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Wind energy plays an important role in many new energy sources. According to the latest report released by the Global Wind Energy Council (GWEC) (
Currently, shortterm wind speed prediction methods are divided into two main categories: physical processdriven models (
In recent years, artificial intelligence models, including machine learning and deep learning models, have become increasingly popular in the field of shortterm wind speed prediction (
Due to the distinct characteristics exhibited by various single models, hybrid models can effectively leverage the advantages of different individual models to achieve enhanced wind speed prediction performance. Consequently, hybrid prediction models based on decomposition and optimization have emerged as a research hotspot in the field of wind speed prediction in recent years. In order to ensure the sufficiency and integrity of feature decomposition and reconstruction, some scholars have proposed a novel hybrid model based on singular spectrum analysis and temporal convolutional attention network with adaptive receptive field (ARFTCAN). The results demonstrate that the proposed model effectively supports the adaptability of shortterm wind power forecasting (WPF) across all four seasons (
In constructing the wind speed hybrid model, usually after signal decomposition of the data, a parameter optimization algorithm is also used to optimize the weights of each IMF to improve the performance of the prediction algorithm. Among the parameter optimization algorithms, the swarm intelligence optimization algorithm is the most commonly used algorithm for wind speed prediction. The swarm intelligence optimization algorithm is a number of algorithms proposed for solving optimization problems through the simulation study of the behavior of animal groups, which overcomes the limitations of the traditional algorithms when dealing with some complex problems such as, nonlinear, multiconstraint, multivariable, etc., and demonstrates a better optimization ability. Some common ones are grey wolf optimizer (GWO) (
In summary, this study proposes the VMDAttention LSTMASSA (VMDAtLSTMASSA) hybrid shortterm wind speed prediction model containing decomposition, prediction, and optimization for shortterm wind speed prediction. The variational mode decomposition (VMD), as a decomposition model in the hybrid model, decomposes the wind speed series data into a series of intrinsic mode functions (IMFs) that can adaptively update the optimal center frequency and bandwidth of each IMF component, which is helpful for the subsequent work of using the long short term memory networks (LSTM) prediction model to incorporate the attention mechanism effectively, which extracts the important slice information in each IMF component for highprecision prediction. Finally, the multiobjective adaptive learning rate salp swarm algorithm (ASSA) model is used to find the optimal weights for each IMF component, which is finally weighted to obtain the highprecision wind speed prediction value.
The main contributions and innovations of this paper are as follows.
(a) The use of long short term memory networks (LSTM) with the inclusion of an attention mechanism to individually predict the intrinsic mode functions (IMFs) obtained through variational mode decomposition (VMD). The Attention mechanism identifies the importance of slice information within each modal component, effectively improving the prediction accuracy and robustness of the LSTM network.
(b) On the basis of the salp swarm algorithm (SSA), improvements are made to address the problems of local optima trapping and premature convergence in the original salp swarm algorithm. This is achieved by proposing the adaptive learning operator and multiobjective operator in the multiobjective adaptive learning rate salp swarm optimization algorithm ASSA. Ultimately, this approach achieves global optimality and improves wind speed prediction accuracy.
(c) Through comprehensive comparisons with popular deep learning prediction models, decomposition models, and optimization models, this paper verifies the superiority of the proposed hybrid wind speed prediction model VMDAtLSTMASSA in terms of individual components as well as overall predictive performance.
The structure of this paper is described as follows:
This section describes the framework structure of the proposed VMDAtLSTMASSA combined model, and the specific flowchart is shown in
Framework and execution process of VMDAtLSTMASSA model. This framework is divided into three steps,
The VMD is a signal decomposition method (
Results of variational mode decomposition (VMD) for three sites.
Assuming that each wind speed’s intrinsic mode functions have a finite bandwidth with a center frequency, now find the decomposed wind speed modes such that the sum of the estimated bandwidths of each wind speed mode is minimized. The specific model is as follows:
Where,
In order to solve the above model, introduce the penalty factor
Iteratively update the parameters,
Where
For a given precision
The subsequent analysis focuses on the 15 intrinsic mode functions (IMFs) obtained through the variational mode decomposition (VMD), which are then utilized for shortterm wind speed prediction using an Attention LSTM model. Additionally, the study investigates the optimization of weights associated with each IMF. The detailed process can be found in the flowchart depicted in
The IMFs obtained by applying the variational mode decomposition (VMD) to the original wind speed sequence are individually predicted using an Attention LSTM model. LSTM network is a special type of recurrent neural network (RNN) (
First, each IMF after decomposition is used as an input to the LSTM
Decide what information to discard from the memory cell state (calculate the “forget gate” state).
In the above equation,
Decide which information is stored in the memory cell state (calculate the “input gate” state) and calculate the candidate values for the memory cell state.
In the above equation,
Update the current moment memory cell state with the “forget gate” state, the “input gate” state, the previous moment memory cell state, and the candidate value of memory cell state:
In the above equation
Determine what information to output from the memory cell state (calculate the “output gate” state):
In the above equation,
When predicting each wind speed IMF component, it is obviously not rigorous enough to assign the same weight to all input slice information. While the Attention mechanism can capture the important features of wind speed, the Attention mechanism evaluates the importance of different input features, focuses the important information with high weights, ignores the less relevant information with low weights, and finally assigns different weights to them reasonably. Therefore, the Attention mechanism is introduced into the LSTM prediction of each IMF component, and the specific implementation steps of the mechanism are as follows: firstly, the weight coefficients are calculated, i.e., the attention distribution of the slices inside each IMF component is calculated; secondly, the weighted summation of the calculated weight coefficients is carried out, i.e., the weighted average of the slices of each IMF component is calculated, and the calculation process is as follows:
Multiply the sliced samples
query and key perform similarity calculation to get the weights
The weights
The normalized weights are weighted and summed with VALUE to get the final output of a certain IMF component prediction
After the prediction of each IMF component sequence, the salp swarm algorithm (SSA) will find the optimal weights of each component, and finally weigh the superposition to get the final shortterm wind speed prediction. The salp swarm algorithm (SSA) simulates the group behavior of salp swarm chains, which is a novel swarm intelligence optimization algorithm (
However, in the SSA, the salp swarm leader is eager to reach the local optimum from the beginning, which leads to insufficient searching and sometimes the algorithm has a low convergence accuracy. Therefore, this paper proposes multiobjective adaptive learning rate salp swarm algorithm (ASSA). Aiming to solve the problem of a lack of global awareness in population updating, we add two different learning operators in leader position updating and follower position updating respectively, which effectively solves the problem of the SSA easily falling into local extremes and improves the optimization accuracy of the algorithm. The flowchart of multiobjective adaptive learning rate salp swarm algorithm (ASSA) is shown in
Population initialization. Let the search space be the Euclidean space of
Leader position update. During the movement and foraging process of the salp swarm chain, the position of the food source is the target position of all salp swarm individuals, so the leader’s position update formula is expressed as:
Where:
Where: l is the current iteration number; L is the maximum iteration number. The convergence factor is a decreasing function from 2 to 0. The control parameters c_{2}, c_{3} are random numbers between 0 and 1, which are used to enhance the randomness of
Follower position update. During the movement and foraging process of the salp swarm chain, the followers move forward sequentially in a chain by influencing each other between the front and back individuals. Their displacements conform to Newton’s laws of motion, and the equation for the follower’s motion displacement is:
Where: t is the time;
Where:
However, in the SSA algorithm, the salp swarm leader runs to the global optimum from the beginning of the iteration, which leads to insufficient global search, and an occasionally low convergence accuracy of the algorithm. To address this problem, this paper proposes the ASSA algorithm. For the problem of lack of global awareness in the population update, we add two different learning operators on the leader position update and follower position update respectively, which effectively solves the problem of the SSA algorithm easily falling into the local extreme value and improves the algorithm’s optimization accuracy.
The learning operator for leader position update is added to make the population search more biased towards largescale search in the early stage and focused towards the global optimal solution in the late stage of the search. The improved salp swarm leader position update process is:
For the position update of a salp swarm follower, the individual position is always affected by the two individuals before and after it, and the fitness of the two individuals is unknown. Therefore, we propose that by calculating the fitness values of the two individuals and restricting the poorly adapted individual, we weaken the influence of the poorly adapted individual on the individual update at the current moment. The improved bottles sea squirt follower position update process is:
Where
This improved optimization algorithm has more than one objective function, thus the optimization problem is changed to a multiobjective optimization problem. We first demeasure the objective functions to ensure that the objective functions have the same measure; then average the objective functions, and then transform the multiobjective optimization problem into a simple singleobjective optimization problem to solve the problem. As follows:
Step4: Judge whether the current iteration number count satisfies the maximum iteration number iter, if so, output the optimal weight results of each IMF component, otherwise return to Step2.
In this section, to verify the effectiveness of the proposed VMDAtLSTMASSA model, we experimentally study the model using wind speed data collected from wind farms in three different regions. The VMDAtLSTMASSA model is compared with popular models in the research field. All experiments are implemented under the deep learning framework under Python 3.7.3. The configuration of the emulated platform is Intel(R) Core(TM) i58250U CPU @ 1.60 GHz 1.80 GHz with 8 GB memory capacity.
The study collected wind speed datasets from three sites on
Characteristics of the threesite wind speed datasets.
Dataset  Number  Statistical indicators  

