Improving the Performance of PCA-Based Chiller Sensor Fault Detection by Sensitivity Analysis for the Training Data Set

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1 Purdue Uversty Purdue e-pubs Iteratal gh Perfrmace Buldgs Cferece Schl f Mechacal Egeerg 016 Imprvg the Perfrmace f PCA-Based Chller Sesr Fault Detect by Sestvty Aalyss fr the rag Data Set Yupeg u Wuha Buzess Uversty, Cha, Peple's Republc f, yupeghu@hust.edu.c Ja Lu Wuha Buzess Uversty, Cha, Peple's Republc f, @qq.cm L Zhu Wuha Buzess Uversty, Cha, Peple's Republc f, @qq.cm Yag Lu Wuha Buzess Uversty, Cha, Peple's Republc f, @qq.cm Qglg Qu Wuha Buzess Uversty, Cha, Peple's Republc f, @qq.cm Fllw ths ad addtal wrks at: u, Yupeg; Lu, Ja; Zhu, L; Lu, Yag; ad Qu, Qglg, "Imprvg the Perfrmace f PCA-Based Chller Sesr Fault Detect by Sestvty Aalyss fr the rag Data Set" 016). Iteratal gh Perfrmace Buldgs Cferece. Paper hs dcumet has bee made avalable thrugh Purdue e-pubs, a servce f the Purdue Uversty Lbrares. Please ctact epubs@purdue.edu fr addtal frmat. Cmplete prceedgs may be acqured prt ad CD-ROM drectly frm the Ray W. errck Labratres at errck/evets/rderlt.html

2 318, Page 1 Imprvg the Perfrmace f PCA-Based Chller Sesr Fault Detect by Sestvty Aalyss fr the rag Data Set Yupeg U*, Ja LIU, L ZOU, Yag LIU, Qglg QIU Wuha Busess Uversty, Departmet f Buldg Evrmet ad Eergy Egeerg, , Wuha, ube, PR Cha * Crrespdg Authr : , Yupegu@hust.edu.c ABSRAC A mprved apprach f fault detect fr chller sesrs s preseted based the sestvty aalyss fr the rgal data set used t tra the Prcpal Cmpet Aalyss PCA) mdel. Sesr faults are evtable due t the agg, evrmet, lcat ad s. Meawhle, because f the wde rage f peratal cdts, the fault f a certa sesr s very dffcult t be drectly detected by ts w hstrcal data. PCA s a multvarate data-based statstcal aalyss methd ad t s very useful fr the sesr fault detect VAC&R. he udetectable ze f a certa sesr by Q-statstc s derved frm the deft f Q-statstc whch s usually emplyed as a budary t detect the sesr fault stuat. Due t the smlar style betwee Q-statstc ad awks, the udetectable ze by awks s als btaed. Udetectable ze s a predctve dex t dcate the detectablty f dfferet sesrs by dfferet statstcs. Sce udetectable ze s the character f the rgal trag data set, t ca dcate the qualty fr the selected trag data. Oe feld data set s emplyed t valdate the preseted apprach. Results shw that the udetectable ze f a certa sesr by Q-statstc s qute dfferet frm that by awks. herefre, the udetectable ze ca be used t mprvg the perfrmace f PCA-based chller sesr fault detect by chsg dfferet fault detect statstcs wth less udetectable ze fr dfferet sesr. 1. INRODUCION Due t lg term perat ad severely wrkg evrmet, sesr faults are evtable VAC&R. here are much dsadvatage because f sesr fault, cludg effectve ctrl, usafe perat, ureasable eergy csumpt ad s Lee ad Yk, 010; Y et al., 011). Fr eergy savg ad cservat, researches sesr fault detect, dagss ad erreus sesr data recstruct FDDR) fr VAC&R system have bee pad mre attet t the last decade. Usually, the mdel-based methds ad the data-drve methds are the tw typcal classes f FDDR methds. Ay faulty sesr cat be easly detfed ust ly frm the hstrcal data f ts w. hus, varus multdmesal data-based methds have bee trduced t the FDDR f VAC&R system the recet years, such as fuzzy ferece systemskcygt, 015), data fussu et al., 010), eural etwrkdu et al., 014; Lee et al., 004), supprt vectr machea et al., 011), prcpal cmpet aalyssl et al., 016), fsher dscrmat aalyssdu et al., 007), Bayesa etwrkzha et al., 015), etc. Recet years, prcpal cmpet aalyss PCA) ärdle ad Smar, 007; Jacks, 1991), a multvarate statstcal aalyss methd, was preseted the sesr FDDR, cludg the whle systemwag et al., 010), AUL ad We, 014; Xa et al., 009), VAVDu et al., 009), chllerche ad La, 009; u et al., 016; Xu et al., 008) ad s. By the dfferet assgmet f sesrs r the cmbat wth ther algrthms, PCA-based appraches were successfully appled t sesr FDDR fr chller. May researchers were dedcated applyg vel data-drve methds t the sesr FDDR f VAC&R system. Fr ay data-drve methd, the aalyss results hghly deped the character f the trag data set. Because the felded data reles samplg terval, samplg lcat, measuremet prcples, ad s, the qualty f trag data s much wrse. wever, rare wrk was reprted hw t predct the qualty f the trag data s as t ehace the FDDR results detal. I ths paper, the udetectable ze fr each sesr assged PCA mdel s 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

