The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan A Software Sensor for Feedwater Flow Montorng * Man Gyun Na ), Yoon Joon Lee ) ) Department of Nuclear Engneerng, Chosun Unversty 375 Seosuk-dong, Dong-gu, Gwangju 50-759, Republc of Korea magyna@chosun.ac.kr ) Department of Nuclear and Energy Engneerng, Cheju Natonal Unversty Ara-l-dong, Jeju-do 690-756, Republc of Korea yjlee@cheju.ac.kr ABSTRACT Ventur meters can decrease the thermal performance of nuclear power plants because the feedwater flowrate can be over-measured because of ther foulng phenomena that make corroson products accumulate n the feedwater flow meters due to long-term operaton. Therefore, n ths paper, a software sensor usng a fuzzy nference system s developed n order to ncrease the thermal effcency by estmatng on lne the feedwater flowrate accurately. The fuzzy nference system to be used for black box modelng of the feedwater system s equpped wth an automatc desgn algorthm that automates the selecton of the nput sgnals to the fuzzy nference system and ts fuzzy rule generaton ncludng parameter optmzaton. The proposed algorthm was verfed by usng the numercal smulaton data of MARS code for Kor- and also, the real nuclear plant data (YG-3). In the smulatons usng numercal smulaton data and real plant data, the RMS error and the relatve maxmum error are so small that the proposed method can be appled successfully to valdate and montor the exstng feedwater flow meters. KEYWORDS feedwater measurement, fuzzy nference system, software sensor, genetc algorthm. INTRODUCTION It s very mportant to accurately measure the feedwater flowrate n order to montor the thermal performance of a nuclear power plant (NPP). Ventur meters are used to measure the feedwater flowrate n most current pressurzed water reactors (PWRs). These meters can nduce measurement drft due to corroson product buldup near the meter orfce because of long-term operaton. Ths ventur meter foulng s known to be the most sgnfcant contrbutor to deratng n PWRs. The
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan amount of deratng ranges from 0.5% to 3%. Therefore, a lot of researchers have been nterested n overcomng the naccurate measurement problem of the feedwater flowrate (Kavakloglu and Upadhyaya, 994, Heo, 000). Due to the foulng phenomena of the ventur meter, the accuracy of the exstng hardware sensors s not suffcent. Therefore, n ths paper, a software sensor s developed to measure the feedwater flowrate by combnng an emprcal data-based model usng a fuzzy nference system and other partal measurements of the reactor system. Software sensor desgn conssts of buldng an estmate of some quantty of nterest. The software sensor can be used ether to replace a physcal measurement or to valdate an exstng one. Recently, many researchers have pad much attenton to software sensors or nferental sensng, whch use other readly avalable on-lne measurements because these software sensors can ether replace the hardware sensors or be used n parallel wth them to provde redundancy and verfy whether the hardware sensors are drftng (Cho and Park, 00, Lnko et al, 00, Masson, 999). When the process model for evaluatng the process varables s a pror unknown or dffcult to model lke the steam generator system at hand, the problem can be stated n terms of black-box modelng. The fuzzy nference system s wdely used for ths black-box modelng. Therefore, n ths work, a fuzzy nference system equpped wth an automatc desgn algorthm s developed n order to ncrease the thermal effcency by estmatng on lne the feedwater flowrate accurately. Partcularly, the selecton of the nput sgnals to the fuzzy nference system and ts rule generaton are automated to optmally estmate the feedwater flowrate.. A SOFTWARE SENSOR USING A FUZZY INFERENCE SYSTEM There are two types of approaches n developng software sensors. One s a method that estmates requred parameters on the bass of a determnstc model and the other s the black-box modelng method that depends only on the measured values. Black-box modelng approaches such as artfcal ntellgence are more favored because they can model complcated processes whch are dffcult to be descrbed by analytcal and mechanstc methods. Therefore, black-box model approaches for buldng software sensors have wdely been attempted. Also, recently, artfcal ntellgence such as fuzzy nference systems and artfcal neural networks has been pad much attenton from many researchers because artfcal ntellgence can model complex nonlnear systems easly (Cho and Park, 00, Lnko et al, 00, Masson, 999). In ths work, a Takag-Sugeno (985) type fuzzy nference system to be used to desgn a software sensor s appled to verfy and montor an exstng ventur meter whch measures the feedwater flowrate. Its -th rule can be descrbed as follows: If x s A AND L AND xm s Am, then yˆ s f ( x, L, x ), () m