Mean (m/s)  Sd. (m/s)  Max (m/s)  Min (m/s)  
Site1  3,000  7.6373  1.7722  14.4030  1.8014 
Site2  3,000  7.2664  1.9386  15.8270  3.0015 
Site3  3,000  8.0485  3.3500  18.1090  0.8450 
To validate the effectiveness and high accuracy performance of the proposed hybrid model, three sets of comparative experiments were conducted. Experiment 1 compared the predictive performance of AtLSTM with currently popular single deep learning models, verifying the superior predictive performance of Attention LSTM. Experiment 2 compared the prediction results of different wind speed sequence decomposition methods combined with Attention LSTM, demonstrating the superiority of VMD followed by Attention LSTM prediction. Experiment 3 compared the prediction results of different deep learning models combined with VMD, as well as the performance of models incorporating the optimization models SSA and ASSA. This experiment validated the superiority of the VMDAttention LSTM hybrid model and the excellent predictive performance and stability of the VMDAtLSTMASSA model. The details of these three sets of comparative experiments will be presented in Sections 3.4–3.6.
In the experiments, three different evaluation indicators, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), were used to present and analyze the experimental results, and according to the value of the evaluation Indicators, the model’s prediction performance was evaluated (
Three evaluation indicators for model evaluation.
Metrice  Definition  Equation 

