Page - 216 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1900 combinationof theseparameters,andthensubstitutes theoptimalcombinationparameters into the supportvectormachinemodel toobtain its regressionmodel. Thespecificstepsareas follows: • Datanormalization: x∗ij= xij−xjmin xjmax−xjmin , (11) where xij, x∗ij aredatabeforeandafternormalization, respectively, and xjmin and xjmax are the respectiveminimumandmaximumvaluesof thecolumnwherexij is located. Thenormalization processof thedependentvariabledata is similar to the independentvariabledata,andwillnotbe describedhere. • Establishingthesupportvectormachineobjective functionbasedontrainingsamples. • Using theparticle swarmoptimization algorithm to select the keyparameters of the SVMto obtain theoptimalcombinationof thekeyparametersof theSVM. • Substituting the optimal combination parameters into the SVM model to obtain its regressionmodel. • Usingthepredictionsampleandthemodelobtainedabove to forecast theenergyconsumptionof thebuilding. 2.3. TheSRCsMethod forSensitivityAnalysis Sensitivityanalysisisusedtostudythemappingrelationsofuncertaintiesofinputparametersand outputs[30]. Therearealotofsensitivityanalysismethodsamongpreviousstudies[31]. Somemethods directly research the input-outputmapgeneratedby theMonteCarlomethodwithout additional runsof themodel. Othermethodspropagate specificsamplesareaimedat thesensitivityanalysis, for example, the screeningmethod ofMorris [32]. The SRCsmethod has been adopted in this paper, ofwhich thebasis is tofit a linearmultidimensionalmodel [20] betweenmodel inputs and modeloutputs. yˆi= β0+∑kj=1βjxij (12) Theregressioncoefficientsβj aredeterminedsuchthat thesumoferrorsquares ∑Ni=1(yi− yˆi)2=∑ N i=1 [ yi− ( β0+∑kj=1βjxij )]2 (13) isminimized. Thefollowingratio, calledthecoefficientofdetermination[20], R2= ∑Ni=1(yˆi−yi)2 ∑Ni=1(yi−y)2 (14) isameasureofhowwell themodel (12)matches thedata. Thecloser to1 thecorrespondingvalueof R2, thegreater themodelmatchesthedata,butconsideringthedifferentunitsandordersofmagnitude ofparameters, thesedrawbacksareeasilyworkedoutreformulatingEquation(12) [20]as yˆ−y σy =∑kj=1 βjσj σy xj−xj σj , (15) wherey is themeanvalueandσy thevarianceof theoutputunder theconsideration σy= [ ∑Ni=1 (yi−y)2 N−1 ]1/2 , (16) 216