Key Variable Based Detection of Sensor Faults in a Power Plant Case

Transcription

1 Key Varable Based Detecton of Sensor Faults n a Power Plant Case Rku-Pekka Nkula*, Vlle aukkanen**, Esko Juuso*, Kauko evskä* *Control Engneerng aboratory, P.O.Box 43, FIN-94 nversty of Oulu, Fnland (e-mal: rku-pekka.nkula@oulu.f) **Indmeas, Tetäjänte, FIN-3 Espoo, Fnland Abstract: In ths study, an approach for detecton of sensor faults s presented. It s based on an dentfcaton prncple, whch takes nto account lnear relatonshps between process varables and a key varable. Smple lnear regresson models are created for varables wth a strong correlaton. Relatve lmts are defned for the varables usng actual values and response values from the lnear models. The lmts are used to scale the varables and to montor exceptonally hgh and low values. The proposed approach s tested wth real data from a coal-fred power plant. To demonstrate the behavour of the approach on a fault stuaton, smulated sensor faults are montored. The results mply that the approach s applcable to cases wth strong lnear relatonshps. The approach asssts n revealng nherent lnear relatonshps n a process to support the development of sensor valdaton approaches and to create lmts for montorng. Keywords: fault detecton, outler detecton, process montorng, sensor valdaton, varable dentfcaton. INTRODCTION Good qualty of sensor data collected from an ndustral process s an essental factor to relable operaton of the process. Sensor faults are almost nevtable even wth the most advanced desgn of nstruments especally n harsh ndustral envronments. A fault s to be understood as a nonpermtted devaton of a characterstc property whch leads to nablty to fulfll the ntended purpose (Isermann, 984). Roughly speakng, sensor faults can be categorzed as hard faults wth abrupt changes and as soft faults, whch are slowly developng falures (Goebel and an, 8), (Frank, 99). Smulaton of four types of sensor faults, ncludng bas, precson degradaton, drftng and complete falure are presented n (Qn and, 999). In real envronments, sensor nose, deteroraton, system dynamcs, and changng condtons brng challenges to detecton of sensor faults. It s mportant to dstngush sensor faults from process changes, because process changes can nterfere wth sensor fault detecton. Process changes can be categorzed nto: () unmeasured, normal process changes; () slow process degradaton; and () abnormal process changes (Qn and, 999). The process s consdered to be stable but t has changes n the operatonal state n ths study. The detecton of sensor values that do not conform to the assumed behavour s related to outler detecton. Outlers can be referred as statstcal anomales. The term outler descrbes a type of data pont that s not representatve of the sample beng consdered. Typcally, outler detecton methods have the assumpton of dentcally and ndependently dstrbuted (..d.) data. In that case, the sample mean and varance gve The research was funded by the Fnnsh Fundng Agency for Technology and Innovaton (TEKES) through the Measurement, Montorng and Envronmental Assessment (MMEA) programme. good estmaton for data locaton and spread. The popular 3σ rule s based on the dea of detectng the observatons lyng further than three standard devatons from the mean (Oakland and Followell, 99). Hampel Identfer replaces the outler-senstve mean wth the medan and the standard devaton wth the medan absolute devaton from the medan (Pearson, ). Chang et al. (3) compare many outler detecton methods on data from the Tennessee Eastman Process smulator n ther study. A physcal system that nvolves several sensors montorng the operatng state has usually certan relatonshps between the sensor values. The expected value of one sensor mght be obtaned from the remanng sensor values nvolved n the same relatonshp. The verfcaton of sensor values wth other nformaton s called sensor valdaton, whch s often based on redundancy of several sensors. Physcal redundancy nvolves redundant sensors measurng the same parameter of the system (Goebel and an, 8). Analytcal redundancy, on the other hand, utlzes a functonal relatonshp between the sensors that are of dfferent types or postoned at dfferent locatons (Walker and Wyatt-Mar, 995). In addton, categorzaton nto spatal redundancy, temporal redundancy and knowledge-based redundancy s presented n lterature (Frank, 99), (ee, 994). Some sensor valdaton methods produce sensor health nformaton from a sngle sensor (Ma et al., 999), (Näs et al., 5). An ndustral plant has probably thousands of sensors montorng numerous targets. When new methods for montorng the plant are put nto operaton, t s tme consumng to fnd and defne parameters for every object ndvdually. In that case, an approach whch takes several process varables and uses the nherent redundances n the process to automatcally dentfy certan characterstcs and parameters s useful. The dentfed parameters can be

