multistep wind speed and wind power prediction based on a...

Research ArticleMultistep Wind Speed and Wind PowerPrediction Based on a Predictive Deep Belief Network andan Optimized Random Forest

Zexian Sun 1 Hexu Sun 1 and Jingxuan Zhang 2

1School of Artificial Intelligence Hebei University of Technology China2College of Electrical Engineering North China University of Science and Technology China

Correspondence should be addressed to Hexu Sun hxsunhebusteducn

Received 11 March 2018 Revised 24 May 2018 Accepted 4 June 2018 Published 24 July 2018

Academic Editor Marco Mussetta

Copyright copy 2018 Zexian Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A variety of supervised learningmethods using numerical weather prediction (NWP) data have been exploited for short-termwindpower forecasting (WPF) However the NWP data may not be available enough due to its uncertainties on initial atmosphericconditions Thus this study proposes a novel hybrid intelligent method to improve existing forecasting models such as randomforest (RF) and artificial neural networks for higher accuracy First the proposed method develops the predictive deep beliefnetwork (DBN) to perform short-term wind speed prediction (WSP) Then the WSP data are transformed into supplementaryinput features in the prediction process of WPF Second owing to its ensemble learning and parallelization the random forest isused as supervised forecasting model In addition a data driven dimension reduction procedure and a weighted voting method areutilized to optimize the random forest algorithm in the training process and the prediction process respectively The increasingnumber of training samples would cause the overfitting problem Therefore the k-fold cross validation (CV) technique is adoptedto address this issue Numerical experiments are performed at 15-min 30-min 45-min and 24-h to indicate the superiority andsignal advantages compared with existing methods in terms of forecasting accuracy and scalability

1 Introduction

The uncertainty of wind energy indeed imposes major chal-lenges on power system operation and planning such aspower system security assessment and reserve management[1] A reliable wind power forecasting plays an important rolein preventing damage to wind turbines and maintaining thestability and security of the power system

Numerous forecasting models which are generally classi-fied into four categories have been proposed for short-termwind power forecasting(1) Physical-based method includes spatial and temporalfactors in a full fluid-dynamics model of the atmosphere[2] NWP is a popular physical approach utilizing complexmathematical models but always suffers from the difficultiesin gaining information and its limited spatial resolution(2) Statistical-based method characterizes the historydata to yield precise performance for short-term forecasting

tasks The dynamical ensemble LSSVR [3] the closed-loopforecasting engine including KIM and EMD[4] and adaptiverobust multikernel regression model [5] have been proposedto yield the research Adaptive neurofuzzy inference systemswere developed to perform a nonlinear mapping betweeninputs and outputs [6](3) Artificial intelligence-based method represents thecomplex nonlinear relationship between inputs and outputswithout predefined mathematical models These modelsinclude Ridgelet ANN [7] bagging neural network [8] andMultilayer Perceptron Networks [9](4) Hybrid-based method based on two or more archi-tectures benefits from the advantages of each approach toreach the optimal results A hybrid approach based on thecombination between least square support vector machineand gravitational search algorithms is proposed [10]

Most methods reported in the current literature havethree disadvantages

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6231745 15 pageshttpsdoiorg10115520186231745

2 Mathematical Problems in Engineering

(1) In most artificial intelligence methods there is onlyone single hidden layer [11ndash14] Due to the finite abilityof searching optimal solution in the parameter spaces ofANN with more than one hidden layer these models cannotprovide accurate outputs(2) Some methodologies require tediously hand-engineered features [13] Due to the lack of sufficientknowledge for a specific domain the selected features maynot be suitable for corresponding models(3)The conventional features in the previous supervisedforecasting models contain the NWP data of the wind farms[15ndash19] However the NWP model usually runs once ortwice a day which is often applied for medium- to long-termforecasts [20]

Deep learning has attracted tremendous attention inrecent years of academia and industrial communities [21] Ithas been successfully used in the field of speed recognition[22] image processing [23] and health status assessment[24 25] However it has not been actively utilized in thewind power or wind speed forecasting fields Deep beliefnetwork due to its strong ability of learning has beenperformed in short-term WSP [26] The stacked denoisingautoencoder combined with rough set was applied to extractfeatures from wind speed series [20] In the literature [27]deep autoencoders act as base-regressors whereas deep beliefnetwork is used as ametaregressor ADNN-MRT schemewasproposed to predict wind power Therefore employing deeplearning to address the problemsmentioned above has a greatpotential

In this paper a hybrid intelligent method for short-term wind power forecasting is proposed First DBN as aprobabilistic generativemodel consisting ofmultiple layers ofrestricted Boltzmann machines (RBMs) provides the unsu-pervised learning features from the wind speed series data inthe pretraining phase and backpropagation neural network(BPNN) as the top layer of the DBN uses the labeled data tofine-tune the parameters of the DBN by stochastic gradientdecent Performance of DBN is affected by its parameterswhich are often limited by hand-engineered features The batalgorithm combined the major advantages between particleswarm optimization and genetic algorithm and HarmonySearch is applied to yield optimal parameters in the DBNSecond random forest is suitable for handling large data dueto its parallelization [28] It has been combined with theSpark [28] heuristic bootstrap sampling method [29] kernelprincipal component analysis [30] and other technologies toperform fault diagnosis and regression tasks [31 32] Owingto the improvement of the forecasting accuracy for high-dimensional and large-scale wind turbine data we proposean optimized random forest method which consists of adimension reduction procedure and the weighted votingprocess for the short-termWPF

The contributions of the paper are as follows(1) Predictive deep belief network is applied as the deeplearning architecture to perform the short-term wind speedprediction The DBN model has better generalized abilitythan the traditional shallow architectures(2) The bat algorithm is incorporated with DBN toimprove the training accuracy and reduce the costing timein wind speed prediction

START

Perform the deep belief network topredict wind speed series

Select the SCADA variables as thesupplementary input features

Conduct a Max Relevance-Min Redundancyindex to reduce the number of dimensions

Apply the random forest to forecastthe wind power

Utilize the stochastic gradient decline to update theweights for each decision tree in real time

END

Figure 1 The process of the proposed method for multistep windspeed and wind power prediction

(3) Benefiting from the dimension reduction andweighted voting procedures the random forest modelavoids the lack of prior knowledge for feature selection andenhances the capacities of tackling new condition data

This paper is organized as follows In Section 2 the DBNand its learning algorithm for short-termWSP are presentedSection 3 presents the optimized random forest and theproposed model for short-term WPF Numerical results andconclusion are presented in Sections 4 and 5 respectively

2 Brief Architecture aboutthe Proposed Method

In this section the proposed method would be brieflyintroduced and its process is shown in Figure 1 Wind speedas the most important variable to the normal running ofwind turbine is hard to predict because of its randomnessand fluctuation Therefore due to the merged advantages ofthe deep learning architectures and the bat algorithm theWSP model based on predictive deep belief network and batalgorithm is firstly performed to capture the characteristics ofwind speed series Then owing to its ensemble learning andparallelization the random forest is used as the WPF modelIn addition a data driven dimension reduction procedureand a weighted voting method are utilized to optimize therandom forest algorithm in the training process and theprediction process respectively

