Study on Operator Reliability of Digital Control System in Nuclear Power Plants Based on Boolean Network

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1 Sudy o Operaor Relably of Dgal Corol Sysem Nuclear Power Plas Based o Boolea Nework Yahua Zou a,b,c, L Zhag a,b,c, Lcao Da c, Pegcheg L c a Isue of Huma Facors Egeerg ad Safey Maageme, Hua Isue of Techology, Hegyag, Cha b School of Nuclear Scece ad Techology, Uversy of Souh Cha, Hegyag, Cha c Huma Facor Isue, Uversy of Souh Cha, Hegyag, Cha Absrac: The curre huma relably aalyss mehod of aalyzg sysem operaor s relably, carred ou from he perspecve of operaors hemselves, s relavely sac, for has ake he effec of sysem evoluo o he operaors performace o cosderao I vew of operaor relably dgal corol sysem uclear power pla, hs paper, based o boolea ework heory, res o explore he operaors behavor he dyamc logc process of sysem evoluo, amg a fdg ou he dyamc evoluo process of huma-sysem eraco A ew echque, called he sem-esor produc of marces, ca cover he logcal sysems o sadard dscree-me dyamc sysems, ad he he dscree-me lear equao ad relably aalyss model are esablshed Daa colleced from smulao expermes carred ou full-sze smulaor LgDog Nuclear Power Pla s foud o be cossece wh he operaor relably model cosruced before Keywords: Boolea ework, Dgal corol sysem, Relably aalyss, Sem-esor produc of marces INTRODUCTION Wh he developme of scece ad echology, he safey ad effcecy of sysem ad equpme have bee mprovg, bu he relably of huma-mache sysem has bee depedg o ma Accordg o sascs, over 60% of faal casuales ad over 80% of serous casuales a home ad abroad are due o huma errors [,] The serous cosequeces caused by operaors have bee fully realzed afer he accdes a he Cherobyl uclear power pla ad he Amerca Three Mle Islad uclear power pla accdes Therefore, research o he relaoshp bewee operaors ad sysem, o qualave aalyss ad quaave assessme o huma operaos, has become creasgly mpora he egeerg feld [3] Ever sce dgal corol sysem was adoped uclear power pla, operaors have bee ejoyg he coveeces has brough abou, he meame, hey have also bee facg rsks of operao relably caused by eormous ad ceralzed formao I he ma corol room of a dgal corol sysem, he ceral dsplay of sysem alarmg, parameers ad pcures has formed a keyhole effec wh eormous formao ad lmed dsplay [,5], for he operaors, sce a radoal corol room, he operaors ca ake everyhg a a glace whle he ma corol room of a dgal corol sysem, hey have o use a compuer o carry ou erface maageme asks o fd formao promply ad effcely Ths shows ha he adopo off dgal echology has brough some ew rsks for operaors, ad wheher he relably of hem ca mee he safe ad ecoomc requremes has become oe of he urge problems a pla has o solve The mehod of Faul Tree Aalyss ad Eve Tree Aalyss are wo of he commo ways probablsc safey assessme However, case of accdes a a uclear power pla, he respose of he sysem or he behavor of a operaor chages wh he process of he accde, so a operaor s behavor a he ex me ode s closely relaed o he suao of he sysem ad he operao a he prevous me ode The radoal mehods of Faul Tree Aalyss ad Eve Tree Aalyss are sac aalyss echology based o Boolea Logc [6], whou akg he dyamc developme bewee Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

