Brief Study of Identification System Using Regression Neural Network Based on Delay Tap Structures

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1 DOI V [ GSTF Journal on Computng (JoC), Vol. 3 No. 3, Dec 03 Bref Study of Identfcaton System Usng Regresson Neural Network Based on Delay Tap Structures Alvn Sahron Abstract ths nvestgaton ams to provde an overvew and nvestgatons of non-lnear dentfcaton system usng neural network approach. Nowadays, a lot of neural network approach was done to provde a satsfyng dentfcaton system. Backpropagaton scheme as the manstream approach for developng dentfcaton system has several lmtatons such as tranng data, computaton tme, archtecture, optmzaton technque for weght value update, and many others. Regresson Neural Network whch s found by specht on 990 contans more advantages compare wth backpropagaton scheme. Wth the mprovement of computaton tme, archtecture, and robustness of ths model and provded 90% of effectveness, promsng a good prospectve to develop non-lnear dentfcaton system. For future works, t can be mplemented n neural network predctve model control system and another control scheme based on dentfcaton system approach. Keywords-GRNN, predctve model Identfcaton System, backpropagaton, I. INTRODUCTION T development of neural networks has been started snce several decades ago. Snce the past decade, many artfcal ntellgence methods such as fuzzy logc, neural networks, etc. has been developed to solvng system modelng for dynamc plants. For nonlnear problems, neural networks have been wdely appled for emprcal process modelng []. The development of Neural networks tself ncrease rapdly snce the mult layer neural networks and backpropagaton was founded and popular related to the ts capablty to be traned to assocate nput data to output data that can be useful to learn unknown dynamc plants. The popularty of ths scheme have been used n complex dentfcaton system []. Currently, neural networks are beng appled to physcal plant modellng wth satsfactory results [3,4]. System modellng and dentfcaton system was appled n control system engneerng. In control engneerng, neural network approach based modellng are generally used as dynamc plant emulators for dong control desgn and also can HE Manuscrpt receved September 3th, 03. Ths work was supported by Electrcal Engneerng Department of UII Yogyakarta, Indonesa. Independent Research Project n Control and Mcroprocessor Laboratory, UII Indonesa. Alvn Sahron s wth the Department of Electrcal Engneerng, UII Yogyakarta Indonesa, Kalurang Street 4.5 (alvnsahron@u.ac.d). DOI: 0.576/5-3043_ be utlze for predctor models n many adaptve control confguratons [5,6,7,8,9]. Many of controller usng drect controllers scheme, but n neural networks as drect controllers to the plant are less popular, however several methos have been reported. The common and best schemes of neural networks controllers are usng predctor model n a control system whch used to estmate the future condton/value. The problem came related to the mplementaton of predctor model that usulally has constrants of lmted network sze, and n many real tme applcatons, fast computaton tme and processng s requred. Based on the problems, usng conventonal multlayer and backpropagaton n complex system gve lacks of system performance. And n realty condtons, many knds of dentfcaton and control confguratons appled onlne schemes whch needs fast and contnuous learnng capablty and large of data to be traned. In many knds of neural networks paradgms, the General Regresson Neural Networks (GRNN) seems to be promsng to posses such as characterstcs [0] thus, t s beng used as the motvaton for ths nvestgaton. GRNN has been appled n many number of applcatons on dentfcaton/modellng system and control []. There also have been nvestgated certan comparson