A Neuro-Fuzzy System for Modelling of a Bleaching Plant

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1 A Neuo-Fuzzy System fo Modelling of a Bleaching Plant R. P. Paiva a A. Douado a B. Duate b a CISUC Cento de Infomática e Sistemas da Univesidade de Coimba Depatamento de Engenhaia Infomática, PÓLO II da Univesidade de Coimba, Pinhal de Maocos, P 3030, Coimba, Potugal Tel , Fax: , uipedo@dei.uc.pt b Companhia de Celulose do Caima, S A, P 2250 Constância, Potugal ABSTRACT: In pape industy, pulp bleaching is a most impotant concen in ode to effectively espond to the high quality standads demanded by maket equiements. Thus, a good knowledge of the bleaching plant is vital to achieve those goals. In this pape a neuo-fuzzy stategy is poposed to aid bleaching quality by pedicting the outlet bightness. It consists of two phases: in the fist one, a fuzzy clusteing technique is applied to extact a set of fuzzy ules; in the second one, the centes and widths of the membeship functions ae tuned by means of a fuzzy neual netwok tained with backpopagation. This technique seems pomising since it pemits good esults with lage nonlinea plants. Futhemoe, it descibes the plant using a set of linguistic ules, which have the advantage of being close to natual human language, so, moe intuitive fo opeatos. Peliminay pomising esults ae pesented and discussed. Keywods : pulp bleaching, fuzzy clusteing, neuo-fuzzy modelling 1. Intoduction Pulp bleaching is known to be a athe nonlinea pocess with significant pooly undestood physical phenomena. Futhemoe, the bleaching sequence is influenced by a lage set of vaiables fo which elative impotance is not so well compehended. So, finding a good model of the plant is not a tivial task. In the absence of an accuate fist-pinciples model, fuzzy modelling appeas to be the most adequate appoach. Howeve, if pocess measuements and some insight of the opeatos ae the only available knowledge, the building up of the fuzzy system is not a simple task. Clusteing - in the input-output space allows to come up with a finite set of linguistic ules. Then, a fuzzy neual netwok, tained with backpopagation, optimally tunes the centes and widths of the membeship functions. One impotant chaacteistic of the pocess is its time-vaying tanspot delay. The effects of this phenomenon will be pesented and discussed. This pape is oganised in five sections. Section 2 descibes the two-phase algoithm fo fuzzy modelling. Section 3 gives a shot desciption of the pulp bleaching plant. In Section 4 the application of the efeed techniques to a nonlinea system is descibed. Simulation esults ae pesented. Finally, Section 5 concludes the pape pointing out the advantages and limitations of the stategy used and the main poblems encounteed, as well as some diections fo futue wok. 2. Fuzzy modelling Conside a Multiple Input Multiple Output (MIMO) system, with p N inputs and q N outputs, descibed by Y k = f θ k, ξ( k ), Y ( k) R q, ξ( k) R q (1) ( ) [ ( ) ] whee f is a linea o nonlinea function, ξ(k) denotes a stochastic distubance and θ(k) epesents pevious inputs and outputs, as follows: θ ( k) = [ y ( k ),, y ( k n ), y ( k 1, ) y ( k n ), u ( k d ), u ( k m d + 1 ), u ( k d ), u ( k m d 1) ] T q q q p p p p p + K (2)

