Neuro-Fuzzy Modeling of Heat Recovery Steam Generator

Transcription

1 International Journal of Mahine Learning and Computing, Vol. 2, No. 5, Otober 202 Neuro-Fuzzy Modeling of Heat Reovery Steam Generator A. Ghaffari, A. Chaibakhsh, and S. Shahhoseini represented in a network struture. he learning tehniques for neural network an be applied in order to tune the parameters of the fuzzy models 8. In ANIFS struture presented by Jang (999), the number of fuzzy rules is equal to the produt of number of membership funtions and the number of inputs 9. In some ases, the required number of fuzzy rules to over entire input spaes is very large, whih auses the training proess beomes time onsuming or pratially impossible. In order to redue the number of fuzzy rules without auray losses, the fuzzy -means (FCM) lustering approah was proposed to define the struture of fuzzy systems 0. In this paper, a ombination of fuzzy -means lustering and least square tehniques are employed to identify the parameters of membership funtions and fuzzy rules in a multi-input single-output (MISO) SK type fuzzy inferene systems (FIS). he FCM lustering is first employed to etrat the number of fuzzy rules and membership funtions for the anteedents. hen, the parameters of onsequents are defined for model based on a given set of input/output data. he auray of developed models is validated by performing a omparison between the responses of developed models and the eperimental data. In net setion, a brief desription of the plant that onsists of a general view of the power plant and its subsystems is presented. Inputs and outputs to the subsystems are also speified in this setion. he neuro-fuzzy model based on the eperimental data and struture of reurrent model and simulation result is presented in Setion IV. In addition, a omparison between the responses of the proposed models with the responses of the real plant is presented to validate the auray of the developed models. Abstrat In this paper, an appliation of dynami neuro-fuzzy systems is presented for modeling the subsystems of the heat reovery steam generator (HRSG). he dynami neuro-fuzzy models were developed based on the formal NARX models topology. he lustering tehniques were employed to define the struture of the fuzzy models by dividing the entire operating regions into smaller subspaes. he optimal luster enters and orresponding membership funtions are aptured by FCM, where the parameters of onsequent were adjusted by reursive LSE method. A omparison between the responses of the proposed models and the responses of the plants ware preformed, whih validates the auray and performane of the modeling approah. Inde erms Power plant; HRSG boiler; fuzzy system; eperimental data; lustering tehnique. I. INRODUCION In reent years, many different modeling approahes have been employed to desribe the nonlinear dynamis of power plant subsystems. he analytial models an be developed based on the fundamental laws of physis suh as mass onservation, momentum, and energy semi-empirial laws for heat transfer and thermodynami state relations. In order to develop suh analytial models, it is neessary to alibrate the model parameters with respet to boundaries, inputs, and outputs in steady state and transient onditions 2. he olleted Input/output data from field eperiments an also be used to develop mathematial models based on identifiation tehniques. here is a vast olletion of blak-bo modeling tehniques whih are developed for the lass of nonlinear systems. In this regard, artifiial neural networks (ANN), fuzzy logi (FL) models or a ombination of these approahes suh as adaptive neuro-fuzzy inferene systems (ANFIS) are etensively used for modeling the industrial proesses inluding power plants. his an be addressed in the works done by Afzalian and Linkens (2000), Liu et al. (2003), Sanhez-Lopez et al. (2004), Vieira et al. (2004), Zhang et al. (2006), Ghaffari et al. (2008), and Mastaan et al. (2009) 3-7. If adequate information from the plant performanes an be aptured, using neuro-fuzzy system would be an appropriate approah to desribe the non-linear systems behaviors. One of the most ommon strutures employed for this propose is ANFIS, in whih the fuzzy if-then rules are II. SYSEM DESCRIPION AND IS SUBSYSEMS In this study, a HRSG boiler of the ombined yle units at Neka power plant (at the north of Iran) is onsidered for investigation. his plant onsists of two gas turbine units and one steam turbine, whih was onstruted by Siemens AG ; in 990. he rated power of gas and steam units are 2 36 MW and 60 MW, respetively. In ombined yle power plants, the ehausted gas from gas turbines is reovered by HRSG. he required heat for this boiler is provided by the hot ehaust gas and three auiliary burners. he output temperature of gas turbine is about 530oC, whih burns natural gas as the main fuel. he HRSG boiler onsists of different parts suh as de-aerator, eonomizer, low-pressure (LP) drum, high-pressure (HP) drum, evaporators, superheaters, and de-superheaters. he outlet water from ondensation system heads to the deaerator, and then is send to the feedwater pump to inrease the feedwater pressure. A part of feedwater goes to low Manusript reeived May 30, 202; revised August 8, 202 A. Ghaffari is with the Department of Mehanial Engineering at the K.N. oosi University of ehnology, ehran, Iran ( ghaffari@kntu.a.ir). A. Chaibakhsh is with the Department of Mehanial Engineering at the University of Guilan, Rasht, Guilan, Iran ( haibakhsh@guilan.a.ir). S. Shahhoseini is M.S. student at South ehran Brah, Islami Azad University, ehran, Iran ( sajjad.shahhoseini@gmail.om) /IJMLC.202.V

