Page - 272 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 of training(i.e., cross-validation).Moreover,eachmodelofferedpredictionresults pi(i∈1,2,. . . ,n) whichwere thencast intoasecondleveldata; theoutcomebecamethe input for thesecondlevelas trainingdata. 2.2.1. EnsemblePruning Ranking-basedsubset selectionmethodranks thecandidatemodelsaccordingtocriteria, suchas themeanabsolutepercentageerror (MAPE),directionalaccuracy (DA),andEuclideanDistance (ED), andincludedonly the topnmodels fromall candidatemodels. 2.2.2. Ensemble Integration This stepdescribes how the selectingmodelswere combined into ensemble forecast. In this context, the stackingmethod isused tobuild the second leveldata, stackingusesa similar idea to K-folds cross-validation to solve twosignificant issues: Firstly, to createout-of-samplepredictions. Secondly, to capture distinct regions,where eachmodel performs the best. The stackingprocess investigates by inferring the biases of the generalizers concerning theprovidedbase learning set. Then, stacked regression using cross-validation was used to construct the ’good’ combination. Considera linearstackingfor thepredictiontask. Thebasic ideaofstackingis to ’stack’ thepredictions f1, . . . , fmbylinearcombinationwithweights ai, . . . ,(i=1,. . . ,m): fstacking(x)= m ∑ i=1 ai fi(x), (1) where theweightvectora is learnedbyameta-learner. 2.2.3. EnsemblePrediction Thesecondlevel learnermodel(s) canbe trainedontheD′data toproduce theoutcomeswhich will beused forfinal predictions. In addition, to selectmultiple sub-learners, stacking allows the specificationofalternativemodels to learnhowtobestcombine thepredictions fromthesub-models. Becauseameta-model isusedtocombinethepredictionsofsub-modelsbest, thismethodissometimes termedblending,as inmixingthefinalpredictions. Inbrief, Figure1demonstrated thegeneral structureofSMLEframework,whichconsistedof various learning steps, after applying this scheme, three SMLEmodelsweregenerated,while the differencebetweentheSMLEmodelswerenot instructure,but in the typeofbasemodel in level#0 andthedifferencesbetweenthe threemodels in thepartofbasemodelcanbeexplainedas follows: • 1stSMLEinbase layerusedSVRlearnerandinMeta layerLRusedasmeta learner. • 2ndSMLEinbase layerusedBPNNlearnerandinMeta layerLRusedasmeta learner. • 3rdSMLEinbase layerusedSVRandBPNNlearnersandinMeta layerLRusedasmeta learner. 2.3. ExperimentStudyDesign 2.3.1.Data TheGOCdatawereusedasbenchmarkdata; thisdatasetwasdownloadedfromthewebsite: https://www.bp.com/en/global/corporate/energy-economics/statistical-review-of-worldenergy.html. ThedatarepresentedtotalOCintheworld; thedatawasyearly typeandhadadurationfrom1965 to 2016. Thedataconsistedof twofactors, thusdependentvariableoil consumption(inMillionTonnes), whichwasa featureover time, anddate (inyears)was the independentvariable in this case study. Therefore, the OC time series for this experiment had 52 data points. For a better explanation, wevisualizedwholeactual timeseries inFigure2,withabluecircle incurve. 272