Page - 404 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies 2018,11, 242 andtheactualobservedvalues.As largererrorshaveadisproportionately largeeffectonMAEand RMSE, theyaresensitive tooutliers. TheMRE,alsoknownas themeanabsolutepercentagedeviation, canremedythisdrawback,anditexpresses thepredictionaccuracyasapercentage throughdividing theabsoluteerrorsbytheircorrespondingactualvalues. Forpredictionapplications, thesmaller the valuesofMAE,RMSEandMREare, thebetter the forecastingperformancewillbe. To better show the validity of themodels, we also consider another two statistical indices, which are, respectively, the Pearson correlation coefficient, denoted as r, and the coefficient of determination,denotedasR2. These twoindicescanbecalculatedas r= K(∑Kl=1 yˆ (l) ·y(l))−(∑Kl=1 yˆ(l)) ·(∑Kl=1y(l))√ (K∑Kl=1(yˆ(l))2−(∑Kl=1 yˆ(l))2) ·(K∑Kl=1(y(l))2−(∑Kl=1y(l))2) , (34) R2= [ ∑Kl=1(yˆ (l)− yˆAve) ·(y(l)−yAve) ]2 ∑Kl=1(yˆ(l)− yˆAve) ·∑Kl=1(y(l)−yAve) , (35) whereK isalsothenumberoftrainingortestingdatapairs,and yˆAve,yAveare,respectively, theaverages of thepredictedandactualvalues. Thestatistic r isameasureof the linearcorrelationbetweentheactualvaluesandthepredicted values. It ranges from−1to1,where−1meansthetotalnegative linearcorrelation,while1 is total positive linearcorrelation. ThestatisticR2 providesameasureofhowwellactualobservedvaluesare replicatedbythepredictedvalues. Inotherwords, it isameasureofhowgoodapredictormightbe constructed fromtheobservedtrainingdata [48]. ThevalueofR2 ranges from0to1. In regression applications, the larger thevaluesof randR2 are, thebetter thepredictionperformanceswillbe. 4.3. EnergyConsumptionPrediction for theRetailStore In this subsection, the energy-consumingpatternof the retail storewill be extracted fromthe retail storedatasetfirstly. Then, theconfigurationsof thefivepredictionmodels forpredicting the retail storeenergyconsumptionwillbeshownindetail.At last, theexperimental resultswillbegiven. 4.3.1. Energy-ConsumingPatternof theRetailStore WeutilizeEquations (6)and(7) toobtain thedaily-periodicenergy-consumingpatternandthe residual timeseriesof theretail store. Figure 8a shows thedaily-periodic energy-consumingpattern. In addition, the residual time seriesof theretail store,which isusedtooptimize theMDBNisdemonstrated inFigure8b. 4.3.2.Configurationsof thePredictionModels Asaforementioned,wewilltakethreedesignfactors, thenumberofhiddenlayers,hiddenneurons andinputvariables,with their corresponding levels intoaccount todetermine theoptimalstructureof theMDBNmodel forbuildingenergyconsumptionprediction.Consequently,33=27 trialsareran. Inaddition, theexperimental resultsareshowninTable2. It isobvious that trail 19canobtain thebest performance. Inotherwords, theoptimalstructureof theMDBNforretail storeenergyconsumption predictionhas fourhiddenlayers,150hiddenunitsandfour inputvariables. Furthermore, theparameter configurationsof theother four comparativepredictors for retail storeenergyconsumptionpredictionare listed indetailas follows. • For the BPNN, there were 110 neurons in the hidden layer that can realize the nonlinear transformation of features by the sigmoid function. Additionally, the algorithmwas ran for 7000 iterations toachieve the learningobjective. • FortheGRBFNN,the6-foldcross-validationwasadoptedtodeterminetheoptimizedspreadofthe radialbasis function. Furthermore, thespreadwaschosenfrom0.01 to2with the0.1step length. 404