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan where x j s the nput lngustc varable to the fuzzy nference system ( j =,,..., m ), Aj the membershp functon of the j -th nput varable for the antecedent of the -th rule ( =,,..., n ), and ŷ the output of the -th rule. Also, the rule output s of the followng form: m f ( x, L, xm ) = qj x j + r, () j= where q s the weghtng value of the -th nput on the -th rule output and j j r the bas of the -th rule output. The output of a fuzzy nference system wth n fuzzy rules s a weghted sum of the consequent of all the fuzzy rules. Therefore, the output of the software sensor s gven by: where n y ˆ = w f = w T q, (3) w = = n w = w m, w = A x ), q = j= j ( [ q q LLq Lq r Lr ] T n n n [ w x Lw x LLw x Lw x w Lw ] T w =. m j m L n m nm n, and 3. AUTOMATIC DESIGN OF A SOFTWARE SENSOR 3.. Automatc Structurng The number of varables to be nput to the fuzzy nference system has to be optmzed for several reasons. Frst, rrelevant nputs wll result n an unstable model. Thus, t becomes mportant to use only hgh nformaton predctors. Secondly, snce the generalzaton may degrade f colnearty s present among the varables, t s necessary to remove hghly correlated varables. Fnally, when buldng a black-box model wth many nput varables, a large number of observatons are requred to span the complete nput space. The number of requred observatons grows exponentally wth the number of nput varables, whch makes a dmenson reducton essental to obtan a good model. In addton, snce the optmum number of fuzzy nference rules depends on selected nputs and ts number, t s requred to select the optmum number of rules for selected nputs n order to prevent overfttng and underfttng problems (Na, 003). The genetc algorthms requre a ftness functon that assgns a score to each chromosome (canddate soluton) n the current populaton. In ths paper, a ftness functon that evaluates the extent to whch each canddate soluton s sutable for the multple objectves that mnmze a maxmum error and a root mean squared error along wth the small number of nput varables and the small number of rules, s suggested as follows:
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan ( µ E µ E µ 3E3 µ 4E4 F = exp ), (4) E N = ˆ N k= ( y k y k ), (5) E max{ yk yˆ k k = }, (6) E = 3 N nput, (7) E = 4 N rule. (8) Snce genetc algorthms are computatonally expensve, t s necessary to reduce the computaton tme of genetc algorthms. A modfed genetc algorthm proposed n the lterature (Na, 003) s used n ths work. 3.. Parameter Optmzaton Snce the genetc algorthm requres much computatonal tme f there are many parameters beng nvolved, the genetc algorthm s combned wth a least-squares algorthm. The objectve of the genetc algorthm for a problem of fuzzy parameters optmzaton s to mnmze the root mean squared errors and the maxmum absolute error (refer to Eqs. (4) through (6)), whch results n achevng the membershp functon optmzaton. If some parameters of the fuzzy nference system are fxed by the genetc algorthm, the resultng fuzzy nference system can be descrbed as a seres of expansons of some bass functons. Ths bass functon expanson s lnear n ts adjustable parameters as shown n Eq. (3), y ˆ = w T T q, snce w has been known by the genetc algorthm. Therefore, the least-squares method can be used to determne the remanng parameters. From a total number of N nput-output tranng data pars that are target values, the consequent parameters q are chosen to mnmze the square of the dfference between the target values y and the estmated values ŷ : y = Wq, (9) [ ] T where y = y y L y. N The parameter vector q can be solved easly by usng the pseudo-nverse of the matrx W. The process for automatcally constructng the structure of the fuzzy nference system s descrbed n Fg.. Frst, the nput sgnals selecton bts of the ntal chromosomes are generated by usng the correlaton coeffcent matrx to reduce the computatonal burden of the genetc algorthm and ts rule number bts are allocated wth more prorty that ther decoded value becomes a hgh number f the number of selected nputs s large. An outer loop for the selecton stage of nput sg-
