Page - 399 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies 2018,11, 242 Ak(X)β=Y, (19) where Y=[y(1),y(2), . . . ,y(N)]TN×1. (20) FromEquation(19), theoutputweightingvectorβ canbederivedbythe least squaresmethod as [36–39] β=Ak(X)†Y, (21) whereAk(X)† is theMoore–Penrosegeneralized inverseofAk(X). 4. Experiments In thissection,firstofall, fourcomparativeartificial intelligenceapproacheswillbe introduced briefly.Next, theapplieddatasetsandexperimental settingwillbediscussed. Then, theproposed hybridmodelwill be applied to thepredictionof the energy consumption in a retail store andan officebuildingthat respectivelyhavedaily-periodicandweekly-periodicenergy-consumingpatterns. Finally,wewillgive thecomparisonsanddiscussionsof theexperiments. 4.1. Introductionof theComparativeApproaches Tomakeaquantitativeassessmentof theproposedMDBNbasedhybridmodel, fourpopular artificial intelligenceapproaches, theBPNN,GRBFNN,ELM,andSVR,arechosenas thecomparative approachesandintroducedbrieflybelow. 4.1.1. BackwardPropagationNeuralNetwork The structure of BPNNwith Lhidden layers is demonstrated inFigure 5. TheBPNNasone popularkindofANNadoptsbackpropagationalgorithmtoobtain theoptimalweightingparameters of thewholenetwork[40–42]. [ [ Q[ O Q Q O / O O x xx xxx xxx ,QSXW OD\HU +LGGHQ OD\HU 2XWSXW OD\HU Q / LZ LMZ LMZ Ö\ /Q Figure5.ThestructureofBPNNwithLhiddenlayers. AsshowninFigure5, thefinaloutputof thenetworkcanbeexpressedas [40–42] yˆ= f( nL ∑ s=1 wL+1s1 · · · f( n1 ∑ j=1 w2jk f( n ∑ i=1 w1ijxi))), (22) 399