FAULT DETECTION AND DIAGNOSIS METHOD FOR VAV TERMINAL UNITS

Transcription

1 ESL-IC FAUL DEECION AND DIAGNOSIS MEHOD FOR VAV ERMINAL UNIS Maao Miyaa*, Harunori Yohida*, Maahiko Aada*, Fulin Wang*, and Shiro Hahiguhi** * Deparmen of Uran and Environmenal Engineering, yoo Univeriy, ** Yamaake, Co., Ld Summary: hi paper propoe wo faul deeion and diagnoi mehod for VAV uni wihou a enor of upply air volume, and he reul of applying hee mehod o a real uilding are preened. One mehod dee faul y applying a aiial mehod o four value alulaed uing he room air emperaure and he demand value of VAV damper opening of eah uni during a eady ae operaion period. From he reul of ae udie, he mehod an redue he numer of uni o e heked a fauly one down o 1% of he oal numer and all he uni ha really have a faul are inluded in hi group. he oher mehod judge he faul y applying dynami yem analyi o he operaional daa when he VAV yem ar up. From he reul of he ae udie, he mehod an redue he numer of uni down o 3%, among whih five uni aually have a faul and only one fauly uni wa no inluded in hi group. Boh mehod an redue ime and o for ommiioning of VAV uni ignifianly y he help of BEMS. eyword: Commiioning, VAV erminal uni, Faul deeion and diagnoi mehod 1. INRODUCION Variale Air Volume (VAV) Air Condiioning Syem are widely ued all over he world eaue of he high energy aving feaure. However i i repored ha he poiiliy of faul ourrene, uh a damper and auaor uk, and defe in onrol logi, i unforunaely high 1) ). Epeially ine he numer of VAV uni inalled in large uilding i omeime more han one houand, deeing he faul i eoming an imporan iue. For example in a uilding, whih he auhor inveigaed, all he VAV uni are manually and rouinely heked every year pending a grea deal of udge and manpower and quie many faul have een aually deeed. o ope wih hi iue, i i needed o develop an auomai faul deeion and diagnoi (FDD) ehnology. In he pa a few ype of FDD mehod, uh a, an Exponenially Weighed Moving Average (EWMA) mehod y J. Seem e al. and an RAR model mehod y H. Yohida e al., were propoed 3) 4) 5) 6). hee mehod require he airflow rae of eah VAV uni for FDD, however, i i no availale in old ype VAV uni eaue of no inallaion of an airflow rae enor. hi paper propoe wo kind of FDD mehod for hi ype of VAV uni. One mehod (Mehod A) i aed on a aiial deeion of oulier daa among onrol ignal of VAV opening raio during eady ae period (non-arup and lunh ime period). he oher mehod (Mehod B) i aed on applying dynami yem analyi o arup period daa. he oh mehod are verified uing operaion daa oained a a real offie uilding.. FDD MEHOD USING HE DAA OF SEADY SAE PERIOD (MEHOD A) Figure-1 repreen a general model of a VAV yem ha i ued o derie propoed FDD mehod. he yem ha an air-handling uni and M N zone, eah of whih ha one VAV uni. Eah zone i named a Zi (, j) and eah uni i named a Ui (, j ) (i =1,,..., M, j =1,,..., N ). he zone urrounding Z (1,1), for example, are defined a Z (,1) and Z (1,). he zone urrounding Z (,1) are defined a Z (1,1), Z (,) and Z (1,3). In he ae of he zone Z (,), he urrounding zone are defined a Z (1,), Z (,1), Z (3,) and Z (,3). All uni do no have an airflow enor. hi aumpion i no proper for he reen VAV produ u here are ill a grea numer of yem equipped wih old ype (1,1) (1,)... (1, N) VAV uni like he uilding udied y preen reearh. In hi paper, wo kind of faul are analyzed, whih are fully-loe damper (,1) (,)... (, N) and fully-open damper. he reaon of eleing hee wo faul i ha he M uni oher kind of faul, for example damper uk a middle-range poiion, were no found in he uilding ha he auhor inveigaed..1 Definiion of FDD Parameer he following four FDD parameer are defined for eah uni uing he zone air emperaure θ r, he e poin of room emperaure θ r and he (M, 1) (M, ) N uni (M, N) Figure-1 Aumed VAV yem Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