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan nals and the number of fuzzy rules goes round untl specfc condtons are met as descrbed by the ftness functon. Also, n every selecton stage of nput sgnals and the number of fuzzy rules (outer loop), an nner loop for parameter optmzaton goes round repeatedly untl specfc condtons are met, too. In addton, n every selecton stage of nput sgnals and the number of fuzzy rules, a part of chromosomes wth very low ftness s replaced by usng the correlaton analyss. Start Generate ntal chromosomes usng a correlaton matrx Rank chromosomes Replace chromosomes wth low ftness usng correlaton analyss Selecton stage of nput sgnals & the number of rules Termnate the selecton stage of nput sgnals & the number of rules? Yes Stop No Genetc operaton such as selecton, crossover, and mutaton Fuzzy nference system Termnate the stage of parameter optmzaton? Yes No Stage of parameter optmzaton Fg.. Automatc desgn of a software sensor. 4. SENSOR FAULT DETECTION The objectve of sensor montorng s to detect the falure as soon as possble wth a very small probablty of makng a wrong decson. In ths work, SPRT (Wald, 945) that uses the resdual are appled. Normally the resdual sgnals are randomly dstrbuted, so they are nearly uncorrelated and have a Gaussan (normal) dstrbuton P ( ε k, m, σ ), where ε k s the resdual sgnal at tme k, and m and σ are the mean and the standard devaton under hypothess, respectvely. The sensor falure can be stated n terms of a change n the mean m or a change n the varance σ. If a set of samples x, =,, L, n, s collected wth a densty functon P descrbng each sample n the set, an overall lkelhood rato s gven by γ P ( ε H ) P ( ε H ) P ( ε H ) P ( ε H ) 3 n n =, (0) P0 ( ε H 0 ) P0 ( ε H 0 ) P0 ( ε 3 H 0 ) P0 ( ε n H 0 )
where The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan represents a hypothess that the sensor s degraded and H represents a hypothess that H 0 the sensor s normal. By takng the logarthm of the above equaton and replacng the probablty densty functons n terms of resduals, means and varances, the log lkelhood rato (LLR, λ ) can be wrtten as the followng recurrent form: λ σ 0 ( ε n m0 ) ( ε n m ) n = λn + ln σ +. () σ 0 σ For a normal sensor, the log lkelhood rato would decrease and eventually reach a specfed bound A, a smaller value than zero. When the rato reaches ths bound, the decson s made that the sensor s normal, and then the rato s rentalzed by settng t equal to zero. For a degraded sensor, the rato would ncrease and eventually reach a specfed bound rato s equal to B, a larger value than zero. When the, the decson s made that the sensor s degraded. The decson boundares B n A and β B are chosen by a false alarm probablty α and a mssed alarm probablty β ; A = ln and α β B = ln. α 5. APPLICATION TO THE FEEDWATER FLOWRATE MEASUREMENT The proposed method was verfed through two applcaton cases. Frst, the proposed method was appled to the numercal smulaton data of the load-decrease transents n Kor- usng a MARS code (Lee et al, 999). Second, the proposed method was appled to the real plant startng data of YG-3. The software sensor usng a fuzzy nference system was automatcally structured usng a half of all the acqured data (tranng data) n the tranng stage and was verfed usng the remanng data (test data) n the test stage. The proposed nput selecton method s compared wth the exstng prncpal component analyss (PCA) method (Wang and L, 999) and a heurstc method. In the heurstc method, nputs are selected through a correlaton analyss among possble nput sgnals. PCA s used to reduce the dmenson of an nput space wthout losng a sgnfcant amount of nformaton. Ths method transforms the nput space nto an orthogonal space. Also, the PCA method makes easy the selecton of the nput to the neuro-fuzzy nference system. Table summarzes the smulaton results usng the numercal smulaton data. Fgure shows smulaton results n case the feedwater flowrate starts to be gradually degraded on purpose from 00 sec. The estmated feedwater flowrate s almost the same as the accurate feedwater flowrate. Ths s a natural result because the estmated feedwater flowrate s not affected at all by usng unaffected sgnals. The gradual degradaton s detected for the frst tme by the proposed method. Table summarzes the smulaton results usng the real plant data. Fgure 3 shows smulaton results n case feedwater flowrate start to purposely be degraded from 0 hr. The estmated feedwater flowrate s almost the same as the accurate feedwater flowrate. The gradual degradaton s detected early by the proposed method.
