Using
Supe ised
Lea ning
Techniques
o
Diagnosis
o
Dynamic
Sys ems
Ped o
J.
Abad
1,
An onio
J.
Su i ez',
Ra ael
M.
Gasca
2,
Juan
A.
O ega
2
Abs ac .
This pape
desc ibes
an
app oach
based
on
supe ised
diagnose
sys ems
aul s
a e
needed
o
main ain he
sys ems
in
lea ning echniques
o
he
diagnosis
o
dynamic
sys ems.
The le els
o
secu i y,
p oduc ion
and
eliabili y.
me hodology
can
s a wi h
eal
sys em
da a
o wi h
a
model
o
Inside
he A i icial
In elligen
communi y
he
dynamic sys ems
he dynamic
sys em.
In
he
second
case,
a se
o
simula ions
o
diagnosis
ask
has
been app oached,
in
mos
o
he
cases,
adap ing
he
sys em
is
equi ed
o
ob ain
he necessa y da a.
In
bo h
cases,
he
echniques coming
om
he s a ic
sys ems
diagnosis
o
he
ob ained
da a
will
be
labelled
acco ding
o
he
unning condi ions
dynamic
beha iou
o
he sys ems. This
way
[2]
o
[3]
y
o
add
o
he
sys em
a
he
ga he ing
da a
ime. Label
indica es
he
empo a y in o ma ion
o
GDE
[4]
unning
s a e
o
sys em:
co ec wo king
o
abno mal
unc ioning
On
he
o he
hand,
quali a i e models ha e
also
been commonly
o
any
sys em
componen .
A e
being
labelled,
da a
will
be
used
o
his
pu pose
[5] [6].
ea ed
o
add
addi ional in o ma ion abou
he
unning
o
sys em.
In
[7]
he undamen s
o
he
based-models
diagnosis,
applied
o
The
inal goal
is
o
ob ain
a se
o
decision
ules
by
applying
a
he
dynamic sys ems,
a e
p esen ed,
and
mo e
ecen ly
[8]
p oposes
classi ica ion
ool
o
he se
o
labelled
and
ea ed da a. This
a
consis ency-based app oach
wi h
quali a i e models.
way,
any
obse a ion
on
he
sys em will
be
classi ied
acco ding
O he echniques, coming
om
he
AL,
ha e
also
en e ed
in
o
hose decision
ules, ha ing
a
e u n
label
indica ing
he
he
diagnosis
ield.
Following
his
line,
lea ning echniques
ies
o
cu en ly
unning
s a e
o
sys em.
Re u ned
label
will
be
he
iden i y he sys em
beha iou basing
on
a
p e ious
aining.
diagnos ic. This
en i e
lea ning
ask
is
ca ied
ou
o -line, be o e
La ely,
some
wo ks
using
lea ning-based echniques
ha e
been
he
diagnosing.
p esen ed,
like
s ochas ic
me hods
[9],
neu al
ne wo k based
lea ning
[10]
and
classi ica ion
sys ems
[11].
Neu al
ne wo k
echniques ha e
ecen ly
been applied
in
di e se
ields,
as
1
INTRODUCTION
medicine
[12]
o powe
supply
[13].
Machine
Lea ning
echniques, inside
he
supe ised lea ning
Diagnosis
de e mines
why
a
sys em,
co ec ly designed, doesn'
ield,
a e
au oma ed
p ocedu es
based
on
logical
ope a ions
ha
wo k
like
i
was
expec ed.
Explana ion,
o his
e oneous
lea n
a
ask
s a ing
om
a
sui e
o
examples.
In
he
classi ica ion
beha iou ,
ep esen s
a
disc epancy
wi h
he sys em
design. One
ield he
a en ion
has
been
cen ed,
conc e ely,
in
app oaches
wi h
diagnosis
ask
is
o
de e mine
he sys em elemen s
ha
could
cause
decision
ees
[14],
whe e
classi ica ion
is
he
esul
o
a
se ies
o
he
e oneous
beha iou
acco ding
o
he sys em
obse a ions.
logical
s eps.
These
app oaches
a e
able
o
ep esen
he
mos
Moni o ing
p ocess
is
undamen al
o
a oid non- eal
aul s
by complex
p oblems
i
hey ha e
enough
da a.
Applied
o
he
small
al e a ions
in
a iables
alues.
[1]
P oposes
a
knowledge
diagnosis,
we
can
ind
hese me hods used
o
he
classi ica ion
o
model
o
dynamic
sys ems
moni o ing.
empo ay
pa e ns
[15]
o
in
p e ious
wo ks
o
he
cu en
one
Faul
de ec ion consis s
on
de e mining,
s a ing
om
he
[16] [17].
sys em
obse a ions,
when
an
inco ec
ope a ion
o
he
obse ed
The
p esen
wo k
is
cen ed
in
quan i a i e models.
I
uses
sys em exis s.
When ailu e
is
de ec ed
hen
diagnosis
will ake
he
supe ised
lea ning echniques
o
ob ain
a
ules-based
model
o
con ol
o
ind
he
easons
o
ha
inco ec
beha iou ,
diagnose
dynamic sys ems
by ecognizing
he co ec
beha iou
Faul
de ec ion
and
diagnos ic
o
aul y
componen s
a e
e y models
and
aul y
beha iou
models.
