process fault detection based on modeling and estimation

8/13/2019 Process Fault Detection Based on Modeling and Estimation

1/18

4utomatica Vo[ . 20 . No . 4 . pp . 3~7-4 M . 1984 0005 1098 ~;4S 3 . 0 0 ~ 0 . 0 0P r i n t e d i n G r e a t B r i t a i n . P e r g a m o n P r e s s L t d .1 9 84 I n t e r n a t i o n a l F e d e r a t i o n o f A u t o m a t i c C o n t r o }

Survey aperProcess Faul t Detect ion Based on Model ing and Est imat ionMethods Survey

ROLF ISERM NNt

A rev iew on de tec t ion an d d iagnos i s i l lus t ra te tha t proces s fau l t s can be de tec ted w henbased on the e s t imat ion o f unmea surable proces s parameter s and s ta t e var iab lesK e y W a r d s - - F a u l t d e t e c t i o n ; s u p e r v i s i o n ; r e l ia b i l it y ; s a f et y ; p r o ce s s m o d e l s ; p a r a m e t e r e s t i m a t i o n : s t a t ee s t im a t ion: d . c . m otor ; c e nt r i fuga l pum p; l e a k de te c t ion; p ipe l ine .

A b s t r a c t - - T h e s u p e r v i s i o n o f t e c h n i c a l p r o ce s s es i s t h e s u b j e c t o fi n c r e a s e d d e v e l o p m e n t b e c a u s e o f t h e i n c r e a s i n g d e m a n d s o nre l i a b i l i ty a nd sa fe ty . The use of proc e s s c om pute r s a ndm i c r o c o m p u t e r s p e r m i t s t h e a p p l i c a t i o n o f m e t h o d s w h i c h r es u l tin a n e a r l i e r de te c t ion of proc e s s f a u l t s tha n i s pos s ib le byc o n v e n t i o n a l l i m i t a n d t r e n d c h e c k s . W i t h t h e a i d o f p r o c e s sm o d e l s , e s t im a t i o n a n d d e c i si o n m e t h o d s i t i s p o s s i b l e to a l som o n i t o r n o n m e a s u r a b l e v a r i a b l e s l i k e p r o c e s s s t a t e s , p r o c e s sp a r a m e t e r s a n d c h a r a c t e r i s t i c q u a n t i t i e s . T h i s c o n t r i b u t i o np r e s e n ts a b r i e f s u m m a r y o f s o m e b a s i c f a u l t d e t ec t i o n m e t h o d s .T h i s i s f o ll o w e d b y a d e s c r i p t i o n o f s u i t a b l e p a r a m e t e r e s t i m a t io nm e t h o d s f o r c o n t i n u o u s - t i m e m o d e l s . T h e n t w o e x a m p l e s a r ec ons ide re d , the f a u l t de te c t ion of a n e le c t r ic a l dr ive n c e nt r i fuga lp u m p b y p a r a m e t e r m o n i t o r i n g a n d t h e l e a k d e t e c t i o n f o rp ipe l ine s t~ y a spe c ia l c or re la t io n m e thod .1. Introduct ionBECAUSE of the inc re a s ing de m a n ds on r e l i a b i l i ty a n d sa fe ty oft e c h n i ca l p l a n t s a n d t h e i r e l e m e n t s m e t h o d s f o r i m p r o v i n g t h es u p e r v i s i o n a n d m o n i t o r i n g a s p a r t o f t h e o v e r a l l c o n t r o l o fproc e s se s a re ge t t ing a n inc re a s ing in te re s t . Thi s hold s a s we ll fora d v a n c e d p r o c e s s e s w i t h h i g h e s t d e m a n d s o n r e l i a b i l i t y a n dsa fe ty , e . g . a e rona ut ic s a nd nuc le a r powe r s t a t ions , a s for m a nyothe r l a rge a nd a l so sm a l l proc e s se s . An e s se nt i a l p re re qui s i t e fort h e f u r t h e r d e v e l o p m e n t o f a u t o m a t i c s u p e r v i s i o n i s a n ear l yprocess faul t detect ion. W h e r e a s p r e v i o u s l y m e t h o d s o f f a u l td e t e c t i o n i n t e c h n i c a l p r o c e ss e s o n l y p e r m i t t e d r e c o g n i t i o n w h e nl i m i t v al u e s o f m e a s u r a b l e o u t p u t s i g n a ls h a d a l r e a d yt r a n s g r es s e d , a n a t t e m p t i s n o w m a d e t o d e t e c t t h e f a u l ts e a r li e ra n d t o l o c a t e t h e m b e t t e r b y t h e u s e o f t h e m e a s u r a b l e s i g n a ls .This i s pos s ib le for a r a n ge of proc e s s f a u l t s by the a pp l ic a t ion ofmathematical process models a n d s ignal models us ing proc e s sc o m p u t e r s a n d m i c r o c o m p u t e r s . M e t h o d s c a n b e u s e d f o rpredicting signals a n d f o r es t imat ing nonmeasurable process s tatevariables, process parameters a n d o t h e r q u a n t i t i e s c h a ra c t e r i st i ct o t h e p r o c e ss . P r o c e s s m o n i t o r i n g b y u s e o f t h e s e a n d d e c i si o nm e t h o d s s e e m s t o d e v e l o p t o a n e w a r e a w i t h i n a u t o m a t i cc ont ro l .I n t h e n e x t s e c t i o n t h e e l e m e n t a r y f u n c t i o n s o f p r o c e s ss u p e r v i s i o n a r e c o n s i d e r e d . T h e n f a u l t d e t e c t i o n m e t h o d s b ym o n i t o r i n g m e a s u r a b l e s i g n a l s a n d n o n m e a s u r a b l e q u a n t i t i e s ,

* Re c e ive d 28 Ma rc h 1983; r ev i se d 3 Augus t 1983. The or ig ina lv e r s io n o f t h i s p a p e r w a s p r e s e n t e d a t t h e 6 t h I F A C S y m p o s i u m o nI d e n t i f ic a t i o n a n d S y s t em P a r a m e t e r E s t i m a t i o n w h i c h w a s h e ldi n W a s h i n g t o n , D . C ., U . S.A . d u r i n g J u n e 1 9 82 . T h e p u b l i s h e dp r o c e e d i n g s o f th i s I F A C m e e t i n g m a y b e o r d e r e d f r o m P e r g a m o nP r e s s L t d , H e a d i n g t o n H i l l H a l l , O x f o r d O X 3 0 B W , U . K . T h i sp a p e r w a s r e c o m m e n d e d f o r p u b l i c a t i o n i n r e v i s e d f o r m b ya s s o c i a t e e d i t o r A . v a n C a u w e n b e r g h e u n d e r t h e d i r e c t i o n o fe di tor H . A . Spa ng, l I I .t I n s t i t u t f u e r R e g e l u n g s t e c h n ik , U n i v e r s i t y o f D a r m s t a d t ,S c h l o s s g r a b e n 1 , 6 1 0 0 D , F e d e r a l R e p u b l i c o f G e r m a n y .

suc h a s s t a te va r ia b le s , p roc e s s pa ra m e te r s a n d o th e r s , a r e br ie flyre vie we d. Be c a use pa ra m e te r e s t im a t ion m e thods forc o n t i n u o u s - t i m e m o d e l s a r e r e q u i r e d , s o m e b a s i c m e t h o d s a r edi sc usse d . The m e thods a nd a ppl ic a t ions for f a u l t de te c t ion a rethe n de sc r ibe d for a d . c . d r ive n c e nt r i fuga l pum p a nd forpipel ines .2. E leme ntary func t ions o f process supervisionA Jaul t i s t o b e u n d e r s t o o d a s a n o n p e r m i t t e d d e v i a t i o n o f ac ha ra c te r i s t i c prope r ty whic h l e a ds to the ina bi l i ty to fu l f i l thei n t e n d e d p u r p o s e .F i g u r e 1 s h o w s a b l o c k d i a g r a m f o r process supervision. I f aproc e s s f a u l t a ppe a r s i t ha s to be de te c te d a s e a r ly a s poss ib le .T h i s c a n b e d o n e b y c h e c k i n g i f p a r t i c u l a r m e a s u r a b l e o ru n m e a s u r a b l e e s t i m a t e d v a r i a b l e s a re w i t h i n a c e r t ai n t o l e r a n c eof the norm a l va lue . I f th i s c he c k i s no t pa s se d , th i s l e a ds to a f a u l tm e ssa ge . The func t ions up to th i s poin t a re usua l ly c a l l e dmonitor ing or , a s ind ic a te d in the f i r s t b loc k of F ig . 1 , a s f a u hdetection. I f ne c e s sa ry , th i s i s fo l lowe d by a fau l t diagnos is : th ef a u l t is loc a te d a nd the c a use of i t i s e s ta b l i she d . Th e ne xt s t e p i s afaul t evaluat ion, t h a t m e a n s a n a s s e s s m e n t i s m a d e o f h o w t h efa ul t w i l l a f f e c t the proc e s s . The f a u l t s c a n be d iv ide d in todi f f e re nt ha z a rd c la s se s a c c ord ing to a n inc ide nt / s e que nc ea na lys i s or a f a u l t t r e e a na lys i s . Af te r the e ff ec t of the f a u l t i sk n o w n , a decision o n t h e a c t i o n t o b e t a k e n c a n b e m a d e . I f t h ef a u l t is e v a l u a te d t o b e t o l e ra b l e , t h e o p e r a t i o n m a y c o n t i n u e a n di f i t i s c ondi t io na l ly to le ra ble a change of operation h a s t o b epe r form e d. H owe ve r , i f the f a u l t i s in to le ra ble , the operation m u s tb e s topped i m m e d i a t e l y a n d t h e f au l t m u s t b e eliminated.Figure 1 indic a te s tha t a loope d s igna l f low e xi s t s in thesupe rv i s ion of proc e s se s in a s im i la r wa y a s in a c lose d loopc ont ro l sys te m . I t i s the re fo re poss ib le to a l so r e fe r to as u p e r v i si o n l o o p . T h i s i s o n l y c l o s e d o n t h e a p p e a r a n c e o f a f a u l ta n d d i s p la y s v e r y d i f fe r e nt d y n a m i c c h a r a c t e r i s ti c s d e p e n d i n g o nt h e e r r o r. T h e t i m e d e l a y o r i g i n a te s m a i n l y i n t h e b l o c k s c h a n g eo p e r a t i o n ( e. g. t r a n s f e r t o a n o t h e r o p e r a t i n g c o n d i t i o n ) , o r s t o po p e r a t i o n a n d f a u l t e l i m i n a t i o n a n d i n t h e p r o c e s s it se lf . I n t h i sc o n t r i b u t i o n t h e p r i m a r y t a s k s o f f a u l t d e t e c t i o n a n d f a u l td ia gnos i s a re c ons ide re d .3. Faul t detect ion methodsPre vious supe rv i s ion of t e c hnic a l proc e s se s wa s r e s t r i c te d toc h e c k i n g d ir e c tl y m e a s u r a b l e v a r i a b l es f o r u p w a r d o r d o w n w a r dt r a n s g r e ss i o n o f f ix ed l i m i ts o r t r e n d s . T h i s c o u l d b e a u t o m a t e dby us ing s im ple l im i t -va lue m oni tor s . Va r ious f a u l t s in thep r o c e s s c o u l d t h e n b e d e t ec t e d , b u t o n l y a f t e r t h e m e a s u r a b l eou tpu t va lue s ha d be e n e f f ec te d c on s ide ra bly . The u se of d ig i t a lp r o c e s s c o m p u t e r s a n d m i c r o p r o c e s s o r s e n a b l e s t h e u s e o ff u r t h e r m e t h o d s w h i c h c a n d e t e c t f a u l ts i n t h e p r o c e ss e a r l ie r a n dw h i c h c a n l o c a t e t h e m b e t t er . T h e p r o b l e m i s t o o r i e n t a t e p r o c e ssf a u l ts w i t h t h e a id o f t h e m e a s u r a b l e i n p u t a n d o u t p u t v a r i a b l e sU ( t ) a n d Y t ) (F ig . 2 ). M a the m a t ic a l m ode l s of the proc e s s a nd i t ss ignals .

