Direct Multistep Wind Speed Forecasting Using LSTM Neural ... - MDPI

applied sciences Article

Direct Multistep Wind Speed Forecasting Using LSTM Neural Network Combining EEMD and Fuzzy Entropy Qiong Qin 1 , Xu Lai 1, * and Jin Zou 2 1 2

*

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, Hubei, China; [email protected] Electric Power Research Institute, China Southern Power Grid, Guangzhou 510080, Guangdong, China; [email protected] Correspondence: [email protected]; Tel.: +86-134-7613-6201

Received: 28 November 2018; Accepted: 19 December 2018; Published: 1 January 2019

Abstract: Accurate wind speed forecasting is of great significance for a reliable and secure power generation system. In order to improve forecasting accuracy, this paper introduces the LSTM neural network and proposes a wind speed statistical forecasting method based on the EEMD-FuzzyEn-LSTMNN model. Moreover, the MIC is used to analyze the autocorrelation of wind speed series, and the predictable time of wind speed statistical forecasting method for direct multistep forecasting is taken as four hours. In the EEMD-FuzzyEn-LSTMNN model, the original wind speed series is firstly decomposed into a series of components by using EEMD. Then, the FuzzyEn is used to calculate the complexity of each component, and the components with similar FuzzyEn values are classified into one group. Finally, the LSTMNN model is used to forecast each subsequence after classification. The forecasting result of the original wind speed series is obtained by aggregating the forecasting result of each subsequence. Three forecasting cases under different terrain conditions were selected to validate the proposed model, and the BPNN model, the SVM model and the LSTMNN model were used for comparison. The experimental results show that the forecasting accuracy of the EEMD-FuzzyEn-LSTMNN model is much higher than that of the other three models. Keywords: wind speed forecasting; long short-term memory; neural network; ensemble empirical mode decomposition; fuzzy entropy; maximal information coefficient; autocorrelation

1. Introduction With the large consumption of fossil energy and the impact of global climate change, increasing attention has turned to renewable energy. As a kind of clean and renewable energy, wind power has been widely valued and promoted in the world. According to the World Wind Energy Association statistics, the total cumulative installed capacity from wind power around the world was approximately 539 GW by the end of 2017. However, with the expansion of wind power generation, its problems have gradually become more prominent. Due to the randomness, fluctuation and intermittence nature of wind speed, the wind power output has great uncertainty [1,2]. Therefore, large-scale wind power integration will bring great hidden dangers to the safe and stable operation of the power system. In order to solve the above problems, it is necessary to effectively improve the controllability and predictability of wind power. Accurate wind power forecasting can provide an important basis for power dispatching and improve the utilization efficiency of wind energy resources. Since wind power has a direct relationship with wind speed, wind power forecasting can be achieved based on wind speed forecasting.

Appl. Sci. 2019, 9, 126; doi:10.3390/app9010126

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The accuracy of wind speed forecasting is not only dependent on the forecasting method but also on the forecasting time horizon. In general, there are two main categories for wind speed forecasting based on the forecasting time horizon, namely, short-term forecast (time horizon of minutes, hours, and days) and long-term forecast (time horizon of days, weeks and months) [3]. The short-term forecast is important for the operation of wind turbines so that dynamic controls can be accomplished to increase the energy conversion efficiency and reduce the risk of overloading. The long-term forecast can provide important references for site location and planning of wind farms. In recent years, researchers have done many studies on the theory and methods of wind speed forecasting. According to the type of input variables of the forecasting model, the wind speed forecasting methods can be divided into physical forecasting methods, statistical forecasting methods and hybrid forecasting methods [4]. The input variables of the physical models are meteorological data from numerical weather prediction (NWP) and terrain feature data. Many physical models have been introduced, and the most popular three are Prediktor [5], LocalPred [6] and Previento [7]. Generally, physical methods have advantages in long-term forecast, while statistical methods have better performance in short-term forecast [1]. The input variables of the statistical models are long-term historical wind speed data. The statistical models achieve the forecasting of wind speed in the future by excavating the hidden change rules in historical wind speed data. Early statistical models include the autoregressive model (AR) [8], the autoregressive moving average model (ARMA) [9], the grey prediction model (GM) [10], etc. With the development of artificial intelligence techniques, support vector machines (SVM) and a large number of artificial neural network (ANN) algorithms have been introduced into wind speed forecasting. For example, Mohandes et al. [11] introduced SVM to wind speed prediction and compared its performance with the multilayer perceptron (MLP) neural networks. Cadenas et al. [12] used the ANN to forecast the wind speed in the region of La Venta, Oaxaca, Mexico, and the results showed very good accuracy for the short-term wind speed forecasting. Flores et al. [13] used back propagation neural network (BPNN) to forecast the wind speed. Li et al. [14] compared three different ANNs (adaptive linear element NN, BPNN, and radial basis function NN) in one-hour ahead wind speed forecasting, and the results showed that even for the same wind dataset, the choice of best-performing model might not be the same with different evaluation metrics. Hybrid forecasting methods are formed by hybridizing physical methods and statistical methods together. In the hybrid methods, NWP data is also used as the input data of the statistical models. Salcedo-Sanz et al. [15] used the output of the fifth generation mesoscale model (MM5 model) as the input variables of the ANN, and the experiment results showed that the hybrid MM5-neural network approach was able to obtain good short-term predictions of wind speed at specific points. Ortiz-García et al. [16] then made improvements to the system proposed in Ref. [15], and used regression SVM instead of ANN to obtain the final prediction. Giorgi et al. [17] trained the ANNs based on the measured wind speed series and on some NWP parameters, and an improvement of the performance had been reached, especially with the longer time horizons. However, the wind speed series has multiscale characteristics. The multiple frequency components existed in the wind speed series are always the challenging parts in forecasting. Currently, the concept of “decomposition and ensemble” (or “divide and conquer”) [18,19] has been used to solve this problem, and a number of various decomposition-ensemble based hybrid models have been developed and widely used. For instance, Liu et al. [20] selected wavelet decomposition (WD) and wavelet packet decomposition (WPD) to decompose an original wind speed series respectively, and then used the ANN models to do the multistep forecasting in each subseries. Guo et al. [21] combined empirical mode decomposition (EMD) and standard feed-forward neural network (FNN), and Liu et al. [22] combined EMD and ANN. The new hybrid model all outperformed the conventional FNN or ANN model. But the WD is sensitive to the wavelet base function and decomposition level, and for the EMD, one major challenge is the frequent appearance of mode mixing [23]. Fortunately, there exists an improved method named ensemble empirical mode decomposition (EEMD), which makes up