2 quckly taken to use and an nsght nto the process characterstcs s ganed. In ths study, a straghtforward dentfcaton and montorng approach for process varables s presented. Offlne dentfcaton takes advantage of strong lnear relatonshps between a key varable and other varables. Relatve lmts for the dentfed varables are defned. These relatve lmts are used n onlne montorng to fnd exceptonally hgh or low sensor values and to scale all the varables to the same range. Scalng s lnear between the relatve lmts and the used slope s defned based on the range, n whch a data pont falls. In contrast to ths, the use of nonlnear scalng for varables has been proposed especally for nonlnear, complex, and hghly nteractve ndustral processes (Juuso, 4). An mportant feature of the scalng approaches s that the varables can be presented n the same range. When the numercal values of varables are gven n the same range, ther comparson s convenent. The approach s tested wth process data from Helsnk Energy Salmsaar power plant. The plant s a combned heat and power unt burnng coal as man fuel. Next Secton explans the dentfcaton prncple, the scalng method and fault smulaton. Identfed varables and ther relatve lmts are presented after that. Results of smulated drft fault detecton are presented and applcablty of the approach dscussed thereafter. Fnally, the study s summarsed.. METHODS. The Proposed Approach to Identfcaton and Montorng Process data from normal operaton of the process s frst fed to the offlne dentfcaton part. Data should be fltered so that t does not contan anomalous perods. One varable s chosen to be a key varable, to whch other varables correlate f defned demands are met. A good startng pont to the selecton of a key varable s to choose a varable, whch already s carefully montored and whch s essental for producton or product qualty. In a power plant, t could be power producton, steam flow rate, steam temperature, and so forth. After the correlated varables have been dentfed, parameters for montorng them are defned and fed to the onlne montorng part. To montor the dentfed varables onlne, each of them needs n addton to ts own sensor value the current value of the key varable and the parameters defned n dentfcaton part. A schema of the approach s gven n Fg... Offlne Identfcaton The dentfcaton part s based on lnear relatonshps, whch are defned by the correlaton coeffcent r x, y. It s calculated by ( x( k) x)( y ( k) y ) k = r =, () x, y N N N ( x( k) x) ( y ( k) y ) k = k = where y s a process varable and x s the key varable. The mean values of x and y are presented as x and y, when k=...n. N s the number of samples. The correlaton coeffcents range from to. Values near suggest there s a postve lnear relatonshp between the varables, whereas values near suggest there s a negatve lnear relatonshp between the varables. Values near suggest the absence of a lnear relatonshp. In ths study, r x, y >.7 was chosen to ndcate a strong lnear relatonshp between y and x. Fg.. The Proposed Approach Smple lnear regresson models are bult for the dentfed varables. The response varable s estmated by usng ŷ y ˆ = a x( t) + b, () where a and b are regresson parameters, and t a tme pont. To fnd the regresson parameters that ft the data, ŷ s set as y and the parameters solved n a least squares sense. The orgnal value y s then dvded by the response varable ŷ to get rato R presented n y R =. (3) yˆ It s possble that the data has some outlers or the lnear regresson model s not suffcently accurate. Therefore, the spread of R needs to be checked. In ths study, the range R [.9.] s consdered to be acceptable. If R =, then the actual value and the response value are the same. If R <.9 or R >. on more than one per cent of N samples, y s rejected. Otherwse, only ponts R [.9.] are chosen for computaton of quantles. Values n R are sorted from the lowest to the hghest and dvded to q equally szed subsets so that the quantles can be taken at chosen ntervals from the cumulatve dstrbuton functon of R. The th k q-quantle s the data value where the cumulatve dstrbuton functon crosses k/q. In ths study, two sets of