2 ESL-IC demand onrol ignal of VAV damper opening φ during eady ae period. a) Differene eween zone emperaure and emperaure e poin = θ θ (1) ai (, j) r r ) Demand onrol ignal of VAV damper opening φ φmin( i, j) i (, j) = 1 φ min( i, j) ) emperaure differene eween he analyzed zone and he average of he urrounding zone = θ ( θ )/ N (3) i (, j) r r( kl,) d) Differene eween demand ignal of VAV damper opening and he average of hoe of urrounding zone = φ ( φ )/ N (4) d ( kl,) One or all parameer of a fauly uni are expeed o e aiially anormal ompared wih hoe of normal uni. Namely, in he ae of a fully-loe damper faul ome of hem are expeed o e larger and in he ae of a fully-open damper faul ome of hem are expeed o e maller during ooling operaion.. Gru e In order o dee a faul auomaially, a aiial mehod alled a Gru e i applied o he aove-menioned four parameer. hi e i a ommon aiial mehod o dee oulier among a e of daa 7). he hypohei and he Gru e aii are defined a follow. Null hypohei Alernaive hypohei Gru e aii : : here are no oulier in he daae : here i a lea one oulier in he daae e xmax x = (5) () Where, x i he ample mean, x max i a ample wih maximum diane from x, and i he andard deviaion. Gru e aii e i he large aolue deviaion from he ample mean in uni of he ample andard deviaion. When he ignifiane level i e α, he null hypohei of no oulier i rejeed if e ( n 1) > SG = n α /n α /n ( n ) + Where, α /n i he riial value of he -diriuion wih ( n ) degree of freedom and a ignifiane level of α /n. hi mehod an hek only one oulier per rial. So if x max i judged a an oulier, i i expunged from he daa e and he e i oninued unil he null hypohei i aeped. he proedure of Gru e i hown in Figure-. Gru e i aed on he aumpion of normaliy. ha i, i mu e verified wheher he daa e an e reaonaly approximaed y a normal diriuion efore applying hi e. (6) Daa Se = { x i i = 1,,...,n} Find x max wih he maximum diane fromx Equion 5 Equion 6 v. < > x max in' unexpeed value x max i unexpeed value Remove x max from Finih Condu Again Figure- Flow of Gru e.3 FDD Proedure Uing Operaional Daa of Seady Sae Period Baed on he aove diuion, he FDD mehod uing operaional daa of eady ae period i propoed a follow. 1) Reord θ r, θ r and φ during eady ae period (non-arup and lunh ime period). ) Calulae he average of eah parameer defined y Equaion (1) o (4), i.e. ai (, j), i (, j), i (, j) and d, for eah VAV uni uing he daa oained a ep 1). 3) Apply Gru e o he ample of ai (, j), i (, j), i (, j) and d eparaely, and dee an exreme value in Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

3 ESL-IC eah daa e. he VAV uni whoe parameer i judged a exreme value i a fauly uni. If he exreme value i larger han he oher value, he uni i upeed o have a fully-loe damper faul. If he exreme value i maller han he oher, he uni i upeed o have a fully-open damper faul. 3. FDD MEHOD USING DYNAMIC MODEL AND DAA OF SARUP PERIOD (MEHOD B) In hi eion a FDD mehod aed on dynami yem analyi i propoed eaue he FDD Mehod A menioned in he previou eion ha a limiaion in deeing faul when φ alway ik o he minimum value. Even hough hi i a kind of a onrol or deign faul we need o dee hardware faul of VAV uni. During he arup ime of air ondiioning, airflow rae generally egin from maximum and dereae o a erain low level. hi period an e defined a a dynami ae and a new FDD mehod aed on a dynami yem analyi an e applied. 