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for the deficiency of EMD. The EEMD is an empirical, intuitive, direct and self-adaptive data processing method created especially for nonlinear and nonstationary signal sequences [3]. For example, Wang et al. [24] proposed a wind speed forecasting method based on EEMD and optimized BPNN (GA-BPNN) for short-term wind speed forecasting, and computational results had shown the good performance of EEMD. In this study, we mainly focus on the wind speed statistical forecasting methods for short-term forecast. The first step is to determine the specific forecasting time horizon. When using statistical methods for direct multistep forecasting of wind speed series, in general, the longer the forecasting length, the lower the forecasting accuracy. Therefore, it is necessary to determine the predictable length of direct multistep forecasting. In this paper, the autocorrelation analysis method based on the maximal information coefficient (MIC) is introduced to measure the predictability of wind speed series. Then, the predictable time of statistical forecasting methods based on historical wind speed data is analyzed. The next step is to choose the wind speed statistical forecasting method. When the ordinary neural networks mentioned above process the wind speed series, the reading and processing of the input wind speed data are independent at each moment. These neural networks cannot fully consider the correlation of the wind speed series itself. When forecasting the wind speed at the next moment, they are unable to share the features learned from the previous input wind speed data. Therefore, the forecasting accuracy of these neural network models is limited. In order to make full use of the correlation between the data of wind speed series at each moment, this paper introduces a new long short-term memory neural network (LSTMNN) model for wind speed forecasting. The LSTMNN has a unique memory and forgetting mode. It can handle the long-term dependence of wind speed series very well, and effectively use the historical input information of the wind speed series. The LSTMNN has been widely used in many fields such as traffic forecasting [25], solar energy forecasting [26], stock price volatility prediction [27] and water table depth prediction [28]. These predictions all get good results [29]. In order to improve the forecasting accuracy of the LSTMNN model, this paper proposes a novel wind speed statistical forecasting method based on the EEMD-FuzzyEn-LSTMNN model. The EEMD-FuzzyEn-LSTMNN model is developed through combining EEMD, Fuzzy Entropy (FuzzyEn) and LSTMNN. In the proposed model, the original wind speed series is firstly decomposed into a series of components by using EEMD. Then, the FuzzyEn is introduced to calculate the complexity of each component, and the components are classified according to the calculated FuzzyEn values. The components with similar FuzzyEn values are classified into one group, and the components of each group are superimposed to obtain a new subsequence. This process can avoid cumbersome calculations caused by forecasting each component separately. Finally, the LSTMNN model is used to forecast each subsequence after classification. The forecasting result of the original wind speed series is obtained by aggregating the forecasting result of each subsequence. The remainder of this paper is organized as follows: Section 2 briefly describes the fundamental methods including EEMD, FuzzyEn and LSTMNN. Section 3 introduces the proposed EEMD-FuzzyEn-LSTMNN model. Section 4 uses MIC to analyze the predictable time of statistical forecasting methods for direct multistep forecasting. Section 5 firstly describes the wind speed data of three cases and selects error evaluation indexes, and then provides the forecasting results of the BPNN model, the SVM model, the LSTMNN model and the proposed EEMD-FuzzyEn-LSTMNN model. Finally, Section 6 gives the conclusions and discusses the future work. 2. Methodology The research methodology used in this study includes EMD, EEMD, FuzzyEn, RNN and LSTMNN. The brief description of those methods is stated as follows.

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2.1. EMD and EEMD EMD was proposed by Huang in 1998 [30]. It is a self-adaptive and efficient method for analyzing nonlinear and nonstationary signals. Since the wind speed series is nonlinear and nonstationary, EMD is efficient to analyze the wind speed signal. The basic idea of EMD is to smooth the fluctuating signals adaptively and to decompose them into fluctuations or trends of different scales. After decomposition, a finite and small number of intrinsic mode functions (IMFs) and a residual component are obtained. An IMF is a function that satisfies the following two conditions: (a) in the whole data set, the number of extrema and the number of zero crossings must either be equal or differ at most by one; and (b) at any point, the average of the envelopes defined by the local maxima and the local minima must be zero [31]. The specific steps for decomposing time series by using the EMD algorithm are detailed in Ref. [30]. Mode mixing is the most significant drawback of EMD [23], which means that a single IMF consists of signals with dramatically disparate scales or a signal of the same scale appears in different IMF components. The mode mixing compromises the stationarity of IMFs and therefore limits the effectiveness of the EMD algorithm. To solve the mode mixing problem in EMD, a new noise-assisted data analysis method EEMD is proposed. In EEMD, the white Gaussian noise is added into the original time series, and the EMD is then applied on noise added time series to obtain IMFs that are free from mode mixing [32,33]. However, the resulting IMFs include white noise, which is then removed by obtaining the mean of multiple trials. Therefore, the true IMF components are defined as the mean of an ensemble of trails and each trail consists of the decomposition results of the signal plus a white Gaussian noise of finite amplitude [3]. For the wind speed series {v(t), t = 1, 2, . . . , N}, the main steps of the EEMD algorithm are described as follows: Step 1:

Add the white Gaussian noise series εj (t) to the original wind speed series v(t) and obtain a new series Vj (t).

Step 2:

Decompose the new series Vj (t) into several IMFs and a residue by using the EMD algorithm.

Step 3:

For j = 1, 2, . . . , NE , repeat Step 1 and Step 2, and add different white Gaussian noise series each time. NE is the number of repeated procedures. Take the mean of all IMF components and the mean of residual components as the final results.

Step 4:

After the decomposition by using EEMD algorithm, the wind speed series {v(t)} can be expressed as: n

v(t) =

∑ ci ( t ) + r n ( t )

(1)

i =1

where {ci (t), I = 1, 2, . . . , n} represents the different IMF component, and rn (t) is the residue after n IMFs are derived. These IMFs contain components of different time characteristic scales of the wind speed series. Their scales range from small to large, and the frequencies range from high to low. 2.2. Fuzzy Entropy Using the EEMD algorithm to decompose the wind speed series, a series of components are obtained. If a forecasting model is built separately for each component, the process is slightly redundant. Moreover, when superimposing the forecasting results of all components, the forecasting errors of each component are also superimposed. In order to reduce the calculation scale and the accumulation of forecasting errors, the components obtained by EEMD can be classified according to certain criteria. Then, the components under each category are superimposed to form a new subsequence, and each subsequence is forecasted separately. The forecasting result of the original wind speed series can be obtained by superimposing the forecasting result of each subsequence. FuzzyEn is a metric of the complexity of time series [34–36]. It measures the complexity of the series by the probability that the time series produces a new pattern as the embedding dimension