3 quantles both havng seven ponts are defned. Fg. presents a block dagram of the dscussed dentfcaton prncple. 5 If R,,,. If 5 R,,,. R [ ] R < [ ] If R (t) s outsde the range defned by the smallest and the largest quantles, = or = dependng on the sde of the range. To smulate a sensor malfuncton, sensor readngs are deflected from the actual values. In ths study, drft type faults are produced by D y = y + c ( t t f ), (5) where y D (t) s a value of malfunctonng sensor; c s a constant and t s the tme pont for begnnng of the drft. f 3. RESTS AND DISCSSION 3. Identfcaton of Varables Nnety-seven process varables around the plant were taken nto dentfcaton together wth the key varable, electrc power output. To dentfy the varables, 377 hours of data wth one hour samplng rate was used. Nneteen correlatng varables were eventually dentfed. Table shows the dentfed varables and Table shows unts, correlaton coeffcents, and regresson parameters a and b. Fg.. A block dagram of the offlne dentfcaton part.3 Onlne Montorng and Smulaton of Drft In montorng part, R (t) s computed wth () and (3). The dentfed quantles n order of magntude correspond to the lmts used n scalng. The seven scalng lmts are -,, -.,,., and. The smallest quantle corresponds to scaled value -; the second smallest quantle corresponds to scaled value, and so on. The lmts - and are supposed to nduce an alarm. The lmts and are supposed to represent an exceptonally low or hgh value. The lmts -. and. are chosen to scale most of the ponts near the centre. (t) s scaled to, by R [ ] = R = R R R ( R R ) ( R R ) + +,, R R 5 R < R The range for R (t) s lmted by consecutve quantles, whch are the lower quantle R and the upper quantle R, and R < R. These quantles have correspondng scalng lmts, whch are the lower l mt and the upper 5 lmt, and <. Medan of R, denote d by R, s chosen as a measure of centra l tendency.. 5 (4) Table. Identfed varables varable explanaton y temperature before feed water heater y temperature after feed water heater y3 feed water flow after feed water heater y4 man condensate flow y5 man condensate temperature y6 man condensate and excess water flow bled steam 4 pressure hgh pressure steam flow y9 flue gas flow y bled steam 5 pressure y bled steam 5 temperature y feed water tank temperature y3 bled steam 6 condensate temperature y4 bled steam 5 condensate temperature y5 supply ar flow y6 feed water temperature before feed water heater bled steam 6 temperature feed water temperature before economzer y9 feed water temperature before control valve Accordng to Table, y 8 has the largest correlaton coeffcent to the key varable, whereas y has the smallest correlaton coeffcent. All the presented correlatons are clearly bgger than the chosen strong correlaton lmt n dentfcaton. Two varables were rejected, because ther spread was not acceptable. The correlaton coeffcents for these varables were smaller than.9. In addton to the 9

4 varables from the 97 nput varables, several computatonal varables correlated also wth the key varable. The computatonal varables are calculated usng process varables from dfferent parts of the plant. However, only real sensors were consdered n ths study. Table. Correlaton coeffcents and regresson parameters varable unt corr. coef. a b y C y C y 3 t/h y 4 t/h y 5 C y 6 t/h y 7 bar y 8 t/h y 9 knm³/h y bar y C y C y 3 C y 4 C y 5 knm³/h y 6 C y 7 C y 8 C y 9 C Computaton of mts Varables y,, and were chosen to be analysed n ths study. These three varables measure dfferent thngs, and have dfferent unts. Varable y 8 has the strongest and varable y the weakest lnear relatonshp to the key varable as t was mentoned before. Table 3 provdes descrptons for the used data n dfferent perods. Bascally, two operatng states on electrc power output were used durng the perod from whch the data was collected. Three hundred and one hours of data was taken from a perod n whch the electrc power output was on the upper operatng state. Seventy-one hours of data was taken to represent the lower operatng state. These perods are separate from the dentfcaton perod. One hour samplng rate was used. Table 3 shows that the mean and the medan of the varables are larger durng the upper than the lower operatng state. Varables y 7 and y have larger standard devaton σ 8 durng the lower than the upper operatng state, whereas the key varable x and y have the opposte stuaton. Standard devatons were larger durng the dentfcaton perod than durng upper and lower