# A Novel Wind Speed Interval Prediction System Based on Neural Network and Multi-objective Grasshopper Optimization

Authors: Zhirui Tian; Jiyang Wang
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

As a clean energy source, the role of wind power in the energy mix is becoming increasingly important. Reliable and high-quality wind speed prediction results are key to wind energy utilization. The traditional point prediction method cannot effectively analyze the uncertainty of wind speed, and the interval prediction model can provide the possible variation range of wind speed under a certain confidence probability and supply more uncertain information to decision makers. However, the previous interval prediction models generally ignore the random characteristics of capturing wind speed and the importance of objective selection of prediction submodels, leading to poor prediction results. To address these problems, a combined model based on data preprocessing, multi-neural network models, multi-objective optimization, and an improved interval prediction method is proposed. The model is applied to five wind speed forecasting examples in Dalian to test the prediction accuracy, multi-step prediction ability, and universality and generalization ability of the model. The experimental results show that the model proposed in this study is satisfactory for various performance evaluation indexes, has high stability and accuracy, and all the solutions obtained by the model are Pareto optimal solutions. Thus, it provides a reliable reference for the effective utilization of wind energy.


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## Body

## 1. Introduction

For a long time, the development mode with overreliance on coal, oil, and other traditional fossil fuels has not only brought economic growth to a majority of countries around the world, but also caused problems that cannot be ignored, such as environmental pollution, abnormal climate change, and frequent natural disasters [1].At present, countries worldwide are trying to find renewable energy to promote the green, efficient, and sustainable economic development. As a safe and sustainable energy, wind energy has naturally become an effective alternative to traditional energy [2].In 2020, the new installed capacity of global wind power was still set a new record, reaching 93 GW [3], owing to the two major markets, China and the United States. In China, by the end of 2020, the cumulative installed capacity of wind power had reached 2.81×108kW, including 2.71×108kW of onshore wind power and approximately 9×106kW of offshore wind power. This makes China the largest country in wind power, with 130% more power than the United States, which ranks second, and 1.2 times the installed capacity all of Europe. However, in terms of the proportion of wind power in total power demand, China lags behind Europe and the United States, and it is also slightly lower than the global average [4]. Figure 1 shows the power generation of each large wind power country.Figure 1
Global wind power generation data in 2020.At present, there are still many difficulties hindering the development of wind power generation, such as unstable and fluctuating wind speed, substandard technology, and difficulty in predicting wind speed, among which the prediction of wind speed is the most important issue. As we all know, wind speed has the characteristics of randomness and instability, which leads to an unsustainable and unstable output of the power grid, which may result in the collapse of the power grid. Therefore, accurate wind speed prediction is the key to improving wind power generation capacity.In the past 10 to 20 years, researchers have provided a number of alternative solutions for accurate wind speed prediction, including physical methods [5] and statistical methods [6]. The physical method does not require the support of historical power data from wind farms and is suitable for new wind farms. However, it requires a large number of accurate numerical weather forecast (NWP) data [7]. Further, the physical information of wind power decreases the accuracy of wind power prediction, and thus it is not suitable for countries with large land areas and complex terrain conditions. The statistical method requires the support of abundant historical data and has high requirements for the consistency of the change law of historical data. Most wind farms find it difficult to complete the establishment of statistical models because the position of measurement is not accurate.As a result, artificial intelligence models have received significant attention. The advantage of the artificial intelligence model is that it does not require high position accuracy for measuring wind speed and does not need any prior assumptions. Common artificial intelligence models for predicting wind speed include the NN neural network, Elman neural network [8], LSTM deep learning [9], and GRU deep learning [10]. For example, Humfeld et al. predicted the wind turbine generation capacity using a neural network (NN) and achieved good results [11]. Choe et al. successfully predicted the power generation efficiency of floating offshore wind turbine blades using LSTM and GRU deep learning [12]. Niu and Wang used the combined model of point prediction to predict the wind speed and achieved good results [13]. Niu et al. proposed a carbon price forecasting system based on error correction and divide-conquer strategies; the use of multi-objective optimization algorithm effectively improves the prediction accuracy [14]. Hao et al. proposed a new combination forecasting model for the prediction of the impact of haze on China’s economy [15]. Gao et al. proposed a multicomponent hybrid system based on predictability recognition and modified multi-objective optimization for ultra-short-term onshore wind speed forecasting [16]. Yang et al. proposed a new novel machine learning-based electricity price forecasting model based on optimal model selection strategy [17]. However, a single artificial intelligence model will fall into the problem of a local minimum or lead to overfitting. Therefore, some experts have proposed a combined model based on artificial intelligence models. For example, the EMD + DBN method [14], after high- and low-frequency data decomposition through the EMD method, predicts and recombines each layer of data to solve the problem of wind speed prediction lag [18]. However, owing to the lack of optimization of the prediction results, there is often a large gap with the real value.In the current research, most wind speed forecast studies are based on point prediction [19]. Point prediction cannot ensure the reliability and controllability of wind speed prediction, whereas interval prediction can quantify the changes of prediction results caused by uncertainty and observe the changes in wind speed at different significance levels. Most importantly, effective interval prediction results can provide more uncertain information for decision-makers and help them carry out risk prediction and assessment.At present, the point prediction (PF) accuracy of the combined model has made great progress, while the accuracy of interval prediction has been improved to a lesser extent. Interval prediction methods mainly include the Mean Variance Estimation Method [20], Delta Method [21], Bayesian Method [22], and Bootstrap Method [23, 24]. In this study, the Bootstrap Method is adopted; however, its performance largely depends on the prediction accuracy of a single neural network. To solve this problem, a combined model based on multiple neural networks is proposed, and a heuristic optimization algorithm is used to obtain the optimal super parameters and weight parameters [25, 26]. The evaluation of existing wind speed forecast models is presented in Table 1.Table 1
Evaluation of existing wind speed forecast model.
CategoryMethodAdvantagesDisadvantagesStatistical methodARMAARIMASARIMAThe prediction accuracy is high, and only endogenous variables are needed without the help of other exogenous variables.It is required that the time series data are stable and can only capture the linear relationship.Neural networkBPELMSVMElmanWAVENNIt has good self-learning, self-organization, and self-adaptability and better performance in the case of large samples.It has the function of realizing any complex nonlinear mapping, which makes it suitable for solving problems with complex internal mechanisms.The performance is poor when the sample size is small and the process cannot be explained.It is difficult to solve the contradiction between the instance scale and the network scale of the application problem.Deep learningLSTMGRUDBNStrong learning ability and wide coverage.It can effectively avoid the problem of RNN gradient disappearing.The amount of calculation is too large and the model is also complex.From the review of a large number of studies, we find that the existing wind speed prediction mostly uses single neural network prediction supplemented by multi-objective optimization model or multiple neural network prediction supplemented with a single-objective optimization model. The single-objective optimization model often ignores the stability of prediction while improving the accuracy, whereas single neural network prediction may not be suitable for all wind speed situations. We develop a combined model based on multiple single neural network prediction models and multi-objective optimization. A number of experiments show that, under the condition that the data requirements are not too stringent, the combined model proposed in this study improves the accuracy of wind speed interval prediction and can effectively improve the wind power generation capacity. In addition, in the comprehensive evaluation module, we use several evaluation indicators of interval prediction ability to evaluate the effectiveness of the combination model proposed in this study on a comprehensive manner and prove its superiority.The contributions and innovations of this study are as follows:(i)
The data preprocessing method is used to reduce the volatility and randomness of wind speed series in an effective way. As the application of decomposition and reconstruction technology, the data preprocessing strategy is used to delete the high-frequency noise and leave the low-frequency effective wind speed data. After decomposition and reconstruction, the volatility and randomness of the original wind speed series are effectively reduced, and the prediction performance is improved.(ii)
A combined system that includes data preprocessing, combined forecasting of multiple neural networks, and a multi-objective optimization and evaluation module is proposed. Four different neural network models are used for interval prediction of data, overcoming the limitations of a single neural network, and the prediction results of the different neural networks are optimized through a multi-objective optimization model. Thus, the different objectives tend to be Pareto optimal solutions at the same time, and the problem that stability and accuracy cannot coexist is overcome.(iii)
Interval forecasts can observe the changes in wind speed at different significant levels, which provides more accurate information on wind speed for decision-makers. In the interval prediction, the combined neural network prediction model is adopted, and a heuristic optimization algorithm is used to improve the Bootstrap method, thus obtaining accurate interval prediction results.(iv)
A comprehensive and exhaustive evaluation system is established to validate the performance and prediction accuracy of the forecasting models. Five experiments are performed to verify the superiority, universality, and generalization of the model.The remaining of this paper is organized as follows: Section2 introduces the selection of data and data processing; Section 3 introduces the combined neural network and its optimization principle and constructs and optimizes the models; Section 4 evaluates and verifies the superiority of the model through multiple groups of data and multiple indicators; and Section 5 discusses the advantages and disadvantages of the model and the directions for further improvement.


## 2. Data and Data Processing

Dalian, which is located at the southern end of the Liaodong Peninsula of China (38.43°–40.12° N and 120.58°–123.31° E), has a wind speed suitable for wind power generation throughout the year, making it an ideal location for wind power plants. In fact, wind power development in Dalian City has been at the leading level in China. In 2015, the power grid received 152.4 million kilowatt-hours of wind power in Dalian City, accounting for 5% of the electricity generation in Dalian City. Wind power has become an important energy source for Dalian.In this study, wind speed monitoring data obtained in January 2011 from four different monitoring sites (WTG03, WTG04, WTG05, and WTG06) in a wind power plant in Dalian are selected. The datasets include four groups, and each group has 1463 sets of wind speed data, at which there is an interval of 10 minutes. Figure2 shows the basics of each dataset.Figure 2
Selection and presentation of 4 groups of data.As the commonly used data preprocessing strategies, the empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) have the drawbacks of modal aliasing and involve a certain white noise fluctuation after reducing the noise in raw datasets, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) proposed by Torres [27] is utilized. CEEMDAN solves the above problems from two aspects.(1)
The intrinsic mode function (IMF) component with auxiliary noise is added after decomposition by EMD instead of the white Gaussian noise signal being directly added to the original signal.(2)
EMD and EEMD [28] are used to calculate the average value of the modal components obtained from empirical mode decomposition, whereas CEEMDAN calculates the average value when the first-order IMF [29] components are obtained; then, the above operations are repeated for the residual parts. In this way, the CEEMDAN has effectively solved the transfer and transmission problem of white noise from high frequency to low frequency.LetEi be the ith eigenmode component obtained by EMD and Φ¯¯1t the ith eigenmode component obtained by CEEMDAN. vj is the Gaussian white noise signal satisfying the standard normal distribution, j=1,2,…,n is the number of added white noise, ψ¯ is the standard table of white noise, and yt is the signal to be decomposed. The EMD process is summarized as follows:(1)
White noise, which is positive and negative pairwise, is added to the signalyt to be decomposed, and a new signal is obtained: yt+−1qvjt, where q=1,2,…,n. Then, decompose the new signal using EMD to obtain the first-order eigenmode component Φ1:(1)Eyt+−1qεvjt=Φ1jt+rj.(2)
Obtain the first eigenmode component of CEEMDAN by averaging generatedN-modal components:(2)Φ¯¯1t=1N∑j=1NEyt+−1qψ¯vjt−rj=1N∑j=1NΦ1jt.(3)
Secondary calculation residual:(3)r1t=yt−1N∑j=1NEyt+−1qΔ∇ψ¯vjt−rj=yt−Φ¯¯1t.(4)
The way to obtain a new signal is to add the positive and negative pairwise Gaussian white noiser1t.Then, the first modal component of the EMD (D1) decomposition and the second modal component of the CEEMDAN are obtained:(4)Φ¯¯2t=1N∑j=1N∑i=1NDijt=1N∑j=1NEyt+−1qψ¯vjt−rjPART2.(5)
The residual after removing the second modal component is calculated:(5)r2t=r1t−1N∑j=1N∑i=1NDijt=r1t−Φ¯¯2t.(6)
Repeat the above steps until the obtained residual signal is a monotone function and cannot be decomposed, and the algorithm ends. The number of eigenmode components obtained isK and the original signal yt is decomposed into(6)yt=Φ¯¯1t+Φ¯¯2t+⋯+Φ¯¯kt+rkt=∑k=1KΦ¯¯kt+rkt.Taking the first set of data (Site 1) as an example, a data preprocessing technique is performed, and the CEEMDAN method is implemented in MATLAB. The parameters of the CEEMDAN are set as follows: Nstd value is 0.2, NR value is 50, and Maxlter value is 500. The original data are divided into 10 different stats with different frequencies, the two groups of data with the highest frequency are filtered out, and the others are used to reconstruct a series that is more stable for the subsequent forecasting stage, as shown in Figure3.Figure 3
Data preprocessing results display.