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changes. The larger the FuzzyEn value, the greater the probability that the sequence will produce aAppl. newSci.pattern, means the sequence is more complex. Each IMF and the residue obtained 2018, 8, xwhich FOR PEER REVIEW 5 ofby 18 EEMD contain components of the wind speed series at different time characteristic scales. Their frequenciesare aredifferent, different,sosothe the complexity each component is also considered be different. In frequencies complexity of of each component is also considered to betodifferent. In this this paper, FuzzyEn is introduced to calculate the complexity of all components, then the paper, FuzzyEn is introduced to calculate the complexity of all components, and then theand components components are classified according the obtained value. For with the components with are classified according to the obtainedtoFuzzyEn value. FuzzyEn For the components similar FuzzyEn similarthey FuzzyEn theyto can considered to have similar complexity and wind speed values, can be values, considered havebe similar complexity and wind speed characteristics, so they can characteristics, they can be classified into one group. be classified intosoone group. Thespecific specificsteps stepsfor forcalculating calculatingthe theFuzzyEn FuzzyEnof oftime timeseries seriesare aredetailed detailedin inRef. Ref.[34]. [34]. The 2.3. 2.3. RNN RNN and and LSTMNN LSTMNN LSTMNN LSTMNN is is developed developed on on the the basis basis of of Recurrent Recurrent Neuron Neuron Network Network (RNN). (RNN). Unlike Unlike ordinary ordinary neural networks, RNN adds a self-connected hidden layer spanning time steps. Therefore, RNN neural RNN adds a self-connected hidden layer spanning time steps. Therefore, RNN can can memorize the input information in front of the time series and apply it to the calculation of memorize the input information in front of the time series and apply it to the calculation of the the current currentoutput. output. A of of three layers: an input layer, a hidden layer layer and anand output layer. Given Asimple simpleRNN RNNconsists consists three layers: an input layer, a hidden an output layer. m as themnumber of forecasting steps of direct multistep forecasting, the structure diagram of the RNN Given as the number of forecasting steps of direct multistep forecasting, the structure diagram of forecasting model formodel wind speed series is shown Figurein1.Figure In this1. figure, 1, i,2,i =. .1, . ,2,t}…, is the RNN forecasting for wind speed series isinshown In this {v figure, i , i = {v the inputinput windwind speed; {Vi +m i =, i1,= 2, , t}t}isisthe t} ismeasured the measured speed; {V, i+m 1, .2,. .…, theforecasted forecastedoutput outputwind windspeed; speed;aai iisisthe the activation activation value value from from time-step time-step i;i;W Wavav,, W Wva va and W Waa aa are the connection connection weights weights between between neurons, neurons, which whichare arethe thesame sameat ateach eachtime timestep. step. V1+m

V2+m

Wva

V3+m

Wva

Wva

a0

a1

a2

Waa

Waa

Waa

Wav

v1

Wav

v2

Vt+m Wva

a3

at-1

Waa

Waa

Hidden layer

Wav

v3

Output layer

Wav

vt

Input layer

Figure Figure 1. 1. The The structure structure of of the the RNN RNN forecasting forecasting model model for for wind wind speed speed series. series.

In the RNN model, the hidden layers of the front and back time steps are connected. It can make In the RNN model, the hidden layers of the front and back time steps are connected. It can full use of the information of the wind speed series before the forecasted time, thereby improving the make full use of the information of the wind speed series before the forecasted time, thereby forecasting accuracy. However, the RNN model may have the vanishing gradient problem during improving the forecasting accuracy. However, the RNN model may have the vanishing gradient the training process [37]. The LSTMNN proposed by Hochreiter and Schmidhuber [38] can solve this problem during the training process [37]. The LSTMNN proposed by Hochreiter and Schmidhuber problem of the RNN model through its special structural design. Moreover, the LSTMNN can better [38] can solve this problem of the RNN model through its special structural design. Moreover, the handle the long-term dependence of time series and effectively utilize the historical input information LSTMNN can better handle the long-term dependence of time series and effectively utilize the of time series. historical input information of time series. The basic LSTMNN also consists of three layers: an input layer, a hidden layer and an output The basic LSTMNN also consists of three layers: an input layer, a hidden layer and an output layer. But compared with the RNN, the hidden layer of the LSTMNN adds some threshold units for layer. But compared with the RNN, the hidden layer of the LSTMNN adds some threshold units for controlling which makes the neural network have ahave unique memory mode [38,39]. controllinginformation informationtransfer, transfer, which makes the neural network a unique memory mode The structures of the RNN forecasting model and the LSTMNN forecasting model at the time-step i [38,39]. The structures of the RNN forecasting model and the LSTMNN forecasting model at the are shown in Figure 2. time-step i are shown in Figure 2. In In the the forward forward propagation propagation process process of ofthe theLSTMNN LSTMNNforecasting forecasting model, model, besides besides the the activation activation value a , a memory cell c is transferred from the previous hidden layer to the latter. In addition, three value ai i, a memory celli ci is transferred from the previous hidden layer to the latter. In addition, gate structures are added to the hidden layer in LSTMNN, namely forget gate, update gate, and output three gate structures are added to the hidden layer in LSTMNN, namely forget gate, update gate, gate. The three gate structures can control the reading and modification of the memory and output gate. The three gate structures canpreservation, control the preservation, reading and modification of cell in the LSTMNN forecasting model. the memory cell in the LSTMNN forecasting model.

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Appl. Sci. 2018, 8, x FOR PEER REVIEW

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Vi+m

sigmoid

sigmiod

ci-1

ci

+

*

tanh

ai ai-1

tanh

ci

ai

* fi

ai-1

forget gate

* c~i

ui update gate

tanh

ai

ai

oi output gate

vi vi

(a)

(b)

Figure 2.2. The The structure structure of of forecasting forecasting model model for for wind wind speed speed series series at at the the time-step time-step i:i: (a) (a) the the RNN RNN Figure forecasting model; (b) the LSTMNN forecasting model. forecasting model; (b) the LSTMNN forecasting model.

In In the the forward forward propagation propagation process process of of the the LSTMNN LSTMNN forecasting forecasting model, model, the the forecasted forecasted output output wind windspeed speedof ofthe thetime-step time-stepi iisiscalculated calculatedas asfollows: follows: ci = tanh a + Wcv ·v cei = tanh vii + +bbc c)) (W( W ca ·caai −i1−1+ Wcv

(

)

(2) (2)

a +W v +b f i =fi σ= W W f a ·faai −i1−1+ W ffvv · vii + bf f

(3) (3)

ui = σ(W(ua ·vii ++bbu u) ) ui = W·uaai− ai1−1++ W Wuv uv

(4) (4)

oi = σ (Woa · ai−1 + Wov ·vi + bo ) oi =  ( Woa ai −1 + Wov vi + bo )