operatng states. Ths s due to the several changes n operaton durng the dentfcaton perod. Durng the chosen perods of upper and lower operatng states, the operaton was notably stable. The unt for the key varable s MW. mts for the varables were computed wth two dfferent quantle sets usng data from the dentfcaton perod. Two sets were chosen for comparson. Scaled lmts, quantle sets and correspondng ratos for the varables are presented n Table 4. Quantles are presented as percentage ponts. Scaled values -,, and are the same on both quantle sets. The quantles correspondng to scaled values, -.,., and dffer. Wth quantle set, these lmts are further from the centre pont than wth quantle set. In other words, most of the data ponts scale closer to wth quantle set compared to quantle set, whch results n larger spread. Varable y 7 has the largest range of ratos correspondng to range [-, ]. Table 3 shows that y 7 also has the smallest standard devaton. The large range mples that R 7 has to dverge from medan more than the other two varables n order to reach the alarm lmts. Bascally, data-drven approaches such as ths have two man problems. Only the close neghbourhood of normal operaton may be covered n dentfcaton f the data ponts do not cover the whole area of operaton. On the other hand, outlers n the data may artfcally wden the actual area of operaton. Therefore, expert help s often needed n addton to data-based defntons. Table 3. Descrpton of data varable mean medan σ The dentfcaton perod y key varable pper operatng state y key varable ower operatng state y key varable Table 4. mts quantle set R R R quantle set R R R

5 3.3 Fault Smulaton Fg. 3 shows the readngs of the key varable durng the tme perods used n smulaton of drft faults. Scaled values are computed by usng (), (3), and (4). Regresson parameters a and b are taken from Table. mts and and correspondng ratos R are taken from Table 4. Equaton (5) s used to smulate a sensor fault. In ths study, c n (5) s chosen to be ±.4 σ dependng on the drecton of the drft. The used standard devatons σ for dfferent varables and perods are taken from Table 3. Durng lower operatng state perod, t f =. Durng upper operatng state perod, t f =. Power (MW) Power (MW) pper operatng state Tme (hours) ower operatng state Tme (hours) Fg. 3. Key varable durng the perods used n smulaton Fg. 4 dsplays the smulated faults n y 8. Table 5 shows 8( t), y 8, the dfference between malfunctonng and actual sensor value (dff.), and x(t) at tme ponts t, n whch lmts ± and ± are crossed the frst tme after t f. Results show that quantle set needs an evdently larger devaton n the sensor value than quantle set to nduce a crossng of lmt ±. Fg. 4 shows that the orgnal sensor values stay n the range from -. to. all the tme when the quantle set s used. Qute the contrary, the use of the quantle set nduces large fluctuatons n the orgnal sensor values. Smulaton results for y 7 ndcate smlar behavour but the results are not presented because of lmted space. The smulatons of faults n y durng the perod of upper operatng state are shown n Fg. 5. Quantle set causes large fluctuatons, whch are seen from pont 8 onwards. Quantle set ndcates that the orgnal value of y s qute constantly near (Fg. 5). These results ndcate that the ratos R correspondng to lmts -. and are too close to the medan of R, whch s.68. In concluson, the selecton of the quantle set s challengng especally for the nner lmts ±. and ±. The problem can be solved by choosng the correspondng ratos further from the measure of the central tendency manually or choosng quantles that are closer to % and % n the dentfcaton part. On the other hand, senstvty becomes then worse. If normal fluctuatons and trend checkng n the data are the targets of nterest, then quantle set type lmts are better than quantle set type lmts. The am of ths study was to detect exceptonally hgh and low values nstead. Therefore, the quantle set s more approprate than the quantle set. Generally speakng, exceptonally hgh and low values may be already found on lmts ± wth the quantle set, whereas these lmts are already crossed durng normal operaton wth the quantle set. However, crossng of ± durng normal operaton s possble wth the quantle set as shown n Fg. 5. Table 5. Smulaton results for ower operatng state quantle set quantle set both ( t) dff x (t) t pper operatng state quantle set quantle set both ( t) dff x (t) t ower operatng state and quantle set n use orgnal drft upward drft downward Tme (hours) ower operatng state and quantle set n use Tme (hours) pper operatng state and quantle set n use Tme (hours) pper operatng state and quantle set n use Tme (hours) - - orgnal drft upward drft downward Quan tle set n use 5 5 Tme (hours) 5 3 Quant le set n use Tme (hours) Fg. 4. Smulatons of drft faults n varable Fg. 5. Smulatons of drft faults n varable y

