Genetic and Evolutionary Algorithms for PSP - Digital Signal Processing in Power System Protection and Control - page 282

• Matrix of the neurones' biases B k ,
• Quality index Q k .
At each consecutive optimization step (for successive population of nets)
appropriate changes in the genome of each individual were carried out, depending
on the genetic operation applied to the net (-s):

• The new layers sizes N k are assigned.
• Elements of the matrices W k and B k are cut away, newly established or inter-
changed between the ANNs.

Optimization of the neural CT saturation detector was performed by going out
of a population of neural networks that consisted of 20 individuals. The ANNs
were being trained with the first half and tested with the second half of pattern
signals originating from EMTP-ATP simulation of current transformer operation.
The ANN input vector consisted of 10 most recent samples of the CT secondary
current, which may be seen as signal windowing with 10 ms long data window (by
sampling frequency f s = 1 kHz). The Levenberg-Marquardt training algorithm
was adopted with the desired output of the ANN set to 1.0 for the periods of linear
CT operation and 0.0 when the CT was saturated.
Implementation of the GA procedure brought about results, which, among the
others, depend on the definition of the ANN quality index (adaptation function). Two
versions of the index were analyzed, i.e. efficiency index Q eff and efficiency/size
index Q eff/size , according to the formulae
Q eff ¼ number of correct decisions
number of all testing cases

ð 13 : 1 Þ

1
ð 1 Q eff Þ 2 n ANN

Q eff = size ¼ ð 13 : 2 Þ

where n ANN stands for ANN size (total number of neurons).
With the quality index ( 13.1 ) the best neural nets from the population con-
sidered were assigned values close to 1.0, while the worst ones were graded with
values approaching 0.0. One has to understand that the assessment of ANN with
use of the efficiency index Q eff is done with respect to the ANN performance
quality only (in terms of percentage of correctly classified cases) without taking
into consideration the ANN size. Such an approach can sometimes lead to quite
big neural networks, implementation of which may create problems if they are
going to be applied in on-line operating protection or control systems (high-
computational burden, proportional to the ANN size). In order to drive the
optimization process in both efficiency and ANN size directions the quality index
( 13.2 ) was proposed. The values of Q eff/size (not limited to 1.0) are inversely
proportional to the total number of neurons of ANNs being assessed, thus giving
a chance of obtaining efficient yet reasonably small (and implementable) neural
networks. In first attempt the simple ratio of Q eff -n ANN was considered; however,
such a quality index could sometimes lead to very small ANNs but of poor