RMSE  Root mean square error 

MAE  Mean absolute error 

MAPE  Mean Absolute percentage error 

In order to verify the validity of the proposed model, the model parameters used in this study are the same, eliminating the influence of model parameter settings on experimental results. The Attention LSTM is commonly referred to as AtLSTM in the experimental setting.
Related parameter settings.
Model  Parameter  Parameter value 

SVR  Step size  60 
Kernal  linear  
RNN  Step size  60 
Dropout ratio  0.1  
Epochs  150  
Batch size  64  
BPNN  Step size  60 
Learning rate  1e4  
Epochs  150  
Batch size  64  
LSTM  Step size  60 
Dropout ratio  0.1  
Epochs  150  
Batch size  64  
Number of hidden neurons  64  
GRU  Step size  60 
Dropout ratio  0.1  
Epochs  150  
Batch size  64  
Number of hidden neurons  64  
AtLSTM  Step size  60 
Dropout ratio  0.1  
Epochs  150  
Batch size  64  
Number of hidden neurons  64  
VMD  noise margin  0 
Alpha  7,000  
number of decomposition modes  15  
ASSA  Population size  10 
Number of iterations  50 
In this experiment, AtLSTM was compared with SVR, BPNN, RNN, GRU, and LSTM models to validate the exceptional predictive performance of the proposed model. The evaluation metrics for model prediction performance are presented in
Comparison of prediction errors of five single models with AtLSTM.
Dataset  Measurement model  Evaluation indicators  

RMSE  MAE  MAPE  
Site1  SVR  0.5831  0.4505  7.0699 
BPNN  0.6044  0.4657  7.2671  
RNN  0.5348  0.3997  6.2173  
GRU  0.5332  0.3967  6.1847  
LSTM  0.5309  0.3954  6.1427  





Site2  SVR  0.5409  0.4424  7.6596 
BPNN  0.5067  0.3988  6.6723  
RNN  0.5078  0.4075  7.1344  
GRU  0.4571  0.3545  5.7271  
LSTM  0.4562  0.3466  5.6348  