3 318, Page preseted t evaluate the detectablty fr chller sesr fault. It s derved frm the trag data ad the deft f statstcs emplyed as fault detect budary. he udetectable ze fr each sesr ca be used t evaluate the fault detect ablty ad relablty wth clear physcal r thermdyamc meags. A felded data set f a real screw chller was emplyed t valdate the detectablty f dfferet statstcs detal.. PCA-BASED SENSOR FDDR.1 PCA-based sesr FDDR 0 m I PCA methd, the rgal data matrx X R usually cssts f m samples rws) ad prcess varables 0 m clums) btaed frm the feld measuremets. he trag data X, whch s cssted f the rgal measured data, s trasferred t a rmalzed matrx,, X x1 x m wth zer mea ad ut varace due t egeerg uts ad rders f magtude. After the egevalue decmpst f the cvarace matrx, R X X 1), ay rmalzed samples x ca be expressed as x xˆ x 1) where ˆx, the estmat f x, s the prect vectr f x t the PC subspace, ad x, the resdual f x, s the prect vectrs f x t the Resdual subspace. A cmm FDDR strategy fr sesr fault based PCA s llustrated as Fgure 1. Its detaled structure ca be referred referece u et al., 01). It eeds t emphasze that the rgal peratal data used t tra PCA mdel s cluded wth may utlers evtably due t measuremet errrs, hardware falure ad s. he am f PCA mdelg s t establsh a fault budary t detect whether there s a faulty sesr system r t. Fgure 1: A cmm FDDR strategy fr sesr fault based PCA Several statstcs ca be emplyed as the budary t detect sesr fault, such as Q, awks ad s. Whe the value f statstcs fr the tested sample s greater tha the budary, the fault ca be detected successfully. herefre, the belw equats mea the sesr fault cat be detected. Q Q ) 3) k; Where, Q α s the threshld f Q statstc ad k; s the threshld f awks. Udetectable Ze by Q-statstc If there s a faulty sesr, the measuremet data f ths sesr make the value f sme statstc s greater tha the threshld. Assumg the certa faulty sesr s the th sesr, there must be a par f lmted upsde ad dwsde f th sesr measuremet data, whch ca ust satsfy the Equat 1) r Equat ). Whe the measuremet data f the th sesr s utsde the par f lmtats, the fault ca be detected. Frm the threshld ad the ther sesrs. 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