Y - - f { U , N , O , X } (1)387

AUTO 2O:~ A


2/18

3 8 8 S u r v e y P a p e r

F ULT C USEOFF~LT H Z RDMESS GE NDLOC TON CL SS

J ] - I I - IE T E T tO N D I G N O S I S E V L U T IO N

FIG. l . Supe rv i s ion loop (onc a n be use d to th i s e nd , whe re N ge ne ra l ly r e pre se nt sn o n m e a s u r a b l d i s t u r b a n c e s i g n a l s f r o m t h e p r o c e s s a n d i t sm a n i p u l a t i n g a n d m e a s u r i n g e q u i p m e n t , 0 n o n m e a s u r a b l eproc e s s pa ra m e te r s , a nd X pa r t i a l ly m e a sura ble a nd pa r t i a l lynon m e a s ura bl in te rna l s t a te va r ia b le s ( s igna ls ) . In the proc e s sm o d e l s c o n s i d e r e d t h e p r o c e s s p a r a m e t e r s a r e c o n s t a n t s o rs lowly t im e -va r ia b le c oe ff i c ie n t s a nd the s t a te v a r ia b le s a re t im e -d e p e n d e n t . T h e m e t h o d s f o r f au l t d e t e c ti o n c a n b e d i v i d e d a sb e i n g m a i n l y b a s e d o n t h e f o l l o w i ng q u a n t i t i e s :(1) Me a sura b le s igna l s U , Y( 2) N o n m e a s u r a b l e s t a t e v a r i a b l e s X .(3) No nm e a sura ble proc e s s pa ra m e te r s 0 .(4) Non m e a s ura bl c h a ra c te r i s t i c qua nt i t i e s ~ / - g{ U , Y, 0} .

I t i s ty p i c al f o r m o r e s o p h i s t i c a te d m o n i t o r i n g m e t h o d s t o u s en o n m e a s u r a b l e q u a n t i t i e s w h ic h c a n b e o b t a i n e d b y p r o c e ssm o d e l s a n d e s t i m a t i o n m e t h o d s . M a n y l i t e r at u r e r e fe r en c e s a r ea va i l a b le on the subje c t of proc e s s supe rv i s ion a nd f a u l t de te c t ionfor c la s s ( I ) , a nd the y a re so w ide ly s c a t t e re d tha t i t i s ha rd lyp o s s ib l e to p r e s e n t a c o m p l e t e s u m m a r y o f t h e m . M u c h l e s s isk n o w n a b o u t c l a s s ( 2 ) a n d o n l y a v e r y l i m i t e d n u m b e r o fre fe re nc e s c a n be g ive n for c la s se s (3) a n d (4).I n t h i s s e c t i o n t h e p r i n d p l e s o f t h e s e m e t h o d s a r e b r i e f l yde sc r ibe d . Re c e nt surve ys on f a i lure de te c t io n m e th ods in ge n e ra la re g ive n by H im m e ib la u (1978) , Pa u (1981 ) , a nd on da s s (2) byWi l l sky (1976) . Som e e xa m ple s for a l l c l a s se s a re g ive n inI s e r m a n n 1 9 8 1 a ) .

3.1. M e a s u r a b l e s i g n a l sM e a s u r a b l e i n p u t s i g n a l s U ( t ) a n d o u t p u t s i g n a l s Y ( t ) c a n b ed i r e c t l y u s e d t o m o n i t o r c h a n g e s i n t h e p r o c e s s . T h e v a r i o u sm e thods a re br ie f ly de sc r ibe d for a m e a sura ble output s igna lY(t ) , the m os t f r e qu e nt c a se .L i mi t a n d t r e n d c h e c k i n g . I n t h e c a s e o f t h e w e l l- k n o w n a n dve ry c om m only use d l im i t c he c k of a s igna l Y ( t ) a s ignal isr e le a se d a s s o o n a s a n a d j u s t a b l e m a x i m u m v a l u e Y ~ i se xce ede d or a m in im u m va lue Y , ,i , f a l le n be low (e .g . the wa te rle ve l in a s t e a m ge ne ra tor drum ) . The norm a l s t a te i s

Y, , i, < Y( t ) < Y , , , , . (2)This i s r e fe r r e d to a s a n a b s o l u t e r a l u e c h e c k . The l im i t s a reusua l ly s e t suc h tha t a l a rge e noug h d i s ta nc e to the a ppe a ra nc e ofd a m a g e i s r e t ai n e d o n t h e o n e h a n d , u n n e c e s s a ry f a u l t a l a r m sbe ing a voide d on the o the r . The l im i t c he c k c a n a l so be a ppl ie do n t h e t rend ~ ( t ) of the s igna l Y ( t ) . I f the l im i t va lue s a re s e t sm a l l

U t P R O C E S S

e_ x_

~ V__

FIG. 2 . Re pre se nta t ion of a proc e s s w i th m e a sura ble inputv a r i ab l e s U , m e a s u r a b l e o u t p u t v a r i a b le s Y a n d n o n d i r e c t lym e a sura ble d i s turba nc e va r ia b le s N . proc e s s pa ra m e te r s 0 a nds ta te va r ia b le s X .

L I o c r

TE REQUIRE9 ISETPOINTS ~ i:OECISION = ~ PERATION P OCESS

appearance of a fault) .

e nou gh the f a u l t a l a rm c a n t a ke p la c e e a rl i e r tha n in the l a s t c ases inc e the t r e nd pe rm i t s a c e r ta in pre dic t ion of the s igna lprogre s s ion i a ppl ic a t ions for , e. g . be a t in g turb ine o i l p re s sure s orv ibra t ions ) . The norm a l s t a te i sf~, < f '(t) < ~'. ,, , . (3)

A l s o a c o m b i n a t i o n o f a b s o l u t e v a l u e a n d t r e n d c h e c k i n g i spossible ( Isermann, 1981a) .Predic t ion of s ignals . I f on ly l im i t c he c king i s a ppl ie d , the l im i t susua l ly a re s e t on the s a fe s ide to a l low su t t ide nt t im e forc ounte ra c t ions . Howe ve r , th i s c a n l e a d to unne c e s sa ry f a l s ea l a r m s i f t h e v a r i a b l e r e t u r n s t o t h e n o r m a l s t a t e w i t h o u t e x t e r n a la c t ion . Thi s d i sa dva n ta ge c a n be a voide d , i f the a f f e cte d s igna l sY ( t ) c a n be pre dic te d . Thi s a l so a l lows to pre dic t the t im e ofe xc e e ding a thre shold .I n o r d e r t o d o t h i s , m a t h e m a t i c a l m o d e l s o f d e t e r m i n i s t i cs igna l s , o r s toc ha s t i c s igna l s , o r a de te rm ini s t i c proc e s s a nd as toc ha s t i c s igna l m ode l ha ve to be use d . The (nonm e a sura ble )p a r a m e t e r s o f t h e se s i g n al m o d e l s c a n b e o b t a i n e d b y a p p l y i n gre c ur s ive pa ra m e te r e s t im a t io n m e thod s , e .g . by us ing a m u l t i s t e p

p r e d i c t i o n d e s c r i b e d b y d e K e y s e r a n d v a n C a u w e n b e r g h e(1981) . An a bsolu te va lue c he c k c a n the n be e m ploye d on thepre dic te d s igna l f ' ( k ) . An a ppl ic a t ion to a s t e a m ge ne ra tor w i thde te rm ini s t i c s igna l s is shown by Ba ur (1977).An a l y s i s o f s i g n a ls . O u t p u t s i g n a l s Y ( t ) of te n c ons i s t o f lowe rfrequency components l~Lr( t)w i th l a rge m a gni tude s whic h m a in lyd e t e r m i n e t h e n o m i n a l v a l u e s o f t h e s i g n a l a n d h i g h e r f r e q u en c yc o m p o n e n t s YaF(t ) with sm a l l a m pl i tude s , whic h g ive a ddi t iona li n f o r m a t i o n o n t h e i n n e r s t a t e o f t h e p r o ce s s. T h e n a t t e m p t s c a nb e m a d e t o i d e n t if y h i g h f r e q u en c y s i g n a l m o d e l s a n d t o p i n p o i n tp r o c e ss e r r o r s f r o m c h a n g e s i n t h e c o r r e s p o n d i n g s i g na l m o d e lp a r a m e t er s . T h e r e a r e m a n y e x a m p l e s i n c o n n e c t i o n w i t hn o n p a r a m e t r i c s ignal mode ls , e . g . a u t o c o r r d a t i o n f u n c t i o n s ,spe c t r a l de ns i t i e s or o the r m e thods for v ibra t ion a na lys i s . Thenoise a na lys i s of t r a nsm is s ion sys te m s , in te rna l c om bus t ion

e n g i n e s a n d t u r b o e n g i n e s a r e w e l l - k n o w n e x a m p l e s . O t h e ra p p l i c a t i o n s a r e r e p o r t e d b y Z w i n g e l s t e i n a n d U p a d h y a y a(1979) , a nd Sa e dt le r (1979) on s igna l a na lys i s f rom vibra t ionse nsor s , p re s se r s e nsor s a nd ne ut ron f lux m e a sure m e nts fornuc le a r r e a c tor s (W i l l i am s a nd She r , 1979) .3.2. N o mn e a s u r a b l e s t a r e v a r i a b l e sI f p roc e s s f a u l t s a re ind ic a te d by in te rna l , nonm e a sura bleproc e s s s t a te va r ia b le s , a t t e m pts c a n be m a de to r e c ons t ruc t ore s t im a te the se s tare var iables f rom the m e a sura ble s igna l s byu s i n g a k n o w n process mode l .

S t a t i c c a s e . A s ta t i c proc e s s m ode l ga ine d f rom the ore t i c a lm od e l ing i s suf fi cien t , i f the r e la t ionship be twe e n th e m e a sura blei n p u t s i g n a ls U a n d t h e o u t p u t s i g n a l s Y c a n b e c o n s i d e re d a ss ta t ic . The s ta te va r ia b le e s t im a te s X re q ui re d a re the n a func t ionof d.c . va lues C; and ~

,f = f', C, Y , (4)Inc lude d in th i s c a se a re, e . g . va r ia b le s in the m on i tor ing ofm a te r ia l s t r e s se s ( e . g . d r i ll b re a ka g e s f rom m e a su re m e n ts ofpre s sure , t e m pe ra ture , a dva nc e m e nt ) or the ove r loa d a nd t i l tp ro te c t ion of c ra ne s .


3/18

Survey Paper 89Dynamic case . In ge ne ra l , dyna m ic r e la t ionships do e x i s t

x t ) f { u , }. t ,. (5)Th e n i t i s e xpe die nt to c ha nge to s t a te r e pre s e nta t ion , whic h is forl i n e a r iz a t i o n a b o u t o n e o p e r a t i n g p o i n t .

k ( t ) = A x ( t ) + B u f f ) (6}y ( t ) = Cx t) t7}

whe re v = AY. u = A U . x = AX a re c ha ng e s of Y. U a nd X . There pre se nta t ion m us t be s e le c te d suc h tha t the s t a te va r ia b le s ofin te re s t x i ( t ) a re e le m e nts of the s t a te ve c tor x ( t ) . T o r e c o n s t r u c tt h e s e s ta t e s f ro m m e a s u r a b l e i n p u t a n d o u t p u t s i g n al s a s t a teva r ia b le obse rve r (de te rm ini s t i c c a se ) or s t a te va r ia b le f i l t e rs toc ha s t i c c a se .)x ( t ) = A Y: ( t ) + B u( t l + HD' ( t ) - C~(t)] (8)

c a n be use d , whe re by the f e e dba c k m a t r ix H m us t be s elec te d orde s igne d prope r ly , a s i s we l l known.A c o m p r e h e n s i v e s u rv e y o f m e t h o d s f o r t h e d e t e c t i o n o f abr up tf a u l t s w h i c h a p p e a r i n t h e s t a t e v a r i a b l e s a n d o u t p u t v a r i a b l e s o fdyn a m ic sys te m s i s g ive n by Wi l l sky (1976). Ce r ta in c ha nge s int h e p r o c e s s, i n i ts n o i s e o r i n t h e a c t u a t o r s c a n b e m o d e l l e d b y v ( t )in: :( t) = A x ( t ) + B u( t ) + F v ( t ) + v ( t ) (9)

a n d c h a n g e s i n t h e s e n s o r s b y # ( t ) i ny ( t ) C x ( t ) + n ( t ) + g ( t ) I 0 )

whe re v ( t ) i s p roc e s s noi se a nd n( t ) m e a s u r e m e n t n o i s e w i t hk n o w n s t a t i st i cs . I f v ( t ) a n d # ( t ) a r e a s s u m e d t o b e d e l t a i m p u l s e so r s t e p f u n c t i o n s, a b r u p t c h a n g e s o f t h e s t a te s a n d t h e o u t p u t sc a n b e m o d e l e d . T h e s e c h a n g e s c a n t h e n b e d e t e ct e d b y t h e u s e o fK a l m a n - B u e y f i lt e rs w h e r e t h e r e s id u a l s

j~( t) = y( t) - - C~( t) (11 )a re ge ne ra te d . F au l t de c i s ions c a n t h e n b e m a d e b y s p ec i al t e s t in gm e tho ds , e . g .(a) 'F au l t s e ns i t i v e i l t e r s ' , w h e r e t h e f e e d b a c k m a t r i x H i s ch o s e ns o t h a t p a r t i c u l a r f a u l t m o d e s m a n i f e s t t h e m s e l v e s a sre s idua l s in a f ixe d d i r e c t ion o r in a f ixe d p la n e (Be a rd , 1971 ;Jone s , 1973) , a de te rm in i s t i c a ppr oa c h .(b) A W h i t e n e s s a n d a c h i - s quar e d te s t o f t h e r e s id u a l s o f t h en o r m a l K a l m a n - f i l t e r ( M e h r a a n d P e s c h o n , 1 9 7 1) .(c) A f ini te b a n k o f K a l m a n - f i l t e r s w i t h a s t a n d a r d m u l t i p l eh y p o t h e s i s t e s t in g t h a t t h e s y s t e m s m o s t l i k e ly r e s p o n d t o

o n e o f t h e a s s u m e d m o d e l s w i t h h y p o t h e s i z e d f a u l t s in c l u d e d( M o n t g o m e r y a n d C a g l a y a n , 1 97 4 ; M o n t g o m e r y a n d P r i ce ,1974):(d) A ge ne r a l i z e d l i k e l ihood r a t io t e s t whic h r e su l t s in ac o r r e l a t i o n o f th e o b s e r v e d r e s i d u a l s w i t h t h e p r e c o m p u t e df i l t e r r e sponse s due to c e r ta in f a u l t s ( f a u l t s igna ture s )(Wi l l sky a nd Jone s , 1974).A r e c e n t d e s c r i p t i o n o f t h e l a s t t w o s t a t is t i c m e t h o d s i s g i v en b yWil l sky (1980). A b loc k d ia gra m of the se s t a te va r ia b lete c hnique s i s shown in F ig . 3 .Of cour se , the se m e thod s r e qui re a r e la t ive ly e xa c t knowle dg e

o f t h e p r o c e s s p a r a m e t e r s ( A , B . C ) a nd the inf lue nc ing s igna l s .

