Page - 40 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 Table8.ResultsofWilcoxonsigned-ranktestandFriedmantest forExample2. ComparedModels WilcoxonSigned-RankTest FriedmanTest α=0.025; W=9264 p-Value α=0.05; W=9264 p-Value α=0.05; SSVRCCSvs. SARIMA(9,1,10)×(4,1,4) 152a 0.00000** 152a 0.00000** H0 : e1= e2= e3= e4= e5= e6 F=149.8006 p=0.0000 (RejectH0) SSVRCCSvs.GRNN(σ=0.07) 396a 0.00000** 396a 0.00000** SSVRCCSvs. SSVRCS 482a 0.00000** 482a 0.00000** SSVRCCSvs. SVRCCS 745a 0.00000** 745a 0.00000** SSVRCCSvs. SVRCS 5207a 0.00000** 5207a 0.00000** aDenotes that theSSVRCCSmodelsignificantlyoutperformstheotheralternativecomparedmodels; * represents that the test indicatesnot toaccept thenullhypothesisunderα=0.05. ** represents that the test indicatesnot to accept thenullhypothesisunderα=0.025. 3.2.6.Discussions TolearnabouttheeffectsofthetentchaoticmappingfunctioninbothExamples1and2,comparing theforecastingperformances(thevaluesofMAPE,RMSE,andMAEinTables3and7)betweenSVRCS andSVRCCSmodels, the forecastingaccuracyofSVRCCSmodel is superior to thatofSVRCSmodel. It reveals that theCCSalgorithmcoulddeterminemoreappropriateparametercombinations foran SVRmodelby introducingthe tentchaoticmappingfunctiontoenrich thecuckoosearchspaceand thediversity of thepopulationwhen theCSalgorithm is going to be trapped in the local optima. InExample1,asshowninTable1, theparametersearchingofanSVRmodelbyCCSalgorithmcould bemoved to amuchbetter solution, (σ,C, ε) = (0.5254, 5885.65, 0.7358)with forecasting accuracy, (MAPE,RMSE,MAE)= (1.51%, 126.92, 87.94) from the local solution, (σ,C, ε) = (1.4744, 17877.54, 0.3231)with forecastingaccuracy, (MAPE,RMSE,MAE)=(2.63%,217.19,151.72). It almost improves 1.12%(=2.63%−1.51%) forecastingaccuracy in termsofMAPEbyemployingTentchaoticmapping function. The same inExample 2, as shown inTable 5, theCCSalgorithmalso helps to improve theresultby1.12%(=3.42%−2.30%). These twoexamplesbothreveal thegreatcontributions from the tent chaoticmapping function. In future research, itwouldbeworthapplyinganother chaotic mappingfunctiontohelp toavoidtrapping into localoptima. Furthermore, the seasonalmechanismcan successfully help todealwith the seasonal/cyclic tendency changes of the electric load data to improve the forecasting accuracy, by determining seasonal length and calculating associate seasonal indexes (per half-hour for Example 1, and perhour forExample2) fromtrainingandvalidationstages for eachseasonalpoint. In thispaper, authorshybridize theseasonalmechanismwithSVRCSandSVRCCSmodels,namelySSVRCSand SSVRCCSmodels, respectively,byusingtheirassociateseasonal indexes,asshowninTables2and6, respectively. Based on these seasonal indexes, the forecasting results (in terms ofMAPE) of the SVRCSandSVRCCSmodels forExample1are further revised from2.63%and1.51%, respectively, toachievemoreacceptable forecastingaccuracy,0.99%and0.70%,respectively. Theyalmost improve 1.64%(=2.63%−0.99%) and 0.81% (=1.51%− 0.70%) forecasting accuracy by applying seasonal mechanism. The same inExample 2, as shown inTable 7, the seasonalmechanismalso improves 2.56%(=3.42%−0.86%)and1.84%(=2.30%−0.46%) forSVRCSandSVRCCSmodels, respectively. Inthemeanwhile,basedonWilcoxonsigned-ranktestandFriedmantest,asshowninTables4and8for Examples1and2, respectively, theSSVRCCSmodelsalsoachievestatistical significanceamongother alternativemodels. Based on above discussions, this seasonalmechanism is also a considerable contribution, and it is worth the time cost to deal with the seasonal/cyclic information during modelingprocesses. Therefore, it couldberemarkedthatbyhybridizingnovel intelligent technologies, suchaschaotic mappingfunctions,advancedsearchingmechanism,seasonalmechanism,andsoon,toovercomesome inherentdrawbacksof theexistingevolutionaryalgorithmscouldsignificantly improveforecasting accuracy. Thiskindofresearchparadigmalso inspiressomeinterestingfutureresearch. 40