COMPARING TWO NONLINEAR STRUCTURES FOR SECONDARY AIR PROCESS MODELLING

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1 Control 004, Unversty of Bath, UK, September 004 COMPARING WO NONLINEAR SRUCURES FOR SECONDARY AIR PROCE MODELLING K. Leppäkosk, M. Paloranta and E. Ikonen Fax: , Emal: kmmo.leppakosk@oulu.f, URL: Systems Engneerng Laboratory, Unversty of Oulu, Fnland Keywords: dentfcaton, nonlnear systems, combuston, power plants, flue-gas emssons Abstract he secondary ar process, as a part of a flue-gas oxygencontent control system n a fludzed bed combustor, was dentfed usng two Hammersten types of structures. A tensor product structure developed especally for the process, as well as a sgmod neural network were examned for modellng the statc part of the Hammersten model. he two approaches were equal n accuracy. he better transparency of the tensor product structure makes t more appealng. Multple data sets could effcently be utlsed snce the structure of the model enables separate dentfcaton of the statc nonlnear and lnear dynamc parts. A more accurate model enables better tunng of the control system, n order to decrease flue-gas oxygen-content and NO x emssons. Introducton he secondary ar process s a part of the flue-gas oxygencontent control system n thermal power plants. A part of the total s blown through a secondary ar process nto the combuston chamber va three or four ar feedng levels. he secondary ar process s nonlnear and, at least n a practcal sense, tme-nvarant. Proper functon of a secondary ar control system s essental, n order to ensure an acceptable control of the combuston process. he tmng of fuel and s not easy n ndustral cases [5] due to lack of sutable models. he amount of excess ar s one of the most mportant free control varables effectng NO x and CO emssons. he hgher flue-gas oxygen-content s, the hgher NO x emssons are, whch was observed also n several experments [6,7]. In most cases, flue-gas oxygen-content s controlled by usng secondary. Consequently, reducng NO x emssons requres a secondary ar process model. here are several methods for dentfcaton of nonlnear plants [0], for example neural networks [] and wavelets. Constrants and a pror knowledge can be ncluded n a proper cost functon, takng account of the msmatch between model predcton and emprcal data, non-smoothness of a model, msmatch between a model and a default model, usng soft constrants and hard constrants [4]. Alternatvely, assumptons can also be embedded n the model structure. In ths case, Wener/Hammersten models provde a reasonable and feasble approxmaton of the general nonlnear tmeseres model [, pp. 4]. In ths paper, the use of the Hammersten structure s consdered. In Hammersten models, a statc non-lnear part precedes a lnear dynamc part. A sgmod neural network and tensor product type structures are consdered as the model canddate structures n the statc part. A frst order lnear transfer functon s used n the lnear part. he paper s organsed as follows. Frst, the flue-gas oxygencontent control system s ntroduced, and the secondary ar process and ts behavour are presented. Second, the process experments are descrbed. Fnally, two types of secondary ar process models are studed and compared. Fludsed bed combuston process In fludsed bed bolers, fuel flows and s are fed nto a combuston chamber n whch heat sand bed dres and grnds fuel before t burns. Prmary ar s blown from the bottom of the boler, n order to fludse the bed; secondary ar s blasted above the bed. he s are staged, n order to control better the combuston process. A process automaton system s used to control a combuston process. A power controller mantans energy producton on a desred level by changng the fuel feed rate. Its control sgnal s transmtted to the lower actuator controllers whch control fuel feedng screws, ar fans and ar dampers. A smulator [6,7] has been developed whch (Fg. ) contans: a power control system, a flue-gas oxygen-content controller system, a fuel feedng system, an ar feedng system, and a flue-gas oxygen-content model. he power control system mtates a power controller. he fuel feedng system contans controllers and screw models. he ar feedng system contans an ar dstrbuton calculaton whch defnes the setponts for the controllers, a prmary ar process, and a secondary ar process. he model for the secondary ar process s utlsed n two ways: n rato control between fuel feed and ar feed, and n flue-gas oxygen-content control. he power controller sends a