2 ma ad sysem o full cosderao, so s of sgfcace o probe o he dyamc relaoshp ad applyg o relably aalyss boh heorecal research ad dusral applcao O he bass of Boolea ework, ow a powerful ool sysem corol, Cheg Dazha pu forward a ew mehod of marx calculao--- sem-esor produc of marx [7,8], wh whch logc varable ca be expressed as vecor form, ad logc fuco as mulple lear mappg form However, uder algebrac expresso, Boolea ework equaos, havg all he formao of Boolea ework, are represeed by geeral dscree-me lear equaos Wh he mehod, Boolea ework equaos ca be esablshed o aalyze he operaos he dgal corol sysem a a uclear power pla by deermg he relaoshp bewee operaos wh daa colleced hrough aalog experme ad vdeo aalyss The d seco of hs paper s abou basc kowledge of sem-esor produc of marx, some basc properes eeded dervao, marx expresso of logc ad Boolea ework model The 3rd seco s abou he esablshme of Boolea ework of operaos, roducg he obame of experme daa ad he specfc process of model cosruco The h seco s cocluso ad dscusso, aalyzg o experme resuls ad dscussg fuure work PRELIMINARIES Frs, we gve some oaos for he saeme ease k ) Dk : = {0,,, }, k ; D: = D = {0,} k k ) Le δ be he h colum of he dey marx I 3) f : D D are logcal fucos ) Δ : Δ = { δ =,,, }, whe =, smply use Δ : =Δ 5) Deoe by COL( A) he se of colums of A 6) Assume a marx M = [ δ,,, s δ δ ] M s, s colums, COL( M ) Δ We call marx, ad smply deoe as M = δ[,,, s] 7) s Kroecher produc M a logcal Defo ad Proposo of he Sem-esor Produc of Marces [7,8,9,0] Defo (): () Le X = [ x,, x s ] be a row vecor, Y = [ y,, y ] T be a colum vecor : If s = The k XY, L : = X yk () k = Where X = [ X,, X ], X, =,, We call X, Y L a sem-esor produc : If = s The T T T XY, L : = ( Y, X L) () X, Y L also called a sem-esor produc () Assume M Mm, N M p q, f s he dvsor of p or p s he dvsor of We call C = M N s he sem-esor produc of M ad N j If C s composed of m q blocks, C = ( C ), meawhle j C = M, N j L, =,, m, j =,, q (3) Where M s a row of M, N s a colum of N j Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

3 Throughou hs paper, he marx produc s assumed o be he sem-esor produc I he followg, he symbol s omed The sem-esor produc has he followg properes Proposo (): () If A Mm p, B M p q The A B= A( B I ) () () If A Mm, B Mp q The A B= ( A I ) B (5) p m Proposo (): Le X R, Y R be wo colums The W[ m, ] X Y = Y X; (6) W[ m, ] Y X = X Y (7) Where W[ m, ] s a m m marx, called he swap marx Proposo (3): Le x Δ The x = Mx r (8) Where M = δ [, ] s called he power-reducg marx r Marces Expresso of Logc [7,8,9,0] A logcal varable meas a proposo Whe he proposo s rue, we say ha he logcal varable akes value T or, ad whe s false, he logcal varable akes value F or 0 I classcal logc a logcal varable ca oly ake values from { 0,} We oe 0 T : = ; 0 F : = 0 ; (9) Four fudameal operaors usually be used are Cojuco P Q, Dsjuco P Q, Codoal P Q, ad Bcodoal P Q A coveoal way o depc he values of a operaor s usg a able, called he ruh able We ca have ruh able for cojuco, dsjuco, codoal, ad bcodoal, respecvely as Table Table : Truh Table p q p q p q p q p q Defo (): Le σ be a r-ary logcal operaor Mσ M s called he srucure marx of σ, r f he vecor form we have σ ( p, pr ) = Mσ p p pr = Mσ p pr (0) Theorem (): Assume f ( x,, x ) s a logcal fuco, ad he vecor form we have f : Δ Δ The here exss a uque logcal marx M f, called he srucure marx of f, such ha followg equao() holds f ( x,, x ) = M x () f Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

