Page 171 - Data Science Algorithms in a Week

The Estimation of Cutting Forces in the Turning of Inconel 718 Assisted … 155

The first step in developing of ANN is selection of data for training and testing
network. The number of training and testing samples were 18 and 9, respectively, as
shown in Table 2. Then, all data were normalized within the range of ±1 before training
and testing ANN. The ANN model, using the BP learning method, required training in
order to build strong links between layers and neurons. The training is initialized by
assigning some random weights and biases to all interconnected neurons.
hid
The output of the k-th neuron in the hidden layer Ok is define as,

1
O hid  (1)
k  I  hid 

1 exp  (1)  k
 T 

with

N inp
(1)
(1)
I k hid   w O inp  b (2)
j
jk
k
j 1

inp
where N is the number of elements in the input, wjk is the connection weight of the
(1)
synapse between the j-th neuron in the input layer and the k-th neuron in the hidden layer,
inp
Oj is the input data, bk is the bias in the k-th neuron of the hidden layer and T is a
(1)
(1)
scaling parameter.
out
Similarly, the value of the output neuron Ok is defined as,

1
O out  (3)
k  I  out 

1 exp  (2)  k
 T 

with

N hid
(2)
I k out   w O i hid  b k (2) (4)
ik
i 1

hid
(2)
where N is the number of neurons in the hidden layer, wik is the connection weight of
the synapse between the i-th neuron in the hidden layer and the k-th neuron in the output
layer, bk is the bias in the k-th neuron of the output layer and T is a scaling parameter
(2)
(2)
for output layer.
During training, the output from ANN is compared with the measured output and the
mean relative error is calculated as: