this paper has good prediction accuracy and robustness.

A short-term wind power prediction model based on BiLSTM–CNN–WGAN-GP (LCWGAN-GP) is proposed in this paper, aiming at the problems of instability and low prediction accuracy of short-term wind power prediction. Firstly, the original wind energy data are decomposed into subsequences of natural mode functions with different frequencies by using the variational mode decomposition (VMD) algorithm. The VMD algorithm relies on a decision support system for the decomposition of the data into natural mode functions. Once the decomposition is performed, the nonlinear and dynamic behavior are extracted from each natural mode function. Next, the BiLSTM network is chosen as the generation model of the generative adversarial network (WGAN-GP) to obtain the data distribution characteristics of wind power’s output. The convolutional neural network (CNN) is chosen as the discrimination model, and the semi-supervised regression layer is utilized to design the discrimination model to predict wind power. The minimum–maximum game is formed by the BiLSTM and CNN network models to improve the quality of sample generation and further improve the prediction accuracy. Finally, the actual data of a wind farm in Jiuquan City, Gansu Province, China is taken as an example to prove that the proposed method has superior performance compared with other prediction algorithms.

Traditional decomposition integration models decompose the original sequence into subsequences, which are then proportionally divided into training and testing periods for modeling. Decomposition may cause data aliasing, then the decomposed training period may contain part of the test period data. A more effective method of sample construction is sought in order to accurately validate the model prediction accuracy. Semi-stepwise decomposition (SSD), full stepwise decomposition (FSD), single model semi-stepwise decomposition (SMSSD), and single model full stepwise decomposition (SMFSD) techniques were used to create the samples. This study integrates Variational Mode Decomposition (VMD), African Vulture Optimization Algorithm (AVOA), and Least Squares Support Vector Machine (LSSVM) to construct a coupled rainfall prediction model. The influence of different VMD parameters α is examined, and the most suitable stepwise decomposition machine learning coupled model algorithm for various stations in the North China Plain is selected. The results reveal that SMFSD is relatively the most suitable tool for monthly precipitation forecasting in the North China Plain. Among the predictions for the five stations, the best overall performance is observed at Huairou Station (RMSE of 18.37 mm, NSE of 0.86, MRE of 107.2%) and Jingxian Station (RMSE of 24.74 mm, NSE of 0.86, MRE of 51.71%), while Hekou Station exhibits the poorest performance (RMSE of 25.11 mm, NSE of 0.75, MRE of 173.75%).