
17-1
17.1 Introduction
A neural network with basis functions that remain invariant under the Fourier transform is pro-
posed
fo
r
fa
ult
di
agnosis
of no
nlinear
sy
stems
. e co
nsidered
ne
ural
ne
twork
is of th
e
fe
edforward
ty
pe
an
d
us
es
Ga
uss–Hermite
po
lynomial
ba
sis
fu
nctions
. i
s
ne
ural
mo
del
fo
llows
th
e
co
ncept
of wa
velet
ne
tworks
[1
–3]
an
d
em
ploys
ba
sis
fu
nctions
th
at
ar
e
lo
calized
bo
th
in sp
ace
an
d
fr
e-
quency,thus
al
lowing
be
tter
ap
proximation
of th
e
mu
ltifrequency
ch
aracteristics
of mo
nitored
no
n-
linear
sy
stem
[4
–8]
. Ga
uss–Hermite
ba
sis
fu
nctions
ha
ve
so
me
in
teresting
pr
operties
[9
,10]:
(1
)
e
y
re
main
al
most
un
changed
by th
e
Fo
urier
tr
ans ...