Page - 79 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3.3. Black-boxModeling Definition Interpretation Nl Numberofnodes in the l-th hiddenlayer (1≤ l≤L) xli(k) Outputof the i-thnode in the l-th layerat timek zl+1j (k) = ∑Nl i=1w l j,i(k) ·xli(k) Inputof the j-thnode in the (l+1)-th layerat timek δlj(k) = ∂JOL(k) ∂zlj(k) Localgradientof the j-thnode in the l-th layerat timek fo, f ′ o(z) := df′o dz Activationfunctionusedin the output layeranditsfirst derivative g, g′(z) := dg ′ dz Activationfunctionusedin the hiddenlayersanditsfirst derivative Table3.3. Parametersusedin theupdateofweights (inNN). ThevaluesYNN,i(k)andYd,i(k)arethe i-thelementfromthevector YNN(k)andYd(k), respectively. For the l-th hidden layer (1≤ l≤L), the corresponding local gra- dientvector is [Hay98][ δl(k) ] = [ δl1(k), δ l 2(k), . . . δ l Nl (k) ] , (3.80) where theelement isdefinedas δli(k) = g ′(zli(k)) · Nl+1∑ j=1 δl+1j (k)w l+1 j,i (k−1), 1≤ i≤Nl. (3.81) 79