An
app oach
o
o e
se e al
impo an
om
he
s a egic
poin
o
iew
o
he companies, due
o
aul causes,
when
he e
isn'
an
only
clea cause,
is
p esen ed.
he economic demands and
en i onmen conse a ion equi ed
o
Res
o
he
documen
has
been o ganized
in
he ollowing
way:
emain
in
compe i i e
ma ke s. This
is
one
o
he easons
causing
in
he
nex
sec ion he
used me hodology
will
be exposed
and
he
ha his
is a
e y ac i e
in es iga ion
ield.
Componen s
aul s
and o m
o
ca y
ou
he
diagnosis.
Nex
a
p oblem
applica ion
p ocess
aul s
can
cause sys ems damages
and
undesi able hal
o
example
is
desc ibed
o
he
de eloped app oach.
To
illus a e
he
he sys em. This causes
he
inc ease
o
cos s
and
dec ease
o
ope a ion
o
hese
echniques
a
wide
se
o
es s
is
p esen ed.
Las ly
p oduc ion.
The e o e
de eloping
mechanisms
o
de ec and
o some
imp o emen s
ha
a e
in
de elopmen p ocess
a e
discussed.
Dp o
de
Ingenie ia
Elec 6nica,
Sis emas
In o m n icos
y
Au omd ica.
2
PROPOSED
METHODOLOGY
Uni e sidad
de
Huel a.
E-Mail:
{abadhe,[email p o ec ed]}
2
Dp o
de
Lenguaje y
Sis emas
1n o md icos.
Uni e sidad
de
Se illa.
To ca y
ou
diagnosis
o
dynamic
sys ems
a se
o
decision
ules
E-
Mail:
{gasca,[email p o ec ed]}
should
be
gene a ed.
I
can
be done s a ing
om
he known
ajec o ies
o
he sys em
o
he
simula ions
gene a ed
om
a
2.
Decision
ules
a e
gene a ed
using
a
supe ised lea ning
ool.
model.
Relabelled
ajec o ies
*
Decision
ules
Be o e s a ing wi h
he
me hodology
some
concep s
need
o
be
3.
Diagnosis
consis s
in
associa ing
an
obse a ion
as
de ined.
co esponding
o
beha iou s
amily
by
using
decision
ules.
Classi ica ion
(obse a ion,
ules)
*
Diagnos ic
label
2.1
De ini ions
and no a ion.
De ini ion
1:
Beha iou s Family.
I
is a
ini e
g oup
o
2.2
Me hodology
ajec o ies ha ing
a
simila
beha iou
om
he
poin
o
iew
o
P oposed me hodology
o
diagnose
is
an
ampli ica ion
o
o he
one
he
diagnosis.
de eloped
in
[16].
This basic
me hodology
may
p esen
some
De ini ion
2:
Co ec
beha iou .
I
is
he
ini e g oup
o
p oblems
when he
same
sys em
beha iou s
can
be associa ed
o
ajec o ies
belonging
o
e olu ions
o
he
sys em
wi hou
any
aul
di e en
aul
easons.
In
o de
o
don'
diagnose inco ec ly hese
ype. cases,
in
his new
app oach,
hose beha iou s
will
be
associa ed
De ini ion
3:
Pe ec beha iou .
I
is
he
ajec o y
desc ibing
he
wi h
all
he
possible
beha iou s
amily ha
can
cause
his
conc e e
sys em
when
all
pa ame e s
ake
he cen al
alues
o
he
anges
beha iou .
In
his
way
se e al
aul
causes
will
be
o e ed
o
de ined
as
co ec . obse a ions
ha
can
co espond
o
di e en
beha iou s
amily.
De ini ion
4:
Obse a ion.
I
is a
eal
ajec o y
o
he
dynamic
Basic
idea
consis s
in
ob aining
a se
o
classi ica ion
ules
om
sys em
con aining alues
o
he
obse a ional
a iables
in he
a
sui e
o
sys em da a
in
di e en
beha iou s
modes:
he co ec
sys em.
beha iou
and
he
aul y
beha iou s.
A e , hose ob ained
De ini ion
5:
Diagnosis.
I
is
he
iden i ica ion
o
he
obse ed classi ica ion
ules
can
be used
o
associa e
an
obse a ion
wi h
beha iou
o
he
sys em
as
belonging
o
a
ce ain
beha iou
amily
model
beha iou .
Thus
diagnosis
o
he
obse a ion
is
ob ained.
(diagnosis
label) and
acco ding o decision
ules.
P ocess
can
s a
wi h
eal
sys em da a
o
wi h
a
model
o
he
P oposed
app oach
can be
gene a ed
om wo
di e en
ways:
dynamic
sys em.
In
he
second
case,
a se
o
simula ions
o
he
"*
Rules
a e
gene a ed s a ing
om
a
g oup
o
di e en sys em
is
equi ed
o
ob ain
he necessa y da a.
In
bo h
cases,
beha iou
models.
ob ained
da a will
be labelled acco ding
o
he
unning
condi ions
Model
(beha iou )
*
labelled ajec o ies o
he sys em
a
he
ga he ing
da a ime.