2 International Journal of Mahine Learning and Computing, Vol. 2, No. 5, Otober 202 f( ) is onsidered as a SK type fuzzy system. Neuro-Fuzzy System he priniple of ANFIS an be desribed by a set of if-then rules as follows 9, pressure drum, where its output pressure and temperature are about 0.85MPa and 235oC, respetively. he evaporated steam goes to the LP superheater, and then enters to the LP steam turbine setion. he other portion of feedwater is pumped to the HP eonomizer and then goes to HP drum to onvert to steam. he steam temperature at the drum header is 300oC and its pressure is about 9MPa. he evaporated steam goes to the primary and final HP superheaters. his steam with the temperature of 520oC and pressure of 9MPa is flashed to the HP stages of steam turbine. he different omponents of this HRSG boiler are shown in Fig. Feedwater outlet from ondensation system with 75 kg/s mass flow rate and temperature about 52oC after a hemial treatment stage, goes to the deaerator. In the deaerator, the gas phase is etrated from the liquid phase, whih is sent to the feedwater pump and the yle is repeated. Ri: if is Ai, and... and k is Ai,k then yi = bi,0 + bi, bi,k k (2) where Ai,k is the membership funtion assoiated with input variables k and N is the number of inputs Fig. 2. he SK ANFIS arhiteture. In this struture, a linear ombination of the input variables are onsidered as the onlusion funtions of fuzzy rules. he firing degrees of the fuzzy rules are alulated through the five layers of the model 9. Layer : Eah node represents a linguisti label. Here, the membership funtion Ai,k is onsidered to be Gaussian, whih is speified by the enter v and the spread σ, Fig.. he heat reovery steam generator boiler. III. HRSG MODELING In order to model the subsystems of HRSG, the input and output data of plant performanes were reorded. Due to the lak of prior information from the performane of gas unit, the reorded data for the transient responses were olleted with respet to the hanges in fuel flow rate at auiliary burners. he gas flow rate was onsidered as onstant value for gas units. wo different data sets were prepared from the plant responses during load hanged, whih were used in the model training and model testing proesses. Dynami systems an be divided into two ategories: first group onsists of systems that have only feedforward onnetions, and the others are systems with feedbak or reurrent onnetions. If the output of the model at a moment is applied as its input at the net moment, the model is alled dynami or reurrent model. In other words, in reurrent models, the output of the model at the eisting moment is influened by the output of the model at previous moments. A dynami fuzzy model an be developed by using the ommon NARX model topology as a disrete-time nonlinear mapping on some previous measured outputs and inputs as follows, y(k) = f (u(k), u(k ),..., u(k nu ), y(k ),..., y(k n y ) Ai,k (r ) = ep( (( r vi,k ) σ i,k ) 2 ) (3) Layer 2: he fulfillment degree of rules are alulated by multiplying all inoming values as follows, N wi = Ai,k ( k ) (4) k = Layer 3: he relative degree of fulfillment of eah rule is alulated by normalizing orresponding degree of fulfillment as follows, wi = wi / wi (5) i = Layer 4: he onsequent of eah rule is alulated by multiplying the orresponding rule in its relative degree of fulfillment as, yi = wi yi (6) Layer 5: he output of the net or the fuzzy system is alulated by adding all inoming weighted onsequents, y = yi () (7) i = where nu and ny are the number of past terms for input u and output y, respetively. Here, the non-linear mapping funtion As a result, all input output patterns an be defined as below, 605