## 3. Theory and Construction of Combined Model

A combined model is used to achieve more accurate forecasting results. In this study, four AI models are selected as the component models for our proposed combined model: limit learning machine (ELM) [30], support vector machine (SVM) [31], back-propagation neuron network (BP) [32], and wavelet neural network (WAVENN) [33]. To improve its accuracy, the four groups of prediction results from the four AI models are weighted again using the multi-objective locust optimization algorithm (MOGOA). The basic theory of each model is as follows.


### 3.1. Theory of Combined Models

The network structure of the ELM is the same as that of a single hidden layer feedforward neural network (SLFN) [34], but in the training stage, the traditional neural network (back propagation) algorithm is no longer used, and the weights and deviations of the input layer are randomly set. In this study, we set the implicit layer neuronal activation function gx, sample size Q, and network output value T.(7)T=t1,t2,t3,…,tQm∗Q,tj=t1jt2jt3j⋯tmjm∗l=∑i=1lβi1g¯¯wixj+bi∑i=1lβi2g¯¯wixj+bi⋯∑i=1lβimg¯¯wixj+bij=1,2,3,4,…,Q.The objective function is as follows:(8)minHβ−T,β∈RL∗M.According to the linear algebra and the matrix theory, the optimal solution can be deduced as follows:(9)β=H†T,where H† is the Moore–Penrose generalized inverse matrix of matrix H.The above problem is transformed into calculating the Moore–Penrose generalized inverse matrix of matrixH using the singular value decomposition method (SVD) [35]. If HTH is nonsingular, we can use the orthogonal projection method, and the calculated results are as follows:(10)H†=HTH−1HT.SVM was first proposed by Vapnik, and it is a two-class classification model. Its basic model is to find a linear classifier with a maximum separation hyperplane in the feature space. The SVM model mainly comprises four parts:(1)
Set the known training as(11)T=x1,y1,…,xi,yi∈X∗Yi.(2)
Choose an appropriate kernel functionK and parameter Θ to construct the optimization problem:(12)min12∑i=1j∑j=1lyiyjaiajKxi,xj−∑j=1laj,s.t.∑i=1lyiai=0,0≤ai≤Θ,i=1,2,3,…,n.Obtain the optimal solution:a∗=a1∗,…,ai∗T.(3)
Choose a positive component of0<ai∗<Θ, and calculate the threshold accordingly:(13)b∗=yj−∑i=1lyiai∗Kxi⟶−xj⟶.(4)
Construct a decision function:(14)fx=sgn∑i=1lai∗yiKx,xi+b∗.(5)
Add a relaxation termξi≥0:(15)minW,b12WTW+C∑i=1nξi,s.t.yiWTxi+b−1+ξi≥0,i=1,2,3,…,n,maxai∑i=1nai−12∑i,j=1naiajyiyjxi,xj,s.t.∑i=1lyiai=0,0≤ai≤Θ,i=1,2,3,…,n.The parameters used in the regression arer2 and MSE, and their formulas are(16)MSE=1n∑i=1nfxi−yi2,r2=n∑i=1nfxiyi−∑i=1nfxi∑i=1nyin∑i=1nfxi2−∑i=1nfxi2n∑i=1nyi2−∑i=1nyi2.We use the LIBSVM-FarutoUltimate Ultimate toolbox to optimize the SVM. The scale for the SVM function in the toolbox can optimize and normalize the parameters reasonably, which further improves the accuracy of prediction [36].WAVENN was originally used to predict traffic flow series. Wavelet analysis is developed to solve the deficiency of the Fourier transform, which has no resolution in time domain. The wavelet basis function of Morlet is used in this study:y=cos1.75xe−x2/2.(17)fxa,τ=1a∫−∞∞xtΦt−τadt,a≥0.In the neural network, we use the first four sets of data of each time node to make a rolling prediction of the node to improve the prediction effect:M=4. The calculation formula and prediction error of the output layer of it are as follows:(18)yk=∑i=1lwikhi,k=1,2,…,m,e=∑k=1mynk−yk.The key point of the WAVENN neural network lies in the use of wavelet transform:(19)tu˜=∑x=0N−1fxsx,u,sx,u˜=αucosμπNx+12,αu=1N,u˜=0,2Nu˜=1,2,…,N−1.Suppose the data can be written in vector form:f∈RN∗1, t∈RN∗1:(20)t⌢=s0Tfs1Tf⋯sN−1Tf=s0Ts1T⋯sN−1T,t⌢=Af,where si=s0,1,s1,i,…,sN−1,iT, A=s0,s1,…,sN−1T.(21)AT=S0TS0S0TS1⋯S0TSN−1S1TS0S1TS2⋯S1TSN−1SN−1TS0SN−1TS3⋯SN−1TSN−1,f=ATt,f1,f2=t1,t2=Af1,Af2.The BP neural network is a neural network which is based on an error back-propagation algorithm. The prediction function of the BP neural network issimnet,x. BP neural network is solved through the following steps:(1)
Hidden layer output calculation:(22)Hj=f∑i=1nwijxi−aj,fx=11+e−x.(2)
Output layer result calculation:(23)Ok=∑j=1lHjwjk−bk,k=1,2,…,n,ek=Yk−Ok,k=1,2,…,n.(3)
Error calculation, weight and threshold update, and output of results:(24)wjk=wjk+ηHjek,wij=wij+ηHi1−Hixi,k=1,2,…,n,aj=aj+ηHj1−Hj∑k=1mwijek,j=1,2,…,n,bk=bk+ek.The gradient matrix is mainly used in the BP neural network:(25)∇AfAij=∂fA∂Aij,∇xfx=∂fx∂x1∂fx∂x2⋯∂fx∂xn.MOGOA is a new type of optimization algorithm [37]. The GOA algorithm has a strong exploration advantage on the whole [38], which ensures that the algorithm has a strong global search ability, and avoids stopping in the local optimization. We use this algorithm to fit the results of the above four models to make the prediction results close to the true value.The algorithm divides the search into exploration and development by simulating the population migration and foraging behavior of locusts in nature. The mathematical formula for the locust algorithm is as follows:(26)Xi=Si+Gi+Ai,where Xi is the position of the ith locust, Si refers to the mutual influence between individuals, Gi is the gravity of the ith locust, Ai is the wind force on the ith locust, and Si is calculated as follows:(27)Si=∑j=1,j≠iNsdijDij,sdijt=f∗esp−dijtl−exp−dijt,Dijt¯=xjt⟶−xit⟶dijt.where dij=xi⟶−xj⟶ is the distance between the ith and the jth locusts and Dij=xj⟶−xi⟶/dij is the unit vector pointing to the jth locust for the ith locust.However, the functions has defects: that is, when the distance between locusts is excessively large, the force will not exist, and thus the distance between locusts should be standardized.(28)Gi=−geg,where g is the gravity constant and ej is the unit vector pointing to the center of the Earth.Ai can be calculated as follows:(29)Ai=−uew.Usually, when the locust swarm reaches the comfort zone, the swarm does not converge. To adapt to the solution of the optimization problem and coordinate the global and local optimization processes, parameters can be introduced to distinguish different stages of optimization. The original model and the improved mathematical models are as follows:(30)Xi=∑j=1,j≠iNsxj⟶−xi⟶xj⟶−xi⟶d+TdXi=∑j=1,j≠iNcubd−lbd2sxj⟶−xi⟶xj⟶−xi⟶dij+Td,where c is the decreasing coefficient, which determines the size of the comfort zone, repulsion zone, and attraction zone, n is the number of locusts, and Td is the best solution of locust position in the d-dimensional space thus far. In the formula, the influence of gravity is not considered, and it is assumed that the wind direction always points to the optimal solution. The internal c helps to reduce the repulsion or attraction between locusts, which is directly proportional to the number of iterations. The external c will reduce the search area around the target with an increase in the number of iterations.The following formula is used to reduce the global search and increase the local precision search.(31)c=cmax−ncmax−cminL.Proof.
It is proved that when the algorithm finds the optimal solution, it will be stored in Archive, and those with high fitness will be selected in the front position. If there is aY∗=X∗+φ, and satisfies FITWY∗≥FITWX∗, then WY∗ will be sorted in front of WX∗. When Archive is full, the value with low fitness will be proposed, so the first few individuals of the final selected Archive are Pareto optimal solutions of MOGOA.


### 3.2. Construction of Combined Model

A new wind speed interval prediction framework is proposed using the model introduced in the previous section. The system mainly includes a combined prediction module and evaluation module, as presented in Figure4 and Tables 2 and 3. We selected the first 1200 data as the training set and the last 203data as the test set. The whole process of the combined prediction model is as follows:(1)
Use the CEEMDAN method to decompose the original data into components with different frequencies and delete the component with the highest frequency as noise to achieve the effect of data noise reduction.(2)
Use 4 different neural networks to predict the processed data and use the multi-objective optimization algorithm to perform unconstrained weighting on the prediction results to obtain a new prediction solution.(3)
Use different indicators to evaluate the prediction results of the combined model to verify its advanced nature.Figure 4
Processing flow of the study.Table 2
Data chosen for training and test sets.
Training setTesting setMean (m/s)Min (m/s)Max (m/s)Data 112002036.31011.913.3Data 212002036.45641.813.5Data 312002036.77012.013.4Data 412002036.23412.113.2Table 3
Parameters and setting value.
ModelParametersSetting valueBPHidden layer modes20Learning rate0.05Training epochs7000ELMHidden layer modes20Training epochs7000SVMCost1Gamma0.002WAVENNHidden layer modes6Learning rate 10.01Learning rate 20.001Training epochs10000MOGOANumber of iterations200Population100Archive max size500Cmax1Cmin0.00004


#### 3.2.1. Combined Prediction Module

The combined model we proposed selects four artificial intelligence models (WAVENN, SVM, ELM, and BP) as component models [39]. The four neural networks have a good prediction accuracy. Through continuous debugging of the number of hidden layer nodes, learning rate, and other parameters, they are suitable for long-term prediction. After obtaining the point prediction, we form different confidence intervals according to the results of point prediction, and set the upper boundary of the confidence interval as Ui and the lower boundary as Li [40].(32)Ui=Y^+Z1−a/2∗σ^y2xi+σ^ε2xi,Li=Y^−Z1−a/2∗σ^y2xi+σ^ε2xi,where Y^ is the estimated value of the real regression mean, σ^y2xi is the variance of the uncertainty of the NN model, and σ^ε2xi is the variance of the noise.To make the interval prediction of the time series more accurate, we use MOGOA to optimize the single predicted value of the above four neural networks and make it as close to the real results as possible (Algorithm1).Algorithm 1: Pseudocode of the MOGOA.
Objective functions:minobj1y=1/N∑i=1Ny^i−y1obj2y=stdy^i−y1Parameters:IterMax: The maximum number of iterationsN: The number of grasshoppersXi: The position of ith grasshoppersXj: The position ofjth grasshopperst: The current iteration numberd: The number of dimensionsWHILE (t<IterMax) DOUpdateμ using μ=μMax−tμMax−μMin/IterMaxFor all agents DONormal distance between grasshoppers in [1, 4]Update grasshoppers-position withXij=μ∑j=1nμHd−Ld/2sdjid^ij+T^dCalculate the fitness function for each search agentFind the non-dominated solutionsUpdateAIF (A is full) THENRun the grid mechanism to one of the currents achieve membersAdd the new solution toAEND IFEND FORt=t+1END WHILERETURE A (Contains PO)


#### 3.2.2. Evaluation Module

After the above process, we apply the combination strategy to predict the data, and through a number of interval prediction indicators for comprehensive evaluation, we verify the superiority of the model performance.We take 1200 sets of data (1th–1200th) in each group of data as the training set and the data (1201th–1403th) as the test set, use the proposed combination model to predict, and draw the prediction results of Site 1, as shown in Figure5. Confidence level is 0.95, respectively.Figure 5
The prediction interval of 95% confidence level is compared with the true value.