4 318, Page 3 measuremet data, we derved the calculat f the lmtats fr the th sesr t t be detected. Obvusly, the par f lmtats s a predctve ze t demstrate the fault detectablty fr the th sesr. Assumg the th sesr s the faulty e, x, the th etry f x, s the erreus measuremet value. e, the th etry f x, ca be rewrtte as 1 RS RS RS RS RS k k k k,: k1 k 1 4) e y x y x y x y x Y x Where, y s the th etry f the th rw f RS drect f the erreus ser ad be wrtte as RS Y. Y RS s the prect matrx f RS. s used t dcate the ,, 1 1,, 5) herefre, Q-statstc ca be derved as Q y x y Y x x Y x RS RS RS RS ),: )),: ) ) Due t the th sesr s faulty e, ts Q-statstc wll satsfy the fllwg equat 7) y ) x y Y x)) x Y x) Q 0 RS RS RS RS,:,: ) Frm the style f Equat, t s a e-varable quadratc equaltes wth the frm f ax bx c>0. Where, a 1 1 y ) RS, RS RS b y Y,: x), 8) RS c Y,: x) -Q 1 he par f sluts f Equat 7), x,m ad x,max, are the lmtats fr the rmalzed sesr fault budary. A ze, 0 0 [ x, x ], ca be btaed by de-rmalzg. If the rgal measured data 0 x s utsde f 0 0 [ x, x ], we,m,max ca easly fd the faulty sesr. herefre, the area, 0 0 [ x,m, x,max ], ca be defed as the udetectable ze f the th sesr by Q-statstc. he udetectable ze ca be emplyed as the dex t evaluate the sesr fault detectablty..3 Udetectable Ze by Smlar wth the deft f Q-statstc, the awks ca be rewrtte as,m,max y x y Y x x Y x ),: )),: ) ) Where, 1/ Y P s the prect matrx f awks. herefre, the udetectable ze f the th sesr by k1, m awks ca be the sluts wth the style f ax bx c>0, where 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

5 318, Page 4 a 1 y ),: ) 1 b y Y x c Y,: x) -k ; 1 10) he udetectable ze by awks s qute dfferet t that by Q-statstc. herefre, the cmpared results ca dcate the dfferet sestvty fr these tw dfferet statstcs..4 PCA mdel fr a water-cled chller Frm the csderat f the eergy balace prcple, there are eght mprtat sesrs the water-cled chller ad ts ctrl lgc. he PCA mdel f a typcal water-cled chller s X M M W V 11) Where, ad are the temperature sesrs f let de ad utlet de f evapratr, respectvely. ad are the cdeser-water system let de temperature ad utlet de temperature, respectvely. M s the water flwrate f chlled-water system ad M s the water flwrate f cdeser-water system, respectvely. W s the electrcal pwer. V s the pst f the slde valve t dcate the mass flwrate f the refrgerat t the screw cmpressr. 3. VALIDAION 3.1 Cases study A felded data u et al., 01; u et al., 016) f a water-cled screw chller were used t valdate the sestvty f Q ad awks fr dfferet sesrs. he udetectable zes f dfferet sesrs by a same trag data set were vestgated. he results f sesr fault detect were used t valdate the predctve ablty f udetectable ze fr the faulty sesr. CASE I: wth -1.5 bas fault Udetectable ze f fr the trag data set s llustrated the Fgure. Fgure : Udetectable ze f fr the trag data set 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

6 318, Page 5 he up lmts f udetectable ze by Q s almst equal t that by awks, as well as the dw lmts f tw statstcs. Obvusly, the fault detectablty f by Q s equal t the ablty by awks. he udetectable ze f by Q s ±1.39, whle that by awks s ±0.67.here are ust the frmer 0 samples shw the hrztal axs rder t make the fgure clear. A bas fault wth -1.5 was trduced t t test the predctve ablty. he fault detect results by Q ad are llustrated Fgure 3 a) ad b). All the Q-statstcs values f tested samples are greater tha the Q α ad the detect effcecy f sesr fault by Q s 100 %. Meawhle, the -1.5 bas fault f s cmpletely detected by awks. herefre, the detectablty dcated by the udetectable ze f s accrdg t the fault detect results f tested samples f. he udetectable ze successfully predcted the fault detect results. CASE II: wth -.0 bas fault a) b) Fgure 3: Fault detect fr wth -1.5 bas fault: a) by Q b) by Udetectable ze f fr the trag data set s llustrated the Fgure 4. Fgure 4: Udetectable ze f fr the trag data set 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