3.3. N o n m e a s u r a b l e p r o c es s p a r a m e t e r sP r o c e s s m o d e l p a r a m e t e r s a r e u n d e r s t o o d a s c o n s t a n t s o rt im e -de pe nd e nt c oe f f ic ie n t s in the proc e s s w hic h a ppe a r s in them a t h e m a t i c a l d e s c r ip t i o n o f t h e r e l a t i o n s h i p b e t w e e n t h e i n p u ta n d o u t p u t s i g n a l s , t h e process model. A d i s t i n c t i o n i s m a d ebe twe e n s ta t i c proc e s s m ode l s , e . g . in the form of a polynom ia le q u a t i o n

Y(U ) = f lo + f l , U + f12U2 + . . . 1 2 )

___.... ..PROCESSF . . . . . . ,

I - ~ [ n l

J 1i . . . . j

Y==~

S T A T E [E S T I M A T IO N [ -

E S I D U A L S I

FAULTDECISION ]

FAULTSF I G . 3. Fa ul t de te c t ion ba se d on s ta te va r ia b le e s t im a t ion .

a nd dyna m ic proc e s s m ode l s whic h , for proc e s se s w i th lum pe dpa ra m e te r s , a r e usua l ly d i f f e re nt i a l e qua t ionsy( t ) + a ~ ( t ) + a2y (t) + . . . + a.y~ )(t) = bou( t )

+ bxfi(t) + b2fi'(t) + . . . + b.,u( )(t) 113)i n t h e s i m p l e s t c a s e l i n c a r i z e d a b o u t o n e o p e r a t i n g p o i n t .T h e p r o c e s s m o d e l p a r a m e t e r s O = [~ of l lB2. . . ] o r O= [ a , . . . a . i b l . . . b . ] a re m os t ly m ore or l e s s in t r i c a tere la t io nsh ips of severa l physica l pro cess coeffic ients, e .g. length,mass , speed , drag coeff icient, viscosi ty, res is tances , capacit ies .F a u l t s w h i c h m a k e t h e m s e l v es n o t i c e a b l e i n t h e s e p h y s i ca l p r o c e s sc ons ta n t s a re the re fore a l so e xpre s se d in the proc e s s m ode lpa ra m e te r s .I f the phys ic a l proc e s s c oe f f i c ie n ts whic h ind ic a te proc e s s f a u l t sa r e n o t di re c t ly m e a s u r a b l e , a n a t t e m p t c a n b e m a d e t o d e t e r m i n et h e i r h a n g e s v i a t h e c h a n g e s i n t h e p r o c e s s m o d e l p a r a m e t e r s O .T h e f o l l o w i n g p r o c e d u r e i s a v a i l ab l e :

a ) E s t a b l i s h m e n t o f t h e p r o c e s s e q u a t i o n f o r t h e m e a s u r a b l ei n p u t a n d o u t p u t v a r ia b l es

Y t t ) = f { U(t ) ,O} 0 4 )m os t ly by the ore t i c a l m ode l ing .

b ) D e t e r m i n a t i o n o f t h e r el a t i o ns h i p b e t w e e n t h e m o d e lp a r a m e t e r s 0 ~ a n d t h e p h y s i c a l p r o c e s s c o e ff i c ie n t s p :0 ---- (p).( c ) Es t im a t ion of the m o de l p a ra m e te r s 01 a s a r e su l t o fm e a s u r e m e n t s o f t h e s i g n a ls Y ( t ) a n d U ( t ) .(d) Ca lc ula t ion o f the proc e s s c oe f f ic ie n t s :

p = f - 1 O ) 1 5 )a n d d e t e r mi n a t i on o f t he i r c h a n g e s A p j .( e) Poss ib le proc e s s fa u l t s c a n b e p inpo in te d ( i f ne e d be byp a t t e r n r e c o g n i t i o n ) b y t h e u s e o f a c a t a l o g u e o f f a u l t s inw h i c h t h e r e l a t i o n s h i p b e t w e e n p r o c e s s f a u l t s a n d c h a n g e s i nthe coeff icients Apj ha s been es tablis hed .

H e n c e , t h e b a s i s o f t h is c l as s o f m e t h o d s i s t h e c o m b i n a t i o n o ft h e o r e t i c a l m o d e l i n g a n d p a r a m e t e r e s t i m a t i o n o f c o n t i n u o u s -t im e m ode ls . A b loc k d ia gra m i s g ive n in F ig . 4 . A ne c e s sa ryr e q u i r ~ a c n t o f t h i s p r o c e d u r e i s, h o w e v e r , t h e e x i s t en c e o f t h einve r se r e la t ion ship e qua t io n (15) . The re fore , i t m a y be r e s t r i c te dto we l l -de f ine d proc e ~ ' s , s e e Se c t ion 5 .T h e p r o c e s s p a r a m e t e r t e c h n i q u e s t r y t o m o n i t o r t h e p r o c e s sdi r e c t ly , ba se d on phys ic a l l a ws whe re a s the s t a te va r ia b le


4/18

3 9 0 S u r v ey P ap e rPROCESS

P- lu r ~ Jl ) y

IPRO ESS~MOO UNO

FAULTSF I G . 4 . F a u l t d e t e c t i o n b a s e d o n p a r a m e t e r e s t i m a t i o n a n dt h e o r e t ic a l m o d e l i n g .

t e c h n i q u e s m u s t a s s u m e t h e p r o c e ss p a r a m e t e r s a s k n o w n a n dt r y t o m o n i t o r t h e s i g n a l s . O f c o u r s e , b o t h t e c h n i q u e sc o m p l e m e n t o n e a n o t h e r .3.4. Nonmeasurable characteristic quantities

The c ur re nt c he c king of c ha ra c te r i s t i c qua nt i t i e s c a n g ivei m p o r t a n t i n f o r m a t i o n o n t h e i n n e r s t a t e w h e n s u p e r v i s i n g l ar g e rp la nt s or s e c t ions .Exa m ple s of c ha ra c te r i s t i c qua nt i t i e s a re :( a ) Ef fi cienc y ( e . g . a l l type s o f e ngine s a nd m a c hine s , s t e a mgenera tors , heat exchangers , furnaces , vehic les) .( b ) F u e l c o n s u m p t i o n p e r p r o d u c t i o n u n i t o r t i m e (e .g . c e m e n tburn ing , m i l l ing , dry ing) .( c ) O i l c ons um pt ion p e r prod uc t io n uni t o r t im e (e .g . in te rna lc om bus t ion e ngine s , c om pre s sor s ) .(d) Te o l usa ge pe r produ c t ion u ni t o r t im e ( e. g . m a c h ine tool s) .( e) We a r pe r produc t ion uni t o r t im e ( e .g . tool s m oto r s , g r indingdevicesl .

T h e c h a r a c t e r i s t i c q u a n t i t i e s m u s t b e d e t e r m i n e d f r o mm e a sura ble va r ia b le s :

= g / u , r ~ . 1 6 )Most ly , s t a t i c r e la t ionships a re suf f i c ie n t . Cha nge s in thequa n t i t i e s c a n po in t to f a u l t s, e. g. c onta m ina t io n , de pos it s we a r ,f r i c tion , ic ing , l e a ks. To th i s e nd , a bso lu te v a lue or t r e nd c he c ksshould be c a r r i e d out on the c ha ra c te r i s t i c qua nt i t i e s .3.5. A general structure o f process fau lt detection methodsLooking a t the va r ious t a sks of proc e s s f a u l t de te c t ionm e t h o d s w h i c h m a k e u s e o f n o n m e a s u r a b l e q u a n t i t i e s a n dthe re fore a re ba se d on proc e s s m ode l s one r e c ogniz e s s e ve ra ls im i lar i t ie s . He nc e, i t is s t r a ight forw a rd to pre se nt the se m e thodsin a ge ne ra l i z e d s t ruc ture (F ig . 5) . Ba se d on the a prioriknow le dge a n d e xpe r ie nc e of the r e a l proc e s s we wi ll use :

( i ) a m ode l of the normal proc e s s ;( ii ) a m od e l of the obserred proc e s s :( i i i ) models of the fizulty process .A s t h e m e t h o d s r el y o n t h e d e t e r m i n a t i o n o f c h a n g e s i nc o m p a r i s o n t o t h e normal status t h e m o d e l o f t h e n o r m a l p r o c e s sm u s t b e k n o w n a n d t r a c k e d w i t h h i g h p r e c i si o n . T h i s a l s o i n c lu d e sthe de f in i t ion of wha t i s norm a l ' , e .g . pa ra m e te r va lue s inc ludin gthe i r ' no rm a l ' ( a l lowa ble ) to le ranc e s . The norm a l m od e l c a n , for

e xa m ple , be the m ode l o bta ine d jus t be fore a f a u l t i s a la rm e d, i .e .the pre vious m ode l . The m ode ls of the f a u l ty proc e s s show theeffec ts of the faults on the analysed quanti t ies . These effec ts arecal led fault s ignatures.De pe nde nt on the f a u l t s to be de te c te d one ha s to use :( i ) s t a te e s t im a t ion m e thods ;( ii ) p a r a m e t e r e s t i m a t i o n m e t h o d s ;( ii i) c a lc u la t ion of c ha ra c te r i s t i c qua n t i t i e s .A c om pa r i son of the se non m e a sura ble qua n t i t i e s x', 0 , ~ a s pa r to f t h e o b s e r v e d m o d e l w i t h t h e c o r r e s p o n d i n g q u a n t i t i e s o f t h enorm a l m ode l ( i . e . p re vious m ode l ) r e su l t s in changes

~ zxO or zx6or in error signals o r residuals e.g.

= y C~ or e = y ~P0i f the e ff e ct of s e ve ra l e s t im a te s on pa r t i c u la r s igna l s i s c ons ide re d(h : s e e ne xt s e c t ion) . The se c ha nge s or r e s idua l s form comparisonquantities a nd a re one ba s i s for the ne xt s t e p , the fault decision.T h e o t h e r b a s i s i s t h e fault s ignatures whic h show the e f f e c t off a u l t s on the se qua nt i t i e s , for e xa m ple , by :