3 DBN for Wind Speed Prediction

Due to the intermittence and volatility of the wind energy itis difficult to gain the efficient future wind speed seriesThusthis sectionwould introduce a novelWSPmethod to performthe wind speed forecasting

Mathematical Problems in Engineering 3

20 40 60 80 1000Sample

0

2

4

6

8

win

d sp

eed

(ms

)

Figure 2 The wind speed series recorded on October 30 2017 innorthern China

RBM RBM

Ｒ1

Ｒ2

ＲN

W

BPNN

Figure 3 Architecture of DBN composed of a number of stackedRBMs and BPNN

31 Short-Term Wind Speed Forecasting The wind speedseries can be described as 119883 = 1199091 1199092 119909119905 where 119909119894 isthe average wind speed in the past 15 minutes as illustratedin Figure 2 For short-term wind speed prediction it is toforecast the future value of 119909119905+120591 by utilizing the previous Ndata where t is the index of the wind speed series and 120591 is theforecast horizonTherefore it is a significant task to build thefunction f to describe the wind speed explicitly

119891 (119909119905minus1 119909119905minus119873 120579) = 119909119905+120591 (1)

where 120579 is the parameter vector

32 Traditional Deep Belief Network The architecture ofDBN is shown in Figure 3 It is composed of several stackedRBMs The unit number of first input layer is N which is thesame as the number of previous data The numbers of unitsfor the hidden layers are gradually reduced The input layerof BPNN as well as the hidden layer of the last RBM consistsof two unitsThe output layer has one unitThen the optimalmapping function can be found through the parameter spacewhich is influenced by the bat algorithm and avoid the effectof personal experience

There are two steps included in the training process oftraditional DBN(1) The pretraining phase As the hardcore of DBNRBM is a stochastic generative model which performs thisprocedure as a technology of greedy layerwise unsupervised

learning Each RBM consists of two layers namely thevisible layer and the hidden layer as shown in Figure 2The probability distribution over an RBM is defined by theconnection weights between visible units and hidden unitsthrough an energy-based model 119864(V ℎ 120579)

119864 (V ℎ 120579) = minus119887V minus ℎ119882V minus 119888ℎ (2)

where 120579 = (119882 119887 119888) represents the model parameters 119882denotes the weights connecting hidden and visible units andb and c are the biases of the visible units and the hiddenunits respectively The conditional probability over visibleunits and hidden units is defined as

119875 (ℎ | V) = exp (minus119864 (V ℎ 120579))119885 (3)

119885 = sumℎ

exp (minus119864 (V ℎ 120579)) (4)

Considering the specific structure of the RBM the neu-rons are binary the probabilistic version of activating a unitis a logistic function which is given by

119901 (ℎ119894 = 1 | V) = 119904119894119892119898 (119888119894 +119882119894V) (5)

119901 (V119894 = 1 | ℎ) = 119904119894119892119898 (119887119894 +119882119894ℎ) (6)

where 119904119894119892119898 is the logistics sigmoid functionThe objective by training the model is maximized log-

likelihood which is defined by

119871 (120579119863) = sum119909isin119863

log119875 (119909 120579) (7)

In the commonly studied case the contrastive divergenceis adopted to calculate the derivative of the log probabilityabout the model parameter

120597 log119875 (119909)120597119882 = 119864119901 [119909 sdot ℎ] minus 1198641199011015840 [119909 sdot ℎ] (8)

120597 log119875 (119909)120597119888 = 119864119901 [119909] minus 1198641199011015840 [119909] (9)

120597 log119875 (119909)120597119887 = 119864119901 [ℎ] minus 1198641199011015840 [ℎ] (10)

where 119864119901 denotes an expectation under the data distributionand1198641199011015840 denotes an expectation under themodel distribution

Then update rules for the parameters can be written as

119882 = 119882 + 120572120597 log119875 (119909)120597119882 (11)

119887 = 119887 + 120572120597 log119875 (119909)120597119887 (12)

119888 = 119888 + 120572120597 log119875 (119909)120597119888 (13)

where 120572 is the learning rate(2)Thefine-tune phase For the DBNmodel the gradientdescent associated with greedy layer-wise training method


is performed in the pretraining phase and this predictivefine-tune is carried out by adopting BPNN The parametersspace of the DBN model would be fine-tuned by minimizingthe error between the predicted value and actual value Theparameters can be updated as

119882119897 = 119882119897 minus 120572 120597120597119882119897 119871 (119882 119887119883) (14)

119861119897 = 119861119897 minus 120572 120597120597119861119897 119871 (119882 119887119883) (15)

where119882119897 and 119861119897 are the weights and bias of the lth layer 120572 isthe learning rate and 119871(119882 119887119883) is the cost function

The DBN model has the capability of forecasting thewind speed in the current condition space after the fine-tuneprocedure When it comes to the new dataset the parametersspace can be further fine-tuned by simply performing the newdataset instead of training from scratch

33 Optimization of the DBN Model To find the opti-mal mapping function in Section 31 an improved DBN isemployed The connecting weights the offsets of the unitsand the learning rate need to be decided when the modelis applied As mentioned above the model parameters areinitialized by random experiments and then updated byiterative training which may take a long time and need themutual experience To address this problem a bat algorithmis employed to help search the optimal parameters spacewhich is composed of the connecting weights between visibleunits and hidden units the biases of the visible units andthe hidden units the learning rate in the RBM and theparameters in the BPNN The detailed steps are shown asfollows

Step 1 Initialize 119894119905119890119903 = 1 bat position 119909119894 velocity V119894frequency 119876119894 pulse rate 119903119894 and loudness 119860 119894 for each of then bats

Step 2 Compute the fitness function value for every bat andselect the best bat

119891119894 = 1119898119898sum119895=1

(119877119895 minus 119877119886119895)2 (16)

119909119887119890119904119905 = argmin (119891119894) (119894 = 1 2 119899) (17)

where119898 is the size of output vector 119877119895 is the predicted valueand 119877119886119895 is the measured value and 119909119887119890119904119905 is the best solution inthe current situation

Step 3 Compute the new solution 119909119905119894 the new velocity V119905119894 andthe new fitness 119891119894

119891119894 = 119891min + (119891max minus 119891min) 120573 (18)

V119905119894 = V119905minus1119894 + (119909119905119894 minus 119909lowast) 119891119894 (19)

119909119905119894 = 119909119905minus1119894 + V119905119894 (20)

START

Compute the fitness functionand select the best solution

Update the parameters spaceaccording to the guide of bat

algorithm

Update the parameters spaceaccording to the guide of BP or

RBM algorithm

Select the new best globalsolution

YES Terminationcondition is false

NO

END

Figure 4 Using bat algorithm to design an optimized DBN

where 120573 is a uniform random value within [0 1] and 119909lowast isthe current global best solution and119891max and119891min denote themaximum and minimum frequency respectively

Step 4 BPNN or RBM updates the parameters space accord-ing to its own learning method

Step 5 Compare the performance of parameters spacesbetween the BPNN or RBM and the bat algorithm using (16)and select the best one as the new best global solution

The second step to the fifth step would be repeateduntil the termination condition is true Figure 4 shows theframework of the DBN model developed in this section

