Page - 413 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies 2018,11, 242 4.5. ComparisonsandDiscussions Asdiscussedpreviously, smallervaluesof theMAE,RMSEandMRErepresentbetterprediction resultswhile lagervaluesof randR2 correspondtobetterperformance.Consideringall thevaluesof such indicesasshowninTables3and5(It isworthnotingthat thevaluesof the indices inTable3are abouttheretailenergyconsumptionwhilethevaluesinTable5areabouttheofficeenergyconsumption. Theretailbuildingconsumedmuchmoreenergies thantheofficebuilding.Asaresult, somevalues of theMAE,RMSEandMREinTable3are larger thanthose inTable5), thepredictorsconstructed byutilizingtheenergy-consumingpatternsperformbetter thanthosedesignedonlybytheoriginal data. TakingtheRMSEindexforexample, in thefirstexperiment, theaccuraciesof theMDBN,BPNN, GRBFNN,ELMandSVRbasedhybridmodelsarepromotedby11.1%,7.0%,4.2%,21.6%and9.6%, respectively,while, in thesecondexperiment, theaccuracy improvementsofsuchmodelsare15.6%, 14.8%,26.5%,16.9%and34.0%, respectively.Asaresult,wecandrawaconclusionthat theperiodicity knowledge ishelpful to improvetheaccuracyforbuildingenergyconsumptionprediction. FromFigures9and12,wecansee that thehybridDBNmodelcannotonlypredict theregular testingdatawell forboth theretail storeandtheofficebuildingenergyconsumptionfromtheglobal perspective,butalsogive thebestpredictionresults for thenoisy irregulardata, e.g., thesampling points from25to50 inFigure9 in theretail storeexperiment. These irregular testingdatacanreflect theuncertainties in theenergyconsumptiontimeseries. Inotherwords, theproposedhybridDBN modelhasthemostpowerfulability todealwiththeuncertainand/ortherandomness inthehistorical buildingenergyconsumptiondata. Figures 10 and13demonstrated theprediction error histogramsof thefivemodels designed throughusingtheperiodicityknowledge inthe twoexperiments. In thehistograms, thehorizontal directiondepicts theexactvaluesof thepredictionerrors,while theverticaldirection indicates the numberof thepredictionerrors indifferentpartitionedintervals. Themore thepredictionerrorsfloat aroundzero, thebetterperformance thepredictorswill achieve. Frombothfigures,wecanclearly observe that theproposedhybridDBNmodelhasmorepredictionerrorsfloatingnearzerocompared with theother fourartificial intelligence techniques—that is tosay, theapproximationcapabilityof the proposedhybridDBNmodel ispromisingfor thetwoexperimentedbuildings. Furthermore, tofurther validatetheaccuracyof theMDBNbasedhybridmodel, scatterplotsof theactualandpredictedvalues in the twoexperimentsaredemonstrated inFigure14a,b, respectively. FromFigure14,wecanobserve that thepredictedvalues fromthehybridDBNmodelcanduplicate theactualvalueswell. Among all the predictors constructed by both the original and residual data, the proposed MDBN based hybridmodel has the best prediction accuracy in the two experiments as shown in Tables3and5. This phenomenon indicates that the proposed deep learning method has the miraculous learningandpredictionabilities in timeseries forecastingapplications. Thisalsoverifies thepowerful feature extraction ability of thedeep learningalgorithmand the effectiveness of the modifiedlearningstrategies. One thing tobementioned is that thenumbersof thedataused in thispaperarenotverybig (about the ten thousandscale). EventhoughthehybridMDBNmodel isnot learnedbybigdata in bothexperiments, it still showsusexcellentperformances. This is also consistentwith someother application resultswhere theDBNswere trainedwithout amass ofdata. For example, in [49,50], theDBNswereappliedto the timeseriespredictionandthewindpowerprediction,whichalsodonot havea largequantityofdata. Inbothapplications, theexperimental resultsdemonstrated that the DBNapproachperformsbestcomparedwith the traditional techniques.All theseapplicationsverified the learningabilityof theDBNmodels fornotvery largedataapplications. 413