studes to demonstrate the modellng capablty of GRNN compare wth another multlayer and common neural networks paradgms [,3]. The nvestgaton results gves advantages by applyng GRNN than usng backpropagaton paradgms. The sgnfcant result related to the computaton tme, neural networks archtectures, and smplfy of neural network algorthms have been provded. Ths nvestgaton also prove the advantages of GRNN based results and performances. Another nvestgaton also reported usng hybrd method between GRNN and fuzzy clusterng measurement n system dentfcaton. The work also related to the smplfed GRNN methods to provde a good performance usng large of tranng data [. Ths nvestgaton tsetlf wll provded several confguraton of delay tap/tme to ncrease the performance of GRNN n system dentfcaton. Ths paper has several parts that organzed as follows, A bref ntroducton and background revew of dentfcaton system usng neural networks and GRNN whch gven n ths part. It s followed by explanaton of GRNN, and dentfcaton

2 GSTF Journal on Computng (JoC), Vol. 3 No. 3, Dec 03 system appled n dynamc plants. The next part wll provde proposed method of dentfcaton system usng GRNN on dynamc plants. The proposed method that has been nvestgated wll be dscussed on the next part and also closed by dong concluson for certan nvestgatons. ndependent varable such as X computes the most probable value of dependent varable Y wthn fnte set of observatons data. Let s f (x ) as the probablty densty functon of a random vector x. Regresson result of by X based on below formula: Y gven II. TRAINING OF GRNN The basc fundamental of GRNN has been proposed [0] (Fg.) by specht and the usng of GRNN has been popular than back-propagaton because the characterstc of GRNN as probablstc soluton and the known as probablstc neural network wth fast computaton and tranng process and ts smplcty [5], then GRNN was the alternatve feed-forward method after back-propagaton n many felds. E y / X y. f ( X, y)dy () f ( X, y)dy The probablty densty functon must be estmated from sample observatons (data sets) of x and y. The general form of estmaton process gven by: f n ( x) Where n x x n () x are ndependent and as dstrbuted random varables wth absolutely contnuous dstrbuton functon. The have constrans to bounds certan value to satsfy several condtons: ( y) dy (3) lm y ( y) 0 (4) y And ( y)dy (5) The functon (n) must be chosen wth: lm (n) 0 lm n (n) Fgure. GRNN Archtecture (Specht, 99) (6) n GRNN has two layers, the frst layer called Radal Bass Layer and the second layer called as Lnearzaton Layer or Specal Lnear Layer (Fg.). Where R = number elements n nput vector, Q = number of neurons. n One useful form of the weghtng functon (7) s the kernel densty functon whch s known as Gaussan functon. There s a constant value for dstrbuton estmator that based on panzer s results that wll converge to the underlyng dstrbuton at the sample pont when t s smooth and contnuous. Based upon sample values X and Y of the random varable x and y, t can provde a good dstrbuton constant value as gven by [9]: f ( X,Y ) n e n ( ) ( p ) / ( X X )T ( X X ) ( p ) e. (Y Y ) (8) p s the dmenson of the vector varable x, n s the Fgure. GRNN Archtecture The concept s the regresson functon performed on an number of observatons, s the wdth spreadng of

