Neuro-Fuzzy Control for Semi-active Dampers - Fuzzy Modeling and Control: Theory and Applications - page 177

Fig. 9.7 Architecture of proposed neuro-fuzzy

number of fuzzy rules are generated. In the current control problem, the proposed
method is suitable due to its optimization possibilities.
The first layer is composed by Radial Basis neuron where their inputs (U i )are
the inputs to the Neuro-Fuzzy System and the output nodes are expressed in the
equation:

2

− (

U i − m ij )

p ij = exp i = 1 ,..., N 1 j = 1 ,..., N 2 . (9.9)

2
ij

σ

As ( 9.9 ) shows there are parameters that must be defined, the centers of the
membership functions m ij , the widths of the membership functions

σ ij where N 1 is
the number of Neuro-Fuzzy System inputs and N 2 is the number of nodes at the
hidden layer.
The second neurons layer represents the rule system and their outputs nodes are
calculated by the expression:

min p 1 j ,..., p N 1 N 2 .

γ j = p ij ,..., (9.10)

The defuzzification is carried out in the third layer providing the Neuro-Fuzzy
output by:

j s

ν jk γ j
j γ j

Y k = k = 1 ,..., N 3 . (9.11)

Summarizing, the described Neuro-Fuzzy system depends on the centers of mem-
bership functions (m ij ), their width ( σ ij ). Before

using the Neuro-Fuzzy system in the control system, a learning phase needs to be
carried out in order to obtain these parameters. This learning algorithm is divided
in two phases (Mitra and Hayashi 2000 ; Al-Hadithi et al. 2007 ; Santos et al. 2010 ).

σ ij ) and the estimated output value ( s