2 The paametes n 1,, n q, m 1,, m p, d 1,, d p ae elated to the system ode and discete pue time delay. Equation (1) models a pocess by a nonlinea auto-egessive with exogenous input (NARX) model. The goal is to somehow obtain an appoximation of function f. In this pape fuzzy modelling is used so, the model will be designated as a fuzzy auto-egessive with exogenous input (FARX) model FARX model stuctue Function f is modelled by Mamdani fuzzy infeence. The pocess is epesented by a fixed set of R ules of type (3): Ri : If y1( k) is A11i and Land yq ( k nq ) is Aqn i andlu k d is B i and and u p k m p d p is B q 1( 1) 11 L ( + 1) pmpi then y1( k + 1) is C1i and Land yq ( k nq + 1) is Cqi whee A jki, B jki and C ji ae linguistic values fo each output and input vaiables, defined by thei membeship functions: µ, µ,, i = 1, 2,, R. A B µ C jki jki ji (3) 2.2. Identification The paametes n 1,, n q, m 1,, m p, d 1,, d p must be popely chosen, based on pio knowledge o by compaison of diffeent values in tems of some citeia. Assuming this poblem is solved, the issue is: 1) to obtain a set of ules of type (3); 2) to adjust the paametes of the membeship functions using data collected fom the system: X = [ θ( 1) L θ( N 1) ] T, Ψ = [ Y( 1) L Y( N 1) ] T (4) whee N is the numbe of data samples available fo the identification pupose Fuzzy clusteing In ode to obtain a set of R ules avoiding the poblems inheent to gid patitioning, e. g., ule base explosion, fuzzy c- means clusteing (Bezdek, 1981) is applied. This technique is employed since it allows a scatte space patitioning. Given the identification data, X and Ψ, and the numbe of clustes, R, this algoithm calculates cluste centes, V R R, and a patition matix, P, that contains the degees of membeship fo each point in each cluste: The classification citeia is given by the objective function (5): N R m' 2 J ( P, V ) = = = ( µ ik ) ( dik) (5) k 1 i 1 In (5) µ ik is the membeship of the k th data sample in the i th class, m is a paamete that contols the extent of fuzziness in the clusteing pocedue m is typically chosen in the inteval ]1.25, 2] - and d ik is the Euclidean distance between the k th data point and the i th cluste cente v i. The centes of each cluste ae computed by: N m' µ x v k ik kj ij = = 1, j = 1, m, x kj an entance in the input matix X (6) N m' µ ik k= 1 The objective of classification is, thus, to obtain a fuzzy patition that minimises the classification citeia J(P,V) (5). This is accomplished by iteatively updating the patition matix and ecalculating the cluste centes. The algoithm is stated with an initial guess fo P, e.g., andom values in the inteval [0, 1]. Then the membeship values ae updated accoding to: 2 ( ' 1) + 1 µ = R m d ik (7) ik j= 1 d jk The algoithm stops when the two consecutive values of the matix U ae below a specified toleance level. Afte obtaining a set of fuzzy ules, these can be included in a fuzzy infeence system. Befoe doing so, centes and widths of the input and output membeship functions must be obtained. Obviously, the centes of the clustes obtained will be assigned to the centes of the input and output membeship functions. Since gaussian memb eship functions ae used in this wok, thei espective standad deviations must be computed. This is accomplished by the heuistic: 1

3 ( x ) min( x ) max kj kj σ ij = m', k = 1,, N (8) Fuzzy neual netwok Afte deiving an initial fuzzy infeence system based on fuzzy clusteing, its paametes, i.e., the centes and widths of membeship functions must be optimised. In this pape, this is accomplished by means of taining a fuzzy neual netwok (FNN) using standad backpopagation. The stuctue of the FNN is pesented in Figue 1. The netwok consists of five layes. Laye 1 contains the input nodes, which epesent input linguistic vaiables. This laye simply passes the inputs to laye 2. The nodes in laye 2 ae the linguistic tems of each input vaiable, epesented by gaussian membeship functions. This laye is esponsible fo the fuzzification of the cisp input values. In laye 3, each node is assigned to a ule of the fuzzy infeence system. The antecedents of each ule ae defined by setting pope links fom nodes at laye 2 to nodes at laye 3. This laye fies each ule based on some fuzzy AND opeation. Since thee ae some ules that shae the same consequent, laye 4 integates those ules using some fuzzy OR opeation. The nodes at laye 4 define the linguistic tems fo each output, epesented by gaussian membeship functions, as in laye 2. Laye 5 is the output laye. The ole of this laye is to pefom defuzzification, i.e., convet fuzzy numbes into cisp numbes. In this wok, the cente of aea defuzzification method is used. y 1 (k) u p (k-m p -d p +1) y 1 (k+1) y q (k+1) Figue 1: Stuctue of the fuzzy neual net As stated befoe, the objective of the pesented FNN is to pefom optimisation of the centes and widths of the gaussian membeship function. Fo that matte, supevised leaning is caied out based on acquied data (4). A detailed desciption of the application of backpopagation to the FNN can be found in (Lin, 1995). 3. Pulp bleaching plant fom washing plant Washes 1 & 2 H 2 O 2 NaOH Na 2 O:SiO 2 O 2 Steam T o w e 1 T o w e 2 H 2 O 2 NaOH Na 2 O:SiO 2 Steam Washe 3 T o w e 3 Washe 4 Buffe tank to wet end Filtate tank Filtate tank Filtate tank to effluent teatment pulp flow Figue 2: The EOP/P sequence chemicals and steam flow "fesh" wate flow effluent flow The main goal of bleaching is to decolouise the lignin pesent in wood fibbes. In ode to achieve this goal, chemicals ae added, which eact with the unbleached chomophoes poducing the desied bleached chomophoes so that pulp