4 Where x = x = Usg Theorem (), he srucure marx of four fudameal operaors are obaed as M : = M = c δ [,,,] ; M : = M = d δ [,,, ] ; M : = M = δ [,,, ] ; M : = M = e δ [,,,] 3 Boolea Nework Boolea ework was frsly roduced by Kaufma o formulae he cell eworks The, becomes a powerful ool descrbg, aalyzg, ad smulag he cell eworks, ad also be used as models of some complex sysems such as eural eworks A Boolea ework s a dreced ework graph, cosss of a se of odes, ad a se of edges Defo (3): A Boolea ework s a se of odes x, x,, x, whch erac wh each oher a sychroous maer A each gve me = 0,,, a ode has oly oe of wo dffere values: or 0 Thus he ework ca be descrbed by a se of equaos: x( + ) = f( x( ),, x ( )) x( + ) = f( x( ),, x ( )) () x( + ) = f( x ( ),, x( )) Where f : D D, =,, are -ary logcal fucos, x () D are sae varables 3 MODEL CONSTRUCTION I dgal corol sysem, a operaor s work volves moorg, suao assessme, respose plag ad respose mplemeao [] Suppose x (), x (), x 3 (), x (), x ( =,,3,) D represe he operaos a (a cera me), x (), x(), x3(), x() represe moorg, suao assessme, respose plag ad respose mplemeao respecvely, dcaes ha a operaor akes some aco, whle 0 o aco For sace, f a a cera me, x (), x(), x3(), x() has he values (,, 0, 0), ha meas he operaor ake he acos of moorg ad suao assessme a hs mome Thus, he operaor s behavor a ay mome ca be expressed a four-dmesoal array, he evoluo of he operaor s behavor s equal o ha of he array Wh hs absrac mehod, he operaor s behavor a dffere me ca be arraged usg he mehod of mome, so as o aalyze he dyamc process of he operaor s behavor he evoluo of he sysem 3 Experme Daa Source ad Explaao The experme daa of hs paper are from he Seam Geeraor Tube Rupure experme Lgdog Nuclear Power Pla carred ou o full-scale smulaor The reaso why SGTR s chose s ha s a ypcal problem of relably relaed o operaos afer al accde a a uclear power pla, ad hey are crucal huma s operaos o be cosdered PSA aalyss [] 8 ses of daa are obaed afer observao ad aalyss: Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

5 ) = 0, ( 0,0,,0) ; =, (0,0,0,) ; =, (,0,0,0); = 3, (0,,0,0); =, (, 0, 0,) ; = 5, (,, 0, 0) ; = 6, (,,,) ; ) = 0, (, 0,, 0) ; =, (0,,0,) ; =, (, 0, 0,) ; 3) = 0, (0,,,) ; =, (,0,0,) ; =, (,,,) ; ) = 0, (0,0,,) ; =, (,, 0,) ; =, (,,,) ; 5) = 0, (,,,0) ; =, (,,,) ; 6) = 0, (0,,,0) ; =, (, 0, 0,) ; 7) = 0, (, 0,,) ; =, (,, 0,) ; 8) = 0, ( 0,0,0,0) ; =, ( 0,0,0,0) ; As 7 experme daa are eeded o deerme a four-oded Boolea ework model, 8 dffere me odes are chose as sarg observao pos o avod beg specal, ad daa are obaed I he above 8 ses of daa, all he me odes are dscree, bu he me odes of each se of experme daa are successve The erval s he me eeded by a operaor o chage hs operao from oe mome o aoher As here are addoal accdes plaed he experme, four operao models happe smulaeously a some me odes As for he 8h se of daa, dcaes ha whe a operaor akes o aco, he suao wll be beer, ad he same wll happe a ex me ode 3 Algebrac Form of Boolea Nework From equao (), he key o buld he dyamc relaoshp bewee hese four varables s o deerme he four logc fuco Defe x() = = x( ), from equao () ad (), we have x( + ) = Mx( ) x( + ) = Mx( ) (3) x3( + ) = M3x( ) x( + ) = Mx( ) Where M M, called he srucure marx of f r Equao (3) s called he compoe-wse algebrac form of () The, x( ) ) x() M x() + = = x( + ) = Mx( ) Mx( M3 () Refer o [7,8,0], (3) ca furher be covered as x ( + ) = Lx() (5) Where L L s called he raso marx of he sysem Equao (5) s called he algebrac form of () Refer o [8], was proved ha (),(3),(5) are equvale o each oher Whle buldg model () drecly seems much more dffcul, we prefer o cosruc model (3) or (5) by calculag he srucure marx of M or he raso marx L Nex sep, we use he expermeal daa colleced seco 3 o cosruc model (3) ad (5) 33 Dyamc Model Cosruco of A Operaor s Performace For he frs expermeal daa, he vecor form [8,3], we have Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

