Page - 276 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 Similarly, Figure 2b demonstrated the residual errors of the prediction, to make a reliable comparisontoquantitativelyanalyze theperformancesof thebasemodels;weconsideredtheMAPE measure indices forperformanceaccuracyprocesses,whichare listed inTable3. Inbrief, asseen inTable3, theMAPEbetweenpredictedandactualvalues for theSVRmodel is 1.24%givenbyrelativeaccuracy(DA)89.9%whichindicatesclearlythattheSVRmodeliswellworking andhasacceptableaccuracy.Regardingthesameaspect,wecanobserve that theSVRhadsuperiority inbothruntimeandsimilarity (0.01and0.034, respectively).However, it isworthmentioningthat the LRmodelsscoredpoorperformancecomparedtoothersinglemodels. Thesimilaritybetweenactual andpredicteddatawasmeasuredusingtheEuclideanDistance (ED),asshowninTable3; theBPNN score0.034,whichwassmall indicates thebestpredictiveperformance,whileLRscores0.074was the worst similarityacross themodels. 3.2. ClassicEnsembleModelsResults In thesecondexperiment,weempirically testedtwoclassicalensemblemodels, includedbagging andadditive regression (AR). To illustrate thebehavior of all classical ensemblefitting, theywere comparedwithactualdata inFigure3a,b, forvisualcomparisonof theresidualerrorofeachmodel. Theevaluationmatrixof single learning, classical ensemblemethods, andproposedSMLEmodels are summarized inTable3. Asobserved fromTable3andFigure3, thebaggingmodelperformed better than theARmodel in all evaluationmeasures, except inDA. Similarly, the baggingmodel performedbetter thanthebest singlemodel (SVR) inperformanceandsimilaritywhileSVRperform best inDAandhas least trainingtime. For thisdataset,weaccordinglydevelopedhomogeneousand heterogeneousensemblesof individualmodels rather thanusingtheirhybridversions. Figure3. Illustrated(a) actualandpredictedconsumptionusingclassicensemble learners (b) errorof classicensemblemodels. 3.3. TheSMLEResults In the thirdexperiment,weempirically testedthreeheterogeneousstackingmodels, eachmodel wascomposedofacombinationofbaseandmeta-models. ThefirstensemblemodelconsistsofSVR asabase learnerandLRasmeta-learner. To illustrate thebehaviorofallSMLEforfitting, theywere comparedwithactualdata inFigure4a,b, forvisualcomparisonof theresidualerrorofeachmodel. Theevaluationmatrixof single learningmethods,andproposedframework is summarized inTable3. 276