Label
indica es
he
"*
Rules
a e
gene a ed
s a ing
om
a
g oup
o
expe imen al unning
sys em
s a e:
co ec
wo king o
abno mal unc ion
o
any
ajec o ies
o
dynamic
sys em
o
he
co ec
beha iou
and
sys em
componen .
Final
esul consis s
in
a
da abase con aining
all
possible
aul
beha iou .
labelled ajec o ies.
T ajec o ies
(beha iou )
*
labelled
ajec o ies.
Ob ained
da abase
con ains
e y
simila ajec o ies
Lea ing
o
one
o
hese
si ua ions
he
p ocess
can
con inue
like
co esponding
o
di e en
beha iou
amily
and he e o e
wi h
ha :
di e en
labels.
To
sol e
his
p oblem
he se
o
all
simila
1.
Simila
ajec o ies
belonging
o
di e en beha iou s
amily
a e
ajec o ies
will
be
elabelled wi h new
labels.
This new
labels
will
iden i ied. These ajec o ies
a e
labelled
again
as
belonging
o
be composed
as
a
mix
o
he
olde labels.
Thus, elabelled
bo h
beha iou s
amily.
ajec o ies
will
be associa ed
wi h anyone
o
he
o iginal
Simila
T ajec o ies
(di e en
beha iou
amily)
•
beha iou s
amily. The
p oblem
is
o
de ine
when wo
o mo e
elabelled
ajec o ies,
ajec o ies
a e
simila .
Decision
aken
is
ha
se e al
ajec o ies
P oblem
Simula ing
Desc ip ion
M14ln
Moe
iuaig
D bae
LbligLble
Sys em
Real
Sys em
Obse a ion
DecisionRc
ble
Rules
ClassiFica ion
Labelled
&
Da a
Da abase
T ea ed
T ea men
D
M hbdasoe
E alua ion
DIAGNOSIS
Figu e
1.
P oposed
Me hodology
a e
simila
when
dis ance
be ween hem
is
lowe
han
a
magni ude.
Sys em
can
be
modelled
by
he
ollowing equa ions,
which
Tha
magni ude should be
speci ied
o
each
ea ed sys em. Used
include
a
cons an
o
each
componen
ha
is
used
o
model
also
dis ance
is
Euclidean dis ance,
he aul y
beha iou
o
he
componen :
A e
being labelled
and
elabelled, ajec o ies
da a
will
be
ea ed
o
add addi ional
in o ma ion abou unning
o
he sys em.
dw
This
addi ional in o ma ion
will
be
e y
use ul
when
classi ica ion
d
(1)
ool
ies
o ind
decision
ules,
because a ailable in o ma ion
will
be g ea e .
This
addi ional in o ma ion
should
cha ac e ize
he
d
sys em u he
han
ga he ing da a and
i
is
speci ied
o
each
I
-
Con olle :
--
=
c,
(d
-
w.)
(2)
ea ed
sys ems.
d
A
new
da abase,
which
con ains
o iginal ajec o ies plus
new
a ibu es
and he
co esponding
label,
is
ob ained.
Senso :
w,,
=
c,
*
w
(3)
Final
s ep,
o
ob ain
decision
ules,
is
o
use
a
classi ica ion
ool
wi h
he
labelled
and ea ed
da abase.
Whe e
T
is
he
ine ia
o
he
mo o ,
c.,
is
he
cons an
o
he
An
aspec
o
highligh
is
ha
all
p ocess,
un il
his
momen ,
mo o ;
c,
is
he
cons an
o
he
con olle
and
c,
is
he
cons an
o
ha e
been de elopmen
o -line, and ime
needed
o
his p ocess
is
he
e olu ion
coun e .
no
impo an
o
he
diagnosis p ocess.
Componen
anomalous ope a ion
is
caused,
mainly,
by
he
Diagnosis
p ocess
consis s
on
e alua ing
an
obse a ion
wi h
de ia ion
o
he
componen
cons an
nominal
alue. These
he
ob ained
decision
ules.
Time
spending
o
diagnose
is
only
he
cons an s
s ay
o
he
conside ed co ec alues
ange
ime
o
e alua ing
ob ained
decision
ules.
Decision
ules e u ns Some aul s ep esen
ha
cons an s
ake
alues
abo e
he
he label
associa ed
o
he
beha iou
by co espondence
be ween co ec ones
and
o he s
aul s
ep esen
ha
cons an s
ake
alues
aining
da a
and
obse ed
da a.
This
e u ned
label
is
o e ed
as
below
he
co ec ones.
Diagnosis
esul
should
indica e,
in
diagnosis.
addi ion
o
he
aul y
componen ,
i
aken
alues
o
he
componen
Nex
a
case
s udy
will
be p esen ed
o
de elop
his
cons an
a e
below
co ec
alues o
abo e hem.
me hodology. Possible
aul
easons
ha
we
wan
o
iden i y
a e
he e o e:
'CmHigh'
when
alues
o
Cm
a e
abo e he co ec ones;
M
4
'CmLow'
when
alues
o
Cm
a e
below
he
co ec
ones;
'CsHigh'
when
alues
o
Cs
a e
abo e
he
co ec
ones;
'CsLow'
when
alues
o
Cs
a e
below
he
co ec ones;
'CcHigh'
when
alues
o
Cc a e
abo e
he
co ec
ones
and
'CcLow'
when
alues
o
Cc
a e
below
he co ec ones.