( i) c ha ng e s (b ia s ) in de f in i t e d i r e c t ions ;( i i ) c ha nge s in oppos i t e d i r e c t ions ;( ii i) c ha nge s due to a c e r ta in pa t t e rn ;( iv) increase of var iances .T h e r ef o r e, t h e c h a n g e s c a n b e e x a m i n e d w i t h r e s p e c t t o t h eindic a t ion of poss ib le f a u l t s . To c om pa re the c ha nge s w i th thef a u lt s i g n a t u r e s j u s t b i n a r y d e c i s i o n s c o m b i n e d w i t h e x c e c d i n gp r e d e t e r m i n e d t h r e s h o l d s c a n b e m a d e , o r m o r e s o p h i s t i c a t e dm e thods l ike c or re la t ions of the c ha nge s w i th the f a i lures igna ture s m a y be use d . Thi s i s obvious ly a f i e ld for thea p p l i c a t io n o f statistical decision theory a n d pattern recognition.The re su l t o f the f a u l t de c i s ion i s the fault type a n d t h e t ime of i ts

occurrence.The ne xt t a sk c ons i s t s of the fault diagnosis w i t h t h e g o a l s t od e t e r m i n e t h e fault location the fault s ize a n d t h e cause of thefault . A g a i n t h e o b s e r v e d a n d n o r m a l p r o c e s s m o d e l m a y b e u s e dto pe r form th i s . Ba se d on th i s inform a t ion the f a u l t e va lua t ioncan start, etc. , see Fig. 1.In the fo l lowing two e xa m ple s proc e s s f a u l t de te c t ion n '~ th odsa r e c o n s i d e r e d w h i c h t r y t o m o n i t o r c h a n g e s o f p r o c e s sp a r a m e t e r s a n d p r o c e ss s t a t e v a r i a b le s . A s p a r a m e t e r e s t i m a t i o nf o r c o n t i n u o u s - t i m e m o d e l s i s r e q u i r e d , s u i t a b l e m e t h o d s a r ec ons ide re d ne xt .4. Param eter estimation for continuous-time modelsF a u l t d e t e c ti o n , b a s e d o n p r o c e s s p a r a m e t e r s w h i c h a r e m o s t l ynot d i r e c t ly m e a sura ble , r e qui re s on- l ine pa ra m e te r e s t im a t ionm e thod s . As the goa l i s no t o nly to de te c t bu t to d ia gnose proc e s sfaul ts , the p roc e s s m ode l s shou ld e xpre s s a s dos e a s poss ib le thephys ic a l l aws whic h gov e rn the proc e s s be ha v iour . The re fore , theproc e s s m ode l s ha ve to be de ve lope d f i r s t by theoretical modelingt h a t m e a n s b y s t a t in g t h e b a l a n c e e q u a t i o n s f o r m a ss , e n e rg y a n dm o m e n t u m , t h e p h y s i c a l - c h e m i c a l s ta t e e q u a t i o n s a n d t h ep h e n o m e n o l o g i c a l l a w s f o r a n y i r r e v e r s i b l e p h e n o m e n a . T h em o d e l s w il l t h e n a p p e a r i n t h e c o n t i n u o u s - t i m e d o m a i n , i n t h eform of ord ina ry or pa r t i a l d i f f e re nt i a l e qua t ions . The i rpara me ters 0~ are ex pressed in de pen den ce on process coeffic ientsp j l ike s tora ge o r r e s i s t a nc e qua nt i t i e s , whose c h a nge s m a y tel la bo ut proc e s s f au l ts . He nc e , the pa ra m e te r s 01 of continuous-timemodels ha ve to be e s t im a te d .A lso , in the c a se of f a u l t de te c t ion m e thods ba se d on s ta teva r ia b le t e c hnique s , pa ra m e t r i c m ode l s a re r e qui re d . I f the i rp a r a m e t e r s a r e n o t k n o w n e x a c t ly e n o u g h , p a r a m e t e r e s t i m a t i o nm e thods a l so ha ve to be a ppl ie d .

A c o m p r e h e n s i v e s u rv e y o n p a r a m e t e r e s t i m a t i o n m e t h o d s f o rc o n t i n u o u s , t i m e m o d e l s w a s g i v e n q u i t e r e c e n t l y b y Y o u n g(1981) . For f a u l t de te c t ion the s ingle pa ra m e te r s m us t bee s t im a te d v e ry a c c ura te ly a n d o ne of the que s t ion s i s, for whic hp a r a m e t e r s a n d f o r h o w m a n y p a r a m e t e r s ( m o d e l o r d e r ) t h i s w il lbe poss ib le in a noi sy e nvi ronm e nt .Ha ving in m ind the se r e qui re m e nts , the ne xt s e c t ions w i l lbr i e f ly d i sc uss som e pa ra m e te r e s t im a t ion m e thods for l ine a r ,


5/18

Survey Paper 39I N y

P RO E S S

M OD ELOBSER VEDPROCESS

GEN ER AT I ON OFC H A N G E S- E RROR SIGNALS- RESIDUALSJJ COMPARISONQU AN T I T I ES

I F A U L T ~ F A U L TD E C I S I O N S I G N A T U R EFAULT ~ ~ FAULTT YP E . . . . . T I M E

FAULTDI GNOSIS

F A U L T F ULT C USEL O C A T I O N SIZE O F F ULT

4

F IG . 5 . G e n e r a li z e d s t r u c t u r e o f f a u l t d e t e c ti o n m e t h o d s b a s e d o n p r o c e s s m o d e l s a n d n o n m e a s u r a b l e ' q u a n ti t ie s .

c o n t i n u o u s - t i m e m o d e l s , b a s e d o n s a m p l e d s i g n a l s, o b t a i n e d b y ap r o c e s s o r m i c r o c o m p u t e r .4.1. L e a s t - s q u a r e s p a r a m e t e r e s t i m a t i o n . I t i s a s s u m e d t h a t as t a b l e p r o c e s s w i t h l u m p e d p a r a m e t e r s i s t i m e - i n v a r i a n t a n dl ine a r iz a ble so tha t i t c a n b e de sc r ibe d b y a l ine a r d i f f e re nti a le q u a t i o n ,

~ ( t ) + a . _ L ~ - l ( t ) + . . . + a l y ~ ( t ) + a oy( t )= b . u ' ( t ) + b = _ l u ' - ~ ( t ) + . . . + b l u l ( t) + b o u (t ) (17)

w h e r e t h e s u p e r s c r i p t n o t a t i o n s m e a n s t h e t i m e d e r i v a t i v eo p e r a t i o n , t h a t m e a n s y J (t ) = d ~ y ( t ) / d t J , a n d y ( t ) a n d u ( t ) a re thed e v i a t i o n sy( t ) = Y ( t ) - Yoo; u ( t ) = U ( t ) - U o o . (18)

T h e m e a s u r e d o u t p u t y ( t ) i s as s u m e d t o b e c o n t a m i n a t e d b y as ta t ion a ry s to c ha s t i c noi se n( t ) , s ee F ig . 4 ,y ( t ) = y , ( t ) + n ( t ) . 0 9 )

S u b s t i t u t i n g f o r .~ ( t ) i n t e r m s o f i t s m e a s u r e m e n t s o n e o b t a i n sy ( t ) = q / T ( t ) O + e f t ) (20)

w h e r e e ( t ) i s t h e e q u a t i o n e r r o r .N o w m e a s u r em e n t s o f th e i n p u t a n d o u t p u t s i g na l s a r e m a d e a n da l l re qui re d de r iv a t ive s a re de te rm ine d a t d i s c re te t im e s t - - k T o ,k - - 0 , 1 , 2 , . . . N w i th T o t h e s a m p l i n g ti m e. T h e n N + 1e q u a t i o n s

y ~ ( k ) = ~ T ( k ) O + e ( k ) (21)

re su l t whe re e ( k ) c a n b e i n t e r p r e t e d a s a n e q u a t i o n e r r o r ,r e s u l ti n g i n a v e c t o r e q u a t i o ny" = ud0 + e. (22)

T h e d a t a m a t r i x c o n s i s ts o f N + 1 rows o f the da ta ve c tor Or (k) .W i t h t h e c o s t f u n c t io nN

V = y e 2 k ) - - - ere a n d d V / d O = 0 (23)k=O

t h e l e a s t s q u a r e s e s ti m a t e o f t h e p a r a m e t e r v e c t o r b e c o m e s t h ew e l l -k n o w n n o n r e c u r s i v e e s ti m a t i o n e q u a t i o n0 = [ o . / T ~ ] I ~ J T j ~ . 24)

H o w e v e r , t h e s e p a r a m e t e r s a r e b i a s e d f o r a n y n o i s e n ( t ) ,The re fore , the l e a s t - squa re s m e th od shou ld not be use d , if thenoise - to- s igna l r a t io i s no t sm a l l .4.2. D e t e r m i n a t i o n o f t h e t i m e d e r i v a t i v e s . T h e p a r a m e t e re s t i m a t i o n o f l e a s t - s q u a r e s r e q u i r es t h e t i m e d e r i v at i v e s o f t h ei n p u t s i g n a l u (t ) a n d t h e ( n o i sy ) o u t p u t s i g n a l y ( t ) u p t o t h e r u t ha nd the (n - ) th de gre e , r e spe c tive ly . Th e re a re m a in ly fo l lowingposs ib i l i t ie s to c a lc u la te the se va lue s f rom sa m ple d m e a sure m e nts

u ( k ) and y(k) .In the c a se of n u m e r i c a l d i f fe r e n t i a t io n the s im ple s t wa y i s tor e p l a c e t h e d e r i v a t i v e s b y t h e c o r r e s p o n d i n g ( b a c k w a r d )d i ff erenc es . T o r e duc e som e wh a t the inf lue nc e of the noi sei n t e r p o l a t i o n f o r m u l a s t h e r e i s a n o t h e r w a y . F o r e x a m p l e ,i n t e r p o l a t i o n b y s p l i n e s ( t h i r d o r d e r p o l y n o m i a l s ) o r N e w t o ni n t e r p o l a t i o n c a n b e u s e d . H o w e v e r , t h e r e m a i n i n g n o i s e i n f lu e n c ere s t r i c t s the a ppl ic a t ion to s e c ond a nd th i rd orde r proc e s se s .T h e u s e o f s t a t e v a r i a b l e f i l t e r i n g a c c o r d i n g t o b o t h t h e i n p u ts ignal u t ) a n d t h e o u t p u t s i g n a l y t ) , s i m u l t a n e o u s l y p r o v i d e s t h e


6/18

392 Survey Papert im e de r iva t ive s a nd f i l t e r s the noi se w i thout d i f f e re nt i a t ion(Young, 1981) .S inc e only the t im e de r iva t ive s of the s igna l s a re r e qu i re d the rei s som e f r e e dom in the c hoic e of the fi l t e r pa ra m e te r s (Yo ung a n dJa ke m a n, 1980) .

4.3. Ins trumental var iables parameter es t imation. T o o v e r c o m et h e b i a s p r o b l e m e s t i m a t i o n o f t h e i n s t r u m e n t a l v a r i a b l e (I V )c onc e pt c a n be use d (You ng, 1970, 1981 ) . Ins t rum e nta l va r ia b le sa re in t rod uc e d whic h a re on ly ins igni f i c a nt ly c or re la te d w i th thenoise - f r e e proc e s s output y , ( t ) . A su i t a b le wa y to ge ne ra te theins t rum e nta l va r ia b le s is to use a n a uxi l i a ry m od e l of the proc e s swhic h ge ne ra te s the ins t rum e nta l va r ia b le s .This m e thod y ie lds c ons i s te n t pa ra m e te r e s t im a te s . To s ta r tthe proc e dure , th e l e a s t - squa re s m e tho ds c a n be use d. I t i s a l sowe l l su i t e d to be progra m m e d in a r e c ur s ive form . For fur the rde ta i l s a nd im prove m e nts s~ e Young (1981) .A m a j o r a d v a n t a g e o f t h e I V m e t h o d i s t h a t n o s t r o n ga s s u m p t i o n s a n d k n o w l e d g e o n t h e n o i s e a r e r e q u i re d . H o w e v e r ,i n d o s e d l o o p c o n f i g u r a t i o n s b i a s e d e s t i m a t e s a r e o b t a i n e d ,be c a use the input s igna l i s c or re la te d w i th the noi se .I f on- l ine r e a l - tim e pa ra m e te r e s t im a t io n i s r e qui re d b oth thel e a s t s q u a r e s a n d t h e i n s t r u m e n t a l v a r i a b l e s m e t h o d c a n b ewr i t t e n in r e c ur s ive form ( l s e rm a nn, 1981b) .4.4. Parameter es t imation v ia discre te - t ime models . As thepa ra m e te r e s t im a t ion m e thods for d i s c re te - t im e sys te m s a refa i rly wel l de ve lope d o ne c a n f i r s t t ry to e s t im a te the pa ra m e te r s oft h e d i s c re t e -t i m e m o d e l a n d t h e n t o c a l c u la t e t h e p a r a m e t e r s o ft h e c o n t i n u o u s - t i m e m o d e l b y s u i t a b le t r a n s f o r m a t i o n r e l a t io n -sh ips . Ma in ly , two a pp roa c h e s a re use d , whic h a re de sc r ibe d , e. g .b y S i n h a a n d L a s t m a n ( 19 8 2) , S t r m r n i k a n d B r e m g a k ( 19 7 9) a n dHung, L iu a nd Chou (1980) .H o w e v e r , th e s e m e t h o d s r e q u i re e x t e n s iv e c o m p u t a t i o n a n da re , in pa r t , no t s t r a igh t forwa rd , so th a t the y a re , a t l e a s t in thepre se nt s t a tus , no t f e a sib le for on- l ine r e a l - t im e a pp l ic a t ions .In c onc lus ion , i t c a n be s t a te d tha t c ont ra ry to d i sc re te - t im e

m o d e l s t h e p a r a m e t e r e s t i m a t i o n m e t h o d s f o r c o n t i n u o u s - t i m em ode ls ha ve no t obta ine d the s a m e s ta tus . Th e re i s s t il l a ne e d forr o b u s t p a r a m e t e r e s t i m a t i o n m e t h o d s w i t h l e s s c o m p u t a t i o n a le ffort w hic h prov ide c ons i s te n t a n d e f f ic ie n t pa ra m e te r e s t im a te su n d e r m a n y n o i s e c o n d i t i o n s a n d a l s o i n c l o s e d l o o p a n d f o rt ime-variant processes .5. Fa ult de tec tion fo r an e lec tromoto r dr iven centr iJugal pum pThe e a r ly de te c t ion of proc e s s f a u l t s i s of c our se e spe c ia l lya t trac t ive for engines . Therefore , as a f i rs t example , a centr ifugalpum p wi th a wa te r c i r c u la t ion sys te m , dr ive n by a spe e d-c ont ro l l e d d i r e c t c ur re n t m oto r i s c ons ide re d (F ig . 6) . The goa l i sto de te c t c ha nge s ( f a u l t s ) in the d . c . m otor , the pum p a nd thec i r c u la t ion sys te m ba se d on the o re t i c a l ly de r ive d proc e s s m ode l sa nd pa ra m e te r e s t im a t ion . I t i s shown how the proc e s sc oe f f i c ie n t s c a n be de te rm ine d . Som e e xpe r im e nts de m ons t r a ter e s u l t s o b t a i n e d b y u s i n g a m i c r o c o m p u t e r c o n n e c t e d t o t h esensors of the engine se t IGeiger , 1982) .