4 Optimized Random Forest forWind Power Forecasting

Random forest has been widely used for prediction problemsThe proposed WPF model is based on WSP and optimizedrandom forest which consists of attribute reduction andweighted voting procedures Figure 5 shows the trainingand prediction process of the WPF model First Pearsonrsquoscorrelation coefficient is conducted on the vector space toselect the favor features Second this paper adopts the WSPand the selected SCADA variables as the input attributesFinally a real-time weighted voting is constructed in theprediction process

41 Random Forest Algorithm Random forest is an ensemblepredictor based on regression tree model It generates kdifferent decision trees by training different data subsets


Training datasubset 1

Train procedurewith k-fold CV

Regressiontree 1

Result 1w1

Start

Select the favor features

Resampling with BootstrapSampling technique


Train procedure

Training datasubset n


Regressiontree n

Result n

Regressiontree 2

Result 2w2

with k-fold CV

Input

Final result

wn

Figure 5 Process of training and prediction of the WPF model

Each regression tree provides a prediction for every testingdata and the final result depended on the vote of these trees

The original training data is denoted as 119878 = (119888119894 119905119895) 119894 =1 2 119871 119895 = 1 2 119863 where 119888 is a sample and 119905 is thefeature sets Namely the training data contains D variablesand L samples The steps of constructing each decision treeof random forest are as follows

Step 6 Select training subsets in a bootstrap manner

Step 7 d features are randomly selected from D variables

Step 8 Construct the tree to the maximum depth withoutpruning

The above three steps are repeated until k decision treesare collected into a random forest model

42TheDimension Reduction forHigh-Dimensional Data Toimprove the prediction accuracy of the random forest modelwe present a Max Relevance-Min Redundancy (MRMR)index by conducting Pearsonrsquos correlation coefficient toreduce the number of dimensions In the training procedureof each decision tree the top d features according to theMRMR index value are selected as the favor features andthen we randomly select the (119897 minus 119889) feature variables fromthe remaining (119863 minus 119889) ones Therefore the dimension isreduced from119863 to 119897 The process in the dimension reductionis presented in Figure 6

First in the training process Pearsonrsquos correlation coef-ficient based on the covariance matrix is adopted to evaluatethe relationship between two vectors 120572119894 and 120573119895

START

Compute the MRMR index value of each featureand sort in the descending order

Select the top d features inthe ordered list

Select the (I-d) features in theremaining features

Obtain the I features

END

Figure 6 Dimension reduction in the training process

119875 (120572119894 120573119895) = cov (120572119894 120573119895)radicvar (120572119894) times var (120573119895) (21)

The relevance of each feature would be calculated by

119877 (119905119895 119884119871) = 1119863sum119905119895isin119905119875 (119905119895 119884119871) (22)

where 119905119895 is the feature D is the size of dimension119884119871 is the tar-get feature and the most relevant feature can be obtained by

119905max = argmax (119877 (119905119895 119884119871)) (23)


(1) Input a training dataset the whole feature set 119865119908 favor feature size 119904 the favor feature set 119865119904 = 120601the remaining feature set 119865119903 = 119865119908 minus 119865119904(2) for k=1 to s

search the favor feature from the remaining feature set according to

119865119900119901119905 = argmax119865119895isin119865119903

[119875(119865119895 119884119871) minus 1119896 minus 1 sum119865119894isin119865119904119875(119865119895 119865119894)] 119896 = 1argmax119865119895isin119865119903

[119875(119865119895 119884119871)] 119896 = 1(3) update the favor and the remaining feature sets 119865119904 = 119865119904 cup 119865119900119901119905 119865119903 = 119865119903 minus 119865119900119901119905end forOutput 119865119904

Algorithm 1 The process of selecting the favor features

Second the redundancy for each input variable is calcu-lated The min redundancy feature can be obtained by

119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)

The MRMR index is a simple form of 119877(119905119895 119884119871) and119877(119905119894 119905119895) and the candidate feature can be selected by

120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)

Given the framework discussed above we adopt theMRMR index to select the favor features the detailed stepsare shown in Algorithm 1 Compared with the traditionalRF model the dimension reduction method balances theaccuracy and diversity of the RF algorithm and prevents theoverfitting efficiently

43 Weighted Prediction Process In the prediction processlimited to the training data it likely leads to the performancereduction of the traditional RF algorithm when the newcondition data is applied To overcome this drawback a real-time update for weighted voting approach is proposed todecrease the prediction error for the testing data

Each sample of testing data is predicted by all the decisiontrees in the RF model The prediction result is weightedaverage value of all decision trees The weighted regressionresult is defined as

119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)

where 119908119895119894 is the weight for the ith decision tree on the jthsample 119910119895119894 is the prediction result for the ith decision treeon the jth sample and 119884119895 is the final prediction result

The objection of the predictor learning is to minimize theprediction error The error function in this paper is definedas

119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)

The stochastic gradient decline is conducted to update theweights for decision trees as follows

Δ119908119895119894 = minus120578120597119864119903119903120597119908119895119894= 120578 (119910119895119894 minus 119884119895)times (119910119895119894 minus 119884119895)[[

119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)

In the weighted voting procedure of RF model a reason-able weight associatedwith each tree is applied to improve theglobal prediction accuracy and reduce the generation errorespecially for the new condition data

44 The Short-Term Wind Power Forecasting Model To fur-ther improve the inferential ability of the proposed methodthe k-fold cross validation partitions the training data intok different subsets Then (k-1) of these subsets are selectedto train the model and the other one is used for testing theperformance of the trained model The root mean squareerror is taken as the criterion to select the optimal model Toclearly describe the process of the WPF the detailed steps oftraining and prediction procedure are given as follows

The training procedure includes the following

Step 1 Select the training features from the input variablesaccording to the dimension reduction method mentionedin Section 42 Twelve SCADA variables are selected as thecandidate features for RF model which are as shown inTable 1

Step 2 Based on the input features selected in Step 1 theregression tree model is built on its traditional way with k-fold cross validation without pruning

Step 3 The above two steps are repeated until the size ofrandom forest model reaches the threshold


Table 1 The list of candidate features

no The list of candidate features1 generator speed (CCU)2 Rotor speed3 Wind speed4 generator speed (PLC)5 The temperature of bearing A6 The temperature of bearing B7 The temperature of gearbox8 The ambient temperature9 The temperature of nacelle10 The temperature of gearbox bearing11 Blade 1 actual value12 Blade 2 actual value13 Blade 3 actual value

Table 2 The size of training sets and testing sets

The size oftraining sets

The size oftesting sets

Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150

The prediction procedure includes the following

Step 1 Each regression tree of the RF model applies thetesting data which consists of the future wind speed seriesobtained from theWSP and the SCADA variables to performshort-termWPF

Step 2 Compute the final prediction result based on theprediction values from all regression trees according to (28)and then update the error weight for each regression tree inreal-time according to (30)-(31)

5 Numerical Results

To verify the performance of the proposed method numer-ical experiments have been carried out on four sets ofhistorical SCADA data The task is to forecast the 15-min30-min 45-min and 24-h wind speed and the correspondingwind power The size of training sets and testing sets in fourcases are as shown in Table 2

51 Performance Index The root mean square error (RMSE)the mean absolute error (MAE) the average percentage error(APE) the bias (BIAS) and the standard deviation of theerror (SDE) are the measurements to compute the errorscores

