Control of Nonlinear Industrial Processes Using Fuzzy Wavelet Neural Network Based on Genetic Algorithm

Transcription

1 Internatonal Journal of Research n Engneerng and Scence (IJRES) ISSN (Onlne): , ISSN (Prnt): Volume 2 Issue 5 ǁ May 2014 ǁ PP Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc Algorthm Navd Lotfzadeh 1, Ahmad Reza Alae 2, Al Pedar Pralman 3 1 Entekhab Elm Karbord Unversty, Esfahan, Iran 2 Deartment of Electrcal Engneerng, K.N.Toos Unversty of Technology, Tehran, Iran 3 Deartment of Electrcal Engneerng, Islamc Azad Unversty Khomenshahr Branch, Esfahan, Iran ABSTRACT: Artfcal ntellgence control technues, becomes one of the maor control strateges and has receved much attenton as a owerful tool for the control of nonlnear systems. Ths aer resents a desgn of Fuzzy Wavelet Neural Network (FWNN) traned genetc algorthm (FWN-GA) for control of nonlnear ndustral rocess. The FWNN s aled to aroxmate unknown dynamc of system and GA s used to tran and otmze the FWNN arameters. In the roosed control scheme, neural control system synthess s erformed n the closed-loo control system to rovde arorate control nut. For ths, the error between desred system outut and outut of control obect s drectly utlzed to tune the network arameters. The controller s aled to a hghly nonlnear ndustral rocess of contnues strred tank reactor (CSTR). Smulaton results show that FWNN-GA controller has excellent dynamc resonse and adat well to changes n reference traectory and system arameters. Keywords - Fuzzy Wavelet neural network; genetc algorthm; nonlnear CSTR. I. INTRODUCTION Fuzzy technology s an effectve tool for dealng wth comlex, nonlnear rocesses characterzng wth ll-defned and uncertanty factors. Fuzzy rules are based on exert knowledge. The constructng of knowledge base for some comlcated rocesses s dffcult. Thus, there are some methods for constructng of fuzzy rules [1, 2]. On the other hand, some characterstcs of neural networks such as learnng ablty, generalzaton, and nonlnear mang are used to deal wth sgnal rocessng, control system, decson makng, and so on. However, the man roblem of neural networks s that they reure a large number of neurons to deal wth the comlex roblems. Moreover, they also result n slow convergence and convergence to a local mnmum. In order to overcome these dsadvantages, wavelet technology s ntegrated nto neural networks [3]. Recently, based on the combnaton of feed-forward neural networks and wavelet decomostons, wavelet neural network (WNN) has receved a lot of attenton and has become a oular tool for functon learnng [4]. The man characterstc of WNN s that some knds of wavelet functon are used as the nonlnear transformaton n the hdden layer of neural network, so tme freuency roerty of wavelet s ncororated nto the learnng ablty of neural networks. However, the man roblem of WNN wth fxed wavelet bases s the selecton of wavelet frames because the dlaton and translaton arameters of wavelet bass are fxed and only the weghts are adustable. The arorate wavelet transform wll result n the accuracy of aroxmaton. Therefore, there are several dfferent methods roosed to solve the roblems [5, 6]. The comlexty and uncertanty of the system can be also reduced and handled by the concets of fuzzy logc. The local detals of non statonary sgnals can be analyzed by wavelet transforms. The aroxmaton accuracy of the lant can be mroved by the self-learnng caabltes of neural networks. Therefore, there are many aers that dscuss the synthess of a fuzzy wavelet neural nference system for sgnal rocessng, control roblems, dentfcaton and attern recognton [3, 7, 8]. In recent years, Fuzzy Wavelet Neural Networks (FWNN) have become very oular and have been aled n many scentfc and engneerng research areas such as system dentfcaton, functon aroxmaton and control of nonlnear systems. Ths s due to ts nformaton rocessng characterstcs such as nonlnearty, hgh arallelsm, fault tolerance as well as caablty to generalze and handle mrecse nformaton [4]. The Contnuous Strred Tank Reactor system (CSTR) s a comlex nonlnear chemcal system that one of ts states, reacton consstence, cannot be measured. Anyway, the value of the state s necessary for control, so state estmaton s used [9]. In ths aer, a FWNN combned wth GA (FWN-GA) s used for dentfcaton and trackng control of a nonlnear contnuous strred tank reactor (CSTR). The FWN s emloyed to estmate the value of the state and unknown dynamc of system. FWNN consst of a set of fuzzy rules that each rule 1 Page