7 Ulke t the results f 318, Page 6, the up ad dw lmts f udetectable ze by Q s qute dfferet t that by awks. he udetectable ze by Q s much greater tha that by awks. he udetectable ze f by Q s ver ±6.0, whle that by awks s less tha ±1. Csequetly, the detectablty f fault by awks s much better tha the ablty by Q. he fault detect results by Q ad are llustrated Fgure 5 ad Fgure 6, respectvely, whe a.0 bas fault was trduced t. here are ly 1% f Q-statstcs values the tested samples are greater tha the Q α. It meas that the fault detect by Q dd t wrkg. Meawhle, the.0 bas fault f s cmpletely detected by awks. Due the trduced fault level,.0, s less tha the udetectable ze by Q, ±6.0, the detectablty by Q s cmpletely wrse tha that by awks. herefre, t s better that the awks s emplyed t detect the fault. Fgure 5: Fault detect fr wth.0 bas fault by Q Fgure 6: Fault detect fr wth.0 bas fault by 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

8 318, Page 7 CASE III: M wth +10% bas fault he predctve results, udetectable ze, f M fr the trag data set s llustrated the Fgure 7. Meawhle the fault detect results f M by Q ad are llustrated Fgure 8. he udetectable ze by Q s early equal t that by awks, s the fault detect results f M by Q are accrdace wth that by. Fgure 7: Udetectable ze f M fr the trag data set a) Fgure 8: Fault detect fr M wth +10% bas fault: a) by Q ad b) by 3. Summary he udetectable zes fr all sesrs the PCA mdel by Q ad by are summarzed the able 1. he detect abltes fr dfferet sesr by Q ad by are qute dfferet. At the step fr chsg the ptmal statstcs t bta the fault budary, the udetectable ze ca drectly predct the detect ablty fr the sesr by a certa statstcs, such as Q r. herefre, the perfrmace f PCA-based sesr Fault detect ca be mprved by chsg the statstcs wth hgher fault detect effcecy by the sestvty aalyss fr the certa trag data set. b) 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

9 318, Page 8 able 1: Summary fr all sesrs Udetectable zes by Q ad by Sesr Ut Udetectable ze by Q Udetectable ze by M l/m M W l/m kw M ref %.78 ±1.39).47 ±1.4) 6.8 ±3.14) ±5.89) 1.77 ±6.39) 7.18 ±3.59) ±68.9) ±0.75) 1.74 ±0.67) 1.68 ±0.84) 6.35 ±3.18) 1.66 ±0.84) 1.61 ±0.81) 5.30 ±.65) ±34.04) 0.33 ±10.17) here s a mprtat pt llustrated by the case study ad the summary. he slut f udetectable ze s derved frm the matrx calculat prcess f dfferet statstcs. he results f udetectable ze ly rely the rgal trag data. herefre, the udetectable ze demstrates the rgal feature f the trag data. 4. CONCLUSIONS Sesr fault detect, dagss ad erreus data recstruct s the fudametal wrk fr the thermdyamc fault slat, the ptmal ctrl, the safety perat ad s. I ths paper, a evaluat dex, udetectable ze, s preseted t predct the detectablty f sesr fault s as t mprve the perfrmace f sesr fault detect. Dfferet calculat algrthm s derved t bta the udetectable ze by dfferet statstcs. Udetectable ze ca be emplyed as a dex t predct ad t evaluate the detectablty f sesr fault by sme statstcs fr a certa trag data set. It ca be used t chse the ptmal statstcs f fault detect fr each sesr. Frm the evaluat f detectablty fr each sesr by dfferet statstcs, the le sesr fault detect ca be mre flexble by chsg the mst sestve statstcs. herefre, the detect effcecy ca be prmted by the predct f udetectable ze. NOMENCLAURE he meclature shuld be lcated at the ed f the text usg the fllwg frmat: temperature ) M water flw rate l/m) W chller electrcal-pwer put kw) V pst f the slde valve -) X rgal matrx -) X 0 rmalzed rgal matrx -) R cvarace matrx -) U ege vectr matrx -) VE varace explaed -) CV cumulatve ctrbut f varace -) FDD fault detect ad dagss -) FDDR fault detect, dagss ad recstruct -) VAC&R heatg, vetlatg, ar-cdtg ad refrgerat -) 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