3 International Journal of Mahine Learning and Computing, Vol. 2, No. 5, Otober 202 Y M = X M + ) N Θ( + ) N (. (8) he parameters of the matri Θ and membership funtions should be adjusted based on the eperimental data. In order to define the parameters of membership funtions, the FCM algorithm is employed for partitioning the data set into predefined subsets. he data partitioning into lusters depends on similarity or dissimilarity of the members of eah luster that defines by the distane of data points from luster enters. i j By defining D( v, ) as the distane between v i and j, i s j s where { v } R and { } R are the vetor of luster enters and unlabeled data set, respetively. he following objetive funtion has to be minimized in order to obtain the best possible solution. A. Eonomizer Fig. 3 presents the shemati diagram of eonomizer reurrent neuro-fuzzy model. It is noted that the number of inputs in this model is, if only 3 linguisti variables be assigned for eah fuzzy input, the number of rules would be as 3 rules. Using fuzzy -mean lustering, the number of rules redues to only 2 rules. n m 2 Minimize : J ( Α, V ) = ( A ) ( D ) (9) m j= i= where A is the membership of the jth data point in the ith luster and the weighting eponent m ( m < ) ontrols the degree of fuzziness of eah luster. Minimization of J m is performed by onsidering the following onstraints on the membership values, whih would lead to the optimal partition. j =... n, i =..., = A = 0 i and A (0) he best possible positions of luster enters and orresponding membership funtions an be obtained using (6) and (7) through an iterative proess. v ~ n m n m i = ( A ) j / ( A ), i () and j= j= 2 m ( D / D ) ), i, j n A ~ = /( ) jk k= /( (2) Fig. 3. he shemati of the neuro-fuzzy model for eonomizer. he effetive variables of the eonomizer output temperature are known as feedwater mass flow, fuel flow rate and input steam temperature and the output variable is the eonomizer temperature. he input/output vetors of the eonomizer model are summarized as follows: Input = m & m& (4) fuel feedwater feedwater Output = _ (5) eo out where outside the braket stands for transpose. he responses of developed model for eonomizer setion are ompared with eperimental data taken from real plant, whih is shown in Fig. 4. he iteration would be stopped if no further improvement was observed in J m (U,V). By defining the fuzzy membership funtions and orresponding fuzzy rules, the parameters of onsequent in Eq. (8) an be obtained by using reursive least square estimator as follows, P θ = P k ( P = θ + P k k k ( Y P ) /( + θ ) k P ) k (3) In the net setion, the modeling approah is applied to different parts of HRSG boiler. Fig. 4. Responses of eonomizer neuro-fuzzy model and atual plant. IV. MODELING AND SIMULAION In this setion, the HRSG boiler is deomposed to smallest subsystems in order to ease the proess of modeling the boiler. Eah part an be presented by a multi-input single-output (MISO) FIS. he input-output data sets and the responses of the developed model for eah setion will be presented. B. Drum he same struture that was used for the eonomizer setion was employed with 4 inputs, and 25 rules were employed for the drum setion. A shemati of drum setion is presented in Fig. 5. As it is shown, the input feedwater and the output steam mass flow rates have the most effets on the 606

4 International Journal of Mahine Learning and Computing, Vol. 2, No. 5, Otober 202 dynamis of drum. he other input and output for this setion are orresponded to evaporator setion, whih an be haraterized by drum pressure and fuel flow rate. Consequently, the input/output vetor for this setion an be summarized as follows, Input= m& feedwater Pdrum Output = Ldrum m& fuel (6) (7) Fig. 7. Responses of the superheater setion. D. De-superheater In order to regulate the output temperature of the superheating setions, the de-superheaters are onsidered between two parts of superheater. By negleting the pressure loss in the attemperator, the output temperature of the de-superheater an be estimated with respet to the inlet temperature and flow of superheated steam and temperature and flow of water spray. he number of inputs for this model is 4 and the number of fuzzy rules is equal to 2. he input/output vetor for the de-superheater setion is as follows, Fig. 5. he shematis of the drum setion. Input = m& spary spary Output = steam _ out A omparison between the responses of the developed model and the responses of the real plants was performed. Obtained results are presented in Fig. 6, whih validates the auray and performane of the modeling approah. C. Superheater For superheater setion, a model with inputs and 9 fuzzy rules are adequate to desribe its dynami behaviors. Fuel flow rate, input steam temperature and mass flow rate to the superheater setion is onsidered as the main variables to predit the superheated output temperature. he input/output vetors of the superheater model are summarized as follows: Output = steam _ out steam _ in steam_ in (20) (2) Also, it is noted that m& steam_out= m& steam_in+ m& spary. he responses of the developed model for the de-superheater are presented in Fig. 8. In order to demonstrate the advantages of the proposed modeling approah, a omparison between the responses of the developed models and the responses of the reursive ANN models is arried out. he performanes of the developed models are evaluated by alulating the error funtions, where the error is defined as the differene between the predited values by models and the eperimental data. Here, the upper bound error (Ma( e )), lower bound error (Min( e )), mean absolute error (MAE) and orrelation oeffiient (R2) are alulated for both transient and steady state onditions over the operating range, whih are presented in able I to IV. Fig. 6. Responses of drum neuro-fuzzy model and atual plant. Input = m& fuel (8) (9) In Fig. 7, the responses of the developed neuro-fuzzy model for superheater setion are ompared with atual plant responses. Fig. 8. Responses of de-superheater model. 607