## 3.1. Theory of Combined Models

The network structure of the ELM is the same as that of a single hidden layer feedforward neural network (SLFN) [34], but in the training stage, the traditional neural network (back propagation) algorithm is no longer used, and the weights and deviations of the input layer are randomly set. In this study, we set the implicit layer neuronal activation function gx, sample size Q, and network output value T.(7)T=t1,t2,t3,…,tQm∗Q,tj=t1jt2jt3j⋯tmjm∗l=∑i=1lβi1g¯¯wixj+bi∑i=1lβi2g¯¯wixj+bi⋯∑i=1lβimg¯¯wixj+bij=1,2,3,4,…,Q.The objective function is as follows:(8)minHβ−T,β∈RL∗M.According to the linear algebra and the matrix theory, the optimal solution can be deduced as follows:(9)β=H†T,where H† is the Moore–Penrose generalized inverse matrix of matrix H.The above problem is transformed into calculating the Moore–Penrose generalized inverse matrix of matrixH using the singular value decomposition method (SVD) [35]. If HTH is nonsingular, we can use the orthogonal projection method, and the calculated results are as follows:(10)H†=HTH−1HT.SVM was first proposed by Vapnik, and it is a two-class classification model. Its basic model is to find a linear classifier with a maximum separation hyperplane in the feature space. The SVM model mainly comprises four parts:(1)
Set the known training as(11)T=x1,y1,…,xi,yi∈X∗Yi.(2)
Choose an appropriate kernel functionK and parameter Θ to construct the optimization problem:(12)min12∑i=1j∑j=1lyiyjaiajKxi,xj−∑j=1laj,s.t.∑i=1lyiai=0,0≤ai≤Θ,i=1,2,3,…,n.Obtain the optimal solution:a∗=a1∗,…,ai∗T.(3)
Choose a positive component of0<ai∗<Θ, and calculate the threshold accordingly:(13)b∗=yj−∑i=1lyiai∗Kxi⟶−xj⟶.(4)
Construct a decision function:(14)fx=sgn∑i=1lai∗yiKx,xi+b∗.(5)
Add a relaxation termξi≥0:(15)minW,b12WTW+C∑i=1nξi,s.t.yiWTxi+b−1+ξi≥0,i=1,2,3,…,n,maxai∑i=1nai−12∑i,j=1naiajyiyjxi,xj,s.t.∑i=1lyiai=0,0≤ai≤Θ,i=1,2,3,…,n.The parameters used in the regression arer2 and MSE, and their formulas are(16)MSE=1n∑i=1nfxi−yi2,r2=n∑i=1nfxiyi−∑i=1nfxi∑i=1nyin∑i=1nfxi2−∑i=1nfxi2n∑i=1nyi2−∑i=1nyi2.We use the LIBSVM-FarutoUltimate Ultimate toolbox to optimize the SVM. The scale for the SVM function in the toolbox can optimize and normalize the parameters reasonably, which further improves the accuracy of prediction [36].WAVENN was originally used to predict traffic flow series. Wavelet analysis is developed to solve the deficiency of the Fourier transform, which has no resolution in time domain. The wavelet basis function of Morlet is used in this study:y=cos1.75xe−x2/2.(17)fxa,τ=1a∫−∞∞xtΦt−τadt,a≥0.In the neural network, we use the first four sets of data of each time node to make a rolling prediction of the node to improve the prediction effect:M=4. The calculation formula and prediction error of the output layer of it are as follows:(18)yk=∑i=1lwikhi,k=1,2,…,m,e=∑k=1mynk−yk.The key point of the WAVENN neural network lies in the use of wavelet transform:(19)tu˜=∑x=0N−1fxsx,u,sx,u˜=αucosμπNx+12,αu=1N,u˜=0,2Nu˜=1,2,…,N−1.Suppose the data can be written in vector form:f∈RN∗1, t∈RN∗1:(20)t⌢=s0Tfs1Tf⋯sN−1Tf=s0Ts1T⋯sN−1T,t⌢=Af,where si=s0,1,s1,i,…,sN−1,iT, A=s0,s1,…,sN−1T.(21)AT=S0TS0S0TS1⋯S0TSN−1S1TS0S1TS2⋯S1TSN−1SN−1TS0SN−1TS3⋯SN−1TSN−1,f=ATt,f1,f2=t1,t2=Af1,Af2.The BP neural network is a neural network which is based on an error back-propagation algorithm. The prediction function of the BP neural network issimnet,x. BP neural network is solved through the following steps:(1)
Hidden layer output calculation:(22)Hj=f∑i=1nwijxi−aj,fx=11+e−x.(2)
Output layer result calculation:(23)Ok=∑j=1lHjwjk−bk,k=1,2,…,n,ek=Yk−Ok,k=1,2,…,n.(3)
Error calculation, weight and threshold update, and output of results:(24)wjk=wjk+ηHjek,wij=wij+ηHi1−Hixi,k=1,2,…,n,aj=aj+ηHj1−Hj∑k=1mwijek,j=1,2,…,n,bk=bk+ek.The gradient matrix is mainly used in the BP neural network:(25)∇AfAij=∂fA∂Aij,∇xfx=∂fx∂x1∂fx∂x2⋯∂fx∂xn.MOGOA is a new type of optimization algorithm [37]. The GOA algorithm has a strong exploration advantage on the whole [38], which ensures that the algorithm has a strong global search ability, and avoids stopping in the local optimization. We use this algorithm to fit the results of the above four models to make the prediction results close to the true value.The algorithm divides the search into exploration and development by simulating the population migration and foraging behavior of locusts in nature. The mathematical formula for the locust algorithm is as follows:(26)Xi=Si+Gi+Ai,where Xi is the position of the ith locust, Si refers to the mutual influence between individuals, Gi is the gravity of the ith locust, Ai is the wind force on the ith locust, and Si is calculated as follows:(27)Si=∑j=1,j≠iNsdijDij,sdijt=f∗esp−dijtl−exp−dijt,Dijt¯=xjt⟶−xit⟶dijt.where dij=xi⟶−xj⟶ is the distance between the ith and the jth locusts and Dij=xj⟶−xi⟶/dij is the unit vector pointing to the jth locust for the ith locust.However, the functions has defects: that is, when the distance between locusts is excessively large, the force will not exist, and thus the distance between locusts should be standardized.(28)Gi=−geg,where g is the gravity constant and ej is the unit vector pointing to the center of the Earth.Ai can be calculated as follows:(29)Ai=−uew.Usually, when the locust swarm reaches the comfort zone, the swarm does not converge. To adapt to the solution of the optimization problem and coordinate the global and local optimization processes, parameters can be introduced to distinguish different stages of optimization. The original model and the improved mathematical models are as follows:(30)Xi=∑j=1,j≠iNsxj⟶−xi⟶xj⟶−xi⟶d+TdXi=∑j=1,j≠iNcubd−lbd2sxj⟶−xi⟶xj⟶−xi⟶dij+Td,where c is the decreasing coefficient, which determines the size of the comfort zone, repulsion zone, and attraction zone, n is the number of locusts, and Td is the best solution of locust position in the d-dimensional space thus far. In the formula, the influence of gravity is not considered, and it is assumed that the wind direction always points to the optimal solution. The internal c helps to reduce the repulsion or attraction between locusts, which is directly proportional to the number of iterations. The external c will reduce the search area around the target with an increase in the number of iterations.The following formula is used to reduce the global search and increase the local precision search.(31)c=cmax−ncmax−cminL.Proof.
It is proved that when the algorithm finds the optimal solution, it will be stored in Archive, and those with high fitness will be selected in the front position. If there is aY∗=X∗+φ, and satisfies FITWY∗≥FITWX∗, then WY∗ will be sorted in front of WX∗. When Archive is full, the value with low fitness will be proposed, so the first few individuals of the final selected Archive are Pareto optimal solutions of MOGOA.


## 3.2. Construction of Combined Model

A new wind speed interval prediction framework is proposed using the model introduced in the previous section. The system mainly includes a combined prediction module and evaluation module, as presented in Figure4 and Tables 2 and 3. We selected the first 1200 data as the training set and the last 203data as the test set. The whole process of the combined prediction model is as follows:(1)
Use the CEEMDAN method to decompose the original data into components with different frequencies and delete the component with the highest frequency as noise to achieve the effect of data noise reduction.(2)
Use 4 different neural networks to predict the processed data and use the multi-objective optimization algorithm to perform unconstrained weighting on the prediction results to obtain a new prediction solution.(3)
Use different indicators to evaluate the prediction results of the combined model to verify its advanced nature.Figure 4
Processing flow of the study.Table 2
Data chosen for training and test sets.
Training setTesting setMean (m/s)Min (m/s)Max (m/s)Data 112002036.31011.913.3Data 212002036.45641.813.5Data 312002036.77012.013.4Data 412002036.23412.113.2Table 3
Parameters and setting value.
ModelParametersSetting valueBPHidden layer modes20Learning rate0.05Training epochs7000ELMHidden layer modes20Training epochs7000SVMCost1Gamma0.002WAVENNHidden layer modes6Learning rate 10.01Learning rate 20.001Training epochs10000MOGOANumber of iterations200Population100Archive max size500Cmax1Cmin0.00004


### 3.2.1. Combined Prediction Module

The combined model we proposed selects four artificial intelligence models (WAVENN, SVM, ELM, and BP) as component models [39]. The four neural networks have a good prediction accuracy. Through continuous debugging of the number of hidden layer nodes, learning rate, and other parameters, they are suitable for long-term prediction. After obtaining the point prediction, we form different confidence intervals according to the results of point prediction, and set the upper boundary of the confidence interval as Ui and the lower boundary as Li [40].(32)Ui=Y^+Z1−a/2∗σ^y2xi+σ^ε2xi,Li=Y^−Z1−a/2∗σ^y2xi+σ^ε2xi,where Y^ is the estimated value of the real regression mean, σ^y2xi is the variance of the uncertainty of the NN model, and σ^ε2xi is the variance of the noise.To make the interval prediction of the time series more accurate, we use MOGOA to optimize the single predicted value of the above four neural networks and make it as close to the real results as possible (Algorithm1).Algorithm 1: Pseudocode of the MOGOA.
Objective functions:minobj1y=1/N∑i=1Ny^i−y1obj2y=stdy^i−y1Parameters:IterMax: The maximum number of iterationsN: The number of grasshoppersXi: The position of ith grasshoppersXj: The position ofjth grasshopperst: The current iteration numberd: The number of dimensionsWHILE (t<IterMax) DOUpdateμ using μ=μMax−tμMax−μMin/IterMaxFor all agents DONormal distance between grasshoppers in [1, 4]Update grasshoppers-position withXij=μ∑j=1nμHd−Ld/2sdjid^ij+T^dCalculate the fitness function for each search agentFind the non-dominated solutionsUpdateAIF (A is full) THENRun the grid mechanism to one of the currents achieve membersAdd the new solution toAEND IFEND FORt=t+1END WHILERETURE A (Contains PO)


### 3.2.2. Evaluation Module

After the above process, we apply the combination strategy to predict the data, and through a number of interval prediction indicators for comprehensive evaluation, we verify the superiority of the model performance.We take 1200 sets of data (1th–1200th) in each group of data as the training set and the data (1201th–1403th) as the test set, use the proposed combination model to predict, and draw the prediction results of Site 1, as shown in Figure5. Confidence level is 0.95, respectively.Figure 5
The prediction interval of 95% confidence level is compared with the true value.


## 3.2.1. Combined Prediction Module

The combined model we proposed selects four artificial intelligence models (WAVENN, SVM, ELM, and BP) as component models [39]. The four neural networks have a good prediction accuracy. Through continuous debugging of the number of hidden layer nodes, learning rate, and other parameters, they are suitable for long-term prediction. After obtaining the point prediction, we form different confidence intervals according to the results of point prediction, and set the upper boundary of the confidence interval as Ui and the lower boundary as Li [40].(32)Ui=Y^+Z1−a/2∗σ^y2xi+σ^ε2xi,Li=Y^−Z1−a/2∗σ^y2xi+σ^ε2xi,where Y^ is the estimated value of the real regression mean, σ^y2xi is the variance of the uncertainty of the NN model, and σ^ε2xi is the variance of the noise.To make the interval prediction of the time series more accurate, we use MOGOA to optimize the single predicted value of the above four neural networks and make it as close to the real results as possible (Algorithm1).Algorithm 1: Pseudocode of the MOGOA.
Objective functions:minobj1y=1/N∑i=1Ny^i−y1obj2y=stdy^i−y1Parameters:IterMax: The maximum number of iterationsN: The number of grasshoppersXi: The position of ith grasshoppersXj: The position ofjth grasshopperst: The current iteration numberd: The number of dimensionsWHILE (t<IterMax) DOUpdateμ using μ=μMax−tμMax−μMin/IterMaxFor all agents DONormal distance between grasshoppers in [1, 4]Update grasshoppers-position withXij=μ∑j=1nμHd−Ld/2sdjid^ij+T^dCalculate the fitness function for each search agentFind the non-dominated solutionsUpdateAIF (A is full) THENRun the grid mechanism to one of the currents achieve membersAdd the new solution toAEND IFEND FORt=t+1END WHILERETURE A (Contains PO)


## 3.2.2. Evaluation Module

After the above process, we apply the combination strategy to predict the data, and through a number of interval prediction indicators for comprehensive evaluation, we verify the superiority of the model performance.We take 1200 sets of data (1th–1200th) in each group of data as the training set and the data (1201th–1403th) as the test set, use the proposed combination model to predict, and draw the prediction results of Site 1, as shown in Figure5. Confidence level is 0.95, respectively.Figure 5
The prediction interval of 95% confidence level is compared with the true value.


