Page - 233 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1893 wecompress the informationofeachcurve intoahandynumberofcoefficients (in total J=[log2(P)]) thatarecalledrelativeenergeticcontributions. Thecompression issuchthatdiscriminativepower is keptevenif informationislost.Dataaresotabulatedinamatrixwherelinescorrespondtoobservations andcolumnstovariables (seeFigure2). Figure2. Fromcurves tomatrices. 3.Wavelets Awaveletψ isasufficientlyregularandwell localizedfunctionverifyingasimpleadmissibility condition. Duringacertain timeawavelet oscillates likeawaveand is then localized in timedue toadamping. Figure 3 represents theDaubechies least-asymmetricwavelet of order 6. Fromthis single function ψ, using translation and dilation a family of functions that form the basic atoms of theContinuousWavelet Transform (CWT) is derived From this single function ψ, a family of functions isderivedusingtranslationanddilationthat formthebasicatomsof theContinuousWavelet Transform(CWT) ψa,b(t)= 1√ a ψ ( t−b a ) ,a∈R+∗ ,b∈R. í :DYHOHW 3LFWXUH 'DXE FPSFW RQ OHDVW DV\PP 1 [ Figure3. Daubechies least-asymmetricwaveletwithfiltersize6. For a function z(t) of finite energy we define its CWT by the function Cz of two real-valuedvariables: Cz(a,b)= ∫ ∞ −∞ z(t)ψa,b(t)dt Eachsinglecoefficientmeasures thefluctuationsof function f atscale a, aroundthepositionb. Figure 4gives avisual representationof |Cz(a,b)|2, alsoknownaswavelet spectrum, for a 10day periodof loaddemandsampledat30min. Thewaves thatonecanvisuallyfindonthe image indicate 233