3.1 Single-Inpu Single-Oupu Dynami Syem A ingle-inpu and ingle-oupu (SISO) dynami yem i onidered a hown in Figure-3. he relaionhip eween he inpu u and he oupu y of he yem an e expreed y he following equaion if aking he yem a he fir order differenial equaion y approximaion. dy y u d + = (7) When he iniial value of y equal zero, he general oluion of Equaion (7) i hown in Equaion (8). he oluion of an impule repone y i and a ep repone y are expreed y Equaion (9) and (1) repeively. ( τ ) y () = e u( τ) dτ (8) yi = e (9) y = (1 e ) (1) Figure-4 and Figure-5 how he ehavior of he impule repone and he ep repone. In he Figure-5, how he eady ae value of y and how he ime onan of he yem. 3. FDD Mehod Uing he Repone Funion Figure-5 Sep repone he repone of zone air emperaure during VAV yem arup period i imilar o he ep repone of SISO yem. herefore he ep repone Equaion (1) i ued in hi FDD mehod. he VAV yem arup period i defined a he period during whih zone air emperaure goe down or up unil i eome eady. he required ime i defined a and he eady zone air emperaure i defined a θr ( ). We define upply air enile hea a he inpu and room air emperaure a he oupu. he inpu u, he oupu y and he eady ae value are expreed a follow. u () = ρv φ()( θ () θ ()) ( ) (11) p max r y () = θr() θr() ( ) (1) = θ () θ ( ) (13) r r For differen VAV yem, he value of θr ( ) and are generally differen. In order o deermine he value of θr ( ) and uiale for he yem, he emperaure of all meaured zone i averaged and he average emperaure θ () i approximaed uing he following equaion. θ () ae + (14) Figure-3 SISO dynami yem Figure-4 Impule repone Figure-6 Convergene ondiion a, and of he equaion are fied uing he meaured emperaure y he lea quare mehod. A hown in Figure-6, θr ( ) i defined a he value of, and i defined a he ime when he differene eween θ () and onvergen value eome 1% of. Alhough he ehavior of zone air emperaure i aumed o e he ep repone a hown in Equaion (1), i i no he.63 Inpu y() y() u() S Oupu y() Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

4 ESL-IC ep repone exaly. In order o imulae he ehavior of y more auraely, he following equaion ha omine he impule repone and he upply air enile hea i ued inead of Equaion (1). j y () = yi ( τ) u ( τ) dτ e u ( j ) (15) j= Uing he meaured daa y ˆ( ) and u ˆ( ), i alulaed y he lea quare mehod. In general, i ake a few minue ha zone air emperaure ge down afer he VAV yem ar up. L i defined a he ime delay and i eimaed uing he operaional daa afer VAV yem ar up exep he daa during he ime delay period L (5 15 min). L τ L min y ˆ() e uˆ( τ + L) = L τ = (16) Beaue migh e differen on differen day and for differen yem, i andardized uing he average µ and he andard deviaion σ of a yem on a ame meaured day a hown in Equaion (17). µ = (17) σ Faul of VAV uni are deeed and diagnoed uing he differene of eween he analyzed uni and he urrounding uni. he definiion of he urrounding uni i he ame a he previou eion. = ( )/ N (18) ( kl,) If a uni ha a fully-loe damper faul, of he uni i larger han he oher uni eaue he peed of repone i mall. If he uni ha a fully-open damper faul, hould e maller han he oher uni. 3.3 FDD Proedure Uing he Dynami Sae Daa Baed on he aove diuion, he FDD mehod uing he dynami ae daa i propoed a follow. 1) Reord θ r (), θ (), φ () in dynami ae. Reommended daa ampling ime i 6 eond. ) Calulae θ () and deermine and θr ( ) uing Equaion (14). 3) Calulae of eah uni uing he operaional daa in minue afer VAV yem ar up. 4) Calulae, he average of in all meaured day. If i larger han he oher uni, he uni migh have fully-loe damper faul. If i maller, he uni migh have fully-open damper faul. 4. VERIFICAION FOR HE WO FDD MEHODS he wo FDD mehod are validaed uing he daa olleed from VAV yem in a real uilding in okyo Japan. he informaion on he VAV yem i deried in he following eion Informaion of he VAV Syem for Verifiaion In order o verify he propoed mehod, operaional daa of he VAV yem in a large offie uilding were olleed. he onfiguraion of he uilding ogeher wih du work, VAV uni and he air-handling uni are hown in Figure-7. Every floor i divided ino four zone and eah zone ha a VAV air handling uni () yem (WN, WS, EN and ES). Eah yem ha 15 VAV uni (W1, W,..., E5). he oal numer of VAV uni in he uilding i aou 1, and no uni i equipped wih an airflow rae enor. Meauremen wa ondued from Augu o Ooer 3. he deail of meauremen are hown in ale-1. In hi Enlarged WN EN WS ES W1 W W3 W4 W5 Figure-7 Building plan and VAV yem plan C1 C C3 C4 C5 E1 E E3 E4 E5 Floor ale-1 Ouline of meaured daa Syem Amoun of meaured daa 11h ES 7 day 1h ES 4 day 13h EN 3 day 15h WS 9 day 16h WS 1 day 5h WN 9 day 6h WN 5 day 1h ES 7 day 1h EN 5 day W3( loe ) C3( open ) W1( loe ) W( open ) C3( loe ) none none none none 13h ES 5 day none Real fauly uni E5( loe ) Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