6 = = δ, ad (0,0,,0) X (0) [,,,] x (0) = δ δ δ δ = δ 6 Smlarly, we ca calculae 5 x () = δ6 ; x () = δ 8 6 ; x (3) = δ6 ; x () = δ 7 6 ; x (5) = δ 6 ; x (6) = δ 6 The followg proposo ca help us o deerme he colum of he raso marx L Proposo ()[3]: If x () = δ ad x ( + ) = δ, he h colum of he raso marx L s j Col ( L) = δ (6) j Usg he Proposo, s kow ha 5 8 Col( L) = δ6 ; Col5( L) = δ6 ; Col8( L) = δ 6 ; 7 Col( L) = δ6 ; Col7( L) = δ6; Col( L) = δ6 The 6 colums of L have bee deermed Usg he same procedure o he oher groups of daa, cera values of colum of ou L ca be fgured Fally, we ca oba L = δ [,,,,3,,,,3,7,7,7,3,5,8,6] (7) 6 Refer o [3], he correspodg rerevers are The S = δ [,,,,,,,,,,,,,,,]; S = δ [,,,,,,,,,,,,,,,]; S = δ [,,,,,,,,,,,,,,,]; 3 S = δ [,,,,,,,,,,,,,,,] M = S L= δ [,,,,,,,,,,,,,,,] ; M = S L= δ [,,,,,,,,,,,,,,,] ; M = S L= δ [,,,,,,,,,,,,,,,]; 3 3 M = S L= δ [,,,,,,,,,,,,,,,] Cosder he logcal expresso of x () x ( + ) = Mx ( ) = δ [,,,,,,,,,,,,,,, ] x ( ) I s easy o verfy ha M ( M I ) = 0; MW ( M I ) 0; [,] MW ( M I ) = 0; [,] MW ( M I ) 0 [,8] Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

7 So x (), x () are fabrcaed varables he dyamc equao of x ( + ) 3 Seg x() = x3() = δ, he x ( + ) = Mx ( ) = Mx( x ) ( x ) ( x ) ( ) 3 = M x() W x() x() x() [,] 3 = M ( I W ) x () x () x () x () [,] 3 = M ( I W )( δ ) x () x () [,] = δ [,,,] x ( x ) ( ) Hece s logcal expresso s x ( + ) = ( x ( )) x ( ) The same procedure ca be used o cosruc he logcal expresso of x (), x (), x () Fally, 3 he logcal expresso of he dyamcs of he operaors performace s obaed as x( + ) = ( x( )) x( ) x( + ) = x( ) [ x3( ) x( )] (8) x3( + ) = x( ) x( ) x( + ) = x( ) x3( ) Is ework graph depced Fg Fg: Nework Graph The above Boolea Nework equaos are he cosruced dyamc model of a operaor I ca be see from equao (8) ha f moorg ad suao assessme are carred ou a a me ode, respose plag wll be carred ou a he ex; ha f suao assessme or respose plag s carred ou a a me ode, a specfc operao wll be doe a he ex; ha f moorg ad /or respose plag ad specfc operao are carred ou a oe me ode, suao assessme o he sysem wll be carred ou a he ex; ad ha f suao assessme or specfc operao s carred ou a a me ode, moorg wll be carred ou a he ex Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