2 Control 004, Unversty of Bath, UK, September 004 sgnal to calculaton block, whch dstrbutes the sgnal to the fuel feed controllers and ar feed controllers. Correct tmng between the fuel feed controllers and ar feed controllers s essental n order to stablse the flue-gas oxygen-content. he qualty of fuel s not homogenous, and especally bomasses may be very heterogenous, resultng n fluctuatons n the flue-gas oxygen-content. he dsturbances are commonly compensated by usng secondary. he flue-gas oxygen-content controller transmts a sgnal to the controllers. he purpose, ntally, was to use an expermental desgn method, such as the aguch-method [8]. Nonetheless, there were often constrants not known n advance, as all alternatves to change the control sgnals were not possble. Durng an experment sere, the bed temperature ncreased too much snce the lower was too strong, resultng that most of fuel burnt n the bed. Durng the next experment seres, the control sgnal of the lower ar level was slghtly decreased, and the bed temperature dd not ncrease. he control sgnals correlate durng normal operaton, and all combnatons do not fulfl n the real process. hus, only the most common cases are necessary to explore. he tranng (7.5 hours) and valdaton data (5 hours) were composed of several separate experments. 4 Model structures Fgure. Man blocks of the smulator. [6] he consdered secondary ar process conssts of three dfferent ar feedng levels, see (Fgure ). A fan pumps the ar, dstrbuted by usng the ar dampers. he upper level s at the top of the boler, the lower level s ust above the fludsed bed, and the mddle level s between the two levels. All the ar levels are separately controlled by the dampers, and the secondary ar pressure s controlled by changng the blower speed. he ar pressure control sgnal has a nonlnear effect on all the s. Every ar control sgnal s nonlnearly coupled wth the pressure and other s. he Hammersten structure conssts of a nonlnear statc part followed by a lnear dynamc part. wo statc types were used n the Hammersten models: a tensor product and a sgmod neural network. he tensor product can be consdered as a grey-box model made for ths specfc process, n order to take better the constrants of the process nto account. he sgmod neural network was used as a reference model, due to ts flexble functon mappng abltes. A frst order output error type of tme-seres model was used n the lnear part. he models were traned teratvely, usng the Levenberg- Marquardt method. he values were scaled to unt nterval. he statc part was frst estmated, and then the lnear part estmated usng the latest statc model. Both models had four nputs and fve outputs. hree ar damper control sgnals and a fan control sgnal were the nputs; three measurements and an ar pressure measurement were utlsed as the outputs. Both the nputs and the outputs were numbered from one to four, from the upper to ar pressure. Snce the ar fan affected all the ar flows, the total was taken as the ffth output. 4. ensor product structure Fgure. Secondary ar system control prncple. [7] Experments Several process experments were conducted n order to dentfy the process models for a paper mll power plant. Some of the controllers and the ar pressure controller were swtched n manual modes, and the control sgnals were changed by usng a sngle varable method. he control sgnals vared between 0-00 % of the maxmum for the ar dampers, 4-00 % for the ar fan. he tensor product structure was composed of a product of logstc sgmod growth functons, modfed logstc sgmod growth functons and power functons. he tensor product calculaton n the statc part can be consdered as a global bass functon. Several dfferent functons were studed, such as exponental, power and asymptotc regresson functons. A power functon was found to be the most sutable to model the effect of the ar fan control sgnal, snce the nherent bounds of the process were easy to set. Usng a pror knowledge of the behavour of the s, dfferent types of sgmod growth functons were compared: the Gompertz, logstc, Rchards, Morgan- Mercer-Flodn and Webull [9, pp. 6-6]. he logstc type was found to be the most sutable.