(5) (5) ci = f i ci−1 + ui cei (6) ci = fi ci −1 + ui c i (6) ai = oi tanhci (7) ai = oi tanh ci (7) Vi+m = σ (Wva · ai + bv ) (8) Vi + m =  ( Wva ai + bv ) (8) where the subscript i represents the time-step i; cei is the candidate for replacing the memory cell; ci is the memory cell; fi , uii represents and oi are the of forget gate, gate output the gate, respectively; where the subscript the values time-step i; ci is the update candidate forand replacing memory cell; ci σ is the sigmoid function; Wca , Wcv , Wfa , Wfv , Wua , Wuv , Woa , Wov , Wva are weight matrices; bc , bf , bu , bo , is the memory cell; fi, ui and oi are the values of forget gate, update gate and output gate, bv are bias vectors. respectively; σ is the sigmoid function; Wca, Wcv, Wfa, Wfv, Wua, Wuv, Woa, Wov, Wva are weight matrices; After the forward propagation process of the LSTMNN forecasting model is completed, the back bc, bf, bu, bo, bv are bias vectors. propagation process is followed. The model is firstly expanded into a deep network in chronological After the forward propagation process of the LSTMNN forecasting model is completed, the order. Then, the BPTT algorithm [40] and chain rule are used to iteratively update the connection back propagation process is followed. The model is firstly expanded into a deep network in weights and thresholds in the model until the optimal solution is obtained. chronological order. Then, the BPTT algorithm [40] and chain rule are used to iteratively update the connection weights and thresholdsModel in the model until the optimal solution is obtained. 3. The EEMD-FuzzyEn-LSTMNN In EEMD-FuzzyEn-LSTMNN this section, the EEMD-FuzzyEn-LSTMNN model is established for wind speed forecasting 3. The Model based on the concept of “decomposition and ensemble”. The flowchart of the proposed model is In this section, the EEMD-FuzzyEn-LSTMNN model is established for wind speed forecasting shown in Figure 3. The main structure of the EEMD-FuzzyEn-LSTMNN model includes the following based on the concept of “decomposition and ensemble”. The flowchart of the proposed model is four steps: shown in Figure 3. The main structure of the EEMD-FuzzyEn-LSTMNN model includes the Step 1: Use EEMD following four steps:to decompose the original wind speed series into a number of IFM components and a residual component. These components are respectively denoted by IMF1 , IMF2 , . . . , Step 1: Use EEMD to decompose the original wind speed series into a number of IFM components IMFn and Rn . and a residual component. These components are respectively denoted by IMF 1, IMF2, …, IMFn Step 2: Calculate the FuzzyEn of each component and classify all components according to the and Rn. calculated FuzzyEn values. The components with similar FuzzyEn values are classified into Step 2: Calculate the FuzzyEn of each component and classify all components according to the calculated FuzzyEn values. The components with similar FuzzyEn values are classified into

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one group, and the components in one group are superimposed to obtain a new subsequence. one group, and the components in one group areby superimposed All subsequences are respectively denoted S1 , S2 , . . . , SNto . obtain a new subsequence. All subsequences are respectively denoted by S 1 , S 2 , …, S N . Step 3: Use the LSTMNN model to forecast each subsequence separately. Step 3: 4: Use Aggregate the LSTMNN to forecast each subsequence separately. Step the model forecasting result of each subsequence to obtain the ultimate forecasting series Step 4: Aggregate the forecasting result of each subsequence to obtain the ultimate forecasting of wind speed. series of wind speed. Wind speed series EEMD IMF1

IMF2

IMF3

IMFn

Rn

Calculate the FuzzyEn of all components and classify

S1

S2

S3

SN

Forecast by using LSTMNN

Forecast result of S1



Forecast result of SN

Aggregate the forecast results of all subsequences The ultimate forecast result

Figure 3. The flowchart of the EEMD-FuzzyEn-LSTMNN model. Figure 3. The flowchart of the EEMD-FuzzyEn-LSTMNN model.

4. The Predictable Time of Wind Speed Series 4. The Predictable Time of Wind Speed Series The MIC is a statistic that measures the correlation between two variables [41]. Based on mutual The MIC is a statistic that measures the correlation between two variables [41]. Based on information, the MIC can measure both the linear correlation and the nonlinear correlation between mutual information, the MIC can measure both the linear correlation and the nonlinear correlation two variables. It has generality and equitability. The calculation method of MIC is detailed in [41]. between two variables. It has generality and equitability. The calculation method of MIC is detailed Since the wind speed series is a well-known nonlinear time series, the MIC with many excellent in [41]. Since the wind speed series is a well-known nonlinear time series, the MIC with many characteristics can be used to measure its autocorrelation. In this section, we use MIC to measure the excellent characteristics can be used to measure its autocorrelation. In this section, we use MIC to predictable time of statistical forecasting methods based on historical wind speed data. measure the predictable time of statistical forecasting methods based on historical wind speed data. 4.1. Selection of Wind Speed Series 4.1. Selection of Wind Speed Series In this paper, we selected wind speed series from three anemometer towers in China. The three In this paper, we are selected wind speed series from anemometer towers inHenan China.province The three anemometer towers in three wind farms which arethree located in Hunan province, and anemometer towers are in three wind farms which are located in Hunan province, Henan province Zhejiang province, respectively. The location, local terrain condition, selected time and measurement and Zhejiang respectively. Thearelocation, condition, selected height of the province, three anemometer towers shown inlocal Tableterrain 1. These wind speed seriestime wereand used measurement height of the threeofanemometer towers are shownOn in Table 1. These wind speed seriesthe to analyze the predictability direct multistep forecasting. the three anemometer towers, were used toNRG analyze the predictability of direct forecasting. three anemometer calibrated measuring instruments were usedmultistep to automatically recordOn the the wind speed data, and the towers, the calibrated NRG measuring instruments were used to automatically record the wind recorded time interval was 10 min. After processing the missing and invalid data of the anemometer speed data, the recorded time interval After processing thespeed missing towers, theand integrity rate of the wind speed was data 10 canminutes. reach 100%. And these wind dataand have invalid data of the anemometer towers, the integrity rate of the wind speed data can reach 100%. passed the reasonableness test. And these wind speed data have passed the reasonableness test. Table 1. Information of wind speed series from three anemometer towers. Number

Location

Local Terrain Condition

1

Hunan province

Mountainous area

Selected Time of Wind Speed Series From April 2014 to March 2015

Height of Wind Speed Measurement (m) 80

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Table 1. Information of wind speed series from three anemometer towers. Number Location Appl. Sci. 2018, 8, x FOR PEER REVIEW 1 22

3 3

Local Terrain Condition

Selected Time of Wind Speed Series

Height of Wind Speed of 18 Measurement8 (m)

Hunan province Mountainous area From April 2014 to March 2015 Henan 2016 to May Henan province Plain area Plain area From June From June 20162017 to May 2017 province From August 2011 to July 2012 Zhejiang province Coastal area Zhejiang province

Coastal area

From August 2011 to July 2012

80 120 120

100 100

4.2. Autocorrelation Analysis of Wind Speed Series Based on MIC 4.2. Autocorrelation Analysis of Wind Speed Series Based on MIC

The MIC was used to measure the autocorrelation of the selected wind speed series. There are The MIC was used measure the autocorrelation of the selected wind speed 36 months of wind speedtoseries. Taking a month’s wind speed series {v(t), t = series. 1, 2, . .There . , N} are as an 36 months of wind speed series. Taking a month's wind speed series {v(t), t = 1, 2, ..., N} as Then, an example, the MIC of {v(t), t = 1, 2, . . . , N} and {v(t), t = 1, 2, . . . , N} was firstly calculated. example, the MIC of {v(t), t = 1, 2, …, N} and {v(t), t = 1, 2, …, N} was firstly calculated. Then, the the MIC of {v(t), t = 1, 2, . . . , N − 1} and {v(t), t = 2, 3, . . . , N} was calculated. Continuing this step MIC of {v(t), t = 1, 2, …, N − 1} and {v(t), t = 2, 3, …, N} was calculated. Continuing this step until the until the MIC of {v(t), t = 1, 2, . . . , N − τ} and {v(t), t = τ + 1, τ + 2, . . . , N} was calculated. In the above MIC of {v(t), t = 1, 2, …, N − τ} and {v(t), t = τ + 1, τ + 2, …, N} was calculated. In the above example, example, N represents the number of wind speed data; τ represents the number of delay time (unit N represents the number of wind speed data; τ represents the number of delay time (unit is 10 min) is 10 min) and this paper took τ as 300. After calculating the auto-correlated MIC of all wind speed and this paper took τ as 300. After calculating the auto-correlated MIC of all wind speed series, the series, the variation law of the MIC with the delay time is shown in Figure 4. variation law of the MIC with the delay time is shown in Figure 4.