8 CONCLUSION AND DISCUSSION I he pas, aalyss o huma s operao was carred ou hrough sac aalyss echology o he bass of Boolea algebra o work ou huma s error probably [3], focusg o aalyss from a operaor s cogve behavor, falg o show how hs operao chaged wh he suao of he sysem, seldom cosderg he dyamc relaoshp bewee operaos a dffere me odes Ths paper, defe he operaor s behavor he sysem process as a sae varables, usg a array of expresso, he evoluo of operaor s behavor wh process of cde could be absrac, he he logcal process could be chaged o algebrac expresso ad cosruc he logcal equao of operaos Ths mehod has shed ew lgh o aalyzg he relably of operaos ad he relaoshp bewee hem, ad has also show he characerscs of some operaos a a uclear power pla For example, a se of daa as (,0,0,0) (0,,0,0) (0,0,,0) (0,0,0,) ca be deduced from model (8), whch shows ha moorg, suao assessme, respose plag ad respose mplemeao, whch ca be overlappg, have o be carred ou repeaedly a a uclear power pla uder he Sae Oreed Procedure(SOP) Though he aalyss mehod pu forward hs paper s of sgfcace makg up he adequacy of he radoal mehod of sac aalyss o huma relably o he bass of Boolea Logc, he Boolea ework models are specal sce hey are deduced accordg o daa obaed from oe aalog experme If dffere aalog expermes ca be carred ou over ad over aga wh hs mehod o aalyze he relaoshp bewee operaos dffere expermes, he geeral dyamc relaoshp bewee operaos may be deduced a dgal corol sysem Ackowledgemes Ths work was suppored by he Naoal Naural Scece Foudao of Cha (Gra No737070, 70705), Naoal Naural Scece Foudao for youg (Gra No730069) ad Research Projec of LgDog uclear Power Co Ld (Gra NoKR7053) Refereces [] Wag Hog-de ad Gao We Sudy o Erroeous Operao due o Huma Facor Based o Huma Cogve Relably (HCR) Model, Cha Safey Scece Joural, volume6, pp 5-56, (006) [] Zhag L Huma Error Aalyss ad Preveves, Nuclear Power Egeerg, volume, pp 9-96, (990) [3] Zhag L The Research o Huma Relably Aalyss Techque Probablsc Safey Assessme, Aomc Eergy Press, 006, Bejg [] Zhag L, Yag Da-x ad Wag Y-qu The Effec of Iformao Dsplay o Huma Relably a Dgal Corol Room, Cha Safey Scece Joural, volume0, pp 8-85, (00) [5] Gu Pegfe, Zhag Jabo ad Su Yogb The Huma Relably he Accde Processg of NPP, Scece & Techology Revew, volume30, pp 5-55, (0) [6] Yu Yu, Tog Jejua, Lu Tao, Zhao Ju ad Zhag Alg Accde Aalyss by Phase-msso Mehods Nuclear Pla, Scece & Techology Revew, volume7, pp 83-86, (009) [7] Cheg Da-zha, Q Hog-sheg ad Zhao Y Aalyss ad Corol of Boolea Neworks: A Sem-esor Produc Approach, Aca Auomaca Sca, volume37, pp 59-50, (0) [8] Cheg Da-zha ad Q Hog-sheg Sem-esor Produc of Marces: Theory ad Applcaos, Scece Press, 007, Bejg [9] Cheg D Marx ad Polyomal Approach o Dyamcs Corol Sysems, Scece Press, 00, Bejg [0] Cheg D Z ad Q H S A lear represeao of dyamcs of Boolea eworks, IEEE Trasacos o Auomac Corol, volume55, pp 5-58, (00) Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa

9 [] Offce of Nuclear Regulaory Research Compuer-Based Procedure Sysems: Techcal Bass ad Huma Facors Revew Gudace, Washgo DC: US Nuclear Regulaory Commsso [] Yu Yua-gao Huma Relably Aalyss Seam Geeraor Tube Rupure Icdes, Shagha Jao Tog Uversy, 008, Shagha [3] Dazha Cheg, Hogsheg Q ad Zhqag L Model Cosruco of Boolea Nework va Observed Daa, IEEE Trasacos o NeuralcNework, volume, pp , (0) Probablsc Safey Assessme ad Maageme PSAM, Jue 0, Hoolulu, Hawa