Page - 184 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2008 forecastingofelectricity. Theyfoundthat thepretrainedDNNperformedbetter, especiallyasnetwork size increased[23]. Giventhesuccessful resultsof thesedeepneuralnetworkarchitecturesonsimilarproblems, it is expected that DNNswill surpassANNs inmany regression problems, including the short-term load forecasting of natural gas. This paper explores the use of DNNs to model a natural gas systembycomparing theperformanceof theDNNtovariousbenchmarkmodels and the current state-of-the-artmodels. 4.ArtificialandDeepNeuralNetworks ThissectionprovidesanoverviewofANNsandDNNsandhowtotrain themtosolveregression problems.AnANNisanetworkofnodes. Eachnodesumsits inputsandthennonlinearly transforms them.Letxi represent the ith input to thenodeofaneuralnetwork,wi theweightof the ith input,b the bias term,n thenumberof inputs,ando theoutputof thenode.Then o=σ ( n ∑ i=1 wixi+b ) , (4) where σ(x)= 1 1+e−x . (5) This typeofneuralnetworknode isasigmoidnode.Howeverothernonlinear transformsmaybe used. Forregressionproblems, thefinalnodeof thenetwork is typicallya linearnodewhere o= n ∑ i=1 wixi+b. (6) Anetworkofnodesis illustratedinFigure3belowforafeedforwardANN,whoseoutputsalways connect tonodes further in thenetwork. Thearrows inFigure3 indicatehowtheoutputsofnodes in one layerconnect to the inputs in thenext layer. Thevisiblenodesare labelledwithaV.Thehidden nodesare labelledwithanHx.y,wherex indicates the layernumberandyindicates thenodenumber. Theoutputnode is labeledO. H1.1 H1.2 H1.3 V1 V2 V3 V4 H2.1 H2.2 Inputs O Figure3.AfeedforwardANNwith fourvisiblenodes, threenodes in thefirsthidden layer, twonodes in thesecondhiddenlayer,andasinglenode in theoutput layer. 184