comparison of two adaptive identification hemods for iio)(itoriffi and diagnosis of an

8/10/2019 Comparison of Two Adaptive Identification Hemods for Iio)(Itoriffi and Diagnosis of An

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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


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*

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.


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

comparison of two adaptive identification hemods for iio)(itoriffi and diagnosis of an

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