Ui T i IPT p / O t d

Pp?P P 2 K , I

FIG. 6 . Sc he m e of a spe e d c on t ro l l e d d . c. m oto r a n d c e nt r i fuga lpum p. p p ressure , ?v lmas s f lo~. c~ ang ula r velocity, T torque . U~oltage . I current . R res is tance . L inductance .

5.1. M a the ma t ic a l pr oc e s s models. T h e d y n a m i c m o d e l s o f t h ed .c . m o tor , the c e nt r i fuga l pum p a nd the p ipe sys te m a re ga ine db y s t a t i n g th e b a l a n c e e q u a t i o n s f o r e n er g y a n d m o m e n t u m a n dby us ing spe c ia l phys ic a l r e la t ionships . In orde r n ot to obta in toom a ny p a ra m e te r s , a ppro pr ia te s im p l i f i c a tions ha ve to be m a de .T h e d e r i v a t i o n o f t h e m o d e l s a n d t h e s y m b o l s u s e d a r e g i v en i nAppe ndix A . Som e sym bols a re a l so indic a te d in F ig . 6 .Ba se d on th e e qua t ions (A6), (AI7) , (A25) a nd (A31 } he b loc kdiagram of Fig. 7 results .I t shows th a t som e proc e s s c oe ff ic ie n ts a re lum p e d toge the r ,e .g. the fr ic t io n coeff ic ients of the m oto r CFM1 an d the pu mp Cw~,an d th e torq ue coeff ic ient g,~ of the pum p.The r e su l t ing four ba s ic e qua t ion s w i ll be use d for pa ra m e te re s t im a t ion in the fo l lowing form :

{a A r matur e c i r c u i td l z ( t ) = a l lA l t ( t ) + a 12Aco( t) + b tA U l t ) .d t 2 5 )

(b) Mechanics . of motor and pump.dco(t__~)= a : l A l l ( r ) + a22Aco t) ~- a23Ah4(t).d t (26)

(c) Pipe sys tem.d M ( t ) = a ~ 3 A M ( t ) + d 3 A Y t } . (27)d t

(d) Pump spec if ic energ_ Y).A Y t ) = ho , t ) + hMAAI(t). (28)

T h e p a r a m e t e r s a r eR l

a l l = - - - L tp

a l 2 ~ - - - -L lT(,/21 -~- 0

we0 M 0[,

CF[ + g ~a 2 2 0gM

a 2 3 =

2 Ra 3 3 = - - _ _a a e

1b~ = L - ~ - z

1d 3 = - - .aa

(29)

A s ta te va r ia b le r e pre se nta t ion.~(t) = .4xlt) + bu f f )v t l = C x l t 30)

c a n now be g ive n w i th fo l lowing de f in i t ionsA I ~ ( t l i a t t a t .,x t t t = / A ~ ( t ) ; .4 -- - a t a , ,L A I tt o a ; :

r A ' ' ; : l / Ao~(r) 0 1 0Y l t l = l A 3 , 1 t ) ; C = 0 0 h L JLAYI t J o h . .h o L ~a 3 2 = - - ; L /3 3 = a 3 3 + - - .~la Ga

a 2 3~t33

(31}


7/18

S u r v e y P a p e r 3 9 3

_ N I l .= A R MA TU RE C IR C U IT - - ~ M EC HA NIC S ---,

D .C.MOTOR D.C.MOTORA N D P U M P

- - , , I q

PP SYST M

F~G. 7 . B loc k d ia gra m of the l ine a r iz e d d .c . m o to r -p um p- pi pe sys te m .

5.2. P r o c e s s p a r a m e t e r m o n i t o r i n g . T h e p a r a m e t e r s o f( 2 5 ) - ( 2 8 ) c a n b e e s t im a t e d b y b r i n g i n g t h e m i n t o t h e f o r m o f ( 2 1 )a n d b y a p p l y i n g , f o r e x a m p l e , th e l e a s t - s q u a r es m e t h o d . O n e o fthe qu e s t ions the n i s , how the va r io us proc e s s c oe f fi cien t s w hic ha re r e qui re d for f a u l t de te c t ion c a n be c a lc u la te d . The re forese ve ra l c a se s of ope ra t ion a nd m e a sure m e nts a re d i sc usse d .(a) D . c . m o t o r a n d p u m p , c l o s e d v a l v e . In th is case 33 ( t) = 0 is va l id,so tha t on ly (25) a nd (26) a re to be use d .

(i) M e a s u r e d s i gn a ls : A U~ , A l l , A wB o t h e q u a t i o n s a r e w r i t te n d u e t o ( 21 )

y,(t) = C , . ~ O ,y: t t ) = ~ ,~ t )O= (32)

w h e r eYA/) = d l , t l / d t y 2 t ) = d w t ) / d t~ / ~ t ) - -- [ A I I t ) A t o t ) A U I t ) ]O = [ a l l ~ = b ~]~br(t) = [ A l ~ t ) A w t ) ]O [ ~a~ a = ] .

(33)

Us ing (29) , the fo l lowing f ive proc e s s c oe f f i c ie n t s c a n bec a l c u l at e d b a s e d o n t h e f i v e p a r a m e t e r e s t i m a t e s 0~ a n d 0 2 :

b ~ / ~ 1 = - a . 1 = - e , l / b ,

= - a l a , = - a , , / / ~ l0 = ~ / ' a , l = - al . / /haa l

3 4 )

He nc e , a l l p roc e s s c oe f f i c ie n t s whic h de sc r ibe the l ine a r iz e dd y n a m i c b e h a v i o u r c a n b e c a l c u l a t e d . H o w e v e r , t h e f r i c t i o nc o e ff i ci e n ts o f th e m o t o r c r m a n d t h e p u m p c vu ,~ a n d t h em o m e n t s o f i n e r t ia 0 M a n d 0 p a r e l u m p e d t o g e t h e r s o t h a t o n l yt h e i r s u m c a n b e g a i n e d .I f n o t t h e d y n a m i c b e h a v i o u r , b u t o n l y t h e s t a t i c b e h a v i o u rc o u l d b e i d e n t i fi e d , L I a n d 0 c o u l d b e n o t o b t a i n e d , s e e (A 6 ) a n d(A25) for d / d t = O . T h i s s h o w s t h a t b y i d e n t i f y in g t h e d y n a m i c sm o r e p a r a m e t e r s c a n b e e s t i m a t e d a n d t h e r e f o r e m o r e p r o c e s sc oe f f i c ie n t s c a n be m oni tore d .A d i s a d v a n t a g e o f t h e i i n e a r iz e d d y n a m i c r e l a ti o n s h i p s i s t h a tthe c oe f f ic ie n t s Cruo a nd Crpo for the a dhe s ive f r i c t ion d o nota ppe a r . Howe ve r , f rom (A3) a nd (A10) i t fo l lows w i th thea s s u m p t i o n t h a t t h e f r i c t io n t o r q u e o n l y d e p e n d s l i n e a rl y o n t h es p e e dT r ~ t l = C r u o + c r m t o t )T ~ t ) = Crpo + C v p l t o t )

d w t~ ~ = ~ I , H ) - Cvo - C w W t )0

(35)

Cl-lb ~- L'FMO --~ C Fp 0CF I ~--- CFM 1 at CFp I .

The n the a bso lu te va lue s w( t t a n d 11( , ) , a nd not the i r de via t ions .a re use d a n d the e s t im a t io n of Cro a l so be c om e s poss ib le (Ge ige r ,1982).(ii) M e a s u r e d s i g n a l s: U I , z x w

I t i s n o w a s s u m e d t h a t t h e a r m a t u r e c u r r e n t l ~ t ) c a n n o t b em e a s ur e d , b u t o n l y t h e in p u t U , ( t ) a n d t h e o u t p u t to t ) . E q u a t i o n( A 6 ) a n d ( A 2 5 ) t h e n l e a d t o t h e m o d e ld a t o t ) d t o t )d t = + ~ l - - - ~ t + ~ t ot O t )- - - f l o A U 1 t ) (36)

w i t hR 1 CFI l ]~ = - E + T ~o = aT-Ic ~,Rl + ~ )

(37)o = - - -~ ( c r , = cvu~ + cFp~ .L~ 'As the re a re f ive unknown proc e s s c oe f f i c ie n t s a nd only thre ee s t im a te d pa ra m e te r s , the proc e s s c oe f f i c ie n t s c a nnot bec a lc u la te d unique ly . Tw o c oe f f i cie n t s ha ve to be know n. I f 0 a ndL~ a re known, R1,1P a nd c vl c a n be de te rm ine d . Thi s e xa m ples h o w s t h a t i t i s i m p o r t a n t t o m e a s u r e a s m a n y v a r i a b l e s a sposs ib le . I f the s t a t i c be ha viour c a n be ide nt i f i e d , on ly onep a r a m e t e r

c ould be e s t im a te d . The n two c oe f f i cie n t s ha ve to b e a s sum e d a sknow n, to de te rm in e one c oe ff ic ie n t. He nc e , a l so in th i s c a se m o rec oe f f i c ie n t s a re obta ine d by the use of dyna m ic m ode ls .I f too l i t t l e or no c oe f f i c ie n t s c a n be a s sum e d a s known, thes ingle proc e s s c oe f f i c ie n t s c a nnot be c a lc u la te d . Howe ve r , the nt h e c h a n g e s o f t h e p a r a m e t e r e s t i m a te s c a n b e m o n i t o r e d . T a b l e 1s h o w s t h e s i g n o f t h e se p a r a m e t e r e s t i m a t e s i n d e p e n d e n c e o n t h ec ha nge s ( f a u l t s) of the proc e s s c oe f f ide nt s . In th i s c a se only o nepa t t e rn i s un ique , tha t for Aq~ . T h e n a l s o t h e m a g n i t u d e s o f t h ec h a n g e s m a y b e t a k e n i n t o a c c o u n t , t o d e t e c t w h i ch o f t h e p r o c e s sc o e f f i c i e n t s h a s c h a n g e d , u s i n g t h e i r n o m i n a l v a l u e s a n dse ns i t iv i ty func t ions .(b) D . c. m o t o r , p u m p a n d p i p e s y s t e m r a h e o p e n e d ) . Now a l l foure qua t ions (25) - (28) ha ve to be use d .

(i) M e a s u r e d s i g n a l s : A U 1 , A l l , Aco, A Y t ) , A33( t )T h e f o u r e q u a t i o n s a r e n o w

y~ t ) = ~br t )Oj j - -- 1,2 ,3,4 ( 3 8 )


8/18

3 9 4 S u r v e y P a p e rTABLE 1. PATTERN FOR THE SIGN OF THE PARAMETERCHANGES

At / t A Af io+ A R t + + 0+ A ~ 0 + ++ AL~ - - -+ / t 0 - - -+ A c v t + + 0

w h e r ey l ( t ) = d l t ( t ) / d t y 2 ( t ) = d t o ( t ) / d t 3 9 )ya ( t ) = dAYt ( t ) / d t y , , ( t ) = A Y( t )~ r l t ) = [ A l 2 ( t ) Ac o( t ) AU~( t ) ]

o r = [ a l a a t 2 h i ]~ , ] ' ( t ) = [ A l l ( t ) A t a ( t) A ~ t ( t ) ]

O = [ a z l a ~ a 2 a ] ( 4 0 ) ~ ( t ) = JA M ( t ) A Y ( t ) ]

O = [ a ~ 3 d 3 ]~ / ( t ) = [ Ac o( t) A M ( t ) ]

o r = [ h ~ h ~ ]B y u s i n g ( 29 ) t e n p r o c e s s c o e f f i c i e n ts c a n b e c a l c u l a t e d f r o m t h et e n p a r a m e t e r e s t i m a t e s 0 j .

1

/ ~ l = - ~ 1 1 ~ = - t i l t / /~l= - - d t2L ~ . = - d t2 /b t

0 = ~ / d 2 1 = - a t 2 b l a 2 tOF, d - g , m - - t i220 m d22 t i l I /b ld 2 t (4 l )gM m -- d230 = a 2 3 a 1 2 b ld Z ld . o = 1/d3

~ M } d i r e c tl y a v a i l a b l e f r o m 0 , .