5 ESL-IC E5 (Cloed) C C3 (Cloed) E5 (Cloed) C5 W Se Poin E3 W3 C3 (Cloed) 6: 8: 1: 1: 14: 16: 18: : :. 6: 8: 1: 1: 14: 16: 18: : : Figure-8 Operaional daa in WS yem on 16h floor (3/8/9) E3 C3 (Opened) 5 Se Poin 4 C3 (Opened) E4 3 E3 6: 8: 1: 1: 14: 16: 18: : :. 6: 8: 1: 1: 14: 16: 18: : : Figure-9 Operaional daa in ES yem on 1h floor (3/9/9) uilding, aou 5 o 1 % of he oal uni have een found o e fauly every year y rouine manual hek aou he airflow rae of he VAV uni. In he preen reearh, aed on he reul of he hek ondued in April 3, we hoe 1 yem and arried ou he meauremen. 5 yem of whih inluded fauly uni and he oher 5 yem didn' inlude any fauly uni. he kind of reorded daa are room air emperaure, e poin of room emperaure, demand ignal of VAV damper opening, and upply air emperaure of eah uni and he ampling ime i 1 minue. Figure-8 and Figure-9 how he example of he meauremen reul. Figure-8 how he operaional daa of WS yem on 16h floor and hi yem ha wo fauly uni wih fully-loe malfunion. One i Uni-E5, whih uanially affe he room emperaure. he oher i Uni-C3, whih doen' muh affe he room emperaure eaue he zone i urrounded y eigh uni wih no faul. Figure-9 how he daa of ES yem on 1h floor and he yem ha one fauly uni wih fully-open malfunion. he zone emperaure of fauly Uni-C3 i lower han he emperaure e poin eaue of he faul. Bu he emperaure of Zone-E3 ha i ounded y Zone-C3 i lower han ha of Zone-C3. he fauly uni omeime affe no only he i zone emperaure u alo hoe of he urround zone. he meaured daa how ha he demand ignal of VAV damper opening of mo uni are auraed a a minimum value e for eah uni. hi mean ha he airflow rae of eah uni i no well onrolled a inended. 4. Verifiaion of he FDD Mehod A In order o verify he effeivene of Mehod A, he mehod i applied o he real operaional daa menioned aove. FDD e i ondued on 15 VAV uni in 1 yem. he exiene of four VAV uni wih a fully-loe damper faul and wo uni wih a fully-open damper faul ou of 15 VAV uni had een repored y he preliminary manual hek o all uni. Alhough he loaion of he fauly uni are known, however, he FDD e i ondued o he yem auming hey are unknown. he period of eady ae are defined a he period from wo hour afer yem arup unil hudown exep lunhime (1: 14:). In hi reearh, he ignifiane level α for he Gru e i.1. he general value of α i.1 or.5, u he faul ouldn e deeed when we ued hee value. If α wa e larger han.1, he numer of fale alarm go larger and he reliane of alarm wa down. From he e, we reommend ha he uiale value of α i.1. Figure-1 o Figure-13 how he hiogram of a,, and d. he hrehold eween normal uni and fauly uni defined y he Gru e are hown on he figure. From Figure-11, i an e aid ha he diriuion of i no normal diriuion and Gru e hould no e applied o he parameer. Bu here are 11 uni whoe value i zero. I mean he demand ignal of VAV damper opening i alway zero over he meauring period. A we an eaily ay ha i i anormal, uh uni an e judged o have fully-open damper faul. Similarly, when he Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

