Page - 293 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1561 2.2. ElmanNeuralNetwork (ENN) Asanimportantbranchofdeeplearning, recurrentneuralnetworkshavebeenwidelyusedin academicand industrialfields. Thecommonneuralnetworkmainlyconsistsof three layers: input layer,hidden layerandoutput layer. For thehiddenlayer, the input informationonlycomes fromthe input layer. Forarecurrentneuralnetwork, the input informationof thehiddenlayerwillnotonly comefromthe input layer,butalso fromthehiddenlayer itselfandtheoutput layer. Invariousstructuresof therecurrentneuralnetwork,Elmanneuralnetwork(ENN)[49] is typical structure inwhichthe lagsofhiddenlayeraredelivered into thecurrenthiddenlayerbyanewlayer calledthecontext layer. Thisstructure takes the former informationof thehiddenlayer intoaccount and commonly has a better performance in the time-series forecasting such as STLF,wind speed forecasting,financial time-series forecasting. Thestructure is showedinFigure1. Thecontext layercanfeedbackthehiddenlayeroutputs in theprevious timestepsandneurons containedineach layerareusedto transmit informationfromone layer toanother. Thedynamicsof thechange inhiddenstateneuronactivations in thecontext layer isas follows: Si(t)= g( K ∑ k=1 VikSk(t−1)+ j ∑ j=1 WijIj(t−1)) (7) whereSk(t)and Ij(t)denote theoutputof thecontextstateandinputneurons, respectively;Vik and Wij denote their correspondingweights; and g(·) is a sigmoid transfer function. Theother related theoriessuchas feed-forwardandbackpropagationaresimilarwith thecommonbackpropagation neuralnetwork. Figure1.Thestructureof the lowerboundandupperboundestimation(LUBE)basedontheElman neuralnetwork. 2.3. LowerBoundandUpperBoundEstimation (LUBE) In the literature, the traditional intervalpredictioncommonlyattempts toconstruct thePIbased on the point prediction. The upper bound and the lower bound are calculated according to the forecastingvalueandtheconfidence level. Theaccuracyof thepoint forecastinghasplayedakeyrole in theaccuracyof thePI. In thispaper,weintroduceanovelmethodof intervalpredictioncalled lower boundandupperboundestimation(LUBE).Thismethoddirectlyoutputs the lowerboundandthe 293