A l s o i n t h i s c a s e a ll p r o c e s s c o e f f i c ie n t s a r e o b t a i n a b l e a n d c a n h em o n i t o r e d . I n a d d i t i o n t o t h e l a s t e a s e, c Fl a n d g ,~ a r e l u m p e dt o g e t h e r .T h e u s e o f d y n a m i c m o d e l s i n s t e a d o f s t a ti c m o d e l s e n a b l e s o n e t oe s t i m a t e L ~ , 0 a n d a ~ .

(ii] S o m e s i g n a l s n o t m e a s u r a b l eT h e p r o b l e m s w h i c h a r is e, , i f I d t ) c a n n o t b e m e a s u r e d , h a v eb e e n a l r e a d y d i s c u s s e d , s e e (3 6 ). T h e r e f o r e i t w i l l b e a s s u m e d t h a ta t l e a s t U t t t ) , l ~ ( t ) a n d ~ o ( t) a r e m e a s u r e d .

Y ( t ) n o t m e a s u r a b l e , b u t ~ ( t ) .

I n t r o d u c t i o n o f (2 8 ) i n t o ( 2 7 ) le a d s t od , ~ t t )- - = ( a ~ 3 + d3 h ~ ) A , ( l( t ) + d3 h~ A~ o( t) . (42)d t

He nce . a s a~3, d 3, hu a n d h ~, a r e n o t o b t a i n e d s e p a r a t e l y , t h eproc e s s c oe f f ic ie n t s a n , a~ . h~ , h~, a nd Cr~ c a nn o t be de te rm ine d

un ique ly . Ho we ve r , al l r e m a in ing s ix c oe f f ic ie n t s c a n s t i l l beo b t a i n e d .l~t(t) n o t m e a s u r a b l e , b u t Y(t) .

Re p la c ing A~Q( t ) in (26) a nd (27) by us e o f t28 ) l e a ds to= a 2 1 A I l ( t ) - - A~( t ) + a 23Y ( t ) ( 4 3 )hM

d Y ( t ) , d to ( t )d---~- = (a~ 3 + d3h M) AY ( t ) + no , T - h~a 33A69(t ) (44 )N o w d 3 , h u a n d a 2 3 a r e n o t o b t a i n a b l e s e p a r a t e l y a n d t h e r e f o r et h e p r o c e s s c o e f f i c i e n t s an , a , , hu , g ~ a n d c v t c a n n o t b ed e t e r m i n e d u n i q u e l y , b u t o n l y t h e r e m a i n i n g f i v e c o e f f ic i e n ts .

M ( t ) a n d Y(t ) n o t m e a s u r a b l e .I n s e r t i n g ( 2 8 ) a n d ( 2 7 ) in t o ( 2 6 ) y ie l d s

d 2 m ( t ) d i n ( t ) d l l ( t )d t 2 = ~ z T + 2 o + / ~ t T + / ~ o A l t ( t ) ( 45 )w i t h

~ 2 = (a33 + d3hM - a22 ) 2 = a22(d3hu - a~3) - a23d3h~f12 = a21f lo = a~3d3hMa2t .

(46)

B a s e d o n ( 25 ), t h r e e p r o c e s s c o e f f i ci e n t s c a n b e e s t i m a t e d : L t , R )a n d ~ /. A s/ J1 e n a b l e s u s t o e s t i m a t e 0 . t h r e e p a r a m e t e r e s t i m a t e sr e m a i n t o d e t e r m i n e s i x co e f f ic i e n t s, w h i c h i s n o t p o s s i b l eu n i q u e l y . T h e r e f o r e t h r e e p r o c e s s c o e f f i c ie n t s a r e a s s u m e d t o b ek n o w n . H e n c e , i n t h i s c a s e. o n l y f o u r p r o c e s s c o e f f i c ie n t s c a n b ec a l c u l a t e d u n i q u e l y .I f t h e s en s o r s d o h a v e d y n a m i c s w h i c h c a n n o t h e n e g l e c te d i nc o m p a r i s o n t o t h e p r o c e s s, t h e y m u s t a l s o b e i n c l u d e d i n t h ep r o c e s s m o d e l .

5.3. E x p e r i m e n t a l r e s u l t s . E x p e r i m e n t s w e r e m a d e w i t h ac e n t r i fu g a l p u m p d r i v e n b y a s p e e d c o n t r o l l e d d . c. m o t o r . T h et e c h n i c a l d a t a a r e( a ) D . c . m o t o r :m a x i m um p o w e r P , , . = 4 k Wm a x i m u m r o t a t i o n s p e e d N m .~ = 3 0 0 0 r e v m i n - 1 .( b ) C e n t r i f u g a l p u m p , o n e s t a g e :

m a x i m u m t o t a l h e a d H m ~ - 3 9 mfor Nm,~ - 3000 rev min - i .( c ) P i p e s y s t e m : l e n g t h : L ~ 1 0 mdia m e te r : d l = 50 r a m .

T h e d . c . m o t o r i s c o n t r o l l e d b y a n a . c. / d .c , c o n v e r t e r w i t hc a s c a d e c o n t r o l o f t h e s p e ed a n d t h e a r m a t u r e c u r r e n t a sa u x i l i a r y c o n t r o l v a r i a b l e . T h e m a n i p u l a t e d v a r i a b l e i s t h ea r m a t u r e c u r r e n t U t . A m i c r o c o m p u t e r D E C - L S I 1 1/ 23 w a sc o n n e c t e d o n . l i n e t o t h e p r o c e s s . F o r t h e e x p e r i m e n t s t h ere fe re nc e va lue W ( t ) o f t h e s p e e d c o n t r o l h a s b e e n c h a n g e ds t e p w i s w i t h a m a g n i t u d e o f 2 ~ / o f N , , ~ , i .e . 6 0 r e v r a i n - t e v e r y6 0 s . T h e m e a s u r e d s i g n a l s w e r e s a m p l e d w i t h s a m p l i n g t i m eT o - - 2 m s o v e r a p e r i o d o f 2 s , s o t h a t 1 0 00 s a m p l i n g s w e r eo b t a i n e d .T h e s e m e a s u r e m e n t s w e r e s t o r e d i n t h e c o r e - m e m o r y . A f t e r 2 sm e a s u r e m e n t s t h e p a r a m e t e r s w e r e e s t i m a t e d o f f - l i n e , u s i n g t h er e c u r s i v e l e a s t - s q u a r e s m e t h o d w i t h s t a t e v a r i a b l e f i l te r s f o r t h ed e t e r m i n a t i o n o f t h e t i m e d e ri v a t i v e s. T h e a v a i l ab l e c o m p u t a t i o nt i m e f o r th e p a r a m e t e r s w a s 5 8 s . H e n c e , o n e s e t o f p a r a m e t e re s t i m a t e s w a s o b t a i n e d e v e r y m i n u t e . A s t h e n o i s e i s n e g l i g i b l ys m a l l , t h e p a r a m e t e r e s t i m a t e s c a n b e a s s u m e d t o b e u n b i a s e d .T h e f i r s t e x p e r i m e n t s w e r e p e r f o r m e d w i t h c l o s e d v a l v e . A s


9/18

Survey Paper 95de sc r ibe d be fore (d . c . m otor a nd pum p, c lose d va lve ) the n twoe q u a t i o n s c a n h e a p p l i e d f o r t h e p a r a m e t e r e s t i m a t io n . I n o r d e rto a l so obta in the a d he s ive f r i c t ion c oe f f ic ie n t , (35) ha s be e n use d

0 dco(t) i p l , ( t) Cro cwoJ t)d t

toge the r w i th (A1) for the a rm a ture c i r c u i td l l ( t )L~ d t U I t ) - R i l l t ) ~ c o ( Z ) .

The re fo re the de via t ions of the s igna l s ha ve to b e r e p la c e d in (33)by the i r a bsolu te va lue s . Th e proc e s s c oe f f i c ie n t s a re obta ine d by(34) with ~vo = - '~ ,30 in add it ion .I n F i g s 8 - 1 1 r e s u lt s o f t h e p a r a m e t e r m o n i t o r i n g a r e p r e s e n te d .F i g u r e 8 s h o w s t h e s t e p r e s p o n s e s a f t e r a s p e e d s e t p o i n t c h a n g e .The r e su l t ing proc e s s c oe f f i c ie n t s a f t e r a s t a r t o f the c o ld e ng ine(F ig . 9) , ind ic a te tha t th e a rm a tur e r e s i s t a nc e inc re a se s dur ing thef i r s t 1 0 m i n , t h e f l u x l i n k a g e d e c r e a s e s d u r i n g 2 0 r a i n a n d t h ef r i c t ion torque c oe f f ic ie n t de c re a se s dur i ng th e f i r st hour . He nc e ,sm a l l c ha n ge s of the p roc e s s c oe f f i c ie n t s c a n be de te c te d .F igure s 10 a nd 11 show the r e a c t ion on a r t i f i c ia l c ha nge s( fa u lt s) . A s igni f i c a nt c ha ng e of the a r m a ture r e s i s t a nc e e s t im a tei s de te c ta b le a f t e r a 7 c ha n ge (F ig . 10) . The e f fe ct of t igh te ninga n d l o o s e n i n g th e s c re w s o f t h e p u m p p a c k i n g b o x c a p i s d e a r l yse e n in F ig . 11 . M ore d e ta i l s a r e g ive n in Ge ige r (1982) . Re sul t s ofm o r e e x p e r i m e n t s i n c l u d i n g m u l t i p l e h y p o t h e s i s t e s t i n g f o r t h efa ul t de c i s ion a re de sc r ibe d in Ge ige r (1984) .T h e k n o w n l i t e r a t u r e s h o w s o n l y v e r y f ew a p p l i c a t i o n s o f t h i swa y of proc e s s pa ra m e te r f a u l t de te c t ion . Re sul t s w i th ah y d r a u l i c d r iv e o f a m a c h i n e t o o l a r e g i v e n i n H o h m a n n ( 19 7 7)a n d w i t h j e t e n g i n e s i n B a s k i o t is , R a y m o n d a n d R a u l t ( 19 7 9) a n dB a s k i o t i s e t a l . (1981). The l a s t r e fe renc e a l so inc lude s pa r a m e te rm o n i t o r i n g o f t h e h u m a n g l u c o se c o n t r o l s y s te m . R e s u l t s f o r a d .c .m o t o r a r e p u b l i s h e d b y F i l b e r t a n d M e t z g e r ( 1 98 2 ).

5 .4 . C o n c l u s i o n f o r p a r a m e t e r m o n i t o r in g . F a u l t d e t e c t i o n a n dd i a g n o s i s b a s e d o n p a r a m e t e r m o n i t o r i n g r e q u i r e p r e c i s et h e o r e t i ca l m o d e l s a n d p a r a m e t e r e s t i m a t i o n m e t h o d s .T h e u s e o f d y n a m i c m o d e l s i n s t e a d o f s t a t i c m o d e l s a l l o w s t om o ni t or m ore p roc e s s c oe ff ic ie n ts , th e m or e the h igh e r the orde r .A unique c a lc u la t ion of the proc e s s c oe f f i c ie n t s a n d ap a r a m e t e r e s t i m a t i o n w i t h h i g h p r e c i s i o n i s o n l y p o s s i b l e f o r lo wo r d e r e l e m e n t s b e t w e e n m e a s u r e d v a r i a b l e s . T h e r e f o r e t h em e a s u r e d v a r i a b l e s s h o u l d b e s e l e ct e d s u c h t h a t t h e p r o c e s s i sd iv ide d in f i r s t o rde r e le m e nts or , in o the r words , a l l s t a tev a r i a b l e s s h o u l d b e m e a s u r a b l e .E a s y t o i m p l e m e n t p a r a m e t e r e s t i m a t i o n m e t h o d s f o rc o n t i n u o u s - t i m e m o d e l s t o b e u s e d o n - l i n e , r e a l - t i m e a n d i nc l o se d l o o p n e e d t o b e d e v e l o p e d .

0.15 iI

0.12 ~10.9

0.6 ' ' ' 1.'5 t0 3 0 6 0 9 1.2 1.8[ s e c ] tF la . 8 . S te p r e sponse s for a c ha nge of the spe e d se tpoin t .u l ff i U 1 / 0 1 a r m a t u r e v o l ta g e 0 1 = 6 0 V , i l = f i l l s a r m a t u r ec ur re n t 11 = 0 .5A , c o = (o l /G 1 a ngula r ve loc i ty ~ = 62 .83s -=( ~ 6 00 r e v m in - ~ ) .

. . . . . v - - v

5

3 _l . . . . . . . . . . . . . . ~ ,_2r2 5 V

, - - ~ - - Fot J , ,0 20 /~0 60 80 100 120 1/.0[ ra in ] tFIG. 9. P r o c e s s c oe f f ic ie n t e s t im a te s a f t e r s t a r t o f the c o ld e ngine .RI a rm a tur e r e s i s t a nc e , ~P f lux l inka ge , C vo friction coefficient.