4 popeties can satisfy the standads demanded by pape industy. A majo concen is to obtain satisfactoy outlet bightness. Chloine is known to be a univesal bleaching agent. Howeve, due to ambient estictions, pulp bleaching must be caied out without any compound containing chloine. This has led to a Totally-Chloine Fee (TCF) bleaching sequence. Some TCF sequences have been used in the past yeas. In ou case an EOP/P sequence is conducted, as pesented in Figue 2 (Caima, 1994) Desciption of the bleaching sequence Afte cooking the wood with acid fo delignification, washing and sceening the pulp, the bleaching stage is eady to begin. Fist of all, the pulp is washed in washes 1 and 2. Then, in the EOP (Extaction with NAOH, Oxygen and Hydogen Peoxide) stage the pulp is mixe d with chemicals, namely hydogen peoxide, oxygen (bleaching agents), caustic soda (to adjust the ph of the eacting mixtue), and sodium silicate (peoxide stabilise). This mixtue eacts within towes 1 and 2 fo appoximately 4 hous. Befoe the P (extaction with Hydogen Peoxide) stage, the pulp is washed in washe 3 in ode to ecove chemicals and enegy. In the P stage the same chemicals as befoe, except fo oxygen ae added. The eaction takes place in towe 3 fo appoximately 1.5 hous. Afte this esidence time, the pulp is washed in washe 4 and is then conducted to the dying section whee it stays fo about 1 hou. The total bleaching time, fom washes 1 and 2 until died pulp is obtained takes about 8 hous. The final bleaching quality is influenced by a geat deal of vaiables. Accoding to expets knowledge the vaiables that have a stonge influence on the final pulp quality ae inlet bightness, inlet pulp flow, inlet pemanganate numbe (which is a lignin concentation measuement), hydogen peoxide in both of the stages and inlet pulp flow Bightness analysis Thee ae a few high-level ules that give some insight on the final bightness achieved: it inceases with peoxide flow; it inceases with ph; it inceases with the consistency; it inceases with tempeatue, until some theshold; it inceases with inlet pulp; it deceases with inlet pemanganate numbe. This infomation can be compaed with the set of linguistic ules obtained by the fuzzy infeence system. In (Duate, 1995), infomation on the delay times elating each input vaiable and the outlet bightness is pesented. Thee, it is said that the delay time fom inlet bightness to outlet bightness is 7-8 hous, which coesponds to the bleaching time efeed above. Fo inlet pulp flow and inlet pemanganate numbe the delay time should be the same. Concening the peoxide flow in the P stage, the effect of a change on it affects outlet bightness fom 3 to 5 hous late. Fo the peoxide flow in the EOP stage, the delay time should coespond to time elapsed since inlet pulp is washed in washes 1 and 2. So, a delay time of hous is assumed. 4. Simulation esults The pesented techniques ae applied to modelling of the pulp bleaching plant descibed above. Some of the measued vaiables ae not sufficiently exciting. Thus, thei contibution fo the achieved bleaching quality is not easily assessed only with measuements. Moeove, accoding to the expets expeience, the most impotant input vaiables ae peoxide flow, inlet bightness and ph. Theefoe, these ae the input vaiables used to model the plant. Some expeiences wee caied out with the full set of vaiables. Howeve, the inclusion of those vaiables did not bing any bette esults (actually, some cases happened to wosen the model). The fuzzy infeence system is obtained fom the input-output measuements using fuzzy clusteing and tuning the membeship functions with the algoithm in Section The sampling inteval was defined in the mill as one hou; this sampling inteval seems to be sufficient since the system s dynamics ae vey slow. Simulations wee caied out with N=400 taining samples. The paametes fo fuzzy clusteing wee defined as m =1.3 and R=50. Figue 3 pesents the taining esults and Figue 4 shows model validation.

5 Figue 3. Taining esults: Real Pocess Data FNN output Fom the plot in Figue 4, it can be obseved that the model obtained has not satisfactoy genealisation capabilities. Some possible easons fo that ae noise in outlet bightness measuements in the outlet bightness and, especially, inconsistent taining and validation sets, esulting fom the vaiable time delay of the system. As stated above, the total pulp esidence time vaies fom 7 to 10 hous (depending on the inlet pulp flow), accoding to the expets. The descibed technique seems not to be able to satisfactoily cope with this situation. Thus, a stategy fo captuing the effect of the vaiable time delay is pesently unde consideation Figue 4. Validation esults: Real Pocess Data FNN output 5. Conclusions In this pape, a neuo-fuzzy modelling scheme was pesented. The model is obtained in two-phases. In the fist one, fuzzy c-means clusteing was applied in ode to obtain a set of fuzzy ules. Then, a fuzzy neual netwok is tained to optimally tune the membeship paametes using backpopagation. This appoach is intended to model a pulp bleaching plant. Howeve, some poblems wee encounteed, which limited the accuacy of the obtained model. Those poblems seem to come, fundamentally, fom the vaiable time delay of the system, which is not captued by the model. Pesently, a model fo the time delay is being developed to be included in the system. The time delay will be estimated fo each sampling instant, so that the outlet bightness can be moe accuately pedicted, in the pope time basis. This will equie an online leaning scheme, which is pesently unde investigation. Refeences Bezdek, J.C Patten ecognition with fuzzy objective function algoithms, J. Math. Biol., Vol. 1, Bown, M.; Hais, C Neuofuzzy adaptive modelling and contol, Pentice Hall Intenational. Buckley, M.; Hayashi Y Neual nets fo fuzzy systems, Fuzzy Sets and Systems, No. 71, Chiu, S Fuzzy model identification based on cluste estimation, Jounal of Intelligent and Fuzzy Systems, Vol. 2, No. 3.

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