Page - 274 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 Table2.Summaryofparameterssettingforall learners. Model Parameters LR Attributemethodselection=Md5,batchSize=100,andridge=1.0×10−8 SVR Kernel=(Poly),C=1,exponent=2andepsilon=0.0001. BPNN MLP(1-3-1) Bagging Base learner=REPTree,bagSizePercent=100%,No. iteration=10. AR Base learner= linearregression,No. iteration=10,Shrinkage=1.0. 1stSMLE Baselearner(SVR(Kernel=(Poly),C=1,exponent=2,epsilon=0.0001)),metalearner(LR),Combinationmethod=Stackedgeneralization 2ndSMLE Base learner (MLP(1-3-1)),meta learner (LR),Combinationmethod=Stackedgeneralization 3rdSMLE Base learner (SVR(Kernel=(Poly),C=1,exponent=2,epsilon=0.0001)andMLP(1-3-1),meta learner (LR),Combinationmethod=Stackedgeneralization 2.3.3. EvaluationMeasure Thissubsectiondescribesseveralaspectsof theevaluationof thedifferentmodels; theevaluation aspects includetheestimationoferror ratesandpairwisecomparisonsofclassifiers/ensembles. 1. PerformanceEvaluation In terms of performance error estimation, themean absolute percentage error (MAPE)was adopted as an indicator of accuracy for all forecasting methods. The accuracy is expressed as apercentagevalue,andisdefinedbytheFormula (2)asbelow: MAPE= 100 n n ∑ i=i ∣∣∣∣∣∣∣∣ ∧ yi−yi yi ∣∣∣∣∣∣∣∣, (2) whereyi is theactualvalueand ∧ yi is the forecastvalue. 2. TimeSeriesSimilarity Thedistancebetween timeseries canbemeasuredbycalculating thedifferencebetweeneach point of the series. TheEuclideanDistance (ED)between two-timeseriesQ= {q1,q2, . . . ,qn} and S={s1,s2, . . . ,sn} isdefinedas: D(Q,S)= √ n ∑ i=1 (qi−si)2. (3) Thismethodismoderatelyeasy tocalculate,andhascomplexityofO(n) [54]. 3. ContinuousGrowthRates (CGR) Calculatingchangegrowthrate indata isuseful foraverageannualgrowthrates that steadily change. It is famousbecause it relates thefinalvalue inseries to the initialvalue in thesameseries, rather than just providing the initial and final values separately—it gives the ultimate value in context [30]. TheCGRvaluecalculatedaccordingtoFormula (4)as follows: k= ln ( yt+1 yt ) t , (4) where k represents theannualgrowthrateyt represents the initialpopulationsize, t represents the future timeinyearsandk isCGR. 274