To
desc ibe
he sys em co ec
beha iou ,
i
is
conside ed
ha
alues
o
all
cons an s don'
ha e only
one
co ec
alue, bu a he
hey
can ake
alues inside
an
in e al
ha will
be conside ed
as
c
_
co ec .
This
way,
ope a ion
lexibili y
is
allowed and
sys em eal
beha iou
is
be e
simula ed,
whe e
he e
is
no
a
co ec alue
bu
d
a he co ec ion
ma gins
a e
lexible. This
p oduces
ha sys em
doesn'
ha e
an
only
co ec
beha iou , bu
a he
a
co ec
beha iou s
amily.
I
ep esen s
all
possible combina ions
o
he
Figu e
2.
The
example
sys em
cons an s alues
ha
a e
inside
o
he de ined
ole ance limi .
A
co ec
beha iou s
amily
does
he
diagnosis
mo e
di icul ,
3
CASE
STUDY
because
i
is
necessa y
o
ecognize
di e en
beha iou s
as
co ec ,
bu
on
he con a y
i
p o ides
a
mo e
ealis ic
ision
o
he
sys em.
As
i
has
been
commen ed
p e iously, me hodology
can
be
used
In
ou
model
he
cons an alues conside ed
as
co ec
a e:
wi h
eal
sys em da a
o
wi h
ob ained
da a
o
a
model
simula ion.
In
ou
case, he
me hodology
will
be
applied
o
a
model, which
is Table
I.
Values
o
OK
beha iou s
an
idealized si ua ion,
bu
i
o e s
us
a
clea
idea
o
he
way o
ac .
Cm
[0.98-1.02]
In
case
o
applica ion
on
a eal
sys em, many
di icul aspec s,
no
Cc
[0.98-1.02]
men ioned
he e
(as
moni o ing
o
small
phase
shi ),
need
o
be
aken
in
accoun ,
bu
wi h
he
model
we a e
only
ying
o p esen
he
app oach.
As
example
o
dynamic sys em
o
diagnose
we
conside
he
O he conside ed cha ac e is ics
in
ou
sys em
a e:
con olle
elec ic
mo o
in
[18]
and
[19].
Figu e
2
ep esen s
1.
Faul
is
p esen
om
he
beginning
and
i
doesn'
e ol e
in he
ea ed
sys em. The
mo o
'M',
whose
o a ional
speed
is
'w',
is
ime.
d i en h ough
a
ol age
' '
by
he
con olle
'C'
which
ac s
based
2.
Beha iou
change occu s
ins an ly
and
s a ing
om
he e
i
on
he desi ed
speed
'd'
and
he
speed
'w,,'
measu ed
by
he
doesn
change
again.
e olu ion
coun e
'S'.
Con olle
'C'
is
conside ed
as an
I-
con olle .
3.
Once he
wan ed
angula
speed
has
been indica ed,
i
doesn'
change
un il
his
angula
speed
is
eached.
This
way,
diagnosis
will
be
ca ied
ou
when
he
desi ed angula classi ica ion
ool
o
ob ain
a se
o
decision
ules, and
i
we
ha e
speed (d)
is
changed.
The
way o
diagnose
is
by
checking
he
simila ajec o ies
wi h di e en
labels
hen
classi ie
can'
e olu ion
o
each
he
inal speed.
I
is
necessa y
o
keep
in
mind
co ec ly
wo k;
ha
is
o
say,
hose
simila
ajec o ies
will
be
ha
in
spi e
o
exis ence
o
a
ailu e
in some
componen ,
I-
inco ec ly classi ied. Figu e
7
shows
an
example
o
his.
con olle
is
able
o
ac
on
he
mo o
o
each
he
equi ed
inal
speed.
O
cou se
e olu ion
o
he
sys em
o
each he desi ed
inal
speed will
be
di e en .
This
di e ence
in
he
beha iou
will
allow
20
he
diagnosis.
T
10
/ % • -
VW
INTEG(F2)
W
= INTE G(/
Cm
Wm'•---
--
cs
F2 = Cc*(d-W.g)
F2
/ F =
(•.y-YV/T
Cc
0
6
12 18
24
30
Time
(Second)
Figu e
4.
OK
Beha iou
P2O
Figu e
3.
Fo es e diag am
Fi s
s ep,
he e o e,
is
pe o ming
sys em
simula ions
in
15
di e en
beha iou s
modes.
In
ou
case,
sys em
has
been
modelled
as
a
Fo es e
diag am
[20],
o be
able
o
simula e
using
he
7 -
simula ion ool
VEMSIM&.
Fo es e
diag am
gene a ed
o
he
10 .... -
-j
-.
sys em
is
p esen ed
in
igu e
3.
J
Simula ed
beha iou s
will
be
hose
ha
we
wan
o
diagnose.
/
They
will
be:
OK
o
co ec
beha iou
and
CmHigh,
CmLow,
CsHigh, CsLow, CcHigh,
CcLow
o
each
componen
aul
abo e
men ioned.
