-
8/10/2019 Comparison of Two Adaptive Identification Hemods for Iio)(Itoriffi and Diagnosis of An
1/3
m 4
CWARISON OF TWO ADAPTIVE DENTIFICATION
HEMO S
FOR IIO)(ITORIffi ND D I A G N O S I S OF
N
EXPERIMENTALNUCLEAR REACTOR
6. Zwingelstein
C m is s a r ia t Ene rg ie Atomique
C.E.N. S A C L A Y
Serv ice Des App l i ca t i on s Ind us t r i e l l es
BP N o 2 91190 6 i f Sur Yvet te
France
Abstract
This paper deals
wh
t h e c m p a r i s o n o f two
adaptive methods based upon se ns i t iv i ty eq ua tio ns
fo r use i n the surv e i l lanc e and d iagnosis o f an
experimentalnuclear eactor.
The sur vei l lan ce and diagn osis are obtained
by a real- t ime comparison o f referenceparameters
and the act ua l parametersgivenby headaptive
a lgo r i t tm .
descent nethod Resu l tsob ta inedwi th h i sa lgo -
rithm
usingexperimentaldata from a reactor are
g iven us ing two d i f f e r e n t c r i t e r i a .
The f i r s t a l g o r i t h u ses an o n - li ne , s te e pe s t
The second algor i Ura uses both s e n s i t i v i t y
equations and a re cu rs iv e eas t squares method.
An example i s given using heexperimental model
o f h e same reac to r .B o tha lgo r i thmdescr ibed
i n t h i s paper are ea si l y implementab le on a
mini
computer and ar e no t se ns i t i ve o a pr io r i know-
le dg e o f t h e . s t a t i s t i c a 1 p r o p e r t i e s o f t h e n oi se .
These a lgo r i t hm a re a l so su i ta b le o r he su r -
ve i l la nc e o f non l in ear processes.
1 . In t roduc t i on
The m onitor ing and diagn osis of a nucl ear
power p lan t a re ve ry mpo r tan t too l s to use i
a c h i e v i n g n c r e a s e d r e l i a b i l i t y .
adap ta t i ve den t i f i ca t i on a lgo r i thm may he lp the
nuc lea r p lan t ope ra to rs o de tec t and iden t i f y a
m a lf u nc t io n i n t h e e a c to r . The p r i n c i p l e o f
t h i smo nit or i ng system i s shown
i n
Fig. 1. A
math ematic al, model where parameters have phy sic al
meanings i s implementedon a min i computer and i s
fed by the same i npu ts as the nuc lea r p lan t .
The adapt ive a l go r i thmo d i f i es he param-
eters i n order o min imize he nstantaneous errOP
o f a un c t i on a l o f he e r ro r be tween the reac to r
and model outputs.
I f
a malfunction o cc ur s i n t h e p l a n t , t h e
su rve i l l ance i s ach ieved by check ing he e r ro r
value. The diagnos is i s provided by theadap t i ve
algor i thm which wi detenninewhichparameter has
s h i f t e d from i t s nominal va lue.
Th is work i s an a t tempt t o demonstrate how an
P .
Blanc
C m i s s a r i a t E ne rg ie A t mi qu e
C.E.N. S A C L A Y
Servi ce Des App l i ca t i o ns nd us t r i e l l es
BP
NO2 91190
Gif
Sur Yvette
France
Since measurements i n nuc lea r p lan ts a re
a lways no isy, a l l t h e parametersobtained by the
adapt ivea lgor i thmsarea lsono isy.For hese
reasons, i t s necessary t o use decis ion h eory
i n o r de r t o g i v e h e a p p r o p ri a t e m a l f u n c t io n
a1 anns.
averyaccuratephysical Rodel, an acc ura te refe r-
ence parameter s e t and ada pt i ve a lg or i thm which
are ndependent o f a p r io r i knowledge and imple-
rnentableon a mini cosputer.
This paper compares two adaptivea lgor i thms
f o r use i n moni tor ing an exper imenta lnuclear
reactor core .
To
be
re l i ab l e , h i s mo n i to r i ng sys tem needs
2 . D e s c r i p t i o no f the NuclearReactor Core
Fig.2shorn heblockd iag ram o f he nuc lea r
core and ind ica tes he ran sfe r un ct i on between
r e a c t i v i t y n s e r t e d by th e c o n t r o l r o d a nd t h e
power level .
eauations
The open loop i s g iven by th e k in et ic s
dCi Bi
= P
-
aici
where P i s
parer
l e v e l
p k i n e t i c s e a c t i v i t y :kmmn
constants
, B i ,B,P a r e
C, i t h d el ay edneutron
' group
The feedback loo p ncl uck s he feedback re a c ti v i t y
e f fec ts due to he power l eve l and the n le t
cool ant temperature.
These two feedback e f fec ts are npor ta nt s ince
they de tenn ine the nuc lea r p lan t s tab i l i t y and th e i r
magni tudes are d i r ec t ly e la t ed o ph ys ica l param-
e te r s o f t h e c or e.
For hese reasons, ada ptiv e algo rith ms were
tes ted i n o rde r to moni o r these feedback e f f ec t s .