## 4. Verification and Evaluation of the Model

After the construction and optimization of the model, we need to establish an evaluation system to verify the superiority of the model. This is divided into five experiments: (1) comparison between the combined model and the single neural network model; (2) comparison of different data preprocessing methods (EMD and EEMD), CEEMDAN, and data nonpreprocessing; (3) universality test of the combined model proposed in this study; (4) generalization ability test of the combined model; and (5) use of multi-step prediction to verify the prediction ability of the model.


### 4.1. Experiment I

To verify the superiority of the combined model over the component neural networks (SVM, BP, WAVENN, and ELM), seven indexes, namely, MAPE [41], PICP [42], MPIW [43], CWC [44], ACE [45], MPICD [46], and NMPICD (min-max) [36] are selected for the comprehensive evaluation. The confidence levels of interval prediction are 0.8, 0.9, and 0.95, respectively. The formula of each evaluation index is presented in Table 4, and the evaluation results are presented in Table 5 and Figure 5.Table 4
A summary of the formulas used in this study.
IndexMathematical expressionMAPEMAPE=1/N∑i=1NOacti−O^fori/Oacti∗100%PICPPICP=1/n∑i=1nciMPIWMPIW=1/n∑i=1nUi−LiCWCCWC=PINAW1+γe−ηPICP−μγ=0,PICP>μ1,PICP<μACEACE=PICP−μMPICDMPICD=1/Ntest∑i=1NtestU^aXi+L^aXi/2NMPICDNMPICD=MPICD/ξTable 5
Accuracy comparison between combined model and single model.
DataMethodMAPEPICPMPIWCWCACEMPICDNMPICD0.80.90.950.80.90.950.80.90.950.80.90.95Site 1CEE-BP5.14320.8330.9240.9671.12841.46741.62621.12841.46741.62620.0330.0240.0170.21090.17CEE-SVM5.38640.8560.9330.9821.18441.43901.68231.18441.43901.68230.0560.0330.0320.30120.35CEE-WAVENN8.79880.7760.9020.9421.28311.36341.75241.44711.36341.7981−0.020.002−0.10.54570.77CEE-ELM4.87530.8870.9510.9841.25841.49001.69171.25841.49001.69170.0870.0510.0340.27820.29MOGOA3.89750.8950.9640.9891.29191.30691.76711.29191.30691.76710.0950.0640.0390.11070.00Site 2CEE-BP4.99870.8420.9280.9591.23111.39771.78691.23111.39771.78690.0420.0280.0090.30130.35CEE-SVM4.68950.8370.9120.9671.10711.37631.72401.10711.37631.72400.0370.0120.0170.38720.38CEE-WAVENN6.49700.8010.9160.9581.26981.45311.65341.26981.45311.65340.0010.0160.0080.67291.00CEE-ELM4.08530.8750.9440.9461.28681.45901.56251.28681.45901.56250.0750.044−0.10.22360.19MOGOA3.25460.9010.9750.9851.23571.33741.55871.23571.33741.55870.0010.0750.1350.22190.19Site 3CEE-BP5.67540.8650.9530.9571.25151.39801.71711.25151.39801.71710.0650.0530.0070.49730.65CEE-SVM5.77860.8120.9180.9481.24861.39811.66491.24861.39811.67820.0120.01800.39850.47CEE-WAVENN6.89730.8190.9260.9391.17841.42931.67241.17841.42931.70190.0190.026−0.10.67121.00CEE-ELM4.27690.8820.9520.9651.23111.44191.55981.23111.44191.55980.0820.0520.0150.38660.46MOGOA4.08760.9230.9690.9721.13421.45091.54461.13421.45091.54460.0230.0690.0220.23790.20Site 4CEE-BP4.67210.8490.9140.9671.24121.43101.77841.24121.43101.77840.0490.0140.0170.28710.31CEE-SVM4.75650.8870.9260.9521.10641.33251.69231.10641.33251.69230.0870.0260.0020.28720.31CEE-WAVENN9.78530.8290.9110.9551.15541.39871.59291.15541.39871.59290.0290.0110.0050.47690.65CEE-ELM3.56010.8760.9290.9711.10921.48961.60331.10921.48961.60330.0760.0290.0210.28790.21MOGOA2.61980.9270.9460.9811.11941.40231.73381.11941.40231.73380.0270.0460.0310.14980.07It is obvious that the accuracy of the combined model after multi-objective optimization is better than that of the single-component model:(a)
The MAPE value can evaluate the accuracy of point prediction, and the lower the MAPE value is, the better the prediction effect of the model is. It can be found that the MAPE value of the combined model is significantly lower than that of each single neural network. For Data 1, theMAPEMOGOACee=3.8975, which is 31.9% higher than MAPEBPCee=5.3864, 38.4% higher than MAPESVMCee=4.8753, 125% higher than MAPEWavennCee=8.7988, and 25.6% higher than that MAPEELMCee=4.8753.(b)
The PICP value indicates the probability of the real value contained in the interval prediction at different confidence levels. When the real coverage is higher than the confidence level,ACE>0, and when the real coverage is less than it, ACE≤0:(33)CWC=PINAW∗PVPenality Value,ACE=PICP−CLConfidence Level.These indicators show the coverage of the interval prediction to the real value. It can be observed from the real data that the actual probability of a small part of the WAVENN neural network is slightly lower than the Confidence Level = 0.8. The other neural network predictions reach the expected level. The PICP value of the combined model proposed in this study is significantly higher than that of the single neural network, which demonstrates the superiority of the combined model. For Data 1, at a confidence level of 0.8, the PICP value of the combined model isPICPMOGOACee=0.895, which is 7.22% higher than that predicted by the BP neural network (PICPBPCee=0.833), 4.70% higher than that of the SVM neural network (PICPSVMCee=0.856), 15.58% higher than PICPWavennCee=0.776, and 6.47% higher than that of the ELM neural network (PICPELMCee=0.887).(c)
MPICD is a measure of the difference between the real level and the intermediate value of the interval, and NMPICD is the normalized value of the former. For the NMPICD, the study uses the min-max normalization method:(34)NMPICD=MPICD−MPICDminMPICDmax−MPICDmin.It can be observed from the data that, for the combined model,NMPICDMOGOACee is all approximately 0.1 and the minimum value (standard value) also appears in the optimized model; at the same time, NMPICDBPCee is approximately 0.2, NMPICDSVMCee is approximately 0.3, and NMPICDWavennCee is approximately 0.7. This indicates that the real value appears more centrally in the middle of the interval prediction, and there is a significant improvement compared with the single model, as shown in Figure 6.Figure 6
The data display of MAPE and NMPICD.Remark 1.
In experiment I, we can observe that the real value coverage and the distance between the real value and the interval center of the combined model proposed in this study are much higher than those of the single neural network model, and the accuracy of the combined model is significantly better than that of the single neural network model.


### 4.2. Experiment II

In this experiment, we verified the improvement of the wind speed prediction accuracy by data preprocessing and the advantages of the CEEMDAN method over EMD and EEMD. First, the component neural network model is directly used to predict the nonpreprocessed data; second, the EMD and EEMD methods are used to denoise the data and compare them with the results of the CEEMDAN method. In this experiment, the training set, test set, and evaluation indicators are the same as above.The proposed combination model is directly used to predict the data without denoising. The results are listed in Table6, and the prediction results of Data1 (confidence level 0.95) are shown in Figure 7.Table 6
Model accuracy without data preprocessing.
DataMethodMAPEPICPACEMPICDNMPICD0.80.90.950.800.90.95Site 1BP14.78490.7310.8670.941−0.07−0.03−0.010.80.67SVM16.89720.7210.8770.921−0.08−0.02−0.030.70.50WAVENN19.88740.6950.8560.921−0.10−0.04−0.030.90.83ELM14.16580.7360.8670.926−0.06−0.03−0.020.60.33MOGOA9.01760.7850.9120.955−0.020.010.010.40.00Site 2BP12.76980.7240.8550.946−0.08−0.05−0.000.90.83SVM15.87690.7460.8460.936−0.05−0.05−0.010.80.67WAVENN16.52970.7150.8260.921−0.08−0.07−0.031.01.00ELM11.78390.7460.8650.951−0.05−0.030.000.80.67MOGOA10.73690.7750.9020.961−0.030.000.010.50.33Site 3BP16.53890.7410.8620.936−0.06−0.04−0.010.80.67SVM15.76980.7570.8520.936−0.04−0.05−0.010.70.50WAVENN19.66540.7360.8370.916−0.06−0.06−0.030.90.83ELM14.82730.7750.8710.956−0.03−0.030.010.50.33MOGOA12.17680.8020.8960.9700.000.000.020.40.00Site 4BP11.46700.7460.8710.941−0.06−0.03−0.010.60.33SVM15.26980.7520.8620.951−0.05−0.040.000.90.83WAVENN18.23480.7060.8470.936−0.1−0.05−0.011.01.00ELM10.78370.7620.8560.956−0.04−0.040.010.70.50MOGOA8.95270.7960.8910.9650.00−0.10.020.50.33Figure 7
Remove data preprocessing from the model and replace the CEEMDAN method with the EMD method.It is obvious from the chart and table that the prediction ability of the model decreases sharply without data preprocessing.PICP1−stepmodel is the ability to contain real values in the prediction interval, and ACE1−stepmodel is the difference between PICP1−stepmodel and confidence level:(35)ACE1−stepmodel=PICP1−stepmodel−CLConfidence Level.Except for some of the optimized models, theACE1−stepmodel value is negative, indicating that most of the interval forecasts do not reach the expected level, and the ability of the model to predict wind speed is not good, where ACEBPNone=−0.07, ACESVMNone=−0.08, ACEWavennNone=−0.10CL=0.08, and NMPICD1−stepmodel are the evaluation indexes of whether the real value is in the center of the confidence interval. From the table, we can clearly see that the MPICD of the prediction result without data preprocessing is significantly larger than that after data preprocessing, which shows that data preprocessing plays a significant role in improving the prediction accuracy of the model.(a)
For MAPE, the MAPE value of the model with data preprocessing is much lower than that of MAPE without data preprocessing. For Site 1, in the single neural network prediction model, theMAPEBPNone=14.7894 decreased by 64.28% compared with MAPEBPCee=5.1432; the MAPESVMNone=16.8972 decreased by 66.13% compared with MAPESVMCee=5.3864; the MAPEWavennNone=19.8874 decreased by 71.72% compared with MAPEWavennCee=8.7988; and the MAPEMOGOANone=9.0716 decreased by 68.19% compared with MAPEMOGOACee=3.8975. For the prediction results of the four sets of data, the MAPE value is reduced by more than 50% in both the single and combined models.(b)
For PICP, the PICP value of the model without data preprocessing, whether a single neural network or the combined model is significantly lower than expected. For Site 1, in a single neural network prediction model, thePICP value of the BP neural network (PICPBPCee=0.833) increases by 13.69% compared with PICPBPNone=0.731 when the confidence level is 0.8, 6.52% when the confidence level is 0.9, and 4.23% when the confidence level is 0.95; the PICP value of SVM neural network (PICPSVMCee=0.856) increases by 19.69% compared with PICPSVMNone=0.721 when the confidence level is 0.8, 11.52% when the confidence level is 0.9, and 5.96% when the confidence level is 0.95. The PICP value of WAVENN neural network (PICPWavennCee=0.776) increases by 17.58% compared with PICPWavennNone=0.695 when the confidence level is 0.8, 9.32% when the confidence level is 0.9, and 8.33% when the confidence level is 0.95. The PICP value of the combined model (PICPMOGOACee=0.895) increases by 14.10% compared with PICPMOGOANone=0.785 when the confidence level is 0.8, 6.19% when the confidence level is 0.9, and 5.77% when the confidence level is 0.95, which shows that data preprocessing is key to the prediction accuracy of the model.(c)
For MPICD, the BP neural network upshifted the true value toward the center of the confidence interval by 0.6 after data preprocessing, and the other neural networks also upshifted it to various degrees, and the combined neural network upshifted it by 0.3. The EMD method is used instead of the CEEMDAN method, and the results are presented in Table7.Table 7
Model accuracy comparison of different data preprocessing methods (EMD and CEEMDAN).
DataMethodMAPEPICPACEMPICDNMPICD0.80.90.950.800.90.95Site 1EMD-BP8.45870.820.910.950.020.010.000.40.17EMD-SVM7.56380.830.920.960.030.020.010.50.33EMD-WAVENN10.23650.790.900.94−0.010.00−0.010.60.50EMD-ELM6.23540.820.930.950.020.030.000.40.17EMD-MOGOA4.78540.850.950.960.050.050.010.30.00Site 2EMD-BP7.34850.830.920.950.030.020.000.50.33EMD-SVM6.89620.820.920.950.020.020.000.50.33EMD-WAVENN9.39820.800.910.950.000.010.000.70.67EMD-ELM6.78320.840.930.950.040.030.000.40.17EMD-MOGOA4.27610.860.940.960.060.040.010.30.00Site 3EMD-BP7.89210.810.920.960.010.020.010.40.17EMD-SVM8.99120.810.930.960.010.030.010.40.17EMD-WAVENN11.45600.800.920.940.000.02−0.010.80.83EMD-ELM6.44890.840.940.950.040.040.000.50.33EMD-MOGOA5.12760.860.940.960.060.040.010.40.17Site 4EMD-BP8.12260.830.920.950.030.020.000.40.17EMD-SVM7.82540.840.920.950.040.020.010.60.50EMD-WAVENN9.12350.820.900.950.020.000.000.91.00EMD-ELM6.56720.850.930.960.050.030.010.40.17EMD-MOGOA4.80170.870.950.970.070.950.020.30.00After EMD denoising, although most of the models meet the expectations, the prediction accuracy is still very different from that of CEEMDAN denoising. Regardless of the single neural network prediction or the combination model, MAPE, PICP, and MPICD are significantly smaller than the CEEMDAN method, which further verifies the superiority and advanced nature of the model proposed in the study, as presented in Figure7.Remark 2.
Through experiment II, it is obvious that data preprocessing plays a significant effect in improving the prediction accuracy of the combined model, and the superiority of the data preprocessing method used in the model is verified by comparing different data preprocessing methods (EMD and CEEMDN).