10 318, Page 9 PC Prcpal Cmpet -) PCA Prcpal Cmpet Aalyss -) SPCA Prcpal Cmpet Aalyss wth a statstcal data-cleag -) P PC subspace prect matrx -) P Resdual subspace prect matrx -) Q α threshld f the Q-statstc -) x a sample -) ˆx estmate f a sample -) x resdual f a sample -) x recstruct f a sample -) rc x the th etry f x -) e the th etry f e -) Greek letters μ σ λ 1,, λ Superscrpt Subscrpt mea stadard devat egevalues let de utlet de chlled-water system cdeser-water system REFERENCES Du, Z. M., J, X. Q. & Wu, L. Z. 007). PCA-FDA-Based Fault Dagss fr Sesrs VAV Systems. VAC&R Research, 13), Du, Z. M., J, X. Q. & Yag, X. B. 009). A rbt fault dagstc tl fr flw rate sesrs ar dampers ad VAV termals. Eergy ad Buldgs, 413), Du, Z., Fa, B., Ch, J. & J, X. 014). Sesr fault detect ad ts effcecy aalyss ar hadlg ut usg the cmbed eural etwrks. Eergy ad Buldgs, 70), a,., Gu, B., Kag, J. & L, Z. R. 011). Study a hybrd SVM mdel fr chller FDD applcats. Appled hermal Egeerg, 314), ärdle, W. & Smar, L. 007). Appled Multvarate Statstcal Aalyss Secd ed.). New Yrk: Sprger Berl edelberg. u, Y., Che,., Xe, J., Yag, X. & Zhu, C. 01). Chller sesr fault detect usg a self-adaptve Prcpal Cmpet Aalyss methd. Eergy ad Buldgs, 54, Jacks, J. E. 1991). A User's Gude Prcpal Cmpets Frst ed.). New Yrk: Jh Wley & Ss, Ic. Kcygt, N. 015). Fault ad sesr errr dagstc strateges fr a vapr cmpress refrgerat system by usg fuzzy ferece systems ad artfcal eural etwrk. Iteratal Jural f Refrgerat, 500), Lee, S.. & Yk, F. W.. 010). A study the eergy pealty f varus ar-sde system faults buldgs. Eergy ad Buldgs, 41), -10. Lee, W., use, J. M. & Kyg, N. 004). Subsystem level fault dagss f a buldg's ar-hadlg ut usg geeral regress eural etwrks. Appled Eergy, 77), L, G., u, Y., Che,., She, L., L,., u, M., Lu, J. & Su, K. 016). A mprved fault detect methd fr cpet cetrfugal chller faults usg the PCA-R-SVDD algrthm. Eergy ad Buldgs, 116, L, S. & We, J. 014). A mdel-based fault detect ad dagstc methdlgy based PCA methd ad wavelet trasfrm. Eergy ad Buldgs, 68, Part A0), Su, Y. J., Wag, S. W. & uag, G. S. 010). Ole sesr fault dagss fr rbust chller sequecg ctrl. 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016

11 318, Page 10 Iteratal Jural f hermal Sceces, 493), Wag, S. W., Zhu, Q. & Xa, F. 010). A system-level fault detect ad dagss strategy fr VAC systems vlvg sesr faults. Eergy ad Buldgs, 44), Xa, F., Wag, S. W., Xu, X.. & Ge, G. M. 009). A slat ehaced PCA methd wth expert-based multvarate decuplg fr sesr FDD ar-cdtg systems. Appled hermal Egeerg, 94), Y, S.., Paye, W. V. & Dmask, P. A. 011). Resdetal heat pump heatg perfrmace wth sgle faults mpsed. Appled hermal Egeerg, 315), Zha, Y., We, J. & Wag, S. 015). Dagstc Bayesa etwrks fr dagsg ar hadlg uts faults Part II: Faults cls ad sesrs. Appled hermal Egeerg, 90, ACKNOWLEDGEMEN he research wrk preseted ths paper s supprted by Natal Natural Scece Fudat f Cha Prect ), ad s fuded by Wuha Scece ad echlgy Bureau f Cha Prect ), ad s fuded by Beg Key Lab f eatg, Gas Supply, Vetlatg ad Ar Cdtg Egeerg Prect NR016K0), Cha, ad s supprted by state key labratry f cmpressr techlgy, Cha. 4 th Iteratal gh Perfrmace Buldgs Cferece at Purdue, July 11-14, 016