1.2r = ~ - - ~

111 00 90 . 8 ' ' ' ' 2 0 0 ' ', 0 8 0 120 160 2~0 280[ m i n l t

FIG. 10 . Cha ng e o f a rm a tu re c i r c u i t r e s i s t a nc e . ARs ,, , 0 . 2f l ,/~1 ~ 3f l , ~1 = ~1//I 1.

6 . L e a k d e t e c t i o n f o r p i p e l i n e sT h e d e t e c t i o n a n d l o c a l i z a t i o n o f l e a k s i n l i q u i d a n d g a sp i p e l i n e s i s i m p o r t a n t b e c a u s e o f s a f e t y , e n v i r o n m e n t a n de c o n o m y . T h e a p p l i e d m e t h o d s w h i c h w o r k d u r i n g n o r m a lo p e r a t i o n a r e m a i n l y b as e d o n b a l a n c in g t h e i n p u t a n d o u t p u tf lows . Howe ve r , le a ks sm a l le r tha n a bou t 2 of the to ta l f low forl i q u i d s a n d a b o u t 1 0 f o r g a s e s c a n n o t b e d e t e c te d b y t h e s em e t h o d s d u e t o n o i s e e ff ec ts a n d i n h e r e n t d y n a m i c s . O p p o s i t e t oe n g i n e s a n d o t h e r i n d u s t r i a l p l a n t s p i p e fi n e s ar e , i n g e n e r a l , n o tw e l l i n s t r u m e n t e d . T h e o n l y a v a i l a b l e s e n s o r s a r e m o s t l y f l o w - r a tea n d p r e s s u re a t b o t h e n d s o f a p i p e l i n e s e c t io n ( F i g . 1 2 ) . T h eq u e s t i o n n o w i s if , b y t h e u s e o f p r o c e ss m o d e l s a n d e s t i m a t i o nte c hnique s , i t w i ll be po ss ib le to de te c t a nd loc a l iz e sm a l l l e a ksra pid ly .T h e f o l lo w i n g c a se s h a v e t o b e d i s t i n g u i s h e d w i t h r e s p e c t t ole a k de te c t ion m e thods (S ie be r t , 1981) :( i ) M e diu m : l iqu id - ga s - m u l t ip le pha se .( i i) Op e ra t io n: s t a nds t i l l - s t a t io na ry - sm a l l c ha nge s -u n s t a t i o n a r y .( i ii ) Si z e o f l e a k ag e : l a r g e - m e d i u m - s m a l l ( p i p e b u r s t) .( iv ) D e v e l o p m e n t o f l e a k a g e: a b r u p t ( c r a ck i n g o f w e l d in g s e a m ) ;s low (hole c or ros ion) or a l r e a dy e xi s t ing .( v ) L e a k m o n i t o r i n g : c o n t i n u o u s l y - o n r e q u e s t .

6

2t t I

0 2 0 8 0 120

. . ~ e r i o d o fh g h t e n i n g ' , f ~ u l t t im e , ~ l o o s e n i n g160 2O0 2hO 280

[ m i n ] f

C Fo

F ZG . 1 I . C h a n g e o f p u m p p a c k i n g b o x f r i ct i o n b y t i g h t e n i n g a n dloose n ing of the c a p sc re ws .

FIG . 12 . Usu a l ins t rum e nta t ion of a p ipe l ine p pre ssure , ~ m a ssflow.


10/18

96 Survey PaperIn th e fo llowing, m e tho ds for l e a k d e te c t ion w i l l be d i sc usse df o r l i q u id s a n d g a s es , s t a t i o n a r y o p e r a t i o n w i t h s m a l l c h a n g e s o ft h e v a r ia b l es , s m a ll l ea k s w h i c h a p p e a r a b r u p t , a n d c o n t i n u o u sm o n i t o r i n g .6.1. M a t h e m a t i c a l p r o c e s s m o d e l s . T h e d y n a m i c m o d e l s o f ap ipe l ine a nd the sym bols use d a re de sc r ibe d in Appe ndix B .B a s e d o n t h e m a s s a n d m o m e n t u m b a l a n c e e q u a t i o n s , t h eq u a d r a t i c f r ic t io n l aw , t h e i s o t h e r m i c g a s s t a t e e q u a t i o n a n dv a r i o u s s i m p li f yi n g a s s u m p t i o n s a n o n l i n e a r h y p e r b o l i c p a r t i a ld i f f e re nti a l e qu a t ion sys te m i s obta in e d , (B9) . Af te r d iv id ing thepipe l ine in 1/2 se c t ions a nd d i sc re t i z a t ion of the d i f f e re nt i a le qua t ion s , a s e t of ord ina ry d i f f e re nt ia l e qua t ions r e su l t s whic hform s a non l ine a r s t a te spa c e m ode l , s e e (B15).Fo r sm a l l c ha ng e s a nd th e flow ~ in the pos i t ive z -d i r e c t ion ,t h e m o m e n t u m b a l a n c e e q u a t i o n o f ( B I 2 ) c a n b e l i n ea r i ze d

0 M jOt = g2(AP~+I - Ap~ _l) + 2g;(~_ I)AMj (47)

whe re a l l c oe l fi c ie n ts a re t a ke n for the s t e a dy - s ta te va lue s p j a ndM ' j. F u r t h e r o n t h e l i n e a r iz e d v al v e e q u a t i o n s a r e i n t r o d u c e d i n t h ef o r m

A p e = C , o A l d o + Ap,o )Ap,, ffi c'...A34 ,. + Ap,~. ? (49)

T h e n a l i n e a r s ta t e r e p r e s e n t a t i o nY c (t ) = A x ( t ) + B u ( t ) (49)y ( t ) = C x { t )

results , withx r ( t ) = [ A M o A M 2 . . . A M I I A p 1 A p ~ . . . A p l - l ]

ur [APi*AP'~ I (50)

Howe ve r , for m os t of the ga s p i p e l i n e s t h e n o n l i n e a r ( B 1 5 ) m u s tbe use d . I t i s be c a use of the i r b ig s tora ge c a pa c i t i e s a nd the t im e -d e p e n d e n t c o n s u m p t i o n t h a t t h e y r a r e ly c o m e t o a s t e a d y s t at e .6.2. M e t h o d s f o r l e a k d e t e c ti o n . I t i s a s sum e d tha t a sm a l l l e a kf low d2~ oc c ur s a t s e c t ion j = . The e f fe c t of the l e a k c a n bem o d e l e d b y i n t r o d u c i n g t h i s l ea k f l ow i n t o t h e m a s s b a l a n c e o fth i s s e c t ion , s e e (BI8) , l e a ding to (B20) . Thi s c ha nge s thel ine a r iz e d s ta te e qua t ion (49) to

. ~ (t ) = A x ( t ) + L v ( t ) + B u f f ) (51)wi th the l e a k f low ve c tor

v r ( t ) = [0 0 . . . l ~ L ~ . . . 0 i 0 . . . 0 ] (5 2)a nd the l e a k inf lue nc e m a t r ix

i 1L = / . . . 0 0 . . . O l 5 3 )6

: qt~ : 0 0L o . .. . - . . .He nc e a l e a k f low a pp e a r s a s a d i s turb a nc e of the s t a te va r ia b le sx ( t ) (Fig. 13).T h e l e ak m o n i t o r i n g t a s k n o w c o n s i s t s i n t h e d e t e ct i o n o f a na ppe a r ing l e a ka ge , i t s loc a l i s a t ion ~ t a long the p ipe l ine a nd thee s t im a t io n of it s si ze , '~ 'L . n m o s t c a se s only m e a s ure m e nts /~ 0( t kp o ( t ) a n d Mr(t ) , p~( t ) a t the in le t a nd the e x i t o f the p ipe l ine a rea va i l a b le .The r e su l t s of s im ula t ions for a ga sol ine a nd a n e thyle ne -ga spipe l ine a s sum ing d i f f e re nt loc a t ions of a sudde nly a ppe a r ing

Z

FIG. 13 . A le a k a pp e a r s a s d i s turba n c e v ( t ) (w i thout noi se t e rm s ) .

l e a k of 5 ~ of tb e f low- ra te a re show n in S ie be r t (1981) . I f the l e a kloc a t ion i s a bou t in the m idd le of the p ipe l ine the f lows .~ o( t ) a ndM d t ) c h a n g e w i t h a b o u t t h e s a m e s e t t l in g t i m e s a n d r e a c h t h e i rn e w s t e a d y - s ta t e s a f te r a b o u t 4 m i n f o r t h e g a s o l i n e p i p e li n e a n d2 h for th e ga s p ipe l ine . I f the l e a k i s c lose r to one e n d , the t im er e s p o n s es a n d t h e m a g n i t u d e s o f t h e f l ow c h a n g e s b e c o m e r a t h e rdifferent .N o w v a r i o u s a p p r o a c h e s f o r le a k m o n i t o r i n g a r e s h o w n ,fo l lowe d by e xpe r im e nta l r e su l t s w i th a r a the r s im ple m e thod.(a) F a u l t s e n s i t i v e fi l t e r s . For the de te c t ion of the l e a k a s t a teva r ia b le f i l t e r

S ; ( t ) = A . ~ ( t ) + B u ( t ) + H [ y ( t ) - C . ~ .( t) ] (54)c a n be de s igne d to e s t im a te the s t a te s a nd to c a lc u la te there s idua l s

. ~ t ) = y t ) - C ~ t ) 0 5 )t h e r e b y a s s u m i n g t h a t a l l p a r a m e t e r s o f t h e p i p e l i n e sy s t em a r ek n o w n .In the f i r s t a d ju s tm e nt pha se , the f i l t e r ga in H c a n b e l a rge sotha t a f a s t a d jus tm e nt oc c ur s in orde r to m a ke the f i l t e r l e s sse ns i t ive to h ig h f r e que nc y r e s idua l c ha nge s . For l e a k de te c t io nthe ga in H i s lowe re d . The n i f a l e a k MLg oc c ur s sud de nly there s idua l s .P(t ) show a va r ia t ion + AM o( t ) a nd - A~ dt ) , i . e . ther e s id u a l s c h a n g e i n p r e d e t e r m i n e d d i r e c t i o n s w h a t c a n b e u s e dfor the f a u l t de te c t ion .O n e d r a w b a c k o f t h i s m e t h o d i s t h a t t h e f i lt e r t r ie s t o m a t c h t h el e ak d i s t u r b e d p r o c e s s a f t er a w h i l e s o t h a t t h e i n f o r m a t i o n o n t h ele a k va ni she s w i th t im e .(b) F a u l t m o d e l f i l t e r s . A n o t h e r m e t h o d c o n s i s ts i n a n e s t im a t i o nof the l e a k f low ve c tor v ( t ) by m od e l ing th e f a u l t in f lue nc e in thef i l te r (F ig. 14) . The inf lue nc e of a sud de nly ( s t e pwise) a ppe a r in gle a k i s m ode le d by

( t ) = v ( t ) (56)so tha t the f i l t e r i s a b le to r e c ons t ruc t a r e m a in ing l e a k ve c tor

L37(t')dt'.(t) = H , (57)I f the f i l te r c onve rge s in the r ight wa y the e s t im a te d l e a k ve c torc ont a ins a s we l l as the s i ze , the s e c t ion n um be r ~ whe re the l e a ko c c u r re d . T o e x t r a c t t h i s i n f o r m a t i o n u n d e r n o i s y c o n d i t i o n s a'ba n k of f il te rs c ould be use d , a s sum ing d i f f e re nt loc a t ions ~ orthe l e a k ve c tor e s t im a te s c ould be c or re la te d w i th a ' f a u l ts igna ture ' , for e xa m ple th e f low prof i l e a f t e r a l e a k . Thi s r e l ie s onthe s t a te va r ia b le f a u l t de te c t ion m e thods d i sc usse d in Se c t ion3.2.A s i m u l a t i o n w i t h m u l t i p l e m o d e l h y p o t h e s i s p r o b a b i l i t yte s t ing for a n o i l p ipe l ine of 30 km le ngth , us ing pa ra l l e l K a lm a nfi l te rs , is descr ibed by Digernes (1980) . A leak of 1% of the tota lf low wa s de te c te d a f t e r a bo ut 160 s .