2 Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc corresondng to a sub-wnn conssts of sngle scalng wavelets. The dffcultes of selectng wavelets are reduced and orthogonal least-suare (OLS) algorthm s used to determne the number of fuzzy rules and to urfy the wavelets for each rule. Also, GA s used to tran and otmze the FWNN arameters. In the roosed control scheme the error between desred system outut and outut of control obect s drectly utlzed to tune the network arameters. The caablty and effcency of the roosed method s llustrated by the temerature control of a nonlnear CSTR. The aer s organzed as follows. To make a roer background, the basc concets of FWN and GA are brefly exlaned n secton II. In secton III, the roosed FWN-GA based controller and ts learnng algorthm are descrbed. Secton IV descred CSTR system. The results of the roosed aroach on the smulaton examle are gven n Secton V and fnally, some conclusons are dawn n Secton VI. II. The basc concets of FWN and GA are brefly descrbed n ths secton. FUZZY WAVELET NETWORK AND GENETIC ALGORITHM A. Fuzzy Wavelet Neural Network A tycal fuzzy wavelet neural network for aroxmatng functon y can be descrbed by a set of fuzzy rules such as follow [4]: R : If x1 s Then And A 1 and x 2 s T A 2 and and x s A, ŷ = ( k) w k, M z, t k R k 1 M, t k M, t tm R, x R (1) w k Where R s the th rule, c s the number of fuzzy rules. x and ŷ are th nut varable of x and outut of the local model for ruler, resectvely. Also M s dlaton arameter andt s the total number of wavelets for the th rule. k k k k k t [ t1, t2,..., t ], where t denotes the translaton value of corresondng wavelet k. Fnally, A s the fuzzy set characterzed by the followng Gaussan-tye membersh functon. 1, A ( x ) ( x 1 ) 2 3 / 2 (( ) ) 2 e (2) 2 R and 3 2, where 1 reresents the center of membersh functon, 2 and 3 determne the wdth and the shae of membersh functon, resectvely. Wavelets ( k) are exressed by the tensor roduct of 1-D wavelet functons: M M ( k) ( ) ( ) ( ) 2 2 k M k (2 ) 2 2 k M k x x t (2 x ) M, t t (3) 1 By alyng fuzzy nference mechansm and let functon y(x) s as follow: c yfwn ˆ yˆ 1 c A ( x ) 1 1 ˆ (4) M, t k ŷ be the outut of each sub-wnn, the outut of FWN for Where ˆ /, ˆ and for current nut x and each functon, satsfes 0 ˆ 1 c and ˆ 1. Also ˆ determnes the contrbuton degree of the outut of the wavelet based model wth 1 resoluton level M. In ths aer the aled structure of FWNN s the same as the structure used n [2]. Also orthogonal least-suare (OLS) algorthm s used to select mortant wavelets and to determne the number of fuzzy rules. Detals of ths OLS algorthm can be found n [10]. 2 Page