(a)

(b)

(c) Figure Thevariation variationlaw law of of the the MIC MIC with with the of of anemometer Figure 4. 4.The the delay delay time: time:(a) (a)wind windspeed speedseries series anemometer tower 1; (b) wind speed series of anemometer tower 2; (c) wind speed series of anemometer tower 3. 3. tower 1; (b) wind speed series of anemometer tower 2; (c) wind speed series of anemometer tower

canbebeseen seenfrom fromFigure Figure 44 that that as as the the delay MIC of of thethe It Itcan delay time time increases, increases,the theauto-correlated auto-correlated MIC wind speed series gradually decreases and finally reaches a steady trend. With the decrease of MIC, wind speed series gradually decreases and finally reaches a steady trend. With the decrease of the correlation between future and historical wind speed series also decreases. At this time, the MIC, the correlation between future and historical wind speed series also decreases. At this time, forecasting error will gradually increase when forecasting the future wind speed based on the the forecasting error will gradually increase when forecasting the future wind speed based on the historical wind speed. Therefore, in order to ensure the forecasting accuracy of the direct multistep historical wind speed. Therefore, in order to ensure the forecasting accuracy of the direct multistep forecasting, a fixed MIC value can be determined, and the delay time corresponding to the MIC forecasting, a fixed MIC value can be determined, and the delay time corresponding to the MIC value value can be used as the predictable time of the wind speed series. According to the calculation results of the three anemometer towers in Figure 4, the variation law of MIC with delay time tends to be gentle when the MIC drops to 0.2. Therefore, we can take the corresponding delay time (or

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can be used as the predictable time of the wind speed series. According to the calculation results of the three anemometer towers in Figure 4, the variation law of MIC with delay time tends to be gentle when the MIC drops to 0.2. Therefore, we can take the corresponding delay time (or correlation length) as the predictable time of the wind speed series when the MIC is equal to 0.2. The calculation results are shown in Table 2. Table 2. Correlation length of wind speed series when MIC equals 0.2. Correlation Length (h) Month

Anemometer Tower 1

Anemometer Tower 2

Anemometer Tower 3

8.17 5.83 14.83 7.50 12.50 4.50 7.00 3.00 6.33 9.67 7.67 9.00

6.17 5.83 4.50 6.00 4.17 3.67 3.33 4.00 3.83 6.00 6.50 4.17

6.67 3.67 6.83 4.67 6.17 4.83 5.33 8.67 6.67 5.17 5.00 8.50

January February March April May June July August September October November December

4.3. Analysis of Predictable Time Because the selected wind speed series in different regions are different, the correlation length of each month’s wind speed series obtained by taking MIC equal to 0.2 is also different. Therefore, this paper compared the influence of different correlation lengths on wind speed forecasting error to obtain a more general wind speed predictable length. In this paper, the basic time series forecasting method, Persistence Model [42], was used to forecast the corresponding correlation length of each month’s wind speed series. Assuming that the wind speed series of a certain month is {v(t), t = 1, 2, . . . , N}, and the correlation length obtained when the MIC equals 0.2 is denoted by l (unit is h). Since the recorded time interval of the three anemometer towers is 10 min, the number of wind speed data with a correlation length of l is 6l. The wind speed series was segmented according to 6l, and then the wind speed of the previous period was used to forecast the wind speed of the next period. That is to say, {v(t), t = 1, 2, . . . , 6l} was used to forecast {v(t), t = 6l + 1, 6l + 2, . . . , 2 × 6l}; {v(t), t = 6l + 1, 6l + 2, . . . , 2 × 6l} was used to forecast {v(t), t = 2 × 6l + 1, 2 × 6l + 2, . . . , 3 × 6l} and so on until the end of the series. After using the persistence model to forecast the 36 wind speed series in different regions, the errors between the measured and forecasted wind speed of each month were counted. Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) were used as the error evaluation index. The formulas for calculating MAE and RMSE are as follows: MAE =

1 N vi − v pi N i∑ =1

v u N u1 2 RMSE = t ∑ vi − v pi N i =1

(9)

(10)

where N is the number of forecasted wind speed data; vi is the measured wind speed, m/s; vpi is the forecasted wind speed, m/s. The variation law of MAE and RMSE with the correlation length is shown in Figure 5. As the correlation length of the wind speed series increases, the forecasting error tends to increase overall.

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However, when the correlation length is less than four hours, the forecasting error is small and stable, and the fluctuation range is small. Therefore, four hours can be used as the predictable time of the wind speed series for direct multistep forecasting based on historical wind speed data. The forecasting time of the wind speed series in the following section was taken as four hours. Appl. Sci. 2018, 8, x FOR PEER REVIEW

(a)

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(b)

Figure Thevariety varietylaw lawof ofMAE MAE and and RMSE RMSE with (b)(b) RMSE. Figure 5. 5.The with correlation correlationlength: length:(a) (a)MAE; MAE; RMSE.

