Page - 359 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1253 x1 x2 xn-1 x3 x4 xn-2 Convolution Convolutional layer xn sampling subsampling layer y1 ym Fully-connection Figure2.Convolutionalneuralnetworkmodel. Inconvolutional layer, theoriginaldata isprocessedbytheconvolutionalkernel toobtain the output,asdescribed inEquation(8). xlj= f ( k ∑ j=m xl−1j w l j+θ l j ) (j=1,2, · · · ,n; 0<m≤ k≤n) (8) where f(I)= 11+e−I , I= k ∑ j=m xl−1j w l j+b l j (1,2, · · · ,n;0<m≤ k≤n). xlj andxl−1j represent theoutput inLayer landthe input inLayer l−1, respectively. j is the localconnectionrangingfromm tok.wlj equals theweightandθlj is thebias. Thesubsamplingprocesscanbeexpressedas follows: xlj= g(x l−1 j )+θ l j (9) whereg(∼) represents the functionthatselects theaverageormaximumvalue. Then, theobtaineddata is linkedto the fullyconnected layeraspresented inEquation(10). xl= f(Il), Il=Wlxl−1+θl (10) whereWl is theweight fromLayer l−1 toLayer landxl represents theoutputdata. In the above calculation, each convolutional kernel plays a role in all the input via the slide. Differentconvolutionalkernelscorrespondingtomultiplesetsofoutputwhere theweightof thesame convolutionalkernel is identical. Theoutputofdifferentgroupsarecombinedandthentransferred to thesubsampling layer.Here, theoutput in thepreviousconvolutional layer is treatedas the input data.At this time, set therangeofvaluesanduse theaverageormaximumasthespecificvalues in the range. Thedataneeds tobecombinedtosatisfyadimensionality reduction. Finally, theresults canbe derivedfromthefullyconnected layer [25]. Theapplicationof theCNNmodelhas twomainadvantages: (a) theexistenceofdeformeddata isallowed; (b) the loadforecastingefficiencyandaccuracycanbe improvedbyparameterreduction throughlocalconnectionandsharedweight.However, thestabilityof thepredictionresultscannot 359