0
A
beha iou
amily
will
ep esen
each
one
o
hese
beha iou s.
0 6
12
1i
24
30
Simula ions
alues
a e
shown
in
able
2.
Time
(Second)
Table
2.
Sys em
alues
o
simula ion
Figu e
5.
CmHigh Beha iou
T
3
D
10
20
W
5
Time
S ep
0.1
15
Fo
he co ec
beha iou
he
cons an alues
a e
in o
[0.98-
10
------- --
1.02].
Values
o
simula e
beha iou s
abo e
he
co ec one
a e
in o
-J
[1.02-5].
Values
o
simula e
beha iou s bellow
he co ec one a e
in o
[0-0.98].
5
7 _
Cons an s
alues
o
simula ed
beha iou s ha e been
elec ed
by
andom
wi h
he
Mon e Ca lo me hod ollowing
a
uni o m
0
dis ibu ion.
Numbe
o
simula ions pe
beha iou
will
be
100.
0 6
12 18
24
30
Label
co esponding
o
beha iou
is
placed
o each
one
o
he
Time
(Second)
ajec o ies.
This
way,
a
da abase
con aining
700
labelled
ajec o ies
is
ob ained.
Figu e
6.
CcLow
Beha iou
T ajec o ies
a e
composed
wi h
alues
o
he a iable
'w,,' in
each ime
s ep.
Reason
o
selec
a iable
'w,,'
and
no
'w'
is
ha
'w,,,'
is
he only
obse able a iable
in
he
eal
sys em.
To
sol e his
p oblem
a
new label
will
be
assigned
o
e y
In
igu es
4,
5
and
6
di e en
sys em
beha iou s
a e
shown,
simila ajec o ies.
A
mix u e
o
labels
o
all
simila
ajec o ies
Ob ained da abase
has
simila ajec o ies
belong
o
di e en
will
compose
he
new label. This
way, nex
s ep
is
o ind
all
beha iou s.
This way
se e al
e y
simila ajec o ies
ha e
simila ajec o ies in o
he da abase
and
assigning
a
new
label.
di e en
labels.
This
is a
p oblem,
because
ou
inal goal
is
o
use
a
I
is
necessa y
o
de ine when
wo
o
mo e
ajec o ies
a e
.Max
speed
ime
(MST).
I
is
he
momen
in
which he
highes
simila .
Two
ajec o ies
a e
conside ed simila
when
dis ance
e olu ion
speed
is
eached.
be ween
hem
is
smalle
han
a
magni ude. Dis ance
be ween This
way
a
new
da abase con aining ajec o ies plus
new
ajec o ies
is
measu ed
as
Euclidean Dis ance
and
magni ude a ibu es
is
gene a ed.
chosen
is
10%
o
he
Euclidean dis ance
be ween
he
wo
u he
Da a
in
new da abase
ha e
he
ollowing
o m:
away
ajec o ies
o
he co ec
beha iou .
This
magni ude
in
ou
RT,
SS,
MS,
MST,
Win[1],
DP[ 1,
111],
.......
Win[n],
DP[n],
I[n],
example
is
0.45.
LABEL
Final
s ep
is
pe o ming supe ised lea ning wi h
he ob ained
da abase. Classi ica ion ool
selec ed
o
pe o m
he
supe ised
20
lea ning
is
C4.5
[21].
Wha
is
go en wi h
his ool
is
o
cha ac e ize
each one
o
he
beha iou
amilies
acco ding
o
he
15-- alues
o
he
a ibu es
ha ha e been
p o ided.
Resul
is
a
decision
ee
and
an
equi alen
se
o
decision
ules. These ules
/
will
be
he
way o
do
he
diagnosis.
In
ou example
classi ie
10
------ -
--
ob ains
27
ules
wi h
an
e o
a e
o
1.2%.
This
mean ha
1.2%
o
ýT
" ajec o ies
a e
no
co ec ly
classi ied wi h hose ules.
3.1
Diagnosis
0 The
way o
do
he
diagnosis
is
e alua e he obse ed da a
wi h
he
0 6
12
18
24
0
ob ained
ules.
Because
in
ules appea
a ibu es ha ha e been calcula ed
and
Time
(Second)
no appea
in
obse ed da a,
same
a ibu es
should
be
calcula ed
o
obse ed
da a
in
o de
o
be
able
o
classi y
wi h hose ules.
Figu e
7.
Beha iou
CcHigh
s
CmHigh
This
way in
he momen
ha
one
obse ed
da a
is
ga he ed
all
possible
a ibu es
should
be
calcula ed.
A e
ha , decision
ules
A e
his p ocess
we
ob ain
a
new
da abase
wi h all
simila
a e
e alua ed
wi h
wo
possible
esul s:
a
label
is
e u ned
o
ajec o ies e-labelled
as
co esponding
wi h
all
beha iou s
o
he
in o ma ion
is
insu icien
o
e alua e
all
ules.
In
he
i s
case
he
simila ajec o ies. e u ned
label
is
he esul
o
he
diagnosis.