119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)

where 119910119895 is the predicted value from the model and 119910119905 is thetrue value119898 is the number of testing samples

52 Short-TermWind Speed Prediction Results The structureof the predictive DBN is determined by human experiencewhich is 10-7-5-4-2-4-1 How to search the optimal structureis still an open problem In this section the proposedmethod is compared with several wind speed forecastingmodels which have been proposed in the literature includingBPNN ELMAN persistence method and traditional DBNTo evaluate the generalization performance the experimentswith the forecast horizon ranging from 15min to 24 hours arecarried out on four sets Case 1-Case 4

The actual wind speed data and their predicted valuesusing predictiveDBN traditional DBN BPNN ELMAN andpersistence model are shown in Figure 7 Figures 7(a)ndash7(j)show the predicted wind speed series in the future 15 minutesand 30 minutes from predictive DBN traditional DBNBPNN ELMAN and persistence model in Case 1 and Case 2Similarly the results for the 45-minute and 24-hour horizonin Case 3 and Case 4 are shown in Figures 7(k)ndash7(t) wherethe green and blue lines denote the actual and predicted windspeed series by these models respectively In the first twocases the estimated values from predictive DBN are veryclose to the real data but the others have obvious errorsHowever as we can see from Figures 7(k)ndash7(t) the perfor-mance of these models decrease gradually as the inferencestep increases where the predictive DBN also generates theminimum prediction errors

To further show the performance of these models theRMSE MAE BIAS SDE and APE as the indexes toevaluate the approximate performance are computed anddemonstrated in Table 3 As shown in Table 3 the deeplearning architectures procure much better results than shal-low networks and persistence model The proposed modelshares nearly the same generalization capacities with thetraditional DBN to predict the future wind speed while theforecasting ability of the persistence model degrades with thegrowth of the time scale Predictive DBN as a deep learningnetwork has improved the RMSE MAE BIAS SDE andAPE by 1505 1427 2439 1134 and 0625 over multiple time


PDBNActual

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(a) The forecasting result of predictive DBN for 15-min

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(b) The forecasting result of traditional DBN for 15-min

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(c) The forecasting result of BPNN for 15-min

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(d) The forecasting result of ELMAN for 15-min

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(e) The forecasting result of persistence model for 15-min

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012345678

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(f) The forecasting result of predictive DBN for 30-min

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(g) The forecasting result of traditional DBN for 30-min

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(h) The forecasting result of BPNN for 30-min

Figure 7 Continued


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eed

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20 40 60 80 100 120 140 160 180 2000Sample

(i) The forecasting result of ELMAN for 30-min

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(j) The forecasting result of persistence model for30-min

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(k) The forecasting result of predictive DBN for 45-min

DBNActual

02468

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(l) The forecasting result of traditional DBN for 45-min

BPNNActual

02468

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(m) The forecasting result of BPNN for 45-min

ELMANActual

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(n) The forecasting result of ELMAN for 45-min

PersistenceActual

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(o) The forecasting result of persistence model for 45-min

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(p) The forecasting result of predictive DBN for 24-h

Figure 7 Continued


DBNActual

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12

Win

d sp

eed

(ms

)

(q) The forecasting result of traditional DBN for 24-h

BPNNActual

50 100 1500Sample

123456789

10

Win

d sp

eed

(ms

)

(r) The forecasting result of BPNN for 24-h

ELMANActual

50 100 1500Sample

123456789

10

Win

d sp

eed

(ms

)

(s) The forecasting result of ELMAN for 24-h

PersistenceActual

50 100 1500Sample

123456789

10

Win

d sp

eed

(ms

)

(t) The forecasting result of persistence model for 24-h

Figure 7 The results of the short-term wind speed prediction

Table 3 The performance of wind speed forecasting models for different horizons

Index Cases Predictive DBN BPNN ELMAN Persistence Traditional DBN

RMSE

Case 1 0446 0721 0479 0462 0494Case 2 0654 0831 0716 0673 0669Case 3 2416 3307 3491 414 2435Case 4 1869 2076 1913 1949 1879

MAE


BIAS

Case 1 0051 0403 0065 0004 0064Case 2 0037 0526 0015 0003 0038Case 3 -0193 -04 0259 0078 0186Case 4 -0093 1484 -1085 01 0024

SDE


APE



Table 4 The performance of wind power forecasting models for different horizons

Models Experiments RMSE MAE BIAS SDE APE

The optimized random forest

Case 1 3341 2148 -926 3211 097Case 2 2184 1437 -773 1939 067Case 3 7272 5461 4206 5932 052Case 4 7185 4404 1528 7021 069

Random forest withoutweights updating


Random forest without favorfeatures

Case 1 5203 3680 252 5197 1093Case 2 3781 2387 -672 3721 107Case 3 17767 8316 555 16878 076Case 4 28905 16076 -5977 28281 255

Table 5 The performance of wind power forecasting models with 10-fold CV for different horizons




Random forest without weightsupdating




horizons compared to BPNN this demonstrates the abilityof deep learning network to handle the highly varying windspeed series As for the proposed model predictive DBNoutperforms traditional DBN with the total improvementof the RMSE MAE BIAS SDE and APE by 0092 00880062 0072 and 0026This is mainly due to the employmentof bat algorithm which can not only reduce the trainingtime but also provide more accurate network architec-tures

53 Short-Term Wind Power Forecasting Results Graphicalrepresentation about the predicted and actual power valuein four cases is shown in Figure 8 Figures 8(a)ndash8(c) denotethe predicted wind power and actual value in Case 1 from theproposed method random forest without the weights updat-ing (RFWWU) and random forest without the favor features(RFWFF) respectively Similarly Figures 8(d)ndash8(f) Figures8(g)ndash8(i) and Figures 8(j)ndash8(l) represent the predicted resultsfrom those models in Case 2 Case 3 and Case 4

6 Discussion

As seen clearly the DBN together with optimized randomforest can provide notably accurate future wind power seriesIn Case 1 Case 2 and Case 3 the lines of predicted valuesand the actual data are almost overlapping It makes a littleerror in Case 4 because of the wind fluctuation and thelonger time horizon as can be seen from Figure 7(p) Tofurther inspect the generalization ability of the proposedmodel Table 4 reports the RMSEMAE BIAS SDE andAPEindexes of the proposed model and unoptimized randomforest What is more Table 5 shows the forecasting indexesby utilizing tenfold cross validation in training procedureof random forest The training data would be divided intoten subsets Each subset of the training data is used oncefor testing while being used nine times for training CVmethod contributes to searching the optimal weights of theRF algorithm From Table 5 the effectiveness of CV can beeasily seen by comparing the indexes with Table 4 Most


proposed methodactual wind power

0

100

200

300

400

500

600

Win

d po

wer

(W)

50 100 150 2000Sample

(a) The forecasting result of proposed method for 15-min

RFWWUactual wind power

20 40 60 80 100 120 140 160 180 2000Sample

0

100

200

300

400

500

600

Win

d po

wer

(W)

(b) The forecasting result of RFWWU for 15-min

RFWFFactual wind power

0

100

200

300

400

500

600

Win

d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample

(c) The forecasting result of RFWFF for 15-min


20 40 60 80 100 120 140 160 180 2000Sample

0

100

200

300

400

500

600

700

Win

d po

wer

(W)