3 GSTF Journal on Computng (JoC), Vol. 3 No. 3, Dec 03 Y s the desred or target data gven by the observed nput data of X. Then defne D by usng equaton: estmated kernel or smoothng factor, and D ( X X )T ( X X ) modelng around neural networks applcaton (Fg. 4). (9) Combnng (8) and (9) and nterchangng the order of ntegraton and summaton and gven by: N Y(X ) Y e D N e D (0) Fgure 4. GRNN Scheme The Y ( X ) result can be used as weghted average of all observed data of Y and each observed data s based on weghted exponentally of related to Eucldean dstance from X. The man dfference between probablstc neural networks and backpropagaton scheme wthn tranng process s the varables characterstc scheme. The GRNN paradgms also depend on the decson of best tranng related to the value of whch can be appled between 0- values and should not be 0 value. The hghest value wll gve good fttng curve and best generalzaton results. Otherwse, the lower value wll gve best fttng curve but wll decrease the capablty of generalzaton (Fg.3). Step : create a GRNN archtecture wth delay tap/tme confguratons Step : Testng and valdatng the archtecture/models and calculate MSE(eq.) value n MSE ( y( ) real y( ) predct ) n () Step 3 : f the MSE of fttng curve s larger than desred value, develop a new scenaros and back to Step. Step 4 : After provdng best archtecture, t wll conclude the best dentfcaton system for the problem As the ttle above, ths nvestgaton wll focused on usng delay tappng/tme confguratons to provde a good archtecture of GRNN s performance. Confguraton tself s how we can desgn certan delay tappng for nput and output layer of GRNN to gan best ft of dynamc plant dentfcaton system (Fg 5.). Fgure 3. A Smple problem to llustrate the nfluence of on the GRNN result a)true functon, b)too small, c)average, d)a perfect parameter, e)too large (Vadm Tmonn, et al., 005[5]) parameter III. PROPOSED METHOD The nvestgaton contans several steps. The steps should be accomplshed to provde desred value based from tranng data sets. There are several schemes that can be appled for dentfcaton system based on neural networks paradgms. Ths nvestgaton wll usng common scheme of system Fgure 5. Step for the proposed method MSE performance wll be the man parameters to measure the feasblty of each scenaro (Table.). Each scenaro wll provde performance nformaton of each archtecture scenaro. Ths nvestgaton wll provde the best

4 GSTF Journal on Computng (JoC), Vol. 3 No. 3, Dec 03 archtecture of GRNN usng delay tap/tme confguraton. TABLE. SEQUENCE TO INVESTIGATE SEVERAL SCENARIO OF DELAY TAPPING/TIME FOR IDENTIFICATION SYSTEM USING GRNN No 3 4 Scenaros st scenaro nd scenaro 3rd scenaro etc. Performance IV. ANALYSIS AND DISCUSSION The nvestgaton wll usng har dryer for the objects whch wll dentfed the system. Har dryer s a devce that processed ar fanned through a tube and heated at the nlet. The ar temperature s measure by a thermocouple at the outlet. The nput u (k ) s the voltage over a mesh of resstor wre to heat ncomng ar; the output Fgure 8. Tranng data set y (k ) s the outlet ar temperature (Fg.6.). Fgure 6. Har Dryer System Fgure 9. Valdaton data set GRNN archtecture wll conduct several confguratons to fnd the best archtecture to dentfy har dryer dynamc plant (Table.). Confguratons of GRNN wll be focused on to fnd the best scheme usng delay tap/tappng as the nput of dynamc plant. For each delay tap/tme, t wll be measured by usng MSE value to compare between real data and valdaton test (eq.). y( k ) f (u ( k 0), u( k ),..u( k n), y( k 0), y( k ),..y( k n) ) () Fgure 7. Relatonshp between u (k ) and y (k ) Snce The relatonshp of nput u (k ) and output y (k ) that seen n (Fg.7) conclude that the nonlnear characterstc s provded by ths system. The data named as tranng data wll be dvded nto two parts, 50% data for modelng/dentfcaton system, and 50% data for valdaton test (Fg. 8 and Fg. 9) from total data set. u( k n ) was the nput that belongs to the actuator value of voltage to har dryer dynamc plant, and y( k n) as the output sequence of process value. The strategy s how to develop GRNN archtectures by combnng them, t wll provde a good qualty of dentfcaton non-lnear dynamc plants. The measurements of MSE wll be ndcatng the best archtecture of GRNN as the dentfcaton system for dynamc plants. In the prevous secton, t has been dscussed about spreadng coeffcent ( ). Ths nvestgaton wll be fxed parameters of, based on prevous nvestgaton that the hgher value of