3 Control 004, Unversty of Bath, UK, September 004 In the tensor product constructon, the model nput s gven by y I, m, = ( k) f ( ϕ( k) β ) = κ ( ϕ, β ) = () where J s the number of the outputs ( =,, 5), and the column vector ϕ of the model nputs s I dmensonal ( =,,, 4). M s the ndex for the type of a bass functon (m =,, ). he logstc sgmod functon s gven by κ( ϕ, β ) = + exp( β β ϕ ), (),, the modfed logstc sgmod functon by κ ( ϕ, β ) and the power functon by β, = β, +, () + exp( β β ϕ ), ( ϕ β ) β ϕ,,,,4 β κ =. (4) he followng models were used: he top ( = ): =, ar damper, κ = and, ar dampers and, κ he mddle ( = ): = and, ar dampers and, κ =, ar damper, κ he bottom ( = ): = and, ar dampers and, κ =, ar damper, κ he ar pressure ( = 4): = -, ar dampers -, κ he total ( = 5): = -, ar dampers -, κ A useful nterpretaton s to thnk that a man control sgnal affects a man output, and other control sgnals are correctng. A maor mpact s that the user of the model can easly comprehend the effects of the control sgnals. For example, the relaton between the lower ar control sgnal and the lower presents one of the fve man nput/output pars. he relatonshp between the man nput control sgnal and the output sgnal has the shape of the ncreasng logstc sgmod functon (equaton ()) n ths case. he upper ar, the mddle ar and the ar fan control sgnals affect the lower, and thus they are correctng. he correctng effects of the upper and mddle s have the shapes of the decreasng sgmod functon (equaton ()). β, s close to one, and β, s a small negatve number. he correctng effects of the s to the lower (man) ar flow are not large. he effect of the ar fan control sgnal s otherwse sgnfcant. In equaton (4), s close to 0.5. β, he relatonshps above are the same when the upper or mddle s the man control sgnal. Let us consder another example. he ar fan control sgnal s the man nput sgnal, and the ar pressure s the output sgnal. hen (n equaton (4)) s close to two (compare wth β, Bernoull s law). he control sgnals are correctng. In equaton, s close to one and s a small β, β, postve number. he correctons are therefore ncreasng when the mnor control sgnals are enlargng. he effects of the mnor control sgnals are qute sgnfcant. 4. Sgmod neural network An output of one-hdden-layer sgmod neural network s gven by, [, pp. 9], y ˆ = f H h g h h H + h= (, α, β ) = α ( ϕ, β, ) + α ϕ (5) where H s the number of hdden nodes, α and β are parameters, and g h ϕ h = (6) I + exp β h, ϕ β h, I + = (, β ) Snce most of the nonlneartes of the process had nherently the shape of the logstc sgmod functon, n ncreasng or decreasng drecton, the sgmod neural networks contaned ten nodes. Logstc sgmod growth functons were used as bass functons. here were four nputs and fve outputs. he network can be consdered as fve MISO models.

4 Control 004, Unversty of Bath, UK, September Expermental comparson he outputs of two Hammersten models, n whch the tensor product structure and the sgmod neural network were used n the statc part, were compared to the tranng and valdaton data. A part of the valdaton s shown n Fgures and 4 for ar pressure, wth whch the dfference between the dentfed models and the measurements was the largest. For zero-mean data Y = K k = Y he root-mean-squared errors (RMSE) are calculated by the followng [, pp. 6] RMSE = K K ( ˆ ) k = Y Y (9) (0) where Y s measured output, Y ˆ s estmated output ( =,,, k), and K s the number of data ponts. Fgure. Measured ar pressure (sold) and tensor product type based model ouput (dashed), on a part of the valdaton data. Upper Mddle Lower Ar pressure otal ar flow R - R - RMSE - RMSE - tp snn tp snn able : ranng results Hammersten model: tensor product and sgmod neural network. Fgure 4. he changes n the four nput sgnals for the ar pressure (the tensor product type), on a part of the valdaton data. he R crteron s a measure for goodness of ft. R s calculated as follows [, pp. 59], where R = = K E k = E ( Y Y )( (7) ˆ Y Yˆ ) (8) for the th output, where Y s measured output and Y ˆ s the estmated output ( =,,, 4, 5). he statstcs n ables and based on RMSE crteron suggest that the tensor product type and the sgmod neural network had not sgnfcant dfference. RMSE on the valdaton data s smallest for the top usng the sgmod neural network model; the contrary holds for the ar pressure. Upper Mddle Lower Ar pressure otal R - R - RMSE - RMSE - tp snn tp snn able : Valdaton results Hammersten model: tensor product and sgmod neural network. he best valdaton result among the outputs usng R was obtaned for the bottom, for whch the data were probably the rchest. he worst results were obtaned for the