In
he second one
we
Nex
s ep
is
o
calcula e
new
a ibu es
o
each
ajec o y wi h
need
o wai
mo e
in o ma ion
in
u he momen s.
he
goal
ha
classi ie
has
mo e
in o ma ion
o
gene a e
decision
I
we
wan
o
diagnose
he
sys em wi h
ano he unning
ules. These
new
a ibu es
mus
be ep esen a i e
o
each
condi ions,
we
should
ha e
p epa ed
he
decision
ules
se o
hose
ajec o y.
speci ic
condi ions.
I.
e.
i
we
wan
o
diagnose
his
sys em
when
Fo
each
ajec o y
poin
nex
a ibu es
ha e been
calcula ed:
cu en o a ional
speed
is
12
ad/sec and
desi ed
o a ional
speed
"
Dis ance
o
pe ec
beha iou .
I
indica es how
a
away
is is
7
ad/sec,
we
should
ha e
gene a ed
a
se
o
decision
ules
o
cu en ajec o y
om
pe ec
beha iou
(abo e de ined).
I
hose
condi ions
and
we
will
use
hem
in he
diagnosis
momen .
is
calcula ed
as:
DP(i)
=
Wm[i]-
Wmp [i]
(4)
4
RESULTS
ON
THE
EXAMPLE
SYSTEM
To
e alua e he
p oposed me hodology
a
se
o
es s
ha e
been
Whe e
Wm[i]
is
he
ea ed
poin
in
he
cu en
ajec o y
and
done.
Wmpj[i]
is
he
co esponden
poin
in
he pe ec
beha iou .
Obse a ional
da a
ha e
been
ob ained
by simula ing
he
sys em
"
In eg al.
I
is
he
magni ude e u ned by nume ical
in eg a ion
wi h
speci ic
condi ions
o
he
es .
This
way
a
es
ajec o y
is
be ween cu en
poin
and he
p eceden
one.
I
ep esen s
he
ob ained
and he
diagnosis
co ec
esul
is
known, because
i
mus
closed
a ea be ween hem.
I
is
calcula ed
by app oxima ing be
he
co esponding
o
he simula ed
condi ions.
as
ollow:
Condi ions
o
he
es
a e
he same
abo e
men ioned.
We
emembe
hem
in
able
3:
p[ijj-
pi~i-1](5
l(i)
=
T's
x
_____ 5
2
Table
3.
Tes s condi ions
T
3
Whe e
Ts
is
he
ime
s ep
in he
simula ion,
p[i]
is
he cu en
D
10
ea ed
poin
and
p[i-1]
he
p eceden
one.
W
ini ial
5
In
addi ion
nex
a ibu es
will
be calcula ed
o
each ajec o y:
Time
S ep
0.1
"*
Rise
Time
(RT).
I
is
he
momen
in
which desi ed
e olu ion
Values o
OK
[0.98
-
1.02]
speed
is
eached
o i s
ime.
Values o
HIGH
[1.02
-5]
"*
S eady
s a e
(SS).
I
is
he
momen
in
which desi ed
Values o
LOW
[0
-
0.98]
e olu ion
speed
is
eached de ini i ely.
"• Max speed (MS).
I
is
he
alue
o
he
highes e olu ion
In
able
4
we
can
see
esul s
o
he es s:
eached speed.

Table
4.
Tes s
esul s
imes,
me hodology
e u ns
an
inco ec diagnosis,
bu
in
gene al
VALUE
OF
THE
DIAGNOSIS
DIAGNOSIS
o e ed
esul s
a e
accep able.
CORRECT
WITH
SIMPLE
WITH
This occu s
because
he e
a e
e y
simila
ajec o ies
belonging
Cm
Cc
Cs
DIAG
S
LABELLED
LEL
o
di e en
beha iou s,
and
classi ie canno co ec ly
selec
he
LABELLED
ules
o
di e ence
hem.
1 1
1.03
CS
HIGH
CS
HIGH
CS
HIGH
To
sol e
his
p oblem
he new
me hodology
p oposes
he
e-
1 1
1.07
CS
HIGH
CS
HIGH
CS
HIGH
labelled
o
all
simila ajec o ies
as
ha e been
abo e
men ioned.
I 1
1.1
CS
HIGH
CS
HIGH
CS
HIGH
Ob ained esul s
show
ha
he
new
me hodology
o e s
a
mul iple
I 1
1.5
CS
HIGH
CS
HIGH
CS
HIGH
diagnosis
when
he
p e ious
one
can'
ind
he co ec aul .
I 1 3
CS
HIGH
CS
HIGH
CS
HIGH
Among
he
mul iple
o e ed
diagnoses,
nea
o
all
es s e u n
he
1
1.03
1
CCGH
CS
OK
OK
co ec
one.
CC HIGH
C
I
is
impo an
o
highligh
ha ,
in
es s
whe e
beha iou
is
a
1
1.07
1
CC
HIGH CM
HIGH CM
HIGH
o
he co ec one,
o e ed diagnosis
is
he co ec one.
CC
HIGH
In
he
se
o
p esen ed
es s he
diagnosis
is
co ec
in 58.33
%
CM HIGH
o
he
cases. Co ec
diagnosis
is
o e ed, among
o he s,
in
30.55
%
1
1.5
1
CC
HIGH
CC
HIGH
CC
HIGH
o
he cases.