(d) The forecasting result of proposed method for 30-min


0

100

200

300

400

500

600

700

Win

d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample

(e) The forecasting result of RFWWU for 30-min


0

100

200

300

400

500

600

700

Win

d po

wer

(W)

50 100 150 2000Sample

(f) The forecasting result of RFWFF for 30-min


20 40 60 80 100 120 140 1600Sample

0200400600800

10001200140016001800

Win

d po

wer

(KW

)

(g) The forecasting result of proposedmethod for 45-min


0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample

(h) The forecasting result of RFWWU for 45-min

Figure 8 Continued



0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

20 40 60 80 100 120 140 1600Sample

(i) The forecasting result of RFWFF for 45-min


0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample

(j) The forecasting result of proposed method for 24-h


50 100 1500Sample

0

200

400

600

800

1000

1200

Win

d po

wer

(KW

)

(k) The forecasting result of RFWWU for 24-h


0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

50 100 1500Sample

(l) The forecasting result of RFWFF for 24-h

Figure 8 The results of the short-term wind power forecasting

Table 6 The MRMR index and the favor features

Attribute name 1 2 3 4 5generator speed (CCU) 07404 -0099 079038 - - - - - - - - - - - - - - - - - -Rotor speed 07398 -0098 07901 04401 0265Wind speed 0846 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -generator speed (PLC) 07404 -0099 079036 04404 - - - - - - - - -The temperature of bearing A 0024 -0102 0064 -0002 -0036The temperature of bearing B 0409 -0098 0427 0238 0144The temperature of gearbox 0509 -0138 0557 0296 0165The ambient temperature -0183 -0132 -0173 -0148 -0136The temperature of nacelle -036 -0069 -0354 -0243 -0188The temperature of gearbox bearing 0675 -0097 0690 0404 0261Blade 1 actual value -0523 02064 - - - - - - - - - - - - - - - - - - - - - - - - - - -Blade 2 actual value -0523 02063 -0658 -03 -0121Blade 3 actual value -0523 02062 -0658 -03 -0121

indexes of the all cases degrade with CV in the trainingprocedure except for some individual situations From thisobservation using the CV technology in the training processof random forest is a reasonable choice It can be observedthat the predicted accuracy of optimized random forest isgreater than that of RFWWU and RFWFF for all casesThe performance of RFWWU is just a little bit worse

than the optimized random forest The predicted valuesfrom RFWFF have the largest errors among those modelswhich from another point of view prove the importance offavor features The results of MRMR index and the favorfeatures are illustrated in Table 6 The favor features sizeis set to 5 and the bold one is chosen to be a favor fea-ture


7 Conclusions

In this paper we proposed a multistep wind speed and windpower forecasting model combined with predictive deepbelief network and optimized random forest to produce thefuture 15-min 30-min 45-min and 24-h wind speed andwind power seriesTheDBNmodels the wind speed series byits deep learning ability and the bat algorithm is employed tofurther enhance its inference performance The performanceof the predictive DBN is verified by four cases and theresults demonstrate that the DBN makes a major predictionaccuracy increase Wind speed has a pivotal effect on thewindpower generation Benefited by the approximated abilityof the DBN model random forest algorithm can procurebetter future wind power data with higher precise wind speedseries than traditional WPF models On the other hand thecompetitive generalization property can be further obtainedwith the dimension reduction and weights updating in real-time

However there are stillmany problems for thewind speedand wind power forecasting model One is that the learningtime will be booming when it has a large scale Therefore aparallel deep learning algorithm is developing in recent yearsThe second one is the parameters selection in this paperwe utilize the bat algorithm to search the parameter spaceHowever it is very difficult to determine the optimal numberof layers number of the units in each layer and the numberof epochsThese setting parameters affect the learning abilityof the deep network significantly Some automatic selectionmodels should be developed to fix this problem

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Hexu Sun has proposed the idea of the optimized modelZexian Sun has implemented the software code JingxuanZhang has collected the experimental data

Acknowledgments

This work obtains the support of Hebei Province Science andTechnology Plan ProjectmdashConstruction and Application ofWind Power ldquoSmart Capsulerdquo Cloud Management PlatformBased on Big Data Technology (17214304D)mdashand fundedproject of Hebei Natural Science FoundationmdashData Schedul-ing Optimization and Demand Forecasting of Discrete Man-ufacturing Industry Based on Big Data (F2018202206)

References

[1] S Fang and H-D Chiang ldquoImproving supervised wind powerforecasting models using extended numerical weather variables

and unlabelled datardquo IET Renewable Power Generation vol 10no 10 pp 1616ndash1624 2016

[2] A Costa A Crespo J Navarro G Lizcano H Madsen and EFeitosa ldquoA review on the young history of the wind power shortterm predictionrdquo Renewable amp Sustainable Energy Reviews vol12 no 6 pp 1725ndash1744 2008

[3] L Rongsheng P Minfang Z Haiyan W Xun and S MeieldquoUltra-short-term wind power prediction based on dynamicalensemble least square support vector regressionrdquo Journal ofHunan University (Natural Sciences) vol 44 no 4 pp 79ndash862017

[4] NAmjady andOAbedinia ldquoShort termwindpower predictionbased on improved kriging interpolation empirical modedecomposition and closed-loop forecasting enginerdquo Sustain-ability vol 9 no 11 2017

[5] YWang Q Hu DMeng and P Zhu ldquoDeterministic and prob-abilistic wind power forecasting using a variational Bayesian-based adaptive robust multi-kernel regression modelrdquo AppliedEnergy vol 208 pp 1097ndash1112 2017

[6] O Karakus E E Kuruoglu and M A Altinkaya ldquoOne-day ahead wind speedpower prediction based on polynomialautoregressive modelrdquo IET Renewable Power Generation vol 11no 11 pp 1430ndash1439 2017

[7] N Amjady F Keynia and H Zareipour ldquoShort-term windpower forecasting using ridgelet neural networkrdquoElectric PowerSystems Research vol 81 no 12 pp 2099ndash2107 2011

[8] W Wu and M Peng ldquoA data mining approach combining K-means clustering with bagging neural network for short-termwind power forecastingrdquo IEEE Internet of Things Journal vol 4no 4 pp 979ndash986 2017

[9] C G Raji and S S VinodChandra ldquoLong-TermForecasting theSurvival in Liver Transplantation Using Multilayer PerceptronNetworksrdquo IEEETransactions on SystemsMan andCyberneticsSystems vol 47 no 8 pp 2318ndash2329 2017

[10] X H Yuan C Chen Y B Yuan Y H Huang and Q XTan ldquoShort-termwind power prediction based on LSSVM-GSAmodelrdquo Energy Conversion and Management vol 101 pp 393ndash401 2015

[11] E Cadenas and W Rivera ldquoShort term wind speed forecastingin La Venta Oaxaca Mexico using artificial neural networksrdquoJournal of Renewable Energy vol 34 no 1 pp 274ndash278 2009

[12] Q Cao B T Ewing and M A Thompson ldquoForecasting windspeed with recurrent neural networksrdquo European Journal ofOperational Research vol 221 no 1 pp 148ndash154 2012

