Artificial Intelligence: Summary and Hybrid Schemes - Digital Signal Processing in Power System Protection and Control - page 306

accuracy. The learning was first done by self-organizing the centers of the fuzzy
sets according to Kohonen's Self-Organizing Map learning laws. After that, the
fuzzy sets and the outputs of the fuzzy rules were initialized. Finally, in the last
phase, the fuzzy sets were tuned by an algorithm similar to Kohonen's Learning
Vector Quantization. Simulation results show good accuracy and fast conver-
gence of the fuzzy-neural scheme.
Another example of the fused hybrid scheme is the so called Adaptive Network
Fuzzy Inference System introduced in [ 4 ]. It is idea based on the fact that hybrid
neuro-fuzzy systems are homogeneous and usually resemble neural networks.
Here, the rule base of a fuzzy system is interpreted as a special kind of neural
network. Fuzzy sets can be regarded as weights whereas the input and output
variables and the rules are modeled as neurons. One can say that the neurons of the
network represent the fuzzy knowledge base. The advantage of such hybrid NFS is
its architecture since both fuzzy system and neural network do not have to com-
municate any more with each other. They are one fully fused entity and thus can
also learn, both online and offline.
One should note that the ANFIS model [ 4 ] implements a Sugeno-like fuzzy
system (Fig. 15.1 a, described also in Chap. 11 ) in a network-like structure.
The possibility of parameters adjusting via training (similar as for neural network
schemes) is an important feature of the ANFIS structure. The paradigm of
ANN-like training is applied here to a FIS system.
The ANFIS hybrid system has been applied e.g. to realize an efficient protection
scheme against out-of-step (OS) conditions of synchronous machines [ 15 ]. The
structure of an ANFIS with three inputs and one output is shown in Fig. 15.1 b.
The ANFIS consists of three layers of nodes performing different operations on
incoming signals. The nodes in particular layers are responsible for determination
of membership grades for each linguistic term, executing the rules and generating
the weighted output. Additional factor is introduced to normalize the firing
strengths of the rules with respect to the sum of all firing strengths. A hybrid
training algorithm being a combination of the least squares method and back-
propagation gradient descent method was used to prepare the FIS for the OS
classification task.
The FL-based OS protection scheme developed has been thoroughly optimized
and tested with ATP-generated case signals. The scheme designed displays almost
perfect efficiency and high speed of OS detection. With the scheme designed the
OS cases are identified much earlier comparing to standard impedance-based
protection schemes. Wide robustness features of the ANFIS-based scheme have
also been achieved.
A fuzzy-neuro hybrid can also be obtained with introduction of fuzzified
neurons. A classical neuron represented by equation

!

y ¼ u X

n

w k x k ð 15 : 1 Þ

k ¼ 1