6 ESL-IC Faul (Opened) Normal Faul (Cloed) ES-C WS-W 1ES-C3 11ES-W WS-W 11ES-W Defferene eween emperaure and emperaure e poin [ o C] Figure-1 Hiogram of Faul (Opened) Normal Mehod 15WS-W 1ES-C3 emperaure differene eween analyzed zone and urrounding zone [ o C] 11ES-W3 Figure-1 Hiogram of Faul (Cloed) Faul (Opened) Demand value of VAV damper opening [-] Figure-11 Hiogram of a 1ES-C3 Normal 15WS-W Differene eween demand of damper opening and ha of urrounding zone [-] Figure-13 Hiogram of d ale- FDD reul of Mehod A Fully-loed damper faul Fully-opened damper faul 11ES 13EN 16WS 16WS 1ES 15WS W3 W1 C3 E5 C3 W Numer of alarm Numer of fale alarm Faul (Cloed) 11ES-W3 Numer of real fauly uni ha an' e deeed Parameer a) 15 1% 1 67% 1 17% Parameer ) 11 7% 9 8% 4 67% Parameer ) 7 5% 4 57% 3 5% Parameer d) 1% % 4 67% a) U ) 17 11% 1 71% 1 17% ) U d) 8 5% 4 5% 33% a) U ) U ) U d) 18 1% 1 67% % 1. value of i one, hoe uni an e judged o have fully-loe damper faul. ale- how wheher he rue fauly uni an e idenified and diagnoed orrely or no y he preen e mehod. he amoun of alarm, fale alarm, and he rue fauly uni ha were deeed are lied in ale-. In he ale, he mark of " " how he VAV uni whoe faul an e idenified and diagnoed orrely y he e and he mark of " " how he fauly uni ha an e idenified u anno e diagnoed orrely. By aking he union of he four e, i.e. (a d ), he numer of upeed fauly uni an e redued from 15 (1%) o 18 (1%) and all he uni ha ruly have faul are inluded in he 18 uni. hi reul mean ha Mehod A an redue he required ime, and manpower or o for 8.5 ommiioning y aou 9% ompared wih hoe needed y he Simulaed preen manual hek, whih i generally done y eing all he uni. 8 Moreover, if he union of he wo e, namely onidering he omparion wih he urrounding uni ( d ), i applied, we an idenify and diagnoe he faul ha ignifianly affe he room air emperaure y heking only 8 uni (5%). If idenifying ju he uni ha ignifianly affe room emperaure i enough, hi mehod i appropriae. In all e mehod, he faul of Uni-C3 in WS yem on 16h floor, whih i urrounded y many normally operaed uni, Average emperaure of all zone Figure-14 Fiing reul of θ Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

7 ESL-IC Meaured Simulaed Meaured Simulaed Meaured Simulaed Figure-15 Uni-C3 in WN yem on 6h floor (3/9/1) Figure-16 Uni-C3 in WN yem on 16h floor (3/8/7) Figure-17 Uni-C3 in WN yem on 1h floor (3/9/1) anno e idenified or diagnoed orrely. When a fauly uni i urrounded y many normally operaed uni, he preen mehod omeime fail. 4.3 Verifiaion of he FDD Mehod B Mehod B i verified y applying i o he real operaional daa of he uilding formerly menioned. A FDD ep ), and θr ( ) of he yem i deided. Figure-14 how he reul of he alulaion. of he yem i 115 minue and θr ( ) i 6.79 o C. i alulaed per meaured day per uni. A he example of he alulaion, he reul of Uni-C3 in WN yem on 6h floor, Uni-C3 in WS yem on 16h floor and Uni-C3 in ES yem on 1h floor are hown in Figure-15 o Figure-17. he figure how ha he auray of he imulaion i no good eaue of he aumpion ha hi yem i he fir order yem. Figure-18 how he hiogram of and ale-3 how he numer of alarm, fale alarm and undeeale real fauly uni when he hrehold hange from µ ± σ, µ ± σ, µ ± 3σ. I i lear ha all real fauly uni exep for Uni-C3 in WS yem on 16h floor an e deeed if he hrehold i µ ± σ, u Uni-W in WS yem on 15h floor anno e diagnoed orrely. he numer of alarm 46 (31% of all uni) i larger han ha of Mehod A and he reduion of o and ime for ommiioning i alo maller han Mehod A. If he hrehold i µ ± 3σ, he mehod give he alarm for four uni and hree of he alarm are righ, and he oher 3 fauly uni anno e deeed. From he ae udie uing he real offie uilding, 16 3σ σ - σ σ σ 3σ Mehod B i no o effiien from he view poin of he 14 numer of alarm and undeeale uni ompared wih 1 Mehod A. We ondued ae udie in variale ondiion, 1 1ES-C3 for example hanging he amoun of daa or load ondiion, 8 15WS-W 11ES-W3 u no aendany of Mehod B over Mehod A wa found. 6 he mehod may no dee and diagnoe faul orrely 4 if he ooling load haraerii of a zone are largely differen from he urrounding zone. In hi ae, he operaional daa of he uni in uh zone mu e removed from he daa e for analyzing. And he mehod are aed Figure-18 Hiogram of on he aumpion ha room emperaure enor are free of ale-3 FDD reul uing Mehod B faul. I mu e heked wheher he emperaure enor indiae proper value efore applying he FDD mehod. 5. CONCLUSIONS wo FDD mehod for VAV uni are propoed in he preen work. Boh mehod only require imple daa, room emperaure, demand onrol ignal of VAV damper opening hrehold Numer of alarm Numer of fale alarm Numer of real fauly uni ha an' e deeed µ ± 46 31% 41 89% 1 17% µ ± 11 7% 8 73% 3 5% µ ± 3 4 3% 1 5% 3 5% Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4