[13] W Zhang J Wang J Wang Z Zhao and M Tian ldquoShort-termwind speed forecasting based on a hybrid modelrdquo Applied SoftComputing vol 13 no 7 pp 3225ndash3233 2013

[14] K Bhaskar and S N Singh ldquoAWNN-assisted wind power fore-casting using feed-forward neural networkrdquo IEEE Transactionson Sustainable Energy vol 3 no 2 pp 306ndash315 2012

[15] D Lee and R Baldick ldquoShort-term wind power ensembleprediction based on gaussian processes and Neural networksrdquoIEEE Transactions on Smart Grid vol 5 no 1 pp 501ndash510 2014

[16] N Chen Z Qian I T Nabney and X Meng ldquoWind powerforecasts using Gaussian processes and numerical weatherpredictionrdquo IEEE Transactions on Power Systems vol 29 no 2pp 656ndash665 2014

[17] J P S Catalao H M I Pousinho and VM F Mendes ldquoHybridintelligent approach for short-term wind power forecasting inPortugalrdquo IET Renewable Power Generation vol 5 no 3 pp251ndash257 2011


[18] S Li P Wang and L Goel ldquoWind Power Forecasting UsingNeural Network Ensembles with Feature Selectionrdquo IEEETransactions on Sustainable Energy vol 6 no 4 pp 1447ndash14562015

[19] Q Xu D He N Zhang et al ldquoA short-term wind powerforecasting approach with adjustment of numerical weatherprediction input by dataminingrdquo IEEE Transactions on Sustain-able Energy vol 6 no 4 pp 1283ndash1291 2015

[20] M Khodayar O Kaynak and M E Khodayar ldquoRough DeepNeural Architecture for Short-Term Wind Speed ForecastingrdquoIEEE Transactions on Industrial Informatics vol 13 no 6 pp2770ndash2779 2017

[21] M Ma C Sun and X Chen ldquoDiscriminative Deep BeliefNetworks with Ant Colony Optimization for Health StatusAssessment of Machinerdquo IEEE Transactions on Instrumentationand Measurement vol 66 no 12 pp 3115ndash3125 2017

[22] F Jia Y Lei J Lin X Zhou and N Lu ldquoDeep neural networksa promising tool for fault characteristic mining and intelligentdiagnosis of rotating machinery with massive datardquoMechanicalSystems and Signal Processing vol 72-73 pp 303ndash315 2016

[23] S Shao W Sun P Wang R X Gao and R Yan ldquoLearn-ing features from vibration signals for induction motor faultdiagnosisrdquo in Proceedings of the 2016 International Symposiumon Flexible Automation (ISFA rsquo16) pp 71ndash76 Cleveland OhioUSA August 2016

[24] H Shao H Jiang H Zhang and T Liang ldquoElectric LocomotiveBearing Fault Diagnosis Using a Novel Convolutional DeepBelief Networkrdquo IEEE Transactions on Industrial Electronicsvol 65 no 3 pp 2727ndash2736 2017

[25] C Zhang P LimAKQin andKC Tan ldquoMultiobjectiveDeepBelief Networks Ensemble for Remaining Useful Life Estima-tion in Prognosticsrdquo IEEE Transactions on Neural Networks andLearning Systems vol PP no 99 pp 1ndash13 2016

[26] C-Y Zhang C L P Chen M Gan and L Chen ldquoPredictiveDeep Boltzmann Machine for Multiperiod Wind Speed Fore-castingrdquo IEEE Transactions on Sustainable Energy vol 6 no 4pp 1416ndash1425 2015

[27] A SQureshi A Khan A Zameer andAUsman ldquoWind powerprediction using deep neural network based meta regressionand transfer learningrdquoApplied Soft Computing vol 58 pp 742ndash755 2017

[28] J Chen K Li Z Tang et al ldquoA Parallel Random Forest Algo-rithm for Big Data in a Spark Cloud Computing EnvironmentrdquoIEEE Transactions on Parallel and Distributed Systems vol 28no 4 pp 919ndash933 2017

[29] W Lin Z Wu L Lin A Wen and J Li ldquoAn ensemble randomforest algorithm for insurance big data analysisrdquo IEEE Accessvol 5 pp 16568ndash16575 2017

[30] C Dai Z Liu K Hu and K Huang ldquoFault diagnosis approachof traction transformers in high-speed railway combiningkernel principal component analysis with random forestrdquo IETElectrical Systems in Transportation vol 6 no 3 pp 202ndash2062016

[31] A M Shah and B R Bhalja ldquoFault discrimination schemefor power transformer using random forest techniquerdquo IETGeneration Transmission ampDistribution vol 10 no 6 pp 1431ndash1439 2016

[32] C Gonzalez J Mira-McWilliams and I Juarez ldquoImportantvariable assessment and electricity price forecasting based onregression tree models Classification and regression treesBagging and Random Forestsrdquo IET Generation Transmission ampDistribution vol 9 no 11 pp 1120ndash1128 2015

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(1) In most artificial intelligence methods there is onlyone single hidden layer [11ndash14] Due to the finite abilityof searching optimal solution in the parameter spaces ofANN with more than one hidden layer these models cannotprovide accurate outputs(2) Some methodologies require tediously hand-engineered features [13] Due to the lack of sufficientknowledge for a specific domain the selected features maynot be suitable for corresponding models(3)The conventional features in the previous supervisedforecasting models contain the NWP data of the wind farms[15ndash19] However the NWP model usually runs once ortwice a day which is often applied for medium- to long-termforecasts [20]

Deep learning has attracted tremendous attention inrecent years of academia and industrial communities [21] Ithas been successfully used in the field of speed recognition[22] image processing [23] and health status assessment[24 25] However it has not been actively utilized in thewind power or wind speed forecasting fields Deep beliefnetwork due to its strong ability of learning has beenperformed in short-term WSP [26] The stacked denoisingautoencoder combined with rough set was applied to extractfeatures from wind speed series [20] In the literature [27]deep autoencoders act as base-regressors whereas deep beliefnetwork is used as ametaregressor ADNN-MRT schemewasproposed to predict wind power Therefore employing deeplearning to address the problemsmentioned above has a greatpotential

In this paper a hybrid intelligent method for short-term wind power forecasting is proposed First DBN as aprobabilistic generativemodel consisting ofmultiple layers ofrestricted Boltzmann machines (RBMs) provides the unsu-pervised learning features from the wind speed series data inthe pretraining phase and backpropagation neural network(BPNN) as the top layer of the DBN uses the labeled data tofine-tune the parameters of the DBN by stochastic gradientdecent Performance of DBN is affected by its parameterswhich are often limited by hand-engineered features The batalgorithm combined the major advantages between particleswarm optimization and genetic algorithm and HarmonySearch is applied to yield optimal parameters in the DBNSecond random forest is suitable for handling large data dueto its parallelization [28] It has been combined with theSpark [28] heuristic bootstrap sampling method [29] kernelprincipal component analysis [30] and other technologies toperform fault diagnosis and regression tasks [31 32] Owingto the improvement of the forecasting accuracy for high-dimensional and large-scale wind turbine data we proposean optimized random forest method which consists of adimension reduction procedure and the weighted votingprocess for the short-termWPF