### 4.3. Experiment III

To verify the universality of the proposed model [47], based on the wind speed test of 10 min each time in this study, the wind speed predictions of 20 min each time and 30 min each time are added to examine the universality and reliability of the model at different test frequencies.To ensure the reliability of the experiment, the time of the experimental data is the same as that in the previous article. The specific training set and test set are listed in Table8, and the test results are presented in Table 9. According to the previous evaluation indexes, the prediction ability of the model at different frequencies is evaluated, as shown in Figure 8.Table 8
Test set and training set in the new model.
DataTraining setTesting setMean (m/s)Min (m/s)Max (m/s)Site 1 (20 min)6001016.31011.913.3Site 2 (20 min)6001016.29651.813.5Site 3 (20 min)6001016.78722.013.4Site 4 (20 min)600676.33872.113.2Site 1 (30 min)400676.48701.913.3Site 2 (30 min)400676.38711.813.5Site 3 (30 min)400676.77012.013.4Site 4 (30 min)400676.43812.113.2Table 9
Model accuracy under different measurement frequencies.
DataMAPEPICPACEMPICDNMPICD0.80.90.950.80.90.95MOGOA (20 min)Site 15.16760.850.930.970.050.030.020.50.67Site 24.98530.860.920.960.060.020.010.40.33Site 35.78510.840.930.950.040.030.000.40.33Site 45.22940.840.930.960.040.030.010.30.00MOGOA (30 min)Site 16.76190.860.920.950.060.020.000.61.00Site 25.98630.830.910.950.030.010.000.61.00Site 36.88700.850.909.960.050.000.010.61.00Site 46.38120.840.920.960.040.020.010.50.67Figure 8
Predictive power of the model at different frequencies.From Table9, it can be observed that the models proposed in this study show high accuracy in the prediction of wind speed at different frequencies. The value PICPn−minCee is higher than the expected confidence level, and the value ACEn−minCee is greater than 0:(36)PICP20−minCee≥CL,PICP30−minCee≥CL,ACE20−minCee≥0,ACE30−minCee≥0.When the frequency is every 20 min, the valuesMAPE20−minCee of the combined model are 5.1676, 4.9853, 5.7851, and 5.2294, respectively; when the frequency is every 30 min, the MAPE30−minCee values of the combined model are 6.7619, 5.9863, 6.8870, and 6.3812, respectively; when the frequency is 20 min once, the PICP20−minCee values are 0.85, 0.86, 0.84, and 0.84, respectively, which are 0.05, 0.06, 0.04, and 0.04 higher than the confidence level, respectively. When the frequency is 30 min once, the PICP30−minCee values are 0.86, 0.83, 0.85, 0.84, and 0.84, which are 0.06, 0.03, 0.05, 0.04, and 0.04, respectively, higher than the confidence level, respectively, and the prediction accuracy is good. For MPICDn−minCee and NPICDn−minCee, the MPICD20−minCee value is 0.5, 0.4, 0.4, and 0.3 when the frequency is 20 min, and the MPICD30−minCee value is 0.6, 0.6, 0.6, and 0.5 at a frequency is 30 min. It can be observed that most of the real values are located in the center of the confidence interval, indicating that the accuracy of the combined model is high. Although the accuracy of the model will be affected to a certain extent with the decrease in the frequency, the model proposed in this study still maintains a good prediction accuracy, which shows that it is reliable and effective.Remark 3.
Experiment III verifies the universality of the combined model, which can play stably under different wind speed frequencies, and gives accurate predicted values, thus laying a good foundation for the final use of the model.


### 4.4. Experiment IV

To verify the generalization ability of the combined model prediction proposed in the study, we use the method of 10-fold cross-validation to redistribute the data. The data are randomly divided into 10 parts, one of them is selected as the test set and the other nine as the training set, and they are cycled until each has done the test set. The results of cross-validation are shown in Table10 (each set of data shows five sets of cross-validation). In the 10-fold cross-validation, the prediction accuracy of the combined model proposed in the study is always stable. Take Site 1 as an example, the MAPE10−cross−validationCM =  3.2346,2.9863,3.0836,3.1643,3.1244,2.9134,3.4243,3.2134 which are all keeping at approximately 3. MPICD10−cross−validationCM value and NMPICD10−cross−validationCM value also reach the expected level, the interval coverage is greater than the confidence level, and the difference between the real value and the center of the interval is approximately 0.3. The prediction accuracy and stability are very satisfactory, which well verifies the generalization ability of the combined model proposed in this study [48].Table 10
Results of cross-validation.
DataFoldMAPEPICPACEMPICD0.80.90.950.80.90.95Site 11-Fold3.23460.860.940.960.060.040.010.32-Fold2.98630.860.930.960.060.030.010.33-Fold3.08360.850.920.970.050.020.020.24-Fold3.24670.850.930.970.050.030.020.45-Fold3.16430.870.940.960.070.040.010.1Site 21-Fold2.86530.870.930.960.070.030.010.22-Fold2.97580.880.930.970.080.030.020.23-Fold3.07840.890.940.980.090.040.030.34-Fold3.13450.870.950.960.070.050.010.35-Fold3.27680.870.930.970.070.030.020.4Site 31-Fold2.93760.860.920.970.060.020.020.22-Fold2.84740.840.940.990.040.040.040.23-Fold2.75360.860.930.960.060.030.010.34-Fold2.44550.850.920.960.050.020.010.45-Fold3.24360.860.930.960.060.030.060.2Site 41-Fold2.46560.870.920.970.070.020.020.32-Fold3.86750.870.940.950.070.040.000.43-Fold3.34660.860.940.980.060.040.030.24-Fold3.64360.860.940.980.060.040.030.35-Fold3.42340.850.930.970.050.030.020.2Remark 4.
Experiment IV validates the generalization ability of the model and shows the reliability of the model through 10-fold cross-validation. The prediction effect of the model is higher than expected under different training sets and test sets.


### 4.5. Experiment V

In the previous experiment, we verified the single-step prediction ability of the model proposed in this study. However, in the actual wind speed prediction, we need to predict the values of multiple time points in the future. In this experiment, we introduced the concept of multi-step prediction, and the prediction ability of the model is further verified by the accuracy of the multi-step prediction.In the experiment, we adopted a direct multi-step prediction strategy. The direct method developed a separate model for each predicted time point. For example, when forecasting the wind speed at the next two time points, we established an independent model to predict it at the first time point and another independent model to predict it at the second time point, as shown in Figure9.Figure 9
Schematic diagram of multi-step prediction.We realize single-step prediction, two-step prediction, and three-step prediction for four groups of data and verify the prediction ability of the model through the evaluation indicators of multiple interval forecasts. The results are presented in Table11.(a)
With an increase in the number of prediction steps, the prediction ability of the model decreases to a certain extent. In terms ofMAPEn−stepCM, the two-step prediction (MAPE2−stepCM=5.2365) is 25.67% lower than MAPE1−stepCM=3.8975, and the three-step prediction is lower than 30.91% (MAPE3−stepCM=6.2982). In terms of MAPEn−stepCM, the two-step prediction (MPICD2−stepCM=0.2988) is approximately 20% lower than the one-step prediction (MPICD1−stepCM=0.1107), and the three-step prediction (MPICD3−stepCM=0.4621) is approximately 35% lower. This shows that the accuracy of the combined model proposed in this study needs to be improved when dealing with multi-step prediction.(37)MAPE1−stepCM≤MAPE2−stepCM≤MAPE3−stepCM,PICP1−stepCM≥PICP2−stepCM≥PICP3−stepCM,PICP1−stepCM≥CL,PICP2−stepCM≥CL,PICP3−stepCM≥CL.(b)
Although the accuracy of the multi-step prediction of the model has declined to a certain extent, the coverage of interval prediction is still satisfactory. For both the two-step prediction and three-step prediction, most of thePICPn−stepCM values are higher than the confidence level. At Site 1, in the two-step prediction, when the confidence level is 0.8, the interval coverage of the combined model (PICP2−stepCM=0.84) is 5% higher than the confidence level; at Site 2, the interval coverage of the combined model (PICP2−stepCM=0.85) is 6.25% higher than the confidence level; at Site 3, the interval coverage of the combined model (PICP2−stepCM=0.84) is 5% higher than the confidence level; and at Site 4, the interval coverage of the combined model (PICP2−stepCM=0.86) is 7.5% higher than the confidence level. At Site 1, in the three-step prediction, the interval coverage of the combined model (PICP3−stepCM=0.83) is 2.5% higher than the confidence level. At Site 2, the interval coverage of the combined model (PICP3−stepCM=0.83) is 3.75% higher than the confidence level. At Site 3, the interval coverage of the combined model (PICP3−stepCM=0.82) is 2.5% higher than the confidence level. At Site 4, the interval coverage of the combined model (PICP3−stepCM=0.82) is 2.5% higher than the confidence level. A few ACEn−stepCM values of the component prediction model are less than 0, but the ACEn−stepCM values of the combined model are all greater than 0. This level is higher than expected.Table 11
The result of multi-step prediction.
Two-step predictionThree-step predictionMAPEMPICDPICPACEMAPEMPICDPICPACE0.80.90.950.80.90.950.80.90.950.80.90.95Site 1CEE-BP6.12870.41980.820.920.950.020.020.008.11280.69810.810.910.950.010.010.00CEE-SVM6.77230.44620.830.910.950.030.010.008.12730.61250.820.920.950.020.020.00CEE-WAVENN9.34720.66270.810.900.940.010.00−0.019.88210.88170.790.890.94−0.01−0.01−0.01CEE-ELM7.12410.37620.820.910.960.020.010.017.12330.71910.810.900.960.010.010.01MOGOA5.23650.29880.840.930.970.040.030.026.29820.46210.820.920.960.020.020.01Site 2CEE-BP5.99820.44380.830.920.960.030.020.018.23640.77160.810.910.960.010.010.01CEE-SVM6.12350.40980.820.910.960.020.010.018.12340.78140.810.900.960.010.010.01CEE-WAVENN8.77630.78920.800.890.950.00−0.010.0010.77230.71260.780.880.95−0.02−0.020.00CEE-ELM6.12330.44290.830.910.960.030.010.017.11450.67120.810.910.950.010.010.00MOGOA4.99640.33180.850.930.970.050.030.026.22750.52790.830.930.960.030.030.01Site 3CEE-BP6.67620.50920.830.910.950.030.010.007.12980.67910.800.910.950.000.010.00CEE-SVM6.77100.47290.830.900.960.030.000.017.88710.69120.810.920.950.010.020.00CEE-WAVENN9.77290.88910.780.880.94−0.02−0.02−0.0111.67230.95380.800.870.940.00−0.03−0.01CEE-ELM6.12760.51650.810.910.960.010.010.016.99810.71530.820.900.950.020.000.00MOGOA5.12870.37800.840.920.980.040.020.035.79820.45710.830.930.960.030.030.01Site 4CEE-BP7.12730.42910.820.920.960.020.020.017.21440.62610.810.900.950.010.000.00CEE-SVM7.12870.43780.830.920.960.030.020.016.88710.71270.810.910.960.010.010.01CEE-WAVENN9.12730.88720.810.900.950.010.000.0010.59230.92360.780.900.94−0.020.00−0.01CEE-ELM6.77620.55190.840.910.960.040.010.018.81250.82140.800.910.950.000.010.00MOGOA4.87410.41170.860.940.970.060.040.026.12330.57180.820.920.970.020.020.02