5 Control 004, Unversty of Bath, UK, September 004 top (tensor product) and the ar pressure (sgmod neural network). he mddle had the most even results n the tranng and valdaton data. here s no partcular reason why goodness-of-ft should vary between tranng and test data sets. Measurement or process nose s not extensve, and all the s have smlar nose characterstcs. Yet, the top model has the largest dfference n goodness-of-fts between tranng and valdaton data; the dfference n the pressure model s also sgnfcant. Instead, the dfference n goodness-of-fts for the bottom ar flow model s mnor. Comparson between tranng and valdaton data ndcates that the rchness of the tranng data could be mproved. 6 Conclusons he Hammersten structure contans a nonlnear statc part and a lnear dynamc part. he use of a tensor product structure and a sgmod neural network n the statc part were studed. here were no sgnfcant dfferences n accuracy between the dentfed models. For ths specfc process, the tensor product structure s more transparent to use, however. Measured data can be effcently utlsed by usng the Hammersten approach, snce the estmaton of the parameters n the statc and dynamc parts can be conducted separately. Separate data blocks from dfferent operatng condtons, possbly wth dfferent samplng frequences, can be easly used n the dentfcaton of the statc part. Notce, that for dynamc modellng the condtons for data are strcter. akng account of the lmted resources durng normal process operaton, ths enables modellng n a wder operatng area usng routnely collected data. Acknowledgements he authors wsh to thank Foster Wheeler Energa Oy, Ar-Ix uotantoteknkka Oy and Fnnsh Natonal echnology Agency. E. Ikonen was fnancally supported by the Academy of Fnland, proects no and 0. optmzaton approach, Automatca : pp 7-56 (996) [5]. Joronen and P.. Nem. Advanced estmaton and compensaton of varatons n sold fuel calorc value, In: Automaton 00, Semnar Days 9- September 00 (uokko, R. (ed.)), Fnnsh Socety of Automaton, Helsnk, Fnland, pp. 87-9, (00) [6] K. Leppäkosk, M. Paloranta, J. Kovács and E. Nemtalo. NO x emsson reducng control desgn by decreasng flue-gas oxygen-content, In: Automaton 00, Semnar Days 9- September 00 (uokko, R. (ed.)), Fnnsh Socety of Automaton, Helsnk, Fnland, pp. 05-0, (00) [7] M. Paloranta, K. Leppäkosk and J. Mononen. A smulator-based control desgn case for a full-scale bubblng fludsed bed boler, In: Proceedngs of the welfth IASED Internatonal Conference on Appled Smulaton and Modellng (M. H. Hamza (Ed.)), September -5 00, Marbella, Span, pp. 0-5, (00) [8] M. S. Phadke. Qualty engneerng usng robust desgn, Prentce Hall, 4 p., (989) [9] D. Ratkowsky. Nonlnear regresson modellng - A unfed practcal approach, Statstcs, textbooks and monographs 48, Marcel Dekker Inc., New York, 76 p., (98) [0] J. Söberg, Q. Zhang, L. Lung, A. Benvevste, B. Delyon, P. Glorennec, H. Halmarsson and A. Judstky. Nonlnear black-box modelng n system dentfcaton: a unfed overvew, Automatca : pp , (995) References [] S. Haykn. Neural networks: a comprehensve foundaton, Prentce Hall, 84 p., (999) [] H. Hyötynem. Multvarate regresson, technques and tools, Helsnk Unversty of echnology, Department of Automaton and Systems echnology, Control Engneerng Laboratory, Report 5, Fnland, 07 p., (00) [] E. Ikonen and K. Nam. Advanced process dentfcaton and control, Marcel Dekker Inc., New York, 0 p., (00) [4]. A. Johansen. Identfcaton of non-lnear systems usng emprcal data and a pror knowledge an