The contributions of the paper are as follows(1) Predictive deep belief network is applied as the deeplearning architecture to perform the short-term wind speedprediction The DBN model has better generalized abilitythan the traditional shallow architectures(2) The bat algorithm is incorporated with DBN toimprove the training accuracy and reduce the costing timein wind speed prediction

START

Perform the deep belief network topredict wind speed series

Select the SCADA variables as thesupplementary input features

Conduct a Max Relevance-Min Redundancyindex to reduce the number of dimensions

Apply the random forest to forecastthe wind power

Utilize the stochastic gradient decline to update theweights for each decision tree in real time

END

Figure 1 The process of the proposed method for multistep windspeed and wind power prediction

(3) Benefiting from the dimension reduction andweighted voting procedures the random forest modelavoids the lack of prior knowledge for feature selection andenhances the capacities of tackling new condition data

This paper is organized as follows In Section 2 the DBNand its learning algorithm for short-termWSP are presentedSection 3 presents the optimized random forest and theproposed model for short-term WPF Numerical results andconclusion are presented in Sections 4 and 5 respectively

2 Brief Architecture aboutthe Proposed Method

In this section the proposed method would be brieflyintroduced and its process is shown in Figure 1 Wind speedas the most important variable to the normal running ofwind turbine is hard to predict because of its randomnessand fluctuation Therefore due to the merged advantages ofthe deep learning architectures and the bat algorithm theWSP model based on predictive deep belief network and batalgorithm is firstly performed to capture the characteristics ofwind speed series Then owing to its ensemble learning andparallelization the random forest is used as the WPF modelIn addition a data driven dimension reduction procedureand a weighted voting method are utilized to optimize therandom forest algorithm in the training process and theprediction process respectively

3 DBN for Wind Speed Prediction

Due to the intermittence and volatility of the wind energy itis difficult to gain the efficient future wind speed seriesThusthis sectionwould introduce a novelWSPmethod to performthe wind speed forecasting


20 40 60 80 1000Sample

0

2

4

6

8

win

d sp

eed

(ms

)


RBM RBM

Ｒ1

Ｒ2

ＲN

W

BPNN



119891 (119909119905minus1 119909119905minus119873 120579) = 119909119905+120591 (1)







119875 (ℎ | V) = exp (minus119864 (V ℎ 120579))119885 (3)

119885 = sumℎ

exp (minus119864 (V ℎ 120579)) (4)


119901 (ℎ119894 = 1 | V) = 119904119894119892119898 (119888119894 +119882119894V) (5)

119901 (V119894 = 1 | ℎ) = 119904119894119892119898 (119887119894 +119882119894ℎ) (6)



119871 (120579119863) = sum119909isin119863

log119875 (119909 120579) (7)



120597 log119875 (119909)120597119888 = 119864119901 [119909] minus 1198641199011015840 [119909] (9)

120597 log119875 (119909)120597119887 = 119864119901 [ℎ] minus 1198641199011015840 [ℎ] (10)



119882 = 119882 + 120572120597 log119875 (119909)120597119882 (11)

119887 = 119887 + 120572120597 log119875 (119909)120597119887 (12)

119888 = 119888 + 120572120597 log119875 (119909)120597119888 (13)




119882119897 = 119882119897 minus 120572 120597120597119882119897 119871 (119882 119887119883) (14)

119861119897 = 119861119897 minus 120572 120597120597119861119897 119871 (119882 119887119883) (15)






119891119894 = 1119898119898sum119895=1

(119877119895 minus 119877119886119895)2 (16)

119909119887119890119904119905 = argmin (119891119894) (119894 = 1 2 119899) (17)



119891119894 = 119891min + (119891max minus 119891min) 120573 (18)


119909119905119894 = 119909119905minus1119894 + V119905119894 (20)

START



algorithm


RBM algorithm



NO

END












Regressiontree 1

Result 1w1

Start




Train procedure



Regressiontree n

Result n

Regressiontree 2

Result 2w2

with k-fold CV

Input

Final result

wn










START





END




119877 (119905119895 119884119871) = 1119863sum119905119895isin119905119875 (119905119895 119884119871) (22)


119905max = argmax (119877 (119905119895 119884119871)) (23)




119865119900119901119905 = argmax119865119895isin119865119903





119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)


120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)




119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)



119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)



119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)













Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






PDBNActual

50 100 150 2000Sample

3

4

5

6

7

8

Win

d sp

eed

(ms

)


DBNActual

50 100 150 2000Sample

3

4

5

6

7

8

Win

d sp

eed

(ms

)


BPNNActual

50 100 150 2000Sample

3456789

10

Win

d sp

eed

(ms

)


ELMANActual

3

4

5

6

7

8

Win

d sp

eed

(ms

)

50 100 150 2000Sample


PersistenceActual

20 40 60 80 100 120 140 160 180 2000Sample

335

445

555

665

7

Win

d sp

eed

(ms

)


PDBNActual

20 40 60 80 100 120 140 160 180 2000Sample

012345678

Win

d sp

eed

(ms

)


DBNActual

50 100 150 2000Sample

1

2

3

4

5

6

7

8

Win

d sp

eed

(ms

)


BPNNActual

20 40 60 80 100 120 140 160 180 2000Sample

0

2

4

6

8

10

12

Win

d sp

eed

(ms

)


Figure 7 Continued


ELMANActual

1

2

3

4

5

6

7

8

Win

d sp

eed

(ms

)

20 40 60 80 100 120 140 160 180 2000Sample


PersistenceActual

50 100 150 2000Sample

1

2

3

4

5

6

7

Win

d sp

eed

(ms

)


PDBNActual

50 100 1500Sample

0

5

10

15

Win

d sp

eed

(ms

)


DBNActual

02468

1012141618

Win

d sp

eed

(ms

)

50 100 1500Sample


BPNNActual

02468

1012141618

Win

d sp

eed

(ms

)

50 100 1500Sample


ELMANActual

50 100 1500Sample

02468

101214161820

Win

d sp

eed

(ms

)


PersistenceActual

50 100 1500Sample

02468

1012141618

Win

d sp

eed

(ms

)


PDBNActual

0

2

4

6

8

10

12

Win

d sp

eed

(ms

)

50 100 1500Sample


Figure 7 Continued


DBNActual

50 100 1500Sample

0

2

4

6

8

10

12

Win

d sp

eed

(ms

)


BPNNActual

50 100 1500Sample

123456789

10

Win

d sp

eed

(ms

)


ELMANActual

50 100 1500Sample

123456789

10

Win

d sp

eed

(ms

)


PersistenceActual

50 100 1500Sample

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6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









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119891 (119909119905minus1 119909119905minus119873 120579) = 119909119905+120591 (1)







119875 (ℎ | V) = exp (minus119864 (V ℎ 120579))119885 (3)

119885 = sumℎ

exp (minus119864 (V ℎ 120579)) (4)


119901 (ℎ119894 = 1 | V) = 119904119894119892119898 (119888119894 +119882119894V) (5)

119901 (V119894 = 1 | ℎ) = 119904119894119892119898 (119887119894 +119882119894ℎ) (6)



119871 (120579119863) = sum119909isin119863

log119875 (119909 120579) (7)



