Page - 280 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1605 Figure6. Illustrated10-aheadconsumptiondirectionalaccuracy(DA)of (a) singlemodels, (b) classic ensemblemodels,and(c)SMLEensemblemodels. Also, comparingdifferentpredictionhorizons, theshort-termpredictionhorizonshowedbetter performance for in all themodel see Table 4. Taking 1-step-ahead forecasting and an average of the10-step-aheadpredictions forexample, forall theSMLE–basedensemble,BPNN,SVR,bagging, ARmodels, the 1-step-ahead forecasting outperformed the average of the 10-step-ahead forecast, no matter the level accuracy or directional accuracy. Apart from the models mentioned above, SMLE-based ensembles andMLmodels and classic ensembles performed better in 1-step-ahead prediction given directional accuracy. However, from the point of level accuracy, both these approachesonlyhadslightsuperiority in6-step-aheadprediction. Except for theLR,whichperformed almost poorer in the 1-step-ahead compared to the averageof 10-step-aheadprediction as shown inFigure7a–c. Third, to furthervalidationofSMLEmodels forecasting, the t-testwasusedto test thestatistical significanceof thepredictionperformance. The t-test resultspresented inTable5, forall ensemble modelsunder this studywerenotsignificant (df =51,p-value>0.05)). Basedonthedetailedstatistical test,nosignificantdifferenceswereobservedbetweentheactualOCandthatpredictedbytheSMLE models. Themeandifferences in the last columnofTable5, indicate that in thepopulation fromwhere thesamplemodelsweredrawn, theactualandpredictedOCwasstatisticallysemi-equal. Therefore, itwaspossible toprove that theSMLEmodelwasuseful inpredictingOCbasedontheheterogeneous modelswithexcellent levelsofaccuracy(seeTable5). So,wecanconcludethat themodeldeveloped structure is sufficientwithmoreparameterssetting(i.e.,kernels,neuron) forOCprediction. Table5.The t-test resultsofactualandpredictedoil consumptionusingSMLEmodels. Model t p-Value MeanDifference 1stSMLE 0.227 0.823 0.8081 2ndSMLE 1.320 0.193 0.6803 3rdSMLE 0.728 0.470 0.6178 Theforecastedvalues foreachmodelandtotalOCgrowthrate from2017to2026 issummarized in Table 6. As seen from the table, allmodelswill still be increasing in the period from 2017 to 280