An
inco ec diagnosis
is
o e ed
in 2.7
%
o
he
cases.
1 2 1
CC
HIGH
CC
HIGH
CC
HIGH
The
aul
is
no de ec ed
in
8.33
%
o
he
cases.
O he wise,
ne e
1 3 1
CC
HIGH
CC
HIGH
CC
HIGH
de ec ailu e when ailu e
doesn'
exis .
1.03
1 1
CM HIGH
OK
OKCI
CS
LOW
1.07
1 1
CM HIGH
CM
HIGH
CC
HIGH
5
CONCLUSIONS
AND
FURTHER
CM
HIGH
CC
HIGHI
O
K
1.1
1 1
CM
HIGH
CM HIGH
CCHGWO K
CM HIGH
P esen ed
me hodology
is
able
o
pe o m diagnosis
o
dynamic
1.5
1 1
CM HIGH CM
HIGH
CM HIGH
2 1 1
CM HIGH CM
HIGH
CM HIGH
sys ems and
i
is
independen
o
he sys em
ype.
In
ac ,
one
o
3_
1 1
CM
HIGH CM
HIGH
CM HIGH
u he wo ks
is
o
apply his me hodology
o
a
non-linea
dynamic
3 1 1
CM
HIGH
CM HIGH CM
HIGHsy m
1 1
.97
S
LO
OKCS
LOW
j
sys em.
1 1
0.97
CS
LOW OK
OK
This capaci y
is
due
o
he
ac
ha
he
me hodology
is
only
1 1
0.93 CS
LOW
CS LOW CS
LOW
cen ed
in
he
e olu ion cha ac e is ics
o
he
sys em
o
he
co ec
1 1
0.89
CS
LOW
CS LOW CS
LOW
beha iou
o
aul y
beha iou s.
1 1
0.85 CS
LOW
CS LOW CS
LOW
Ano he
cha ac e is ic
o
he
me hodology
is
ha
he
diagnosis
1 1
0.5 CS
LOW
CS LOW CS
LOW
can be
pe o med
in
a
e y
simple way,
and
a
e y li le
1 1
0.1
CS
LOW
CS LOW CS
LOW
compu a ional
ime
is
equi ed.
1
0.97
1
CC LOW
OK
OK
Ce ain
sys ems,
as
he
p esen ed
in
he example, can
p oduce
1
0.93
1
CC
LOW
CC
LOW CC
LOW
j
simila
beha iou s
o
di e en
aul
easons. This
is
due
o
CM
LOW
ela ionship among a iables
ha
go e n he
sys em
beha iou .
1
0.89
1
CC
LOW
CC
LOW
CC
LOW
j
This
ela ionship,
among
sys em
a iables,
can
p oduce
ha
an
1 0.89 1 CCLM
CCLW
I_
CM
LOW
al e a ion
o
a
a iable would be compensa ed by
he
al e a ion
o
1
0.85
1
CC LOW
CC LOW
CC
LOW
ano he
a iable
in
con a y
sense.
To
sol e
his
p oblem,
____
CM
LOW
1
0.5
1
CC LOW
CC LOW
CC
LOW
me hodology
assigns
mul iple
aul
easons
o
sys em
beha iou s
1
0.1
1
CC LOW
CC LOW
CC
LOW
ha
could
be
p oduced
by di e en
aul easons. This
way
a
0.97
1 1
CM
LOW OK
OK
mul iple diagnosis
is
o e ed
in
hose
si ua ions.
0.93
1 1
CMLOW
CCLow
CC
LOW
j
Ano he
u he
wo k
is
o
be
able
o
diagnose
dynamic sys em
CM
LOW
when
mul iple
aul
occu s
a he
same
ime,
is
o
say,
iden i ying
CM
LOW
CM
LOW
CC
LOW
j
sys em
beha iou s
when mo e han
one
componen
is
aul y.
0.89
1 CMC
LOLOWLO
CM
LOW
CC
LOW
0.85
1 1
CM
LOW
CM
LOW
CM
LOW
CM
LOW
ACKNOWLEDGMENTS
0.5
1 1
CM
LOW
CM
LOW
CM LOW
0.1
1 1
CM
LOW
CM
LOW
CM
LOW
This wo k has
been
pa iali y
inanced
by
he
Comisi6n
0.99
0.98
1.02
OK
OK
OK
In e minis e ial
de
Ciencia
y
Tecnologia (DP12000-0666-C02-02)
1
1.02 1.02
OK
OK
OK
and
he
Modelizaci6n
Ma emdi ica
Redes
y
Mul imedia
0.98
1
0.98
OK
OK
OK
in es iga ion
g oup
o
he
Uni e si y
o
Huel a.
0.98
1.02 1.02
OK
OK
OK
0.99
1.01
1.01
OK
OK
OK
1.01
1
0.99
OK
OK
OK
REFERENCES
We can
see
ha
diagnosis me hodology
wi h simple
labelled
doen' o aco ec
digno icin
es
a
e
e yea o
he
[1]
C. J.
Alonso,
J.
A.
Maes o,
J. B.
Pulido
y
C.