3 Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc B. Genetc Algorthm GA s an otmzaton technues nsred by natural selecton and natural genetcs. Unlke many search algorthms, whch erform a local, greedy search, GA s a stochastc general search method, caable of effectvely exlorng large search saces. A genetc algorthm s manly comosed of three oerators: reroducton, crossover, and mutaton. As a frst ste of GA, an ntal oulaton of ndvduals s generated at random or heurstcally. The ndvduals n the genetc sace are called chromosome. The chromosome s a collecton of genes where genes can generally be reresented by dfferent methods lke bnary encodng, value encodng, ermutaton encodng and tree encodng. Gene s the basc buldng block of the chromosome. Locus s the oston of artcular gene n the chromosome. In each generaton, the oulaton s evaluated usng ftness functon. Next comes the selecton rocess, where n the hgh ftness chromosomes are used to elmnate low ftness chromosomes. The commonly used methods for reroducton or selecton are Roulette-wheel selecton, Boltzmann selecton, Tournament selecton, Rank selecton and Steady-state selecton. But selecton alone does not roduce any new ndvduals nto the oulaton. Hence selecton s followed by crossover and mutaton oeratons. Crossover s the rocess by whch two-selected chromosome wth hgh ftness values exchange art of the genes to generate new ar of chromosomes. The crossover tends to facltate the evolutonary rocess to rogress toward otental regons of the soluton sace. Dfferent tyes of crossover by and large used are one ont crossover, two-ont crossover, unform crossover, multont crossover and average crossover. Mutaton s the random change of the value of a gene, whch s used to revent. III. PROPOSED CONTROL SCHEME The FWNN and ts learnng algorthm are used for dentfcaton and control of nonlnear CSTR system. Followng, the archtecture of roosed control strategy and ts otmzaton method based on GA are descrbed n subsectons A and B, resectvely. A. Archtecture of Proosed FWNN-GA controller The structure of control system s gven n Fg. 1. As can be seen, n ths dagram FWNN s utlzed as a controller and dentfer. r(t) e(t) GA otmzer FWNN Controller Plant y(t) FWN Plant model Fgure 1. Proosed FWNN-GA control scheme. The control scheme conssts of the FWNN lant model, FWNN controller and the otmzaton block. Where r(t) s desred outut and y(t) s the outut of control system. In the roosed control strategy, neural control system synthess s erformed n the closed-loo control system and e (t) s used for tunng network weghs to rovde arorate control nut. By mnmzng a uadratc measure of the error between desred system outut and the outut of control obect,.e. e (t), the desgn roblem can be characterzed by the GA formulaton. On the other hand, the genetc algorthm s used to correct the network arameters for adustng of FWNN controller and dentfer n real tme oeraton. B. FWNN Tranng. In the learnng ste, the FWNN arameters are calculated by mnmzng a ftness functon that usng the dfference between the desred and real outut as follow: H 2 Ek yˆ RNN ( x( l)) y( l) (5) k l 1 And, the Kth chromosome s reresented as N N kn N FN [ 1 2 t w ] (6) M 3 Page

4 Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc Whch are all free desgn arameters that to be udated by GA n our FWNN model. H s number of network tranng data. Accordng to Fg. 1, the outut s measured n each teraton and wll be gven to the GA otmzer after beng comared to the reference. Then the soluton vector s obtaned by GA by mnmzng the ftness functon whch gves the FWNN arameters. By usng the obtaned arameters, the network outut s calculated and aled to system followed by calculatng the new outut. The rocedure contnues untl a termnaton crteron s met. The termnaton crteron could be the number of teratons, or when a soluton of mnmal ftness s found. N N kn N Euaton (6) shows that the free arameters to be traned n FWNN are [ 1 2 t w ].Our task s to M desgn the FWNN structure such that the error between outut and reference s mnmzed. Therefore GA s aled for tunng arameters of FWNN by otmzng the (5) obectve or cost functon. Where E N s the ftness of Nth chromosome. In the GA, each oulaton s a soluton to the roblem whch determnes the arameters of N N kn N FWNN,.e. [ 1 2 t w ]. M IV. THE CONTINUOUS STIRRED TANK REACTOR SYSTEM Contnuous strred tank reactor (CSTR) s a hghly nonlnear rocess. A schematc of the CSTR system s shown n Fg.2. The rocess model conssts of two nonlnear ordnary dfferental euatons [11]: dca Q Ea ( CAf CA) k0 ex( ) CA dt V RT dt Q H a ( ) r E UA T f T k0 ex( ) CA ( T T) dt V c V RT c dt dt UA c V ( T T ) u V ( T f T ) (7) Fgure 2. CSTR lant model where the x = [x 1 ; x 2 ; x 3 ] state-varables of the model are the CA (mol/m 3 ) concentraton of the A comonent n the reactor, the T ( o C) reactor temerature, and the T ( o C) temerature of the ackect of the reactor, whle the nut of the rocess s the u [m 3 /mn] flow rate of the coolng materal. The controlled outut y of the rocess s the reactor temerature, y = x 2. The arameters and ts nomnal values of the model are gven n Table 1. Detals of the system data and ts roertes are gven n [12]. V. Smulaton Study In the frst stage, we should generate nut-outut data for obtanng the FWNN model of the rocess (Fg. 2). The tranng data was generated by closed-loo exerment and the roosed aroach n secton III s used to tran the model. Fg. 3 shows the obtaned tranng data set. The combned servo and regulatory control roblem was defned between two unstable oeratng onts: 70 0C C. The coolant feed temerature changed from 10 0C to 20 0C at t = 10 h what was the unmeasured dsturbance. Fg. 4 shows the model's outut and the real outut. From Fg. 4 can see that erformances of the controllers are good, and the FWNN controller based on GA acheved good dynamc erformance. TABLE I. Notaton Descrton Value and unt NOMINAL VALUES OF THE MODEL PARAMETERS 4 Page