120597 log119875 (119909)120597119888 = 119864119901 [119909] minus 1198641199011015840 [119909] (9)

120597 log119875 (119909)120597119887 = 119864119901 [ℎ] minus 1198641199011015840 [ℎ] (10)



119882 = 119882 + 120572120597 log119875 (119909)120597119882 (11)

119887 = 119887 + 120572120597 log119875 (119909)120597119887 (12)

119888 = 119888 + 120572120597 log119875 (119909)120597119888 (13)




119882119897 = 119882119897 minus 120572 120597120597119882119897 119871 (119882 119887119883) (14)

119861119897 = 119861119897 minus 120572 120597120597119861119897 119871 (119882 119887119883) (15)






119891119894 = 1119898119898sum119895=1

(119877119895 minus 119877119886119895)2 (16)

119909119887119890119904119905 = argmin (119891119894) (119894 = 1 2 119899) (17)



119891119894 = 119891min + (119891max minus 119891min) 120573 (18)


119909119905119894 = 119909119905minus1119894 + V119905119894 (20)

START



algorithm


RBM algorithm



NO

END












Regressiontree 1

Result 1w1

Start




Train procedure



Regressiontree n

Result n

Regressiontree 2

Result 2w2

with k-fold CV

Input

Final result

wn










START





END




119877 (119905119895 119884119871) = 1119863sum119905119895isin119905119875 (119905119895 119884119871) (22)


119905max = argmax (119877 (119905119895 119884119871)) (23)




119865119900119901119905 = argmax119865119895isin119865119903





119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)


120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)




119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)



119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)



119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)













Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






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SDE


APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018










119882119897 = 119882119897 minus 120572 120597120597119882119897 119871 (119882 119887119883) (14)

119861119897 = 119861119897 minus 120572 120597120597119861119897 119871 (119882 119887119883) (15)






119891119894 = 1119898119898sum119895=1

(119877119895 minus 119877119886119895)2 (16)

119909119887119890119904119905 = argmin (119891119894) (119894 = 1 2 119899) (17)



119891119894 = 119891min + (119891max minus 119891min) 120573 (18)


119909119905119894 = 119909119905minus1119894 + V119905119894 (20)

START



algorithm


RBM algorithm



NO

END












Regressiontree 1

Result 1w1

Start




Train procedure



Regressiontree n

Result n

Regressiontree 2

Result 2w2

with k-fold CV

Input

Final result

wn










START





END




119877 (119905119895 119884119871) = 1119863sum119905119895isin119905119875 (119905119895 119884119871) (22)


119905max = argmax (119877 (119905119895 119884119871)) (23)




119865119900119901119905 = argmax119865119895isin119865119903





119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)


120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)




119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)



119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)



119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)













Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






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RMSE


MAE


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APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018











Regressiontree 1

Result 1w1

Start




Train procedure



Regressiontree n

Result n

Regressiontree 2

Result 2w2

with k-fold CV

Input

Final result

wn










START





END




119877 (119905119895 119884119871) = 1119863sum119905119895isin119905119875 (119905119895 119884119871) (22)


119905max = argmax (119877 (119905119895 119884119871)) (23)




119865119900119901119905 = argmax119865119895isin119865119903





119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)


120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)




119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)



119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)



119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)













Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






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PersistenceActual

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(ms

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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018











119865119900119901119905 = argmax119865119895isin119865119903





119877 (119905119894 119905119895) = 11198632 sum119905119894 119905119895isin119905119875 (119905119894 119905119895) (24)

119905min = argmin119877 (119905119894 119905119895) (25)


120593 = 119877 (119905119895 119884119871) minus 119877 (119905119894 119905119895) (26)

119865119900119901119905 = argmax120593 (27)




119884119895 = sum119896119894=1 119908119895119894119910119895119894sum119896119894=1 119908119895119894 (28)



119864119903119903 = 05 times (119910119895119894 minus 119884119895)2 (29)



119910119894sum119896119894=1 120596119895119894 minus sum119896119894=1 120596119895119894119910119895119894(sum119896119894=1 120596119895119894)2 ]]

(30)

120596119895119894+1 = 120596119895119894 minus Δ120596119895119894 (31)













Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018














Case 1 13873 195

Case 2 13783 285

Case 3 10000 150

Case 4 10000 150




5 Numerical Results



119877119872119878119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905)2 (32)

119872119860119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 11991011990510038161003816100381610038161003816 (33)

119861119868119860119878 = 1119898119898sum119895=1

(119910119895 minus 119910119905) (34)

119878119863119864 = radic 1119898119898sum119895=1

(119910119895 minus 119910119905 minus 119861119868119860119878)2 (35)

119860119875119864 = 1119898119898sum119895=1

10038161003816100381610038161003816119910119895 minus 1199101199051003816100381610038161003816100381610038161003816100381610038161199101199051003816100381610038161003816 (36)






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PersistenceActual

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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









PDBNActual

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PersistenceActual

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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









ELMANActual

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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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Figure 8 Continued



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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









DBNActual

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RMSE


MAE


BIAS


SDE


APE





















6 Discussion




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Figure 8 Continued



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7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018



























6 Discussion




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100

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Win

d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample



20 40 60 80 100 120 140 160 180 2000Sample

0

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Win

d po

wer

(W)



0

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d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample



0

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d po

wer

(W)

50 100 150 2000Sample



20 40 60 80 100 120 140 1600Sample

0200400600800

10001200140016001800

Win

d po

wer

(KW

)



0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample


Figure 8 Continued



0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

20 40 60 80 100 120 140 1600Sample



0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample



50 100 1500Sample

0

200

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600

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1000

1200

Win

d po

wer

(KW

)



0

500

1000

1500

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Win

d po

wer

(KW

)

50 100 1500Sample








7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018










0

100

200

300

400

500

600

Win

d po

wer

(W)

50 100 150 2000Sample



20 40 60 80 100 120 140 160 180 2000Sample

0

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Win

d po

wer

(W)



0

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Win

d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample



20 40 60 80 100 120 140 160 180 2000Sample

0

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700

Win

d po

wer

(W)



0

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d po

wer

(W)

20 40 60 80 100 120 140 160 180 2000Sample



0

100

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600

700

Win

d po

wer

(W)

50 100 150 2000Sample



20 40 60 80 100 120 140 1600Sample

0200400600800

10001200140016001800

Win

d po

wer

(KW

)



0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample


Figure 8 Continued



0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

20 40 60 80 100 120 140 1600Sample



0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample



50 100 1500Sample

0

200

400

600

800

1000

1200

Win

d po

wer

(KW

)



0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

50 100 1500Sample








7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018










0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

20 40 60 80 100 120 140 1600Sample



0200400600800

10001200140016001800

Win

d po

wer

(KW

)

50 100 1500Sample



50 100 1500Sample

0

200

400

600

800

1000

1200

Win

d po

wer

(KW

)



0

500

1000

1500

2000

2500

Win

d po

wer

(KW

)

50 100 1500Sample








7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018









7 Conclusions



Data Availability






Acknowledgments


References










































Journal of












Journal of







Volume 2018






Volume 2018































Journal of












Journal of







Volume 2018






Volume 2018








multistep wind speed and wind power prediction based on a...

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