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan Table. Results for the Numercal Smulaton Data. Proposed Algorthm Relatve maxmum error(%) Root mean square error(%) Maxmum Ftness Tranng Data 0.3 0.05 0.9647 Test Data.70 0.0 - PCA Tranng Data 0.39 0.3 0.977 method Test Data 0.37 0.3 Selected Inputs S/G steam flowrate, S/G pressure, S/G wde-range level, hot-leg temperature Number of rules 4 prncpal components 4 4 Heurstc Tranng Data 0.8 0.06 0.963 Input Selecton Test Data 0.50 0.06 - S/G steam flowrate, S/G narrow-range level, S/G temperature, reactor power 4 feed flowrate (kg/sec) 400 350 300 measured (degraded) mesaured (no error) estmated (proposed) estmated (PCA) estmated (Heurstc) 50 0 00 00 300 400 500 600 700 800 tme (sec) proposed PCA Heurstc Fg.. Estmaton of feedwater flowrate sgnal n case t s gradually degraded (numercal smulaton data)..0 0.8 0.6 0.4 0. 0.0 fal flag feed flowrate (kg/sec) 000 800 600 400 00 0 0 0 0 30 40 50 60 70 80 90 00 tme (hr) proposed PCA Heurstc.0 0.8 0.6 0.4 measured (degraded) mesaured (no error) 0. estmated (proposed) estmated (PCA) estmated (Heurstc) 0.0 Fg. 3. Estmaton of feedwater flowrate sgnal n case that t s gradually degraded (real plant data). fal flag Table. Results for the Real Nuclear Plant Data. Proposed Algorthm PCA method Relatve maxmum error (%) Root mean square error (%) Maxmum Ftness Tranng Data.0 0.4 0.89 Test Data.88 0.4 - Tranng Data 6.7.43 0.605 Test Data 7.97.53 Heurstc Tranng Data.48 0.7 0.8807 Input Selecton Test Data 3.8 0.9 - Selected Inputs hot-leg temperature, cold-leg temperature, PZR temperature, S/G temperature Number of rules 6 prncpal components 4 S/G wde-range level, S/G narrow-range level, feedwater temperature, reactor power 4 4
The Semnar of JSPS-KOSEF Core Unversty Program on Energy Scence & Technology November -, 004, Tohoku Unversty, Senda, Japan 6. CONCLUSIONS A software sensor usng a fuzzy nference system that has an automatc desgn algorthm has been developed to valdate and montor the exstng feedwater flowrate. The developed software sensor actually estmates the feedwater flowrate sgnal usng other sgnals, whch removes the effect of the foulng degradaton of the venture meters. The proposed algorthm was verfed by usng the numercal smulaton output of MARS code for Kor- and also, the real plant data of YG-3. Although the applcaton to the real plant has larger error than that to the numercal smulaton data, these errors are small enough and also, the results for the test data are almost the same as that for the tranng data. So the developed software sensor can be appled successfully to valdate and montor the exstng feedwater flow meters. REFERENCES Kavakloglu, K. and Upadhyaya, B.R., Montorng Feedwater Flow Rate and Component Thermal Performance of Pressurzed Water Reactors by Means of Artfcal Neural Networks, Nuclear Technology, 07, (994). Heo, G., Cho, S.S. and Chang, S.H., Thermal Power Estmaton by Foulng Phenomena Compensaton Usng Wavelet and Prncpal Component Analyss, Nuclear Engneerng and Desgn, 99(-), 3 (000). Cho, D.-J. and Park, H., A Hybrd Artfcal Neural Network as a Software Sensor for Optmal Control of a Wastewater Treatment Process, Water Research, 35(6), 3959 (00). Lnko, S., Luopa, J. and Zhu, Y.-H., Neural Networks as Software Sensors n Enzyme Producton, Journal of Botechnology, 5(3), 57 (997). Masson, M.H., Canu, S., Grandvalet, Y. and Lynggaard-Jensen, A., Software Sensor Desgn Based on Emprcal Data, Ecologcal Modelng, 0(-3), 3 (999). Takag, T. and Sugeno, M., Fuzzy Identfcaton of Systems and Its Applcatons to Modelng and Control, IEEE Trans. Systems, Man, Cybern.,, 6 (985). Na, M.G., Sm, Y.R., Park, K.H., Lee, S.M., Jung, D.W., Shn, S.H., Upadhyaya, B.R., Zhao, K. and Lu, B., Sensor Montorng Usng a Fuzzy Neural Network wth an Automatc Structure Constructor, IEEE Trans. Nucl. Sc., 50, 4 (003). Wald, A., Sequental Analyss, John Wley & Sons, New York (947). Lee, W.-J., Chung, B.-D., Jeong, J.-J., Ha, K.-S. and Hwang, M.-K., Improved Features of MARS.4 and Verfcaton, Korea Atomc Energy Research Insttute, KAERI/TR-386-99 (999). Wang, X.Z. and L, R.F., "Combnng Conceptual Clusterng and Prncpal Component Analyss for State Space Based Process Montorng," Ind. Eng. Chem. Res., 38, 4345 (999).