5 Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc Q Feed flowrate 0.2 m 3 /mn V Reactor volume 2 m 3 K 0 Reacton rate coeffcent /mn E a Actvaton energy kj/mol R Ideal gas constant kj/mol C H r Heat of reacton 500 kj/mol C Af Concentraton of A n feed 1000 mol/m 3 T f Feed temerature 30 o C Densty of soluton 1000 kg/m 3 c Heat caacty of soluton 4.2 kj/kg o C UA Heat transfer coeffcent 252 kj/mn o C V Jacket volume 0.4 m 3 T f Inlet temerature of coolant 10 o C Iacet Reactor Fgure 3. Tranng date 5 Page

6 Flowrate [m 3 /mn] Temerature [C] Control of Nonlnear Industral Processes Usng Fuzzy Wavelet Neural Network Based on Genetc Reference Outut Tme (h) Fgure 4. Model s outut and real outut VI. CONCLUSION Ths aer resented the develoment and evaluaton of an FWNN based GA controller. The controller was desgned to control the temerature of a CSTR. The nonlnear lant dentfcaton was done on-lne usng the genetc algorthm for uck learnng. Wth ths method any changes n the arameters of the system could be detected and remedal functons can be done. Smulaton results show good dynamc erformance of the roosed FWNN-GA controller. REFERENCES [1] R. R. Yager and L. A. Zadeh, Eds., Fuzzy Sets, Neural Networks and Soft Comutng. (New York: Van Nostrand Renhold, 1994). [2] S. R. Jang, C. T. Sun, and E. Mzutan, Neuro-Fuzzy and Soft Comutng.Englewood Clffs, (NJ: Prentce-Hall, 1997, ch. 17). [3] S. Tang Tzeng, Desgn of fuzzy wavelet neural networks usng the GA aroach for functon aroxmaton and system dentfcaton, Fuzzy Sets and Systems, 16(1), 2010, [4] D.W.C. Ho, P.A. Zhang, J. Xu, Fuzzy wavelet networks for functon learnng, IEEE Transactons on Fuzzy Systems 9 (1), 2001, [5] Q. Zhang, Usng wavelet networks n nonarametrc estmaton, IEEE Transactons on Neural Networks, 8(4), [6] J. Chen, D.D. Bruns, WaveARX neural network develoment for system dentfcaton usng s systematc desgn synthess, Industral & Engneerng Chemstry Research, 34(3), 1995, [7] E. Bam, M. Shahrar-kahkesh, M. Zekr, Shuffled Frog Leang Algorthm combned wth Fuzzy Wavelet Neural Network for Functon Learnng, The 4th Internatonal Conference on Intellgent Informaton Technology Alcaton (IITA 2010) [8] R.H. Abyev, O. Kaynak, Fuzzy wavelet neural networks for dentfcaton and control of dynamc lants a novel structure and a comaratve study, IEEE Transactons on Industral Electroncs, 55 (8), 2008, [9] H. Khodadad, H. Jazayer-Rad, Alyng a dual extended Kalman flter for the nonlnear state and arameter estmatons of a contnuous strred tank reactor, Comuters & Chemcal Engneerng, Comuters & Chemcal Engneerng, 35(11), (2011). [10] S. Chen, C.F.N. Cowan, P.M. Grant, Orthogonal least suares learnng algorthm for radal bass functon networks, IEEE Trans. Neural Networks, 2,1991. [11] M. Nkravesh, A. E. Farell, T. G. Stanford, Control of nonsothermal CSTR wth tme varyng arameters va dynamc neural network control (DNNC), Chemcal Engneerng Journal, vol. 76,. 1-16, January [12] J. Madar, J. Abony, F. Szefert, Feedback Lnearzng Control Usng Hybrd Neural Networks Identfed by Senstvty Aroach, Engneerng Alcatons of Artfcal Intellgence, vol. 18, Page