Page 272 - PVT Property Correlations

238 PVT Property Correlations

Applying the chain rule, the change in total error with respect to the net-
work weights is given by

@E total @E total @O @N
5 3 3 ð10:5Þ
@w @O @N @w
By calculation of the delta weight variation for the W5 (as an example),
the three terms in Eq. (10.5) are evaluated as follows:
@E total @ 2 2
5 0:5 RequiredO12OutputO1Þ 1 0:5 TargetO22OutputO2ð Þ
ð
@O1 @O1
ð10:6Þ
@E total 221
5 2 3 0:5 RequiredO12OutputO1Þ 321Þ 1 0 ð10:7Þ
ð
ð
@O1
It follows that
@E total
ð
52 RequiredO1 2 Output O1Þ 52 0:01 2 0:741Þ 5 0:731 ð10:8Þ
ð
@O1
The second term represents the partial derivative for the output node with
respect to its activation function. It is given by the following equation:
@O @ 1
5 5 O1 3 1 2 O1Þ ð10:9Þ
ð
@N @N 1 1 e 2O1
@O
5 0:745 3 1 2 0:741Þ 5 0:192
ð
@N
The last term is to calculate the partial derivative of the output node with
respect to the weight change. It is calculated as follows:
N 5 W5 3 H1out 1 W6 3 H2out 1 B2 3 1 ð10:10Þ

@N
5 H1out 1 0 1 0 5 H1out ð10:11Þ
@W5
Therefore
@N
5 H1out 5 0:583
@W5
The error influenced by W5 is given by the multiplication of the three
partial derivatives. With the use of Eq. (10.5), it follows that
@E total
5 0:731 3 0:192 3 0:583 5 0:082
@W5
To decrease the error between the required value and the calculated value
from first iteration, the new weight (W5) should be decreased by this error