5. Case Study 5. Case Study Thethree threeforecasting forecasting cases cases of of wind wind speed series The series selected selected inin this thispaper paperarearefrom fromthree three anemometertowers towersininmountainous mountainous area, area, plain plain area and and coastal thethe anemometer coastal area, area, respectively. respectively.Then Then EEMD-FuzzyEn-LSTMNNmodel modelwas was establishedtoto forecast the wind speed series future EEMD-FuzzyEn-LSTMNN established forecast the wind speed series forfor thethe future four four hours. Furthermore, the applicability and effectiveness of the EEMD-FuzzyEn-LSTMNN hours. Furthermore, the applicability and effectiveness of the EEMD-FuzzyEn-LSTMNN model were modelby were verified by comparing with the BPNN model andmodel. LSTMNN model. verified comparing with the BPNN model, SVM model, model SVM and LSTMNN Wind Speed DataDescription Descriptionofofthe theCases Cases 5.1.5.1. Wind Speed Data The wind speed data selected in Case A, Case B and C iswind the wind from The wind speed data selected in Case A, Case B and CaseCase C is the speedspeed series series from October October to December of the anemometer tower 1, 2 and 3 respectively. The detailed information of to December of the anemometer tower 1, 2 and 3 respectively. The detailed information of the three the three anemometer towersinisTable shown1.in Table 1. anemometer towers is shown The direct multistep forecasting time of the wind speed series was taken as four hours The direct multistep forecasting time of the wind speed series was taken as four hours according according to the conclusion of Section 4. In each case, 864 wind speed data from 6 days in December to the conclusion of Section 4. In each case, 864 wind speed data from 6 days in December were were randomly selected as the test set of the forecasting model, and the wind speed data from the randomly selected as the test set of the forecasting model, and the wind speed data from the previous previous two months were used as the training set of the forecasting model. Taking the wind speed two months were used as the training set of the forecasting model. Taking the wind speed series {v(t), series {v(t), t = 1, 2, …, N} of a certain case as an example, the training and test set of the forecasting t = 1, 2, . . . , N} of a certain case as an example, the training and test set of the forecasting model are model are illustrated as follows. The training set is {v(t), t = 1, 2, …, N − 864 − 24}, in which {v(t), t = illustrated set isinput {v(t), sample t = 1, 2,and . . . ,{v(t), N −t864 ... , 1,2, …, Nas − follows. 864 − 24 ×The 2} istraining the training = 24−+ 24}, 1, 24in+ which 2, …, N{v(t), − 864t =− 1,2, 24} is N− 864 − 24 × 2} is the training input sample and {v(t), t = 24 + 1, 24 + 2, . . . , N − 864 − 24} is the training output sample. Similarly, the test set is {v(t), t = N − 864 – 24 + 1, N − 864 – 24 + 2,…, N},the training output Similarly, −is864 24 + 1, Nsample − 864 and – 24 {v(t), + 2, .t.=. N , N}, in which {v(t), sample. t = N − 864 – 24 + 1, the N − test 864 –set 24is+ {v(t), 2, …, tN=−N 24} the–test input in –which {v(t), t = N − 864 – 24 + 1, N − 864 – 24 + 2, . . . , N − 24} is the test input sample and {v(t), t= 864 + 1, N – 864 + 2, …, N} is the test output sample.

N – 864 + 1, N – 864 + 2, . . . , N} is the test output sample. 5.2. Error Evaluation Index

5.2. Error Evaluation Index

The selection of evaluation indexes has an important impact on the assessment of wind speed

The selection of evaluation indexesindexes has anselected important on the wind speed forecasting methods. The evaluation in impact this paper are assessment MAE, RMSEofand Mean forecasting The evaluation indexes selected in this paperof areMAE MAE,and RMSE and are Mean Absolute Absolute methods. Percentage Error (MAPE). The calculation formulas RMSE given by Percentage (MAPE). The and RMSE are given by Formulas (9) and FormulasError (9) and (10), and thecalculation formula forformulas MAPE isof asMAE follows: (10), and the formula for MAPE is as follows: 1 N vi − vpi (11) MAPE =  1N Ni =1 vi v− i v pi MAPE = ∑ (11) N i =1 vi 5.3. Parameter Settings of the BPNN Model, the SVM Model and the LSTMNN Model When the BPNN model, the SVM model and the LSTMNN model were used to forecast the wind speed series in the cases, a series of parameter settings for the models are shown in Table 3. In addition to the parameters specified in the table, the default values given by the corresponding

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5.3. Parameter Settings of the BPNN Model, the SVM Model and the LSTMNN Model When the BPNN model, the SVM model and the LSTMNN model were used to forecast the wind speed series in the cases, a series of parameter settings for the models are shown in Table 3. In addition to the parameters specified in the table, the default values given by the corresponding software toolbox were used for other parameters. The wind speed data should be normalized before being input into Appl. Sci. 2018,model. 8, x FOR PEER 11 function, of 18 the forecasting TheREVIEW normalization function used in this paper is the mapminmax which normalizes the wind speed series to [−1, 1]. software toolbox were used for other parameters. The wind speed data should be normalized before being input into the forecasting model. The normalization function used in this paper is the Table 3. Parameter settings of wind speed forecasting model. mapminmax function, which normalizes the wind speed series to [−1, 1].

Forecasting Models

Parameters

Number or Type

Number of neurons in the hidden layer Parameters Learning rate of training Number ofTraining neurons in the hidden layer target

20

Table 3. Parameter settings of wind speed forecasting model.

Forecasting BPNN modelModels

Number or Type 0.001 20 0.00001 BPNN model Learning rate of training 0.001 Type of svm epsilon-SVR Training target 0.00001 SVM model Type of kernel function linear kernel function Type of svm epsilon-SVR SVM model Number Type of neurons in function the LSTM layer 20 of kernel linear kernel function Type of activation function of the output Number of neurons in the LSTM layerlayer 20 tanh LSTMNN model adam Type of activationOptimizer function of the output layer tanh LSTMNN model Learning rate 0.0001 Optimizer adam Learning rate 0.0001

5.4. Decomposition Results by EEMD

5.4. Decomposition Results by EEMD

In order to improve the overall forecasting performance, this paper firstly adopted EEMD to In order to improve the overall forecasting performance, this paper firstly adopted EEMD to decompose the original windwind speed series of the cases separately, andand the the decomposition results decompose the original speed series of three the three cases separately, decomposition are listed in Figure 6. It is obvious that each wind speed series is decomposed into 13 components results are listed in Figure 6. It is obvious that each wind speed series is decomposed into 13 whichcomponents are respectively denoted by IMF , . IMF . . , IMF R from top to bottom. which are respectively denoted 1, IMF …, IMF 12 and R from top to bottom. 1 , IMF2by 122,and

(a)

Figure 6. Cont.

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(b)

(c) Figure 6. The decompositionresults resultsof ofwind wind speed speed series: A; A; (b)(b) Case B; (c) C. C. Figure 6. The decomposition series:(a)(a)Case Case Case B;Case (c) Case

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5.5. Classification of Components Based 5.5.Appl. Classification Components Based on on FuzzyEn FuzzyEn Sci. 2018, 8, x of FOR PEER REVIEW

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The by The original original wind wind speed speed series series of of the the three three cases cases are are all all decomposed decomposed into into 13 13 components components by 5.5. Classification of Components Based on FuzzyEn EEMD. Then, the FuzzyEn values of each component were calculated respectively, and the results are EEMD. Then, the FuzzyEn values of each component were calculated respectively, and the results shown in Figure 7. wind The original are shown in Figure 7. speed series of the three cases are all decomposed into 13 components by EEMD. Then, the FuzzyEn values of each component were calculated respectively, and the results are shown in Figure 7.

Figure 7. 7. The The FuzzyEn FuzzyEn of of each each component component obtained obtained by by EEMD. EEMD. Figure Figure 7. The FuzzyEn of each component obtained by EEMD.

