Page - 80 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3. ModelingMicrowaveHeating with [ wl+1(k−1)]=       wl+11,1 (k−1) wl+11,2 (k−1) · ·· wl+11,Nl(k−1) wl+12,1 (k−1) wl+12,2 (k−1) · ·· wl+12,Nl(k−1) ... ... ... ... wl+1Nl+1,1(k−1) wl+1Nl+1,2(k−1) · ·· wl+1Nl+1,Nl(k−1)       . (3.82) The L + 1-th hidden layer is defined as the output layer ( [ wL+1(k−1)]= [wo(k−1)],Nl+1=No). Weightupdate: forweightsof linksconnectingtotheoutputlayer, theupdaterule isgivenby[Hay98] [wo(k)] = [wo(k−1)]−η ·(xL(k)δo(k))T, (3.83) with theoutputvector isdefinedas xL(k) = [ xL1(k), x L 2(k), . . ., x L NL(k) ]T . (3.84) For weights of links only connecting with hidden layers, the up- daterule isgivenby[Hay98][ wl(k) ] = [ wl(k−1)]−η ·(xl−1(k)δl(k))T, 1≤ l≤L (3.85) with theoutputvector isdefinedas xl(k) = [ xl1(k), x l 2(k), . . ., x l Nl (k) ]T . (3.86) When the value l = 1, the vector xl−1(k) is defined as the input vectorof theNN x0(k) =UNN(k). (3.87) 3. Procedure2 isexecutedonceper timestep. There are mainly two rounds of calculations in the backpropagation algorithm. One is the forward pass which calculate the output of each node from the input layer to the output layer. The other one 80