6 The proposed montorng approach s not proper f the key varable has quck and farly large changes, and other varables do not follow the changes on tme; leadng temporarly to low correlaton. Results n Table 6 demonstrate such behavour. Quantle set and the medans of varables on the upper operatng state were used to test the behavour. Ratos from Table 4, medans from Table 3, and regresson parameters from Table were used n () and (3) to get the key varable values n Table 6. Results dffer sgnfcantly based on the varable consdered. The scaled medan of y 8 ( t/h) stays n the range [-, ] wth power output roughly from 57.9 MW to 7.5 MW. The dfference s.6 MW. The scaled medan of y (3.574 C) stays n the range [-, ] wth power output roughly from 36. MW to 77. MW. The dfference s 4. MW. As concluson, y 8 gves an alarm wth much smaller change n the power output than y. A fast change from 6 MW to 9 MW, for example, would therefore nduce alarms on the dentfed varables. The rato between a varable and ts estmate may dverge from the medan before the process stablzes to the new operatng state. Table 6. Key varable behavour n upper operatng state quantle set y y CONCSIONS Ths study proposed an approach, whch s a combnaton of varable dentfcaton and montorng amng at sensor fault detecton. The emphass was on fndng of exceptonally hgh and low sensor values. The approach s based on strong lnear relatonshps between process varables. A rato of a varable to a response varable from a smple lnear model s montored, and crossngs of relatve lmts are montored. Accordng to the results, the approach can be used n systems wth strong lnear relatonshps between varables and wth smlar dynamc behavour. Settng the montored lmts far from the measure of the central tendency of a probablty dstrbuton sets the emphass on exceptonally hgh and low values. Settng the lmts closer to the measure of the central tendency gves an approach for montorng the trends of smaller devatons. However, such an approach may cause false alarms. ACKNOWEDGEMENTS Contrbuton of Helsnk Energy s greatly acknowledged. REFERENCES Chang,.H., Pell, R.J., and Seasholtz, M.B. (3). Explorng process data wth the use of robust outler detecton algorthms. Journal of process control, vol. 3 (5), pp Frank, P.M. (99). Fault dagnoss n dynamc systems usng analytcal and knowledge-based redundancy a survey and some new results. Automatca, vol. 6 (3), pp Goebel, K., and an, W. (8). Correctng sensor drft and ntermttency faults wth data fuson and automated learnng. IEEE systems journal, vol. (), pp Isermann, R. (984). Process fault detecton based on modelng and estmaton methods a survey. Automatca, vol. (4), pp Juuso, E.K. (4). Integraton of ntellgent systems n development of smart adaptve systems. Internatonal journal of approxmate reasonng, vol. 35, pp ee, S.C. (994). Sensor value valdaton based on systematc exploraton of the sensor redundancy for fault dagnoss KBS. IEEE transactons on systems, man, and cybernetcs, vol. 4 (4), pp Ma, J., Zhang, J.Q., and an,. (999). Wavelet transform based sensor valdaton. IEEE Colloquum n ntellgent and self-valdaton sensors, Oxford, K, June, 999, pp. //4. Näs, J., Sorsa, A., and evskä, K. (5). Sensor valdaton and outler detecton usng fuzzy lmts. Proceedngs of the 44 th IEEE conference on decson and control, and the European control conference, Sevlle, Span, December 5, 5, pp Oakland, J.S., and Followell, R.F. (99). Statstcal process control: a practcal gude,.ed.. Henemann Newnes, Oxford. Pearson, R.K. (). Outlers n process modelng and dentfcaton. IEEE transacton on control systems technology, vol. (), pp Qn, S.J., and, W. (999). Detecton, dentfcaton, and reconstructon of faulty sensors wth maxmzed senstvty. AIChE journal, vol. 45 (9), pp Walker, Jr., N.D., and Wyatt-Mar, G.F. (995). Sensor sgnal valdaton usng analytcal redundancy for an alumnum cold rollng mll. Control engneerng practce, vol. 3 (6), pp Consderng future development, buldng of a graphcal user nterface to choose the key varables and dentfy the related varables based on the proposed approach s encouraged. pgradng of the proposed approach could be pursued through practcal experence on dfferent cases.