In the three cases, the FuzzyEn values of the 1st component to the 13th component gradually In firstly, the three cases, FuzzyEn valuesThe of the 1st component to the 13th component gradually decrease and then become smooth. FuzzyEn component firstly, and thenthe become smooth. of the high-frequency component is large, decrease firstly, and then become smooth. The FuzzyEn of the high-frequency component is large, is which means itit isismore complicated. On the ofofthe low-frequency component which means more complicated. Onthe thecontrary, contrary, theFuzzyEn FuzzyEn the low-frequency component which means it that is that more complicated. the contrary, the FuzzyEn of the low-frequency component small, indicating itsits complexity The with similar FuzzyEn can be is small, indicating complexityisOn issmall. small. Thecomponents components with similar FuzzyEn values values is small, indicating that its complexity is small. The components with similar FuzzyEn values can front be intoone one group. In Figure the FuzzyEn values of the components the classified into group. In Figure 7, the7,FuzzyEn values of the components at the frontatdescending classified into one group. In Figure 7, the FuzzyEn values of the components at the front curve segment are segment quite different, so each component be regarded subsequence. FuzzyEn descending curve are quite different, so eachcan component canasbea regarded as a The subsequence. descending curve segment are quite different, so each component can be regarded as a subsequence. The FuzzyEn values of the 7th to 13th component at the final stationary segment values of the 7th component to component 13th component at the final stationary curve segmentcurve are almost the The FuzzyEn values of the 7th component to 13th component at the final stationary curve segment same, so they cansame, be grouped superimposed formsuperimposed a new subsequence. the are almost the so theytogether can beand grouped togethertoand to formAfter a new are almost the same, so they can be grouped together and superimposed to form a new subsequence.was After the classification was completed, 7 subsequences classification completed, 7 subsequences were finally obtained. were finally obtained. subsequence. After the classification was completed, 7 subsequences were finally obtained.

5.6. 5.6. Forecasting Forecasting Results Results and and Analysis Analysis

5.6. Forecasting Results and Analysis

The BPNN model, the SVM model, the LSTMNN model and the EEMD-FuzzyEn-LSTM model The BPNN model, model and andthe theEEMD-FuzzyEn-LSTM EEMD-FuzzyEn-LSTM model The BPNN model,the theSVM SVMmodel, model, the the LSTMNN LSTMNN model model were used toto forecast the the 864 wind speedspeed data randomly selectedselected from thefrom three cases. The forecasting were used forecast 864 wind data randomly the three cases. The were used to forecast the 864 wind speed data randomly selected from the three cases. The results are shown in Figure 8 and the forecasting error is shown in Figure 9. forecasting results are shown in Figure 8 and the forecasting error is shown in Figure 9. forecasting results are shown in Figure 8 and the forecasting error is shown in Figure 9.

(a) (a) Figure 8. Cont.

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Appl. Sci. Sci. 2018, 2018, 8, 8, xx FOR FOR PEER PEER REVIEW REVIEW Appl.

14 of of 18 18 14

(b)

(c) Figure 8. Forecastingresults resultsof ofwind wind speed speed series: series: (a) (a) Case A; (b) Case B;B;(c) (c)(c)Case Case C.C. Figure Forecasting results of wind speed C. Figure 8.8. Forecasting series: (a)Case CaseA; A;(b) (b)Case CaseB; Case

(a)

(b) Figure 9. Cont.

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15 18 15 of 19


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(c)

(c) Figure 9. Forecasting error of wind speed series: (a) Case A; (b) Case B; (c) Case C.

Figure Forecastingerror errorof ofwind wind speed speed series: series: (a) C.C. Figure 9.9.Forecasting (a) Case CaseA; A;(b) (b)Case CaseB;B;(c)(c)Case Case

As is shown in Figure 8; Figure 9, the forecasting effect of the BPNN model is similar to that is shown Figure 8; Figure the forecasting the BPNN model is similar to that AsAs is shown in in Figure 8; Figure 9, the9,forecasting effecteffect of theofBPNN model is similar to that of the of the SVM model, and the forecasting effect of the LSTMNN model is slightly better than that of of the SVMand model, and the forecasting effect of the LSTMNN is better slightly better that of SVM model, the forecasting effect of the LSTMNN model ismodel slightly than thatthan of the BPNN the BPNN model and the SVM model for wind speed series in different regions. However, the the BPNN model and the SVM model for wind speed series in different regions. However, the model and the SVM model for wind speed series in different regions. However, the forecasting effect forecasting effect of the EEMD-FuzzyEn-LSTMNN model is greatly improved compared with the forecasting effect of the EEMD-FuzzyEn-LSTMNN model is greatly improved compared model, with the of the EEMD-FuzzyEn-LSTMNN model is greatly improved compared with the LSTMNN and LSTMNN model, and the forecasting error is obviously reduced. LSTMNN model, and the forecasting error is obviously reduced. the forecasting error is obviously reduced. The subsequences are forecasted separately in the the EEMD-FuzzyEn-LSTMNNmodel, model, and the The subsequencesare areforecasted forecasted separately separately in in and thethe The subsequences the EEMD-FuzzyEn-LSTMNN EEMD-FuzzyEn-LSTMNN model, and fluctuation of wind speed forecasting results obtained by the superposition is smoother. fluctuation of wind speed forecasting results obtained by the superposition is smoother. ByBy fluctuation of wind speed forecasting results obtained by the superposition is smoother. By analyzing analyzing the first first few few high-frequency high-frequencysubsequences subsequences have analyzingeach eachsubsequence, subsequence, itit was was found found that that the have each subsequence, it was found that the first few high-frequency subsequences have strong randomness strong randomness low. MIC MICwas wasused usedtotoanalyze analyzethe the autocorrelation strong randomnessand andtheir theirregularity regularity is is very very low. autocorrelation of of and their regularity is very low. MIC was used to analyze the autocorrelation of the first three thethe first three the variation variationlaw lawofofMIC MICwith withdelay delay time is shown first threehigh-frequency high-frequencysubsequences, subsequences, and the time is shown high-frequency subsequences, and the variation law of MIC with delay time is shown in Figure 10. in in Figure MIC of of autocorrelation autocorrelationdecreases decreasesrapidly. rapidly. Figure10.10.As Asthe thedelay delay time time increases, increases, the MIC In In thethe Asforecasting the delay time increases, the MIC of autocorrelation decreases rapidly. In the forecasting of wind windspeed speedseries seriesfor for the the future future four of of these forecasting ofofwind four hours hours (24 (24××10 10min), min),the theautocorrelation autocorrelation these speed series for the future four hours (24 × 10 min), the autocorrelation of these high-frequency high-frequencysubsequences subsequencesisispoor, poor, which which leads to thethe forecasting high-frequency to large largeforecasting forecastingerrors. errors.When When forecasting subsequences issubsequences poor, whichare leads to large forecasting errors. When the forecasting results ofisall results superimposed, the speed series results ofofallallsubsequences are superimposed, the high-frequency high-frequencypart partofofthe thewind wind speed series is subsequences are superimposed, the high-frequency part of the wind speedgentle series is weakened to weakeneddue due thelow lowforecasting forecasting accuracy, which of due thethe weakened totothe accuracy, which results results ininmore more gentlefluctuation fluctuation of theforecasting low forecasting results.accuracy, which results in more gentle fluctuation of the forecasting results. forecasting results.