#### 4.5.1. Sensitivity Analysis

To further explore the influence of the key parameters of the MOGOA algorithm on the sensitivity of the combined model, we propose a sensitivity analysis mechanism. Under the condition of keeping other parameters unchanged, the mechanism only changes one parameter value at a time, and then the fluctuation degrees of the prediction results are analyzed. We measured the sensitivity using the standard deviation of the four evaluation indicators.The equation is defined as(38)SDM=∑i=1mMi−M¯∗1m,where Mi refers to the value of metric M (MAE, RMSE, MAPE, and SSE), M¯ refers to the average of all testing times, and a smaller SDM value indicates stronger stability.Definition 1.
It is assumed thatA=a1,a2,…,a∗,…,ai, B=b1,b2,…,b∗,…,bi, and C=c1,c2,…,c∗,…,ci. When the value of A is tested from the first value to the last value, the values of B and C remain the same; that is, B=b∗, C=c∗, and it is defined as A⟶ΦBC↔.
We set the vectors of the Tunicate Number, Iteration Number, and Archive Size as20,40,60∗,80,100; I⟶=50,100,150,200∗,250; A⟶=100,200,300∗,400,500, respectively, and the number marked with an asterisk (∗) is the best value.
We testA⟶ΦIT↔, I⟶ΦTA↔, and T⟶ΦAI↔, respectively, and calculate their standard deviations according to the differences in the number of prediction steps, for example, SD1−stepCM, SD2−stepCM, and SD3−stepCM. Let us take Data 1 as an example, and the results are listed in Table 12. We can clearly observe from the table that the volatility of A⟶ΦIT↔ is obviously smaller than that of I⟶ΦTA↔ and T⟶ΦAI↔.
From the above table, we can observe that the SD values all fluctuate in a small range, indicating that the sensitivity of the three parameter models is low, which shows that our model has high stability in practical applications.Table 12
Sensitivity analysis.
StepPatternData 1SDMAESDRMSESDMAPESDSSEOne-stepA⟶ΦIT↔0.00140.00310.08010.2214I⟶ΦTA↔0.00320.00440.09810.3981T⟶ΦAI↔0.00800.00980.12810.7980Two-stepA⟶ΦIT↔0.00180.00360.08210.2671I⟶ΦTA↔0.00390.00490.10210.4023T⟶ΦAI↔0.00840.01020.13420.8123Three-stepA⟶ΦIT↔0.00210.00390.08630.2981I⟶ΦTA↔0.00440.00450.11290.4502T⟶ΦAI↔0.00890.01020.14660.9167Remark 5.
Experiment V verified the prediction ability of the combined model using two-step and three-step predictions. Although the forecast accuracy of the model decreases as the number of prediction steps increases, the coverage rate and other indicators are still higher than the expected value. Therefore, the combined model is still stable and reliable.


### 4.6. Experiment

In this experiment, the traditional official test functions are used to test the ability of the optimization algorithm. We selected (ZDT1, ZDT2, ZDT3, ZDT1-Line) to test the MOGOA. The test function is shown in Table13, and the picture of Pareto frontier is shown in Figure 10.Table 13
Formula of ZDT1, ZDT2, ZDT3, ZDT-Line.
Test functionFormulaZDT 1Obj 1:minf1x=x1Obj 2:minf2x=gx1−mxgx=1+9∑t=2mxi/m−1mx=f1/gZDT 2Obj 1:minf1x=xObj 2:minf2x=gx1−mx2gx=1+9∑t=2mxi/m−1mx=f1/gZDT 3Obj 1:minf1x=x1Obj 2:minf2x=gx1−mx−mxsin10πf1gx=1+9∑t=2mxi/m−1mx=f1/gZDT 1-LineObj 1:minf1x=x1Obj 2:minf2x=gx1−mxgx=1+9∑t=2mxi/m−1mx=f1/gFigure 10
Picture of Pareto frontier.Remark 6.
Experiment VI tests the performance of the multi-objective algorithm (MOGOA) through four groups of classical test functions. From the image, it is clear that the performance of the algorithm is good, it has a strong optimization ability when multiple objective functions exist at the same time.


## 4.1. Experiment I

To verify the superiority of the combined model over the component neural networks (SVM, BP, WAVENN, and ELM), seven indexes, namely, MAPE [41], PICP [42], MPIW [43], CWC [44], ACE [45], MPICD [46], and NMPICD (min-max) [36] are selected for the comprehensive evaluation. The confidence levels of interval prediction are 0.8, 0.9, and 0.95, respectively. The formula of each evaluation index is presented in Table 4, and the evaluation results are presented in Table 5 and Figure 5.Table 4
A summary of the formulas used in this study.
IndexMathematical expressionMAPEMAPE=1/N∑i=1NOacti−O^fori/Oacti∗100%PICPPICP=1/n∑i=1nciMPIWMPIW=1/n∑i=1nUi−LiCWCCWC=PINAW1+γe−ηPICP−μγ=0,PICP>μ1,PICP<μACEACE=PICP−μMPICDMPICD=1/Ntest∑i=1NtestU^aXi+L^aXi/2NMPICDNMPICD=MPICD/ξTable 5
Accuracy comparison between combined model and single model.
DataMethodMAPEPICPMPIWCWCACEMPICDNMPICD0.80.90.950.80.90.950.80.90.950.80.90.95Site 1CEE-BP5.14320.8330.9240.9671.12841.46741.62621.12841.46741.62620.0330.0240.0170.21090.17CEE-SVM5.38640.8560.9330.9821.18441.43901.68231.18441.43901.68230.0560.0330.0320.30120.35CEE-WAVENN8.79880.7760.9020.9421.28311.36341.75241.44711.36341.7981−0.020.002−0.10.54570.77CEE-ELM4.87530.8870.9510.9841.25841.49001.69171.25841.49001.69170.0870.0510.0340.27820.29MOGOA3.89750.8950.9640.9891.29191.30691.76711.29191.30691.76710.0950.0640.0390.11070.00Site 2CEE-BP4.99870.8420.9280.9591.23111.39771.78691.23111.39771.78690.0420.0280.0090.30130.35CEE-SVM4.68950.8370.9120.9671.10711.37631.72401.10711.37631.72400.0370.0120.0170.38720.38CEE-WAVENN6.49700.8010.9160.9581.26981.45311.65341.26981.45311.65340.0010.0160.0080.67291.00CEE-ELM4.08530.8750.9440.9461.28681.45901.56251.28681.45901.56250.0750.044−0.10.22360.19MOGOA3.25460.9010.9750.9851.23571.33741.55871.23571.33741.55870.0010.0750.1350.22190.19Site 3CEE-BP5.67540.8650.9530.9571.25151.39801.71711.25151.39801.71710.0650.0530.0070.49730.65CEE-SVM5.77860.8120.9180.9481.24861.39811.66491.24861.39811.67820.0120.01800.39850.47CEE-WAVENN6.89730.8190.9260.9391.17841.42931.67241.17841.42931.70190.0190.026−0.10.67121.00CEE-ELM4.27690.8820.9520.9651.23111.44191.55981.23111.44191.55980.0820.0520.0150.38660.46MOGOA4.08760.9230.9690.9721.13421.45091.54461.13421.45091.54460.0230.0690.0220.23790.20Site 4CEE-BP4.67210.8490.9140.9671.24121.43101.77841.24121.43101.77840.0490.0140.0170.28710.31CEE-SVM4.75650.8870.9260.9521.10641.33251.69231.10641.33251.69230.0870.0260.0020.28720.31CEE-WAVENN9.78530.8290.9110.9551.15541.39871.59291.15541.39871.59290.0290.0110.0050.47690.65CEE-ELM3.56010.8760.9290.9711.10921.48961.60331.10921.48961.60330.0760.0290.0210.28790.21MOGOA2.61980.9270.9460.9811.11941.40231.73381.11941.40231.73380.0270.0460.0310.14980.07It is obvious that the accuracy of the combined model after multi-objective optimization is better than that of the single-component model:(a)
The MAPE value can evaluate the accuracy of point prediction, and the lower the MAPE value is, the better the prediction effect of the model is. It can be found that the MAPE value of the combined model is significantly lower than that of each single neural network. For Data 1, theMAPEMOGOACee=3.8975, which is 31.9% higher than MAPEBPCee=5.3864, 38.4% higher than MAPESVMCee=4.8753, 125% higher than MAPEWavennCee=8.7988, and 25.6% higher than that MAPEELMCee=4.8753.(b)
The PICP value indicates the probability of the real value contained in the interval prediction at different confidence levels. When the real coverage is higher than the confidence level,ACE>0, and when the real coverage is less than it, ACE≤0:(33)CWC=PINAW∗PVPenality Value,ACE=PICP−CLConfidence Level.These indicators show the coverage of the interval prediction to the real value. It can be observed from the real data that the actual probability of a small part of the WAVENN neural network is slightly lower than the Confidence Level = 0.8. The other neural network predictions reach the expected level. The PICP value of the combined model proposed in this study is significantly higher than that of the single neural network, which demonstrates the superiority of the combined model. For Data 1, at a confidence level of 0.8, the PICP value of the combined model isPICPMOGOACee=0.895, which is 7.22% higher than that predicted by the BP neural network (PICPBPCee=0.833), 4.70% higher than that of the SVM neural network (PICPSVMCee=0.856), 15.58% higher than PICPWavennCee=0.776, and 6.47% higher than that of the ELM neural network (PICPELMCee=0.887).(c)
MPICD is a measure of the difference between the real level and the intermediate value of the interval, and NMPICD is the normalized value of the former. For the NMPICD, the study uses the min-max normalization method:(34)NMPICD=MPICD−MPICDminMPICDmax−MPICDmin.It can be observed from the data that, for the combined model,NMPICDMOGOACee is all approximately 0.1 and the minimum value (standard value) also appears in the optimized model; at the same time, NMPICDBPCee is approximately 0.2, NMPICDSVMCee is approximately 0.3, and NMPICDWavennCee is approximately 0.7. This indicates that the real value appears more centrally in the middle of the interval prediction, and there is a significant improvement compared with the single model, as shown in Figure 6.Figure 6
The data display of MAPE and NMPICD.Remark 1.
In experiment I, we can observe that the real value coverage and the distance between the real value and the interval center of the combined model proposed in this study are much higher than those of the single neural network model, and the accuracy of the combined model is significantly better than that of the single neural network model.


