Page - 302 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1561 4.3. Experiment I:CaseswithLargerWidthCoefficients In thisexperiment,weset the intervalwidthcoefficientα=0.05,which isequivalent tosetting theoutput to [0.95×X,X,1.05×X] forasinglesample in the trainingprocessof theneuralnetwork. Basedonthisstructure, thePIscanbeoutputgivenaninputtestset. Inordertoguaranteethediversity of thesamples,westudiedfourdifferentquarterlydata for fourdifferentstates. Themodels involvedinourresearchcanbedividedinto threegroups forbetterexplanations for the impactofdifferentcomponents. ThefirstgroupincludedLUBEandE–LUBE,andthedifference between themwere thestructuresof theneuralnetwork. ThestructureofLUBEconsistedof three layerswhichweresimilar to the traditionalBPneuralnetwork.Moreover, in theE–LUBE,anextra context layerwas added to the structure so thatwe couldvalidate the impact of the context layer inpredictionbycomparing theperformanceof these twomodels. The secondgroup included the PO–E–LUBEandIO–E–LUBE,andthedifferencebetweenthemincludedtheoptimizationalgorithm in the trainingprocess. PO–E–LUBEused the error andvariance of point prediction to construct thecost function inMOSSA,wherebythe targetofminimizingthecost functioneffectivelydenotes arequirement forbetterpredictionaccuracy. Inaddition, IO–E–LUBEemployedtheCPandPIWof the intervalpredictiontoconstruct thecost function inmulti-objectiveoptimization,while the target ofminimizing sucha cost functiondenoted the requirements for a better performance in interval coverage,which ismorerational forourgoalof intervalprediction. Thecomparisonbetweensuch models can reflect the influence of different cost functions in theparameter optimizationprocess. Furthermore, inthefirstgroup, theparametersof theneuralnetworkaredeterminedbyaconventional gradientdescentalgorithm,andin thesecondgroup, theparametersaredeterminedbyaheuristic optimizationalgorithm.Therefore, the impactofdifferentoptimizationalgorithmscanbeshownby comparingthemodels indifferentgroups. Inaddition, in the thirdgroup, thedatapreprocessing is introduced. Basedon themodels in thefirst twogroups,CEEMDANwasused to refine the input dataset. The resultsof themodels in thisgroupwilldisplay theeffectofdatapreprocessing in the hybridmodel. The simulation results are shown inTables 2 and3. Also shown inFigure 5are theprincipal indicesof intervalprediction,namely,CPandPINAW.Basedontheconductedcomparisonsreferred toearlier, several conclusionscanbe inferred: (1) By comparing themodels in thefirst group,wecanconclude that theE–LUBE is superior to LUBEinmostcases, suchas the fourthquarter inNSWandthefirstquarter inTAX,asshownin Table2andFigure5. TheCPofE–LUBEreached87.17%,while theCPofLUBEwas72.36%for the fourthquarter inNSW.Therateof improvementwasmore than15%with themaintenanceof PINAWandPINRW.However, insomecases, the improvement isnot remarkable, suchas the fourthquarter inQLD,asshowninTable3andFigure5. Theperformancesof these twomodels arealmost thesame. Ingeneral, theperformanceofE–LUBEisbetter thanLUBE,whichmeans thatE–LUBEwithanextra context layer can improve theperformance. In theory, thecontext layers are able toprovidemore information compared toprevious outputs of hidden layers. Thissuperiorityhasbeenprovedinourexperiments.However,owingtothe instabilityof the parameters in theneuralnetwork, the improvement isnotadequatelyremarkable ina fewcases. (2) Intermsoftheoptimizationmethods,andaccordingtotheresultsshowninFigure5,andTables2 and3, theCPsof thesecondgroup(PO–E–LUBEandIO–E–LUBE)performbetter thanE–LUBE inmostcases. E–LUBEusesthegradientdescentalgorithm,whichissensitivetotheinitialization, inorder toobtain theparameters inNN.Furthermore, themodels in thesecondgroupuse the heuristic swarmoptimization algorithmwhich can synthesize the initialization results using anadequatepopulationsize. Thus, themodels in thesecondgroupsshouldhaveelicitedbetter performancesintheoryunlesstherandominitializationsofE–LUBEareperfect.Moreover,within thesecondgroup, IO–E–LUBEhasalargerCPvaluethanPO–E–LUBE,withlowlevelsofPINAW andPINRW.It is just the influenceof thecost functionthatmakessuchadifference. Themain 302