8 ESL-IC and upply air emperaure, whih are eaily oained from BEMS. he following are he onluion aed on he ae udie uing real uilding operaional daa. 1) A mehod i propoed o dee faul y applying he Gru e o four parameer alulaed from he room air emperaure and he demand onrol ignal of VAV damper opening of eah uni under eady ae operaion. When omining all he FDD reul of he four parameer, he numer of upeed fauly uni an e redued down o 1% of he oal numer and every uni ha ruly ha a faul i inluded in he uni. hu, he 9% o or manpower for he ommiioning an e redue ompared wih he preen e proedure hrough whih all uni are manually heked. ) When omining he FDD reul of he wo parameer aed on omparing he room emperaure and he demand ignal wih hoe of he urrounding VAV uni, he numer of he upeed fauly uni an e redued down o 5% of he oal numer. In hi ae however, a fauly uni ha doe no ignifianly affe he room air emperaure urrounded y normal uni i very diffiul o e deeed. 3) A FDD mehod uing dynami yem analyi i propoed. In hi mehod he operaion during arup period i regarded dynami. he numer of upeed uni y hi mehod i aou 3% of he whole VAV uni and five uni wih a rue faul an e deeed ou of ix uni. However deeing a fauly uni urrounded y a few normal uni i alo diffiul. NOMENCLAURE a,, : Fiing parameer of Equaion (14) [ -] p : Speifi hea of air [kj/kg * ] : Gain of a fir order yem L : ime delay of SISO yem [min] n : Numer of ample in daa e [-] N : Numer of zone urrounding Zi (, j ) [-] α : Criial Value of diriuion wih ( n ) /n degree of freedom and a ignifiane level α /n : ime onan of a fir order yem u : Inpu of SISO yem : Sandard deviaion of daa e V max : Maximum value of upply air volume [m 3 /h] x : Sample mean of daa e x max : Sample wih he maximum diane from x in daa e y : Oupu of SISO yem y : Iniial value of y : Sandardizaion value of µ : Average of σ : Sandard deviaion of θ r : Zone air emperaure of Zi (, j ) [ o C] θ r : Se poin of room air emperaure [ o C] θ : emperaure of he zone urrounding Zi (, j ) r( kl,) [ o C] θ () : Average air emperaure in all meaured day [ o C] θ : Supply air emperaure [ o C] φ : Demand onrol ignal of VAV damper opening of Ui (, j ) [-] φ : Demand onrol ignal of VAV damper opening of ( kl,) he zone urrounding Ui (, j ) [-] φ min( i, j) : Minimum value of VAV damper opening [-] ρ : Air deniy [kg/m 3 ] REFERENCES 1) IEA Annex 5, Building Opimizaion and Faul Diagnoi Soure Book, Ed. J. Hyvarinen and S. arki, ehnial Reearh Cener of Finland, 1996 ) Harunori Yohida: ypial Faul of Air Condiioning Syem and Faul Deeion y AR Model and Exended alman Filer, ASHRAE ranaion, Vol.1, Par 1, pp , Fe ) Seem, J.E., Houe, J.M. and Monroe, R.H.: On-Line Monioring and Faul Deeion, ASHRAE Journal, Vol.41, No.7, pp1-6, ) Galler, M.A., Park, C., Coa, N.S., Buhy, S..: Uing he Virual Cyernei Building eed and FDD e Shell for FDD ool Developmen, NISIR ) Daniel Choiniere, Samuel Beaudoin: Faul Deeion and Diagnoi ool for VAV Boxe, IEA Annex 34 Deeion and Diagnoi Mehod in Real Building, Ed. A. Dexer and J. Pakanen, Seion C., pp , 1 6) Harunori Yohida, Sanjay umar, Yaunori Moria: Online Faul Deeion and Diagnoi in VAV Air Handling Uni y RAR Modeling, Energy and Building, Vol.33, pp , 1 7) NIS/SEMAECH e-handook of Saiial Mehod: hp:// Gru e for Oulier Proeeding of he Fourh Inernaional Conferene for Enhaned Building Operaion, Pari, Frane, Ooer 18-19, 4