## 4.2. Experiment II

In this experiment, we verified the improvement of the wind speed prediction accuracy by data preprocessing and the advantages of the CEEMDAN method over EMD and EEMD. First, the component neural network model is directly used to predict the nonpreprocessed data; second, the EMD and EEMD methods are used to denoise the data and compare them with the results of the CEEMDAN method. In this experiment, the training set, test set, and evaluation indicators are the same as above.The proposed combination model is directly used to predict the data without denoising. The results are listed in Table6, and the prediction results of Data1 (confidence level 0.95) are shown in Figure 7.Table 6
Model accuracy without data preprocessing.
DataMethodMAPEPICPACEMPICDNMPICD0.80.90.950.800.90.95Site 1BP14.78490.7310.8670.941−0.07−0.03−0.010.80.67SVM16.89720.7210.8770.921−0.08−0.02−0.030.70.50WAVENN19.88740.6950.8560.921−0.10−0.04−0.030.90.83ELM14.16580.7360.8670.926−0.06−0.03−0.020.60.33MOGOA9.01760.7850.9120.955−0.020.010.010.40.00Site 2BP12.76980.7240.8550.946−0.08−0.05−0.000.90.83SVM15.87690.7460.8460.936−0.05−0.05−0.010.80.67WAVENN16.52970.7150.8260.921−0.08−0.07−0.031.01.00ELM11.78390.7460.8650.951−0.05−0.030.000.80.67MOGOA10.73690.7750.9020.961−0.030.000.010.50.33Site 3BP16.53890.7410.8620.936−0.06−0.04−0.010.80.67SVM15.76980.7570.8520.936−0.04−0.05−0.010.70.50WAVENN19.66540.7360.8370.916−0.06−0.06−0.030.90.83ELM14.82730.7750.8710.956−0.03−0.030.010.50.33MOGOA12.17680.8020.8960.9700.000.000.020.40.00Site 4BP11.46700.7460.8710.941−0.06−0.03−0.010.60.33SVM15.26980.7520.8620.951−0.05−0.040.000.90.83WAVENN18.23480.7060.8470.936−0.1−0.05−0.011.01.00ELM10.78370.7620.8560.956−0.04−0.040.010.70.50MOGOA8.95270.7960.8910.9650.00−0.10.020.50.33Figure 7
Remove data preprocessing from the model and replace the CEEMDAN method with the EMD method.It is obvious from the chart and table that the prediction ability of the model decreases sharply without data preprocessing.PICP1−stepmodel is the ability to contain real values in the prediction interval, and ACE1−stepmodel is the difference between PICP1−stepmodel and confidence level:(35)ACE1−stepmodel=PICP1−stepmodel−CLConfidence Level.Except for some of the optimized models, theACE1−stepmodel value is negative, indicating that most of the interval forecasts do not reach the expected level, and the ability of the model to predict wind speed is not good, where ACEBPNone=−0.07, ACESVMNone=−0.08, ACEWavennNone=−0.10CL=0.08, and NMPICD1−stepmodel are the evaluation indexes of whether the real value is in the center of the confidence interval. From the table, we can clearly see that the MPICD of the prediction result without data preprocessing is significantly larger than that after data preprocessing, which shows that data preprocessing plays a significant role in improving the prediction accuracy of the model.(a)
For MAPE, the MAPE value of the model with data preprocessing is much lower than that of MAPE without data preprocessing. For Site 1, in the single neural network prediction model, theMAPEBPNone=14.7894 decreased by 64.28% compared with MAPEBPCee=5.1432; the MAPESVMNone=16.8972 decreased by 66.13% compared with MAPESVMCee=5.3864; the MAPEWavennNone=19.8874 decreased by 71.72% compared with MAPEWavennCee=8.7988; and the MAPEMOGOANone=9.0716 decreased by 68.19% compared with MAPEMOGOACee=3.8975. For the prediction results of the four sets of data, the MAPE value is reduced by more than 50% in both the single and combined models.(b)
For PICP, the PICP value of the model without data preprocessing, whether a single neural network or the combined model is significantly lower than expected. For Site 1, in a single neural network prediction model, thePICP value of the BP neural network (PICPBPCee=0.833) increases by 13.69% compared with PICPBPNone=0.731 when the confidence level is 0.8, 6.52% when the confidence level is 0.9, and 4.23% when the confidence level is 0.95; the PICP value of SVM neural network (PICPSVMCee=0.856) increases by 19.69% compared with PICPSVMNone=0.721 when the confidence level is 0.8, 11.52% when the confidence level is 0.9, and 5.96% when the confidence level is 0.95. The PICP value of WAVENN neural network (PICPWavennCee=0.776) increases by 17.58% compared with PICPWavennNone=0.695 when the confidence level is 0.8, 9.32% when the confidence level is 0.9, and 8.33% when the confidence level is 0.95. The PICP value of the combined model (PICPMOGOACee=0.895) increases by 14.10% compared with PICPMOGOANone=0.785 when the confidence level is 0.8, 6.19% when the confidence level is 0.9, and 5.77% when the confidence level is 0.95, which shows that data preprocessing is key to the prediction accuracy of the model.(c)
For MPICD, the BP neural network upshifted the true value toward the center of the confidence interval by 0.6 after data preprocessing, and the other neural networks also upshifted it to various degrees, and the combined neural network upshifted it by 0.3. The EMD method is used instead of the CEEMDAN method, and the results are presented in Table7.Table 7
Model accuracy comparison of different data preprocessing methods (EMD and CEEMDAN).
DataMethodMAPEPICPACEMPICDNMPICD0.80.90.950.800.90.95Site 1EMD-BP8.45870.820.910.950.020.010.000.40.17EMD-SVM7.56380.830.920.960.030.020.010.50.33EMD-WAVENN10.23650.790.900.94−0.010.00−0.010.60.50EMD-ELM6.23540.820.930.950.020.030.000.40.17EMD-MOGOA4.78540.850.950.960.050.050.010.30.00Site 2EMD-BP7.34850.830.920.950.030.020.000.50.33EMD-SVM6.89620.820.920.950.020.020.000.50.33EMD-WAVENN9.39820.800.910.950.000.010.000.70.67EMD-ELM6.78320.840.930.950.040.030.000.40.17EMD-MOGOA4.27610.860.940.960.060.040.010.30.00Site 3EMD-BP7.89210.810.920.960.010.020.010.40.17EMD-SVM8.99120.810.930.960.010.030.010.40.17EMD-WAVENN11.45600.800.920.940.000.02−0.010.80.83EMD-ELM6.44890.840.940.950.040.040.000.50.33EMD-MOGOA5.12760.860.940.960.060.040.010.40.17Site 4EMD-BP8.12260.830.920.950.030.020.000.40.17EMD-SVM7.82540.840.920.950.040.020.010.60.50EMD-WAVENN9.12350.820.900.950.020.000.000.91.00EMD-ELM6.56720.850.930.960.050.030.010.40.17EMD-MOGOA4.80170.870.950.970.070.950.020.30.00After EMD denoising, although most of the models meet the expectations, the prediction accuracy is still very different from that of CEEMDAN denoising. Regardless of the single neural network prediction or the combination model, MAPE, PICP, and MPICD are significantly smaller than the CEEMDAN method, which further verifies the superiority and advanced nature of the model proposed in the study, as presented in Figure7.Remark 2.
Through experiment II, it is obvious that data preprocessing plays a significant effect in improving the prediction accuracy of the combined model, and the superiority of the data preprocessing method used in the model is verified by comparing different data preprocessing methods (EMD and CEEMDN).


## 4.3. Experiment III

To verify the universality of the proposed model [47], based on the wind speed test of 10 min each time in this study, the wind speed predictions of 20 min each time and 30 min each time are added to examine the universality and reliability of the model at different test frequencies.To ensure the reliability of the experiment, the time of the experimental data is the same as that in the previous article. The specific training set and test set are listed in Table8, and the test results are presented in Table 9. According to the previous evaluation indexes, the prediction ability of the model at different frequencies is evaluated, as shown in Figure 8.Table 8
Test set and training set in the new model.
DataTraining setTesting setMean (m/s)Min (m/s)Max (m/s)Site 1 (20 min)6001016.31011.913.3Site 2 (20 min)6001016.29651.813.5Site 3 (20 min)6001016.78722.013.4Site 4 (20 min)600676.33872.113.2Site 1 (30 min)400676.48701.913.3Site 2 (30 min)400676.38711.813.5Site 3 (30 min)400676.77012.013.4Site 4 (30 min)400676.43812.113.2Table 9
Model accuracy under different measurement frequencies.
DataMAPEPICPACEMPICDNMPICD0.80.90.950.80.90.95MOGOA (20 min)Site 15.16760.850.930.970.050.030.020.50.67Site 24.98530.860.920.960.060.020.010.40.33Site 35.78510.840.930.950.040.030.000.40.33Site 45.22940.840.930.960.040.030.010.30.00MOGOA (30 min)Site 16.76190.860.920.950.060.020.000.61.00Site 25.98630.830.910.950.030.010.000.61.00Site 36.88700.850.909.960.050.000.010.61.00Site 46.38120.840.920.960.040.020.010.50.67Figure 8
Predictive power of the model at different frequencies.From Table9, it can be observed that the models proposed in this study show high accuracy in the prediction of wind speed at different frequencies. The value PICPn−minCee is higher than the expected confidence level, and the value ACEn−minCee is greater than 0:(36)PICP20−minCee≥CL,PICP30−minCee≥CL,ACE20−minCee≥0,ACE30−minCee≥0.When the frequency is every 20 min, the valuesMAPE20−minCee of the combined model are 5.1676, 4.9853, 5.7851, and 5.2294, respectively; when the frequency is every 30 min, the MAPE30−minCee values of the combined model are 6.7619, 5.9863, 6.8870, and 6.3812, respectively; when the frequency is 20 min once, the PICP20−minCee values are 0.85, 0.86, 0.84, and 0.84, respectively, which are 0.05, 0.06, 0.04, and 0.04 higher than the confidence level, respectively. When the frequency is 30 min once, the PICP30−minCee values are 0.86, 0.83, 0.85, 0.84, and 0.84, which are 0.06, 0.03, 0.05, 0.04, and 0.04, respectively, higher than the confidence level, respectively, and the prediction accuracy is good. For MPICDn−minCee and NPICDn−minCee, the MPICD20−minCee value is 0.5, 0.4, 0.4, and 0.3 when the frequency is 20 min, and the MPICD30−minCee value is 0.6, 0.6, 0.6, and 0.5 at a frequency is 30 min. It can be observed that most of the real values are located in the center of the confidence interval, indicating that the accuracy of the combined model is high. Although the accuracy of the model will be affected to a certain extent with the decrease in the frequency, the model proposed in this study still maintains a good prediction accuracy, which shows that it is reliable and effective.Remark 3.
Experiment III verifies the universality of the combined model, which can play stably under different wind speed frequencies, and gives accurate predicted values, thus laying a good foundation for the final use of the model.


## 4.4. Experiment IV

To verify the generalization ability of the combined model prediction proposed in the study, we use the method of 10-fold cross-validation to redistribute the data. The data are randomly divided into 10 parts, one of them is selected as the test set and the other nine as the training set, and they are cycled until each has done the test set. The results of cross-validation are shown in Table10 (each set of data shows five sets of cross-validation). In the 10-fold cross-validation, the prediction accuracy of the combined model proposed in the study is always stable. Take Site 1 as an example, the MAPE10−cross−validationCM =  3.2346,2.9863,3.0836,3.1643,3.1244,2.9134,3.4243,3.2134 which are all keeping at approximately 3. MPICD10−cross−validationCM value and NMPICD10−cross−validationCM value also reach the expected level, the interval coverage is greater than the confidence level, and the difference between the real value and the center of the interval is approximately 0.3. The prediction accuracy and stability are very satisfactory, which well verifies the generalization ability of the combined model proposed in this study [48].Table 10
Results of cross-validation.
DataFoldMAPEPICPACEMPICD0.80.90.950.80.90.95Site 11-Fold3.23460.860.940.960.060.040.010.32-Fold2.98630.860.930.960.060.030.010.33-Fold3.08360.850.920.970.050.020.020.24-Fold3.24670.850.930.970.050.030.020.45-Fold3.16430.870.940.960.070.040.010.1Site 21-Fold2.86530.870.930.960.070.030.010.22-Fold2.97580.880.930.970.080.030.020.23-Fold3.07840.890.940.980.090.040.030.34-Fold3.13450.870.950.960.070.050.010.35-Fold3.27680.870.930.970.070.030.020.4Site 31-Fold2.93760.860.920.970.060.020.020.22-Fold2.84740.840.940.990.040.040.040.23-Fold2.75360.860.930.960.060.030.010.34-Fold2.44550.850.920.960.050.020.010.45-Fold3.24360.860.930.960.060.030.060.2Site 41-Fold2.46560.870.920.970.070.020.020.32-Fold3.86750.870.940.950.070.040.000.43-Fold3.34660.860.940.980.060.040.030.24-Fold3.64360.860.940.980.060.040.030.35-Fold3.42340.850.930.970.050.030.020.2Remark 4.
Experiment IV validates the generalization ability of the model and shows the reliability of the model through 10-fold cross-validation. The prediction effect of the model is higher than expected under different training sets and test sets.