Llamas.
doesn'
o e
a
co ec diagnos ic
in
es s
ha
a e
e y
nea
o
he
Moni o izaci6n
de
Sis einas
Dinmicos:
hacia
una
Ca ac e izaci6n
co ec
beha iou .
In
hose
cases
he aul
is
no
de ec ed.
O he
en
el Ni el
de
Conocimien o.
In
p oceedings
o
he
I
Jomadas
de
T abajo
sob e
Diagnosis.
Valladolid
2001.
[2]
W.
Hamsche .
Diagnosis
de ices
wi h
hie a chic
s uc u e
and
known
componen
jailu e
models.
In
p oceedings
o
he 6 h
Con e ence
on
Al
Applica ions..
1990
[3]
Dague,
P
y o os.
When
Oscilla o s
s op
oscilla ing.
In
p oceedings
o
IJCAI-91
[4]
J.
De
Klee
y
B.
Williams.
Diagnosing
mul iple
aul s.
A i icial
In elligence
32,
97-130,
1987
[5]
K.
Bousson,
y
L.
T a e-Massuyes
A
compu a ional
causal model
o
p ocess
supe ision. Technical Repo 92147, LAAS-CNRS,
Toulouse,
F ance.
1992
[6]
P.
Mos e man
llyb id
dynamic
sys ems:
a
hyb id
bond
g aph
modeling
pa adigm
and
i s
applica ions
in
diagnosis.
Tesis Doc o al
Vande bil
Uni e si y,
Nash ille,
Tennessee, USA.
1997.
[7]
P.
S uss. Fundamen als
o
model-based diagnosis
o
dynamic
sys ems.
P oc.
IJCAI'97.
1997.
[8]
B.
Pulido,
C.
Alonso
y
F.
Acebes.
Consis ency-based
Diagnosis
o
Dynamics
Sys ems
using
quan i a i e
models
and
o -line
dependency- eco ding.
In
p oceedings
o
DX-01.2001
[9]
A.D.
Pouliezos
y
G.S.
S a akakis.
Real
ime
aul
moni o ing
o
indus ial p ocess. Mic op ocesso -based
sys ems
enginee ing.
Kluwe
Academic Publishe s, Do d ech ,
1994.
[10]
V.
Venka usub amanian
and
K.
Chan.
A
neu al
ne wo k
me hodology
jb
p ocess
jaul
diagnosis.
Jou nal
o
A i icial
In elligence
in
Chemical
Enginee ing,
35:1993-2001.
1995
[11]
S.
Leonha
y
M.
Ayoubi.
Me hods
o iaul
diagnosis.
Con ol
Enginee ing
P ac ice,
5.
1997.
[12]
A.
Sim6n,
L.
Alonso
y
A.
An 6n.
Sis ema
hib ido
bo oso
pa a
ayuda
del
diagnds ico
del glaucoma.
In
p oceedings
o
he
I
Jo nadas
de
T abajo
sob e
Diagnosis.
Valladolid
2001.
[13]
S.
Saludes,
A.
Va gas
y
J.
R.
Pe in.
Aplicacidn
de
la
ed
neu onal
SOM
pa a
la
de eccidn
de
iallos
desconocidos
en
un
g po
hid oeldc ico.
In
p oceedings
o
he
I
Jomadas
de
T abajo
sob e
Diagnosis. Valladolid
2001.
[14]
J.
Ross
Quinlan.
Induc ion
o
decision
ees.
Machine lea ning,
1986
[15]
Juan J.
Rod iguez,
Ca los
J.
Alonso
y
Q.
Isaac
Mo o.
Clasi icaci6n
de
pa ones
empo ales
en
sis emas
dinimicos
median e Boos ing
y
Alineamien o
dinamico empo al.
In
p oceedings
o
he
I
Jomadas
de
T abajo
sob e
Diagnosis. Valladolid
2001.
[16]
Ped o
J.
Abad
y
An onio
J.
Sua ez.
Diagnosis
de
Sis emas
Dindmicos Basada
en
Ap endizaje Supe isado
Q -line.
In
p oceedings
o
he
I
Jomadas
de
T abajo
sob e
Diagnosis.
Valladolid
2001.
[17]
An onio
J.
Sua ez y Ped o
J.
Abad.
Aplicaci6n
de
Thcnicas
de
Ap endizqje
a
la
diagnosis
de
Sis emas
Dinumicos
con
E ique ado
M l iple.
In
p oceedings
o
he
IX
CAEPIA
-TTIA.
2001.
[18]
A.
Pana i
and
D.
T.
D up6
S a ed based
s
simula ion-based
diagnosis
o
dynamic
sys em.
ECA12000. !4Th
Eu opean Con e ence
on
A i icial
In elligen .
2000.
[19]
A.
Malik
and
P.
S uss.
Diagnosis o
Dynamic
Sys ems
does
no
necessa ily
equi e
simula ion.
Wo kshop No es
o
he Se en h
In e na ional Wo kshop
on
P inciples
o
Diagnosis
DX-96 Mon eal.
1996.
[20]
J.
W.
Fo es e
P inciples
o
sys ems.
W igh -Allen
P ess
1968.
[21]
J.
Ross
Quinlan.
C45:P og am
o
Machine
Lea ning.
Mo gan
Kau man,
1993.