5 International Journal of Mahine Learning and Computing, Vol. 2, No. 5, Otober 202 ABLE I: ERROR FUNCIONS FOR HE ECONOMIZER MODELS ANFIS e ANN e ABLE II: ERROR FUNCIONS FOR HE DRUM MODELS ANFIS e ANN e ABLE III: ERROR FUNCIONS FOR HE SUPERHEAER MODELS ANFIS e ANN e ABLE IV. ERROR FUNCIONS FOR HE DE-SUPERHEAER MODELS ANFIS e ANN e Obtained results show the performane and feasibility of the modeling approah in terms of more auray and less deviation between the predited values by the developed models and the eperimental data. V. CONCLUSION his paper presents an appliation of neuro-fuzzy modeling approah in order to desribe the nonlinear behavior of a heat reovery steam generator. he reurrent struture of SK fuzzy system was hosen for this aim. A ombination of fuzzy lustering tehniques (FCM) and least square estimation was employed for adjusting the parameters of membership funtions and the fuzzy rules, respetively. he responses of the developed models were ompared with the eperimental data in order to validate their auray. In addition, the performanes of the developed models were ompared with the performanes of reurrent ANN models in order to show the feasibility of modeling approah. Obtained results indiate the auray and performane of the models in both transient and steady state onditions. REFERENCES S. Lu and B. W. Hogg, Dynami nonlinear modeling of power plant physial priniples and neural networks, Journal of Eletrial Power and Energy Systems, vol. 22, pp.67-78, K. J. Astrom and R. D. Bell, Drum-boiler dynamis, Automatia, vol. 36, pp , A. Afzalian and D. A., Linkens, raining of neuro-fuzzy power system stabilizers using geneti algorithms, International Journal of Eletrial Power & Energy Systems, vol. 22, pp , A. Sanhez-Lopez, G. Arroyo-Figueroa and A, Villavienio-Ramirez, Advaned ontrol algorithms for steam temperature regulation of thermal power plants, International Journal of Eletrial Power & Energy Systems, vol. 26, pp , J. Vieira, F. Morgado Dias and A. Mota, Artifiial neural networks and neuro-fuzzy systems for modeling and ontrolling real systems: a omparative study, Engineering Appliations of Artifiial Intelligene, vol. 7, pp , J. Zhang, M. Fei, K. Li and Q. Zhu, Fuzzy modeling of a medium-speed pulverizer using improved geneti algorithms, Leture Notes in Computer Siene, vol. 43, pp , A. Ghaffari, A. Chaibakhsh and C. Luas, Soft omputing approah for modeling power plant with a one-through boiler, Engineering Appliations of Artifiial Intelligene, vol. 20, pp , R. Babuška and H. Verbruggen, Neuro-fuzzy methods for nonlinear system identifiation, Annual Reviews in Control, vol. 27, pp , J. R. Jang, ANFIS: adaptive-network-based fuzzy inferene, IEEE ransations on Systems, Man, and Cybernetis, vol. 23, pp , A. Chaibakhsh, N. Chaibakhsh and M. B. Abdul Rahman, Fuzzy modeling and optimization of biohemial proesses: a ase study. in Pro. International Conferene on Chemistry and Chemial Engineering, vol., 200, pp. -5. G. Beliakov and M. King, Density based fuzzy -means lustering of non-onve patterns, European Journal of Operational Researh, vol. 73, pp , Ali Ghaffari (948) reeived his B.S. degree in 970 from Sharif University of ehnology (in ehran), M.S. degree in 974 from Georgia eh., and his Ph.D. degree in 978 from Berkeley, all in Mehanial Engineering. He is a Professor with the Department of Mehanial Engineering at the K.N. oosi University of ehnology (ehran) sine 987. He teahes ourses in the areas of automati ontrol, advaned and fuzzy ontrol. His researh interests are in the areas of ontrol systems and biomehanis. He is one of the founders of the ARAS Researh Center for Design, Manufaturing and Control of Roboti Systems, and Automati Mahineries. Ali Chaibakhsh (980) reeived his B.S. degree in 2002 from University of Guilan in Mehanial Engineering, Rasht, Iran, and his M.S. and Ph.D. degrees in Mehanial Engineering in 2004 and 2009 from K.N. oosi University of ehnology, ehran, Iran. He is now an Assistant Professor at the Department of Mehanial Engineering, University of Guilan. His researh intersets are intelligent system inluding neural networks, fuzzy logi, and soft omputing tehniques and their appliations in industrial proesses modeling and ontrol. Sajjad Shahhoseini (985) reeived his B.S. and M.S degrees both in Mehanial Engineering, in 2008 and 20 from South ehran Brah, Islami Azad University. His researh intersets are in modeling and ontrol of thermal power plants. 608