Page - 275 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 2.4. TheAlgorithmforStackingMulti-LearningEnsemble (SMLE) In thisstudy,SMLEoffersadynamicELmethod.TheSMLRmethoddependsonthesequence characteristic ofOCdata. For accurateOCprediction, we express the algorithmof SMLEwhen predictingthenextmthmomentOCatthetime t. Thegeneraldesignoftheproposedmodelconsidered bothdiversitymanagementandaccuracyenhancement forbasemodels.Here thealgorithmofSMLE isdescribedbelowaspseudocode inAlgorithm1: Algorithm1: StackingMulti-LearningEnsemble (SMLE). Input:DatasetD={(x1,y1),(x2,y2), . . . ,(xm,ym)}; First-level learningalgorithmsL1,L2, . . . ,Ln; Second-level learningalgorithmL; Process: %Trainafirst-level individual learnerht byapplying thefirst-level learningalgorithmLt to theoriginaldatasetD for t=1,. . . ,T: ht=Lt(D) end; %generate anewdata set D′=φ; for i=1,. . . ,m: for t=1,. . . ,T: zit= hi(xi) %Useht topredict trainingexample xi end; D′=D′∪{((zI1,zi2, . . . ,zT),yi)} end; %Train the second-level learnerh′byapplying the second-level learningalgorithmLto thenewdata setD′ h′=L(D′). Output:H(x)= h′(h1(x1), . . . ,hT(xT)) 3.Results In this section, we evaluated variousmodels onGOC 52-year data sets using BPNN, SVR, andLR as the basemodels to demonstrate their predictability of both single andEL forecasting. Hence, there were single models used as benchmark model compared to ensemble predictors. In the second experiment, we tested two classic ensemblemodels include bagging and additive regression(AR).Moreover, the thirdexperiment testedthreeensemblemodelsbasedonSMLEscheme. Toestablish thevalidityof theevaluatedmethod, a furtherprocedurewasdonebycomparing the obtainedresultsof singlemodelswith theoutcomeof theensemblemodels. Evaluationcriteriawere usedtocompareandanalyze theprediction, suchasT-Time,DA,MAPE,andED,whichareexcellent methods forpredictingGOC.Meanwhile,wecompare theevaluationcriteriaofmultistep(10-ahead) with single step (1-ahead) forecasting to find the better SMLEmodel for predictingGOC in both short-term and term-long horizon situations. Finally, consumption growth rate evaluated for all predictionoutcome. 3.1. SingleModelsResults Regardingtheexperimentdesignandtheoverall stepsdescribedinSection2.2, thefirst test in thisexperimentwas tocompare theperformanceofallbasemodelsseparately. Theoutputof10-fold cross-validation tests runon the initial trainingwereused todeterminewhether eachmodelwas sufficient forOCdata tomakethe forecastingresultsmorestable. Figure2apresents thecomparison of thebest-obtainedresults fromallbasemodelswith therealOCdata. It isevident that theresults obtainedaccording to theSVRmethodfor the52knownyears (1965–2016)wereclose to theactual onesandcomparable to thoseproducedbytheBPNNandLRmodels. 275