An oth e r r e fe re nc e on a f a u l t - s e ns i tive s t a te va r ia b le de te c to r i sC a n d y a n d R o z s a { 1 9 8 0 ) . H e r e a s i m u l a t i o n s t u d y o n t h ed e t e c t io n o f d i v er t e d o r s t o l e n n u c l e a r m a t e r i a l ( c o r r e s p o n d i n g t oa l e a k) in a p lu ton ium c o nc e n t ra tor by us in g s ta t i s t i c a l de c i s ionm e t h o d s f o r t h e r e s i d u a ls o f a n e x t e n d e d K a l m a n f i lt e r i s sh o w n .Re la t ive ly l a rge c om puta t ion t im e a nd s tora ge wa s r e qui re d .In ord e r to e s t im a te the l e a k loc a t ion for a p ipe l ine of I00 kmle ngth w i th a n a c c ura c y of a bo ut + 1 km a t l e a s t 50 se c t ions ha ve


11/18

S u r v e y P a p e r 3 9 7

Til

[Lr-

L E A K ~ ==={> ,.-.PIPELINE

t ,-PIPELINIST TEV RI BLEIFILTERI._1

F I G . 1 4 . P i p e l i n e s t a t e v a r i a b l e f i l t e r i n c l u d i n g a l e a k i n f l u e n c e m o d e l .

t o b e m o d e l e d s o t h a t a h i g h s y s t e m o r d e r r e s u l t s , w h i c h c a u s e sc o m p u t a t i o n a l p r o b l e m s f o r s t a n d a r d p r o c e ss c o m p u t e r s .A d d i t i o n a l l y , s ev e r a l p r o c e s s p a r a m e t e r s a r e n o t k n o w n p r e c is e l ye n o u g h , i . e . t h e f r i c t i o n c o e f f i c i e n t s , a n d a l s o s e v e r a l t e m p e r a t u r ee f fe c ts , s o th a t t h e m o d e l s h a v e t o b e u p d a t e d b y p a r a m e t e re s t i m a t i o n m e t h o d s ( B i l l m a n n , 1 9 83 ).T h e r e f o r e , a s i m p l e r m e t h o d w a s d e v e l o p e d f i rs t fo r l iq u i dp i p e li n e s , t a k i n g i n t o a c c o u n t s e v e r a l p r a c t i c a l r e q u i r e m e n t s a n ds p e c i a l c a s e s o f p i p e l in e o p e r a t i o n .( c ) A c r o s s - c o r r e l a t i o n m e t h o d .f o r l e a k d e t e c t i o n o f s t a t i o n a r yl i q u i d p i p e l i n e s . I t is a s s u m e d t h a t a l i q u i d p i p e l i n e o p e r a t e s i n as t a t i o n a r y s t e a d y - s t a t e a n d t h a t o n l y t h e f l o w - r a te s a t t h e i n le t, ~ l o k ) a n d t h e e x i t b ~ l (k ) c a n b e m e a s u r e d .

T h e s i m p le s t w e l l- k n o w n m e t h o d o f l e a k a g e m o n i t o r i n g i s th e nb y s t a t i n g a s t a t i c b a l a n c e e q u a t i o nM r( k) - -- A 'J 'o (k ) - - A , l , (k ) (58)

a n d b y t r i g g e r i n g a n a l a r m i f t h e l e a k f l o w M X ~ d S a c e r t a i nl im i t . T h i s p u r e b a l a n c i n g m e t h o d i s, h o w e v e r , n o t s u i t a b l e fo r t h ed e t e c t i o n o f s m a l l e r l e a k s, b e c a u s e o f t h e n o i s e s i g n a l s, d r i f ti n gm e a s u r e m e n t s a n d t h e d y n a m i c c h a n g e s o f b o t h f lo w s.A n i m p r o v e m e n t o f t h is m e t h o d i s o b t a i n e d b y d e t e r m i n i n g th el o w f r e q u e n c y c o m p o n e n t s o f t h e f l o w s b y d i s c r e t e - ti m e l o w - p a s sf i l t e r i n g

M ~ ' ( k ) = r M ~ * ( k - I ) + ( l - - r M ) ~ * ( k ) ( j = O , 1 ).( 5 9 )

b l ~ ' (k ) a n d M T ' ( k) a r e t h e n r e f e r e n c e v a l u e s , w h i c h m a y b ed i f fe r e n t b e c a u s e o f c a l i b r a t i o n e r r o r s o f t h e s e n s o r s , a n d c h a n g es l o w l y d u e t o t e m p e r a t u r e a n d v i s c o si t y c h a n g e s a l s o i n t h e c a s eo f c o n s t a n t p u m p i n g . A l e a k i s t h e n o b t a i n e d b y

AA4 o(k) = A,lo(k ) - J~,l~(k)a Y t , k ) = M ? k ) - M * k ) 6 O )

J~J'~.(k) = a A'J*o( k - aA,l~( k)o r b y f u r t h e r l o w - p a s s f i lt e r in g

~3(k ) = KLM L(k - - 1 ) - - ( I - - rL)A l~ . (k ) (61)w h e r e r L < r u i s r e q u i r e d i n o r d e r t o b e a b l e t o d e t e c t su d d e n l y -a p p e a r i n g l e a ks . I f M ~ ( k ) e x c e e d s a c e r t a i n t h r e s h o l d

~ ( k ) > ~a l e a k a l a r m i s g i v e n .B y t h e d e s c r i b e d l o w - p a s s f i l t e r i n g , n o i s e e f f e c t s a n d s l o w d r i f te f fe c t s c a n b e p a r t l y e l i m i n a t e d , b u t c h a n g e s o f t h e f lo w sa c c o r d i n g t o t h e i n h e r e n t fl u id d y n a m i c s c a u s e t h e a d j u s t m e n t o fi - e la t iv e l y l a r g e t h r e s h o l d s M L ~ i n o r d e r t o a v o i d t o o f r e q u e n t f a l s ea l a r m s .

T h i s i s o n e o f t h e r e a s o n s t h a t i t w a s p r o p o s e d t o c r o s s -c o r r e l a t e t h e d i f f e r e n c e s

tO ~ M( T ) = - - ~ A A ' / o ( k - c ) A M l ( k ) ( 6 2 )N k = l( l s e r m a n n a n d S i e b e r t , 1 97 6 , 1 9 77 ) . T h i s c r o s s - c o r r e l a t i o nf u n c t i o n r e a c t s s e n s i t i v e l y e v e n t o s m a l l l e a k s , r e d u c e s n o i s ee f fe c ts a n d m o d e l s i n h e r e n t d y n a m i c r e l a t i o n s h i p s b e t w e e n t h ef l o w c h a n g e s . F o r f u r t h e r n o i se r e d u c t i o n t h e c o r r e l a t i o n f u n c t i o ni s a v e r a g e d w i t h r e s p e c t t o

1 e1 ~ ( 1 )M M ( ~ ) ( 6 3 )O z = 2 P + = = _~,

A f t e r a le a k h a s o c c u r r e d t h e f a u l t s i g n a t u r e c o n s i s t s i n c h a n g e s+ A ~ o a n d - A 3 d t s o t h a t th e p r o d u c t s b e c o m e n e g a t i v e a n d O zd e c r e a s e s . A n a l a r m i s g i v e n , i f

~ < ~ . 6 4 )T h e c r o s s - c o r r e l a t i o n f u n c t i o n i s c a l c u l a t e d r e c u r s i v e ly w i t hf a d i n g m e m o r y P M u T ,k ) = 2 @ u M z , k - - 1 ) + ( 1 - - 2 ) [A A 4 o ( k - ~ ) A J ~ t ( k ) ]

( 6 5 )w h e r e 0 . 9 < 2 < 1. L a r g e r v a l u e s o f 2 r e s u l t i n i m p r o v e ds m o o t h i n g a n d t h u s r e d u c e t h e n o i s e , b u t le a d i n t u r n t o a d e l a y e da l a r m .A s s u m i n g s t a t i o n a r y o p e r a t i n g c o n d i t i o n s , t h e l o c a t i o n o f th el e a k c a n b e e s t i m a t e d b y c a l c u l a t i o n o f t h e p o i n t o f i n t e r se c t i o n o ft h e p r e s s u r e c u r v e s . T h e i r g r a d i e n t i s g i v e n f o r a t u r b u l e n t f l o w b y

~ p ~ 3 ~~ z c p = . ( 6 6 )Po - PaH e r e , t o o , i t i s a d v a n t a g e o u s t o u s e t h e d e v i a t i o n s f r o m ar e f e re n c e v a l u e. T h e r e f o r e , t h e p r e s s u r e g r a d i e n t s a r e e s t i m a t e db y r e c u r s i v e a v e r a g i n g w i t h f a d i n g m e m o r y

, . ~ / ] ( k )c j k ) = r c c .~ k - 1) + (1 - r d p o k ~ _ p : k ) j = O , I). ( 6 7 )

T h e n r e f e r e n c e m a s s f l o w s a r e d e t e r m i n e d4 , , k ) - -- - c j k ) ~ p o k ) - p~(k)] ( j = 0 ,1 ) . (68 )

A s s o o n a s a l e a k a g e a l a r m i s t r ig g e r e d , C o a n d c t a r e n o l o n g e rc a l c u l a t e d b u t f i xe d a n d t h e d i f f e re n c e sA ~ j ( k ) - - l V l f k ) - M ~ 2 ( k ) ( j = 0 , 1 ) ( 6 9 )


12/18

398 Survey Papera r e d e t e r m i n e d a n d s u m m e d u p . A s s u m i n g s m a l l l ea k s t h e l ea kloc a t ion i s g ive n by

2r = L ( l ZAMtk)l- ~ / 7 0 )

se e S ie be r t a nd I se rm a nn (1977). In a s im i la r wa y the l e a k f low i se s t im a te d .6.3. Experimental results with pipel ines Figure 15 shows thec ourse of the p ipe l ine c ons ide r ing the he ight a bove se a l e ve l a sw e ll a s t h e l o c a t i o n o f p u m p s . T h e t w o m a i n p u m p s a r e d r i v e n b yt w o 4 0 0 k W a s y n c h r o n o u s m a c h i n e s , w h i c h m a y b e o p e r a t e di n d i v i d u a ll y o r t o g e t h e r . A t f ul l p o w e r a b o u t 3 3 0 m 3 h - ~ a r ede l ive re d a t a n in i t i a l p re s sure of 69 ba r . Th i s pre s sure i sm e a sure d a f t e r the pum ps , but be fore the e n t r a nc e va lve .T h e l i n e h a s a d i a m e t e r o f 2 7 3 m m a n d a w a l l t h i c k n e s s o f8 ra m . In te rm e d ia te de pots a re loc a te d a t 21 .1 , 27 .3 , 35.8, 43.9 a nd46.7 km.The v olum e f lows a re m e a sure d by m e a n s of m e a sur ing or i fi ce sa nd Ba r ton c e l l s , p re s sure s w i th Ba r ton c e l l s ( a c c ura c y a bout0 .1 ~ ) . T h e v o l u m e f l o w V (l ) a t t h e e n d o f t b e l i n e i s t r a n s m i t t e dby a t e le m e t r i c de vic e, i . e. de via t ions f rom the ope ra t ing p oi n t - -a b o u t 1 /1 0 o f t h e t o t a l m e a s u r in g r a n g e ( 0 - 4 0 0 m 3 h - t } - - a r ee n c o d e d i n t o a n 8 - b i t- w o r d . T h i s c o r r e s p o n d s t o a r e s o l u t i o n o f0 . 1 6 m 3 h - t o r 0 . 0 5 ~ w i t h r e sp e c t t o 3 3 0 m 3 h - t .S i n c e t h e p r e s s u r e a t t h e e n d o f t h e l i n e w a s a l m o s t c o n s t a n t l ye q u a l t o a t m o s p h e r i c p r e s s u r e, r e c o r d i n g a n d p r o c e s si n g o f t h em e a s u r e m e n t v a r i a b l e p ( l) w a s d i s p e n s e d w i th . T h u s o n l y b o t hvolum e t r i c f lows F (0) a nd V ( l ) , a s we l l a s th e pre s sure a t theb e g i n n i n g o f t h e p i p e li n e , w er e u s e d f o r l e a k a g e m o n i t o r i n g . F o rf u r t h e r d et a i ls o n t h e p i p e l i n e a n d t h e e q u i p m e n t s e e S i e b e r t a n dKlaiber (1980) .A n I N T E L M D S 8 0 0 m i c r o c o m p u t e r d e v e l o p m e n t s y s t em w a su s e d t o c a r r y o u t t h e o n - l i n e e x p e r i m e n t s w i t h t h e p i p e l i n ed e s c r ib e d a b o v e . A n 8 - b i t m i c r o c o m p u t e r w i t h t h e 8 0 8 0 A c e n t r a lproc e s sor wa s use d. Th e sys te m i s e x te nd e d to 48 k of RAM .A n e x t e ns iv e p ro g r a m p a c k a g e - - 1 6 k b y t e s o f p r o g ra mm e m o r y - - f o r l e a k a g e m o n i t o r i n g w a s i m p l e m e n t e d o n t h em i c r o c o m p u t e r s y s te m i n t h e A S M 8 0 a s s e m b l e r l a n g u a g e .A se r ie s of e xpe r im e n ts for l e a ka ge de te c t ion we re c a r r i e d o uton th e p ipe l ine de sc r ibe d a bove , whe re l e a ks c ould be ge ne ra te da r t i f i c ia l ly a t the bra nc he s to the in te rm e dia te de pots .The fo l lowing va lue s we re a s sum e d for the c ons ta n t s :

xc

process fault detection based on modeling and estimation

Documents