The process learning and the process recalling the learning processstep
methodologies to incorporate data about the machining process through actual cuts. These methodologies were also employed to construct a control system that predicts surface roughness during the execution of the machining process. These two learning methodologies are artificial neural networks (ANN) and fuzzy neural (FN) systems. An overview of these two approaches follows in the next section.
16.2.1 Neural Networks Model
Step 2: Initialize the beginning weights and biases:
Set all the initial weights and biases values randomly.Step 3: Load the input vector X and the target output vector T of a training example. Step 4: Calculate and infer the actual output vector Y.
net  h  =  ∑i  W  _  xh  ih  •  X  i  –  θ _  h  Equation (16.1)  

H  = ( f ne  )=  1  net h  Equation (16.2)  
h  h  1 exp– 
net  j  =  h  W  _  hy  hj  〈  H  h  −  θ _  y 





Y  j 

)=  1  −  

j  
δ j  =  Y  j  (  1–  Y  j  )(  T  j  –  Y  Equation (16.5)  

δ h  =  H  h  ( 1–  H  h  ) 

Equation (16.6)  
∑j  
W  _  hy  hi 
∆W  _  hy  hj  =  ηδ j  H  h  , , 
∆θ _  y  j  =  –ηδ j  Equation (16.7)  

∆W  Equation (16.8)  
_  xh  ih  =  ηδ h  X  i  ∆θ _  h  h  =  – 

Step 7: Adjust and renew the weight matrix and the bias vector. (a) For the output layer:
16.2.1.2 The Recalling Process
Step 1: Set all the network parameters.
net  h  =  ∑i  W  _  xh  ih  •  X  i  –  θ _  h  Equation (16.11)  

H  = ( f ne  )=  1  net h  Equation (16.12)  
h  h  1 exp– 
(b) Infer the actual output vector Y.
net  j  =  ∑h  W  _  hy  hj  •  H  h  –  θ _  y  j  Equation (16.13)  

Y  = ( f ne  )=  1  Equation (16.14)  
j  j 

–  net j 
16.2.2 FuzzyNets Modeling
16.2.2.1  

Assume that the domain intervals of input variable xi are  [  x  i– ,  x  +  ]  , and that the domain intervals of  
i 