(a) (a)

(b)

(b)

(c)

(c)

Figure 10. The variation law of MIC with the delay time for high-frequency components: (a) Case A; Figure 10. The The variation law of of MIC MIC with with the the delay delay time time for for high-frequency components: components: (a) Case A; Figure 10. (b) Case B; (c)variation Case C. law (b) Case Case B; B; (c) (c) Case Case C. C. (b)

The error evaluation indexes of the four forecasting models are calculated and presented in The evaluation of the models and presented The4.error error evaluation indexes the four fourofforecasting forecasting models are are calculated calculated andare presented in Table In the table, the indexes evaluation indexes the EEMD-FuzzyEn-LSTMNN model the best in Table the the evaluation indexes of the EEMD-FuzzyEn-LSTMNN model are the Table In thetable, table,accuracy the evaluation indexes of the EEMD-FuzzyEn-LSTMNN model are best the and best and4.4. itsIn forecasting is the highest. its forecasting accuracy is theishighest. the LSTMNN with the BPNN model, the MAE, MAPE and RMSE of the and its Comparing forecasting accuracy themodel highest. three cases are bymodel 0.01–0.04 m/s (1–3%), 0.004–0.01 (1–3%), 0.02–0.03 Comparing the LSTMNN with the BPNN model, the the MAE, MAPE and RMSE of(1–2%), theof three Comparing thereduced LSTMNN model with the BPNN model, MAE, MAPE andm/s RMSE the respectively. In the study of this paper, the(1–3%), default (1–3%), values given by the toolbox were used for cases are reduced by case 0.01–0.04 m/s (1–3%), 0.02–0.03 m/s (1–2%), respectively. three cases are reduced by 0.01–0.04 m/s0.004–0.01 0.004–0.01 (1–3%), 0.02–0.03 m/s (1–2%), most parameters of the LSTMNN which maybylead agiven small increase in most thewere evaluation In the case study of this paper, the values the to toolbox were used for parameters respectively. In the case study of default thismodel, paper, thegiven default values by the toolbox used for indexes. Since the training process of the LSTMNN involves the adjustment of many parameters, of the parameters LSTMNN model, maymodel, lead towhich a small increase in athe evaluation Since the most of the which LSTMNN may lead to small increaseindexes. in the evaluation the forecasting accuracy of this model will be further improved after systematic training process of the LSTMNN involves theLSTMNN adjustment of many parameters, theofforecasting accuracy indexes. Since the training process of the involves the adjustment many parameter parameters, optimization. Comparing the EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the errorthe of model will be further parameter optimization. Comparing thethis forecasting accuracy of improved this modelafter willsystematic be further improved after systematic parameter

optimization. Comparing the EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the error

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EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the error evaluation indexes are greatly improved. The MAE, MAPE and RMSE of the Case A are reduced by 0.4413 m/s (29.18%), 0.11 (29.7%), 0.6014 m/s (30.04%), respectively. The MAE, MAPE and RMSE of the Case B are reduced by 0.2773 m/s (19.74%), 0.1051 (21.74%), 0.3076m/s (16.81%), respectively. The MAE, MAPE and RMSE of the Case C are reduced by 0.3397m/s (26.99%), 0.0882 (26.27%), 0.4009m/s (25.66%), respectively. The values in the parentheses above are all relative values. Table 4. Calculation results of error evaluation indexes for the four forecasting models. Case

Forecasting models

MAE (m/s)

MAPE

RMSE (m/s)

Case A

BPNN model SVM model LSTMNN model EEMD-FuzzyEn-LSTMNN model

1.5308 1.5264 1.5122 1.0709

0.3800 0.3742 0.3704 0.2604

2.0371 2.0211 2.0022 1.4008

Case B


1.4406 1.4523 1.4045 1.1272

0.4875 0.4861 0.4835 0.3784

1.8626 1.8694 1.8295 1.5219

Case C


1.2697 1.2733 1.2585 0.9188

0.3397 0.3374 0.3358 0.2476

1.5798 1.5767 1.5624 1.1615

In addition, compared with the anemometer towers in other areas (Case B and Case C), the forecasting accuracy of the mountainous anemometer tower (Case A) is improved more greatly. Therefore, the EEMD-FuzzyEn-LSTMNN model is more advantageous for forecasting the wind speed series which has large forecasting errors by using ordinary neural networks. 6. Conclusions This paper first introduces the LSTM neural network for the forecasting of wind speed series. Then, in order to further improve the forecasting accuracy, a wind speed statistical forecasting method based on the EEMD-FuzzyEn-LSTMNN model is proposed. And the autocorrelation analysis based on the MIC is used to obtain the predictable time of wind speed series for direct multistep forecasting. The main conclusions of this paper are as follows:

•

•

•

MIC is used to analyze the autocorrelation of wind speed series from different terrain conditions, and some suitable correlation lengths are obtained. As the correlation length of the wind speed series increases, the forecasting error tends to increase overall. The forecasting error analysis shows that four hours can be taken as the predictable time of the wind speed series for direct multistep forecasting based on historical wind speed data. The wind speed series from different terrain conditions is forecasted for the future four hours, and the forecasting accuracy of the LSTMNN model is slightly higher than that of the BPNN model and the SVM model. It shows that the LSTM neural network can make better use of the historical input information of the wind speed series, and it is more suitable for the wind speed statistical forecasting method. Under different terrain conditions, the forecasting accuracy of the EEMD-FuzzyEn-LSTMNN model is much higher than that of the LSTMNN model. Comparing the EEMD-FuzzyEn-LSTMNN model with the LSTMNN model, the MAE, MAPE and RMSE of the three cases are reduced by 0.2773–0.4413 m/s (19.74–29.18%), 0.0882–0.11 (21.74–29.7%), 0.3076–0.6014 m/s (16.81–30.04%), respectively. Moreover, the EEMD-FuzzyEn-LSTMNN model has more advantages for forecasting the wind speed series which has large forecasting errors by using ordinary neural networks.

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The current forecasting method in this paper is to directly forecast the same steps for each subsequence. However, due to the strong randomness of the high-frequency subsequence, it is not appropriate for the high-frequency subsequence to make a direct multistep forecasting of the same steps as the low-frequency subsequence. Therefore, the autocorrelation of each subsequence can be analyzed to determine its own appropriate steps for the direct multistep forecasting. Then, each subsequence is forecasted separately according to its corresponding forecasting steps, and all the forecasting results of subsequences are superimposed to get the final forecasting results. This method will help to further improve the forecasting accuracy of the EEMD-FuzzyEn-LSTMNN model, and it will become our next research goal. Author Contributions: Conceptualization, Q.Q.; Formal analysis, Q.Q. and J.Z.; Funding acquisition, X.L.; Methodology, Q.Q.; Software, Q.Q.; Validation, Q.Q.; Visualization, Q.Q.; Writing—original draft, Q.Q.; Writing—review & editing, Q.Q., X.L. and J.Z. Funding: This research was funded by National Natural Science Foundation of China under Grant 51379159 and Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20130141130001. Conflicts of Interest: The authors declare no conflict of interest.

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