The mathematical models were developed and
experim ents consis t ing o f s tep responses where
achieved a t he p l an t . The opt imizat ion echn iques
were used on the plan t data o obta in he ol low -
ing models:
436
-
8/10/2019 Comparison of Two Adaptive Identification Hemods for Iio)(Itoriffi and Diagnosis of An
2/3
*
Power Feedback Effect
akP( t ) = a k d t ) + akp2( t )
6kp1(t)= a1 P ( t )
6kp2( t ) + a26kp2(t) = a3 P ( t ) (neasured)
*Temperature Feedback E ff e c t
akT( t )
=
akTl(t)
+
skT2( t )
6kTO( t )
+
a5 bkT2(t)
=
a6T( t )ature (measured)
P ( t )
Power
Level
a k T l ( t ) = a 4 T ( t ) T ( t )n l e t t e n p e r -
3. A l go r i th m and Resul ts
The fol lowin g algo r i thm s are based upon sensi-
t i v i t y e qu at io ns . I n o r d e r t o de mo ns tr at e t h e
d e te n ni na ti on o f s e n s i t i v i t y c o e f f i c i e n t s , e t us
cons ider a first o r d e r d i f f e r e n t i a l e q u a t i o n
S+alS
=
a2e wi thS ( o u t p u t ) ,e n p u t
he
p a r t i a l d e r i v a t i v e s
aal
=
- as
sal' *a2
-
a re c a l l e d t h e p ar am et er s e n s i t i v i t i e s o f t h e
f i r s t o r d e r and i f we assune t h a t a t
t=Op O)=S O)
= 0,
t he approx imate sens i t i v i t y equa t i ons
[l]
re
given by
i lalaal = - S 'Jal(0) = 0
aa2 + azoa2 e
with
ua2(0)
= 0
F i
s t A 1 g o r i hm
d ' t b e i n s t a n t a T u s squared e r r o r C l ( t ) = d ( t ) =
IS
t) - S,,, t)] between the
neasured
process out-
puand th e nodeloutput.Let A r ep resen t he
parameter ve ct or AT=[a1 .
a 6 ( T
denotes
t r anspos i t i on ) .
The f i r s t a l go r i t t n n tends t o m in im ize f o r each
The gradient
9
s g i ven by
m
i
-1
a6
Thisvector , &; i s o b ta in e d by i n t e g r a t i o n o f h e
sen s i t i v i ty eq uat ion s assuming tha t between two
sampling ins tan ts he parametervalues are cons tant.
The adap t ive a lgor i thm
w s
t h e o l l o w i n g
4kH) L ( k ) + ATK (AT sampl ingime)
( K p o s i t i v eo n s t a n t ) .
Fig. 3ashows the ad ap t ion of one parameter f o r a
s im u la t ed 10% chang e i n a l l o f t h e p ar am ete r i n
the model obtained by fitti t h e e s tdata (K=1
was u s e d i n h i s c a l c u l a t i o y . n o r d e r o
damp os c i l l a t i o ns n he adap t i on , he o l low ing
c r i t e r i o n was chosen:
Second A1 g o r i
tho
be
th
process
ou tpu t , h ( A . t ) be
t h e
m
utput.
I f
ALA,
then
SP(A,t):S&t) + ( -a cT[A,t]
To desc r ibe he second algor i thm, l e t Sp(A,t)
The vector
(4-3
s ob ta ined by so l v i ng an
Us ing the r ecur s l ye eas t square a l go r i t hm
overdetermined l inear system.
t h e s ti m a te o f
A-AJ
when (k) measurements
a r e a v ai la b le i s given by
Thea1
r i t h
s
no
s e n s i t i v e
t o
t h e n i t i a l v a lu e
o f P ( 0 Y a n d h i s a l g o r i t h m s s t i l l e f f i c i e n t even
F ig.4 epresen ts he same parameter, but
wh
a
change o f -20 on a l l t h e parameters and us ing
simulated nputs.
It seems
th at he response of
t h i s a l g o r i t h m i s f a s t e r t h a n t h e p r e v i o u s one.
p r o p e r t i e s i s a v a i la b l e,
i t
s p o s s i b l e o i n d
t h e s t a t i s t i c a l p r o p e r t i e s o f h e e s t i m a t e s n
order t o improve the dec i s i on r u l e .
Concl us
i
ns
equa t i onsareuse fu l oo l s o r he surve i l l ance
and the d iagnos is o f nuc lear p lants .
l edge o f no i s e p ro per t i es and a re no t sens i t i ve
t o a choice o f parameters.
f o r r e a l t i m e a n a l y s is . o n a d n i c oa pu te r w i t h
small m r y 4-8k words).
=k0.5A and never d iverged dur ing severa l tes ts .
Moreover, i f a p r i o r i kn ow le dge o f n o i s e
These two a l g o r l t h r r b a s e d upon s e n s i t i v i t y
N e i t h e r a l g o r i t h m
requi res
a pr ior i know-
M oreover, t he se a t g o r i m a re s pl et ne n ta b le
5. References
1.Eykhoff, System Id e n t i f i ca t i o n , Wi ley, 1974.
2. P. C. Young. "ADDlYinq Parameter Es tim at ion
t o Dynami i-Sys tem,"ControlEngineer ing,
Novenber 1969.
- -
Fig. 3bshows the ad ap tion o f t h e same parameter
us ing he C c r i t e r i o n . Then a lgo r it hmsare ens i -
t i v e t o K c2oice and even diverge i f the gain, K,
i s to ohigh.
-
8/10/2019 Comparison of Two Adaptive Identification Hemods for Iio)(Itoriffi and Diagnosis of An
3/3
-
inputs
PROCESS
I&
1
I
MODEL
I
ADAPTIVE
I
--
ALWRITHM r
f ig
1
P
1
80 00 160 00 zGo.oo s)
f ig
4
fig
2