## 4.5. Experiment V

In the previous experiment, we verified the single-step prediction ability of the model proposed in this study. However, in the actual wind speed prediction, we need to predict the values of multiple time points in the future. In this experiment, we introduced the concept of multi-step prediction, and the prediction ability of the model is further verified by the accuracy of the multi-step prediction.In the experiment, we adopted a direct multi-step prediction strategy. The direct method developed a separate model for each predicted time point. For example, when forecasting the wind speed at the next two time points, we established an independent model to predict it at the first time point and another independent model to predict it at the second time point, as shown in Figure9.Figure 9
Schematic diagram of multi-step prediction.We realize single-step prediction, two-step prediction, and three-step prediction for four groups of data and verify the prediction ability of the model through the evaluation indicators of multiple interval forecasts. The results are presented in Table11.(a)
With an increase in the number of prediction steps, the prediction ability of the model decreases to a certain extent. In terms ofMAPEn−stepCM, the two-step prediction (MAPE2−stepCM=5.2365) is 25.67% lower than MAPE1−stepCM=3.8975, and the three-step prediction is lower than 30.91% (MAPE3−stepCM=6.2982). In terms of MAPEn−stepCM, the two-step prediction (MPICD2−stepCM=0.2988) is approximately 20% lower than the one-step prediction (MPICD1−stepCM=0.1107), and the three-step prediction (MPICD3−stepCM=0.4621) is approximately 35% lower. This shows that the accuracy of the combined model proposed in this study needs to be improved when dealing with multi-step prediction.(37)MAPE1−stepCM≤MAPE2−stepCM≤MAPE3−stepCM,PICP1−stepCM≥PICP2−stepCM≥PICP3−stepCM,PICP1−stepCM≥CL,PICP2−stepCM≥CL,PICP3−stepCM≥CL.(b)
Although the accuracy of the multi-step prediction of the model has declined to a certain extent, the coverage of interval prediction is still satisfactory. For both the two-step prediction and three-step prediction, most of thePICPn−stepCM values are higher than the confidence level. At Site 1, in the two-step prediction, when the confidence level is 0.8, the interval coverage of the combined model (PICP2−stepCM=0.84) is 5% higher than the confidence level; at Site 2, the interval coverage of the combined model (PICP2−stepCM=0.85) is 6.25% higher than the confidence level; at Site 3, the interval coverage of the combined model (PICP2−stepCM=0.84) is 5% higher than the confidence level; and at Site 4, the interval coverage of the combined model (PICP2−stepCM=0.86) is 7.5% higher than the confidence level. At Site 1, in the three-step prediction, the interval coverage of the combined model (PICP3−stepCM=0.83) is 2.5% higher than the confidence level. At Site 2, the interval coverage of the combined model (PICP3−stepCM=0.83) is 3.75% higher than the confidence level. At Site 3, the interval coverage of the combined model (PICP3−stepCM=0.82) is 2.5% higher than the confidence level. At Site 4, the interval coverage of the combined model (PICP3−stepCM=0.82) is 2.5% higher than the confidence level. A few ACEn−stepCM values of the component prediction model are less than 0, but the ACEn−stepCM values of the combined model are all greater than 0. This level is higher than expected.Table 11
The result of multi-step prediction.
Two-step predictionThree-step predictionMAPEMPICDPICPACEMAPEMPICDPICPACE0.80.90.950.80.90.950.80.90.950.80.90.95Site 1CEE-BP6.12870.41980.820.920.950.020.020.008.11280.69810.810.910.950.010.010.00CEE-SVM6.77230.44620.830.910.950.030.010.008.12730.61250.820.920.950.020.020.00CEE-WAVENN9.34720.66270.810.900.940.010.00−0.019.88210.88170.790.890.94−0.01−0.01−0.01CEE-ELM7.12410.37620.820.910.960.020.010.017.12330.71910.810.900.960.010.010.01MOGOA5.23650.29880.840.930.970.040.030.026.29820.46210.820.920.960.020.020.01Site 2CEE-BP5.99820.44380.830.920.960.030.020.018.23640.77160.810.910.960.010.010.01CEE-SVM6.12350.40980.820.910.960.020.010.018.12340.78140.810.900.960.010.010.01CEE-WAVENN8.77630.78920.800.890.950.00−0.010.0010.77230.71260.780.880.95−0.02−0.020.00CEE-ELM6.12330.44290.830.910.960.030.010.017.11450.67120.810.910.950.010.010.00MOGOA4.99640.33180.850.930.970.050.030.026.22750.52790.830.930.960.030.030.01Site 3CEE-BP6.67620.50920.830.910.950.030.010.007.12980.67910.800.910.950.000.010.00CEE-SVM6.77100.47290.830.900.960.030.000.017.88710.69120.810.920.950.010.020.00CEE-WAVENN9.77290.88910.780.880.94−0.02−0.02−0.0111.67230.95380.800.870.940.00−0.03−0.01CEE-ELM6.12760.51650.810.910.960.010.010.016.99810.71530.820.900.950.020.000.00MOGOA5.12870.37800.840.920.980.040.020.035.79820.45710.830.930.960.030.030.01Site 4CEE-BP7.12730.42910.820.920.960.020.020.017.21440.62610.810.900.950.010.000.00CEE-SVM7.12870.43780.830.920.960.030.020.016.88710.71270.810.910.960.010.010.01CEE-WAVENN9.12730.88720.810.900.950.010.000.0010.59230.92360.780.900.94−0.020.00−0.01CEE-ELM6.77620.55190.840.910.960.040.010.018.81250.82140.800.910.950.000.010.00MOGOA4.87410.41170.860.940.970.060.040.026.12330.57180.820.920.970.020.020.02


### 4.5.1. Sensitivity Analysis

To further explore the influence of the key parameters of the MOGOA algorithm on the sensitivity of the combined model, we propose a sensitivity analysis mechanism. Under the condition of keeping other parameters unchanged, the mechanism only changes one parameter value at a time, and then the fluctuation degrees of the prediction results are analyzed. We measured the sensitivity using the standard deviation of the four evaluation indicators.The equation is defined as(38)SDM=∑i=1mMi−M¯∗1m,where Mi refers to the value of metric M (MAE, RMSE, MAPE, and SSE), M¯ refers to the average of all testing times, and a smaller SDM value indicates stronger stability.Definition 1.
It is assumed thatA=a1,a2,…,a∗,…,ai, B=b1,b2,…,b∗,…,bi, and C=c1,c2,…,c∗,…,ci. When the value of A is tested from the first value to the last value, the values of B and C remain the same; that is, B=b∗, C=c∗, and it is defined as A⟶ΦBC↔.
We set the vectors of the Tunicate Number, Iteration Number, and Archive Size as20,40,60∗,80,100; I⟶=50,100,150,200∗,250; A⟶=100,200,300∗,400,500, respectively, and the number marked with an asterisk (∗) is the best value.
We testA⟶ΦIT↔, I⟶ΦTA↔, and T⟶ΦAI↔, respectively, and calculate their standard deviations according to the differences in the number of prediction steps, for example, SD1−stepCM, SD2−stepCM, and SD3−stepCM. Let us take Data 1 as an example, and the results are listed in Table 12. We can clearly observe from the table that the volatility of A⟶ΦIT↔ is obviously smaller than that of I⟶ΦTA↔ and T⟶ΦAI↔.
From the above table, we can observe that the SD values all fluctuate in a small range, indicating that the sensitivity of the three parameter models is low, which shows that our model has high stability in practical applications.Table 12
Sensitivity analysis.
StepPatternData 1SDMAESDRMSESDMAPESDSSEOne-stepA⟶ΦIT↔0.00140.00310.08010.2214I⟶ΦTA↔0.00320.00440.09810.3981T⟶ΦAI↔0.00800.00980.12810.7980Two-stepA⟶ΦIT↔0.00180.00360.08210.2671I⟶ΦTA↔0.00390.00490.10210.4023T⟶ΦAI↔0.00840.01020.13420.8123Three-stepA⟶ΦIT↔0.00210.00390.08630.2981I⟶ΦTA↔0.00440.00450.11290.4502T⟶ΦAI↔0.00890.01020.14660.9167Remark 5.
Experiment V verified the prediction ability of the combined model using two-step and three-step predictions. Although the forecast accuracy of the model decreases as the number of prediction steps increases, the coverage rate and other indicators are still higher than the expected value. Therefore, the combined model is still stable and reliable.


## 4.5.1. Sensitivity Analysis

To further explore the influence of the key parameters of the MOGOA algorithm on the sensitivity of the combined model, we propose a sensitivity analysis mechanism. Under the condition of keeping other parameters unchanged, the mechanism only changes one parameter value at a time, and then the fluctuation degrees of the prediction results are analyzed. We measured the sensitivity using the standard deviation of the four evaluation indicators.The equation is defined as(38)SDM=∑i=1mMi−M¯∗1m,where Mi refers to the value of metric M (MAE, RMSE, MAPE, and SSE), M¯ refers to the average of all testing times, and a smaller SDM value indicates stronger stability.Definition 1.
It is assumed thatA=a1,a2,…,a∗,…,ai, B=b1,b2,…,b∗,…,bi, and C=c1,c2,…,c∗,…,ci. When the value of A is tested from the first value to the last value, the values of B and C remain the same; that is, B=b∗, C=c∗, and it is defined as A⟶ΦBC↔.
We set the vectors of the Tunicate Number, Iteration Number, and Archive Size as20,40,60∗,80,100; I⟶=50,100,150,200∗,250; A⟶=100,200,300∗,400,500, respectively, and the number marked with an asterisk (∗) is the best value.
We testA⟶ΦIT↔, I⟶ΦTA↔, and T⟶ΦAI↔, respectively, and calculate their standard deviations according to the differences in the number of prediction steps, for example, SD1−stepCM, SD2−stepCM, and SD3−stepCM. Let us take Data 1 as an example, and the results are listed in Table 12. We can clearly observe from the table that the volatility of A⟶ΦIT↔ is obviously smaller than that of I⟶ΦTA↔ and T⟶ΦAI↔.
From the above table, we can observe that the SD values all fluctuate in a small range, indicating that the sensitivity of the three parameter models is low, which shows that our model has high stability in practical applications.Table 12
Sensitivity analysis.
StepPatternData 1SDMAESDRMSESDMAPESDSSEOne-stepA⟶ΦIT↔0.00140.00310.08010.2214I⟶ΦTA↔0.00320.00440.09810.3981T⟶ΦAI↔0.00800.00980.12810.7980Two-stepA⟶ΦIT↔0.00180.00360.08210.2671I⟶ΦTA↔0.00390.00490.10210.4023T⟶ΦAI↔0.00840.01020.13420.8123Three-stepA⟶ΦIT↔0.00210.00390.08630.2981I⟶ΦTA↔0.00440.00450.11290.4502T⟶ΦAI↔0.00890.01020.14660.9167Remark 5.
Experiment V verified the prediction ability of the combined model using two-step and three-step predictions. Although the forecast accuracy of the model decreases as the number of prediction steps increases, the coverage rate and other indicators are still higher than the expected value. Therefore, the combined model is still stable and reliable.


## 4.6. Experiment

In this experiment, the traditional official test functions are used to test the ability of the optimization algorithm. We selected (ZDT1, ZDT2, ZDT3, ZDT1-Line) to test the MOGOA. The test function is shown in Table13, and the picture of Pareto frontier is shown in Figure 10.Table 13
Formula of ZDT1, ZDT2, ZDT3, ZDT-Line.
Test functionFormulaZDT 1Obj 1:minf1x=x1Obj 2:minf2x=gx1−mxgx=1+9∑t=2mxi/m−1mx=f1/gZDT 2Obj 1:minf1x=xObj 2:minf2x=gx1−mx2gx=1+9∑t=2mxi/m−1mx=f1/gZDT 3Obj 1:minf1x=x1Obj 2:minf2x=gx1−mx−mxsin10πf1gx=1+9∑t=2mxi/m−1mx=f1/gZDT 1-LineObj 1:minf1x=x1Obj 2:minf2x=gx1−mxgx=1+9∑t=2mxi/m−1mx=f1/gFigure 10
Picture of Pareto frontier.Remark 6.
Experiment VI tests the performance of the multi-objective algorithm (MOGOA) through four groups of classical test functions. From the image, it is clear that the performance of the algorithm is good, it has a strong optimization ability when multiple objective functions exist at the same time.


## 5. Practical Application and Conclusion

With the breakthrough of the key technology of wind power and the expansion of the wind farm construction scale, the large fluctuation range of wind farm output power needs to be taken into account when analyzing the wind farm connected to the power system. Wind energy has intermittent and random fluctuations. The change in wind speed directly leads to a change in the active power and reactive power of the wind farm, and the output power becomes very unstable. When the wind power penetrates the full operation, it not only has a serious impact, but also affects the power quality, economic dispatching, and power bidding. Therefore, it is of practical significance to conduct research on wind power forecasting and improve the accuracy of wind speed prediction. This is of practical significance to power grid dispatching, improving the access capacity of wind power, and reducing the operating cost of the system.In this paper, CEEMDAN is used for data preprocessing, and then four kinds of neural networks are used to predict the data after noise reduction. Finally, the unconstrained weighting algorithm based on multi-objective optimization is used to weight the results of four groups of neural networks, and the final interval prediction results are obtained. It is proved that the interval prediction results are advanced and can provide more effective information for wind farm decision-makers. Our combination strategy effectively combines the method of machine learning and improves the prediction accuracy of the combination forecasting model. The generalization performance of the model is good, and it has good accuracy in all kinds of complex situations. It is obvious that the model has high application significance.In view of the shortcomings of the existing wind speed prediction, this study proposes a combined forecasting model and carries out a multi-objective optimization of the combined neural network on the basis of wind speed data noise reduction. The accuracy and superiority of the model are demonstrated through the verification of several indicators.Although the combined model has achieved good prediction results, there are still some shortcomings, which may be considered in our future work and are the development direction of wind speed prediction:(1)
The operating time of our model is a little longer than some other models, but a high-profile computer may simplify the procedures to address this issue.(2)
We only study one-dimensional time series data and lack consideration of other factors that affect wind speed, such as humidity and temperature. Moreover, environmental factors or physical conditions may not be predicable and controllable and may be considered in future work.



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*Source: 5823656-2022-05-06.xml*