Site3  SVR  0.6314  0.5270  9.4655 
BPNN  0.3089  0.2229  3.9711  
RNN  0.2058  0.1386  2.5879  
GRU  0.2039  0.1333  2.5565  
LSTM  0.2024  0.1252  2.5397  




The best values for the evaluation indicators are bolded.
Bar charts of the fitting curves and metrics for 5 individual models and Attention LSTM.
From
To demonstrate the superiority of AtLSTM based on the VMD decomposition model over other decomposition methods in improving wind speed prediction accuracy, we compared it with EMDAtLSTM, EEMDAtLSTM, and CEEMDANAtLSTM to validate the superior predictive performance of VMDAtLSTM. The evaluation metrics for model prediction performance are presented in
Model error comparison of four decomposition methods combined with AtLSTM.
Dataset  Measurement model  Evaluation indicators  

RMSE  MAE  MAPE  
Site1  EMDAtLSTM  0.3472  0.2673  4.1494 
EEMDAtLSTM  0.1830  0.1445  2.2421  
CEEMDANAtLSTM  0.4289  0.3472  6.0182  





Site2  EMDAtLSTM  0.2323  0.1743  2.7800 
EEMDAtLSTM  0.2058  0.1712  2.8656  
CEEMDANAtLSTM  0.2296  0.1725  2.7366  





Site3  EMDAtLSTM  0.1440  0.1052  1.9368 
EEMDAtLSTM  0.1281  0.1037  1.7263  
CEEMDANAtLSTM  0.1169  0.1095  1.4721  




The best values for the evaluation indicators are bolded.
Circular bar charts comparing the fitting curves and error metrics of the four decomposition methods combined with AtLSTM.
From
In order to validate the superior predictive performance of the proposed VMDAtLSTMASSA model, we first compared the prediction errors of VMDSVR, VMDBPNN, VMDRNN, VMDGRU, and VMDLSTM models, and then evaluated the superiority of VMDAtLSTM. Furthermore, we verified the effectiveness of incorporating SSA in improving the accuracy of VMDAtLSTM. Subsequently, a comparison of prediction errors was conducted between the VMDAtLSTMSSA and VMDAtLSTMASSA models, ultimately confirming the significant positive impact of the proposed VMDAtLSTMASSA on prediction accuracy.
Comparison of prediction errors based on VMD combined with various deep learning prediction models.
Dataset  Measurement model  Evaluation indicators  Running time(s)  

RMSE  MAE  MAPE  
Site1  VMDSVR  0.3687  0.2902  4.4368  30.8748 
VMDBPNN  0.1916  0.1497  2.3733  220.6907  
VMDRNN  0.1867  0.1435  2.2144  850.7612  
VMDGRU  0.1825  0.1409  2.1041  1990.3243  
VMDLSTM  0.1810  0.1402  2.1066  2100.4321  


















Site2  VMDSVR  0.5746  0.4599  8.1926  28.5463 
VMDBPNN  0.2030  0.1581  2.8487  180.6700  
VMDRNN  0.1790  0.1420  2.3702  780.3212  
VMDGRU  0.1723  0.1375  2.3942  1897.5009  
VMDLSTM  0.1707  0.1361  2.3410  1901.3221  


















Site3  VMDSVR  0.5082  0.4252  7.1296  26.1276 
VMDBPNN  0.1023  0.0734  1.3104  175.3435  
VMDRNN  0.1004  0.0823  1.3261  809.9987  
VMDGRU  0.1060  0.0851  1.4559  1799.3212  
VMDLSTM  0.1090  0.0764  1.4377  1831.3221  




