Page - 403 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies 2018,11, 242 4.2.2.DesignFactors forMDBN Todetermine theoptimalstructureof theMDBNforbuildingenergyconsumptionprediction, wewill take threedesignfactors, thenumberofhiddenlayers,hiddenneuronsandinputvariables, with their corresponding levels intoaccount. The threedesignfactorsandtheircorresponding levels arepresented inTable1anddiscussed indetailbelow. Table1.Designfactorsandtheircorresponding levels. DesignFactors Level 1 2 3 i 2hiddenlayers 3hiddenlayers 4hiddenlayers ii 50hiddenunits 100hiddenunits 150hiddenunits iii 4 inputvariables 5 inputvariables 6 inputvariables • DesignFactor i: thenumberofhidden layers k ThenumberofhiddenlayersdetermineshowmanyRBMsarestacked. In this study,weconsider thenumberofhiddenlayers2,3and4asLevels1,2and3, respectively. • DesignFactor ii: thenumberofuthhiddenunitsnu Thenumberofhiddenunits is an important factor that greatly influences theperformanceof theMDBNmodel.Here,weassumethat thenumbersofneurons inallhiddenlayersareequal, i.e.,n1=n2= · · ·=nk. In thispaper,weset thenumberofneurons50,100and150asLevels1, 2 and3, respectively. • DesignFactor iii: thenumberof inputvariables r In this paper, we utilize r energy consumption data in the building energy consumption time series before time t to predict the value at time t. In other words, we utilize x=[y(t−1),y(t−2), . . . ,y(t−r)] topredictthevalueofy= y(t).Here,weconsiderthenumber of inputvariables4,5and6asLevels1,2and3, respectively. 4.2.3.ComparisonSetting Inthisstudy, theperformancesofall thepredictorsconstructedbyutilizingtheenergy-consuming patternsarecomparedwith thosedesignedbytheoriginaldata. Toevaluate theperformancesof the models,weutilize the followingtwokindsof indices. Wefirst consider themeanabsoluteerror (MAE), the rootmeansquareerror (RMSE), and the meanrelativeerror (MRE),andcalculate themas MAE= 1 K K ∑ l=1 ∣∣∣yˆ(l)−y(l)∣∣∣ , (31) RMSE= √ ∑Kl=1(yˆ(l)−y(l))2 K , (32) MRE= 1 K K ∑ l=1 ∣∣∣yˆ(l)−y(l)∣∣∣ y(l) ×100%, (33) whereK is thenumberof trainingor testingdatapairs, and yˆ(l),y(l) are, respectively, thepredicted valueandactualvaluewithrespect to the inputx(l). TheMAE,RMSEandMREarecommonmeasuresof forecastingerrors in timeseriesanalysis. Theyserve toaggregate themagnitudesof thepredictionerrors intoasinglemeasure. TheMAEisan averageof theabsoluteerrorsbetweenthepredictedvaluesandactualobservedvalues. Inaddition, theRMSErepresents thesamplestandarddeviationof thedifferencesbetweenthepredictedvalues 403