Page - 279 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 fromTable 4, theMAPEvalues of the SMLE-based BPNN-SVRmodelwere 0.61 in 1-ahead and 0.74asanaverageof the10-step-aheadpredictions,whichwas less thanothermethods.Also, in the short-termpredictionstep,betterperformancewasobservedwhencomparingensemblemethodswith singlemodels, the results indicate that theensemblemethodsoutperformed the single andclassic ensemblemethods inall cases. Theprinciple reasoncouldbe that thecross-validationdecomposition methodology did efficiently enhance the forecast execution. Interestingly, the 1-step-ahead and multi-step-ahead prediction horizon of singlemodel forecastswere inferior to ensemblemodels. Focusingonthesinglemethodsandclassicensembles,all theMLmodelsoutperformedtheLRmodel; thereasonmaybethatLRisa typical linearmodel,which isnotsuitable forcapturingthenonlinear andseasonal characteristicsofOCseries. InMLmodels (i.e., SVR,BPNN), it canbeseen thatSVR performedslightlybetter thanBPNNinall10-step-aheadpredictionsandBPNNperformpoorest in all thestepprediction. Themainreasonleadingto thismaytheparameterselection. TheMAPEvalues ofLRwere from2.91 to2.40,whichwere slightly inferior toSVRandBPNNmodels. Thepossible reasonwasthat thepredictionresultsofLR,whichwasunder the linearhypothesisweremorevolatile thanthoseof theMLmodels. Second, the high-level exactness does not necessarily imply that therewas a highhit rate in forecastingdirectionofOC.Thecorrect forecastingdirection is essential for thepolicymanager to makeaninvestmentplan inoil-relatedoperations (production,price,anddemand). Table4. 10-aheadforecastingperformanceamongallmodelsonGOCdata. Model MAPE(%)over10-AheadHorizon Avg. 1-ahead 3-ahead 5-ahead 7-ahead 10-ahead LR 2.91 3.76 2.76 1.77 1.30 2.40 SVR 1.08 1.30 1.17 1.23 1.36 1.24 BPNN 1.39 1.33 1.28 1.48 1.61 1.42 Bagging 1.31 1.70 1.99 1.86 1.19 1.66 RF 1.39 1.33 1.28 1.45 1.61 1.41 1stSMLE 0.62 0.82 0.83 1.03 1.05 0.90 2ndSMLE 0.73 0.80 0.79 0.77 0.80 0.78 3rdSMLE 0.61 0.74 0.74 0.78 0.83 0.74 Therefore, theDAcomparisonisnecessary. InFigure6a–c,somesimilarconclusionscanbedrawn regardingDAcriterion. (i)Theproposed3rd SMLEmodelperformedsignificantlybetter thanallother models inall cases, followedbytheother twoensemblemodels, thentwoof thesingleMLmodels (i.e., SVR,BPNN), (LR,AR)hadequalvalues,andbaggingmodelhadtheworstvalues. Individually, theDAvalues of all SMLE-basedensembleswere similar 92.31% for the 1 step-aheadpredictions andshowedsuperioritywith 91.24%for average10-ahead step forecasts for the 3rdSMLEmodel. (ii) The three ensemblemethodsmostlyoutperformed the singlepredictionmodels. Furthermore, amongtheensemblemethods, theSMLE-basedBPNN-SVRmodelperformedthebest,andSMLE- basedBPNNmodeloutperformedSMLE-basedSVRmodel, except for the2-aheadforecast. (iii)SVR modeloutperformedothermethods,BPNNhadthesimilarperformanceasSVRinthe2,3,5step-ahead forecasts,except thatSVRexceededBPNNinboth1-aheadandaverageaheadprediction. Thepossible reason leadingto thisphenomenonmaybethechoiceofoptimalparameters for themodels.Wealso foundthatbaggingmodelhadthe lowestdirectionalaccuracyof66.17%. 279