2108.8876  











Values of evaluation metrics for VMDAtLSTM,VMDAtLSTMSSA,VMDAtLSTMASSA are bolded.
Curve fitting and regression fitting graphs of VMD combined with each model for prediction.
The results from
Results of ASSA weight searching.
Generally, the complexity of a model is related to its computational time.
With the rapid development of China’s economy, the consumption of traditional nonrenewable resources (oil, coal, etc.) is huge, and wind energy, as a renewable and clean energy source, is becoming an important green power generation method for the modern power grid. However, due to the nonlinear and nonstationary nature of wind speed, this trait seriously affects the safe and reliable operation of the power system, and finally leads to problems such as, difficult grid scheduling of wind farms. Therefore, the development of a highprecision and highreliability shortterm wind speed prediction model can, on the one hand, provide efficient and reliable planning for wind power, and on the other hand, stabilize the power grid and reduce the volatility. Numerous researchers have continuously invested in the study of wind speed prediction models, and a steady stream of wind speed prediction models have been proposed. Some examples of such models are, physical models based on meteorological data prediction; statistical models to establish the relationship with future wind speed function by calculating the historical wind speed; artificial intelligence prediction models based on training the model on training samples.
However, the above methods do not work well for fluctuating and complex data, so this paper proposes a shortterm wind speed prediction model based on a mixture of the VMD model, the Attention LSTM prediction model, and an improved salp swarm algorithm (multiobjective adaptive learning rate salp swarm algorithm). In this study, the VMD model is employed to decompose the original wind speed sequence into multiple stable intrinsic mode functions (IMFs). Subsequently, the AtLSTM model is utilized to individually forecast each IMF component. Finally, the proposed ASSA algorithm is applied to assign weights to each IMF component, resulting in a weighted aggregation that yields highly accurate shortterm wind speed predictions.
In this study, by simulating wind speed data from three wind farms and designing three aspects of comparison experiments, the experimental results illustrate that the data preprocessing strategy based on VMD technology can effectively reduce the volatility and complexity of the wind speed sequence, and significantly improve the accuracy of shortterm high wind speed prediction. Furthermore, in the prediction module, the Attention LSTM (AtLSTM) with an incorporated attention mechanism is introduced. This attention mechanism enables the LSTM network to analyze the importance of each temporal slice of input data, assigning higher weight values to slices that have a significant impact on the prediction results. As a result, the predictive accuracy is enhanced. Finally, the multiobjective adaptive learning rate salp swarm algorithm (ASSA) proposed in the weight optimization part adds two operators on the basis of salp swarm algorithm (SSA) that effectively solve the problem of local optimal solution, which the original algorithm is prone to, so as to improve its accuracy in optimization searching. In summary, by setting up a large number of different comparison experiments, it has been verified that the hybrid shortterm wind speed prediction model proposed in this paper based on the multiobjective adaptive learning rate salp swarm algorithm (ASSA), Attention LSTM, and VMD has fully demonstrated the accuracy advantage of the model.
In this study, a hybrid VMDAtLSTMASSA shortterm wind speed prediction model with decomposition algorithm and optimization algorithm is proposed to address the characteristics of shortterm wind speed unsteadiness and nonlinearity and the lack of prediction accuracy of a single model for complex data. This proposed model shows excellent prediction performance. Nevertheless, this model still has more application scenarios and room for expansion. Firstly, this study mainly focuses on the processing and prediction of wind speed time series information, and other data inputs, such as, wind direction information, seasonal information, and spatial information between wind farms, can be considered to expand the model’s environmental adaptability. Secondly, the K value of the variational modal decomposition algorithm used in this study is determined by judging whether the center frequency of each IMF is aliased or omitted, also, the α value is limited to 7,000, so the K value in this paper is selected for the experimental data in this paper, and it is not adaptive, so the introduction of optimization algorithms can be considered to achieve adaptive modal decomposition. Furthermore, within this research, we have observed that VMDGRU demonstrates remarkable predictive accuracy and computational efficiency. Therefore, in future studies, we plan to introduce additional advanced models for comparative analysis. Additionally, we aim to conduct comprehensive optimizations addressing both the accuracy and model complexity limitations identified in these models during our research. In addition, the optimization algorithm for the machine learning algorithm in this study is the salp swarm algorithm (SSA). Considering the rapid progress in the research of swarm intelligence algorithms, more efficient swarm intelligence optimization algorithms can be added to the future research, and other optimization algorithms can be replaced to improve the prediction performance of the model. Finally, the hybrid VMDAtLSTMASSA shortterm wind speed prediction model proposed in this paper is also suitable for other datasets with complex data, high volatility, and high accuracy requirements, such as, crude oil prices and nuclear energy consumption.
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.
LW: Conceptualization, Formal Analysis, Investigation, Methodology, Software, Visualization, Writing–original draft, Writing–review and editing. YL: Formal Analysis, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing–original draft, Writing–review and editing.
The author(s) declare financial support was received for the research, authorship, and/or publication of this article. The work was supported by a grant from the National Natural Science Foundation of China (Grant No: 42171419), awarded to YL.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.