5 GSTF Journal on Computng (JoC), Vol. 3 No. 3, Dec 03 wll not promse a good performance. Apparently, to generalze the predcted output, t should been done farly by gvng halfway value (between ). Indeed that the maxmum value of wll gve lack of performance wthn valdaton phase. But, n the other case, reducng wll mprove the tranng performance phase, but lack of capablty to generalze predctng phase. Therefore, by choosng fxed value that related to prevous nvestgaton wll help ths nvestgaton to confgure the best delay tap/tme on GRNN archtecture. Ths nvestgaton wll use = nput ( y( k )..(k 4), u( k )..(k 4) ) 5 nput ( y( k )..(k ), u( k )..(k 3) ) nput ( y( k )..(k 4), u( k )..(k 4) ) 6 nput ( y( k )..(k 8), u( k )..(k 4) ) [7] S Omatu, M Khald, and R Yusof, Neuro-Control and Its Applcaton. London: Sprnger-Verlag, 995. [ B.G. Hyun and K. Nam, "Fault Dagnoses of Rotatng Machnes by ] Usng Neural Networks:GRNN and BPN," n Proceedng of the 995 IEEE IECON, 995, pp ( y( k ), u( k ) ) 5 [6] A Draeger, S Engell, and H Ranke, "Model Predctve Control Usng Neural Network," IEEE COntrol Sys. Mag Vol : 5, pp. 6-66, 995. [0] D.F Specht, "Probablstc and General Regresson Neural Network," n Fuzzy logc and Neural Network Handbook.: McGraw-Hll Companes, Inc, 996. ( y( k )..(k ), u( k ) ) nput [5] G Irwn, M Brown, Hogg B, and E Swdenbank, "Neural Network modellng of a 00MW Boler System," IEEE Proc. Control Theory Applcatons Vol : 4, pp , 995. [9] K.J hunt and D Sbarbaro, "Adaptve Flterng and Neural Networks for realsaton of nternal model control," Intellgent System Engneerng, pp , 993. Scenaros 3 nput [4] D. Gornevsky, "On the persstency of exctaton n radal bass functon network dentfcaton of nonlnear systems," IEEE trans. on neural networks, pp , 995. [8] M Smth, Neural Networks for Statstcal Modellng. USA: Van Nonstrand Renhold, 993. TABLE. SCENARIOS No ntellgent control of systems," Internatonal Journal Control, pp. 6389, 99. [] L. Marquez and T. Hll, "Functon Approxmaton Usng Backpropagaton and General Regresson Neural Networks," n Proc. 6th Hawa Internatonal Conf. on System Scences, Hawa, 995, pp [3] Alvn Sahron, "Tme Seres Predcton Comparson Study based on General Regresson Neural Network (GRNN) and Backpropagaton Neural Network n Electrcty Peak Load Predcton n Indonesa," n TEKNOIN 0, Yogyakarta Indonesa, 0. V. CONCLUSION The nvestgaton has provded several conclusons that GRNN as the dentfcatons tool has a feasblty performance and shown good performance. The dentfcaton of the system depends on nput characterzaton. The characterzaton refers to delay tap/tme confguraton wthn GRNN archtecture. The performance affected by two parameters. Spreadng coeffcents ( ) wll gve better result based on generalzaton usng a hgher value (between ). In tranng phase, a hgher value of wll not gve a best fttng performance. Otherwse, usng lower value of affected to the smooth fttng curve performance n tranng performance and gves a lack of generalzaton capablty. Other parameters that affected the performance of GRNN n the dentfcaton problem s whle choosng archtecture for GRNN nput nclude delay tap/tme confguraton as the nput neuron. Whle ncreasng the amount of neuron ndcatng delay tap/tme, cannot be surely as the most optmze result of dentfcaton dynamc system. For future works, t wll compare wth statstcal model for dynamc plants such as ARX and ARMAX dentfcaton based system. REFERENCES [] Teo Lan Seng, Marzuk Khald, and Rubyah Yusof, "Adaptve GRNN Modellng of Dynamc Plants," n Proceedngs of the 00 IEEE Internatonal Symposum on Intellgent Control, Canada, 00, pp. 7. [4] Sh-jun Zhao, Jn-Le ZHang, Xunl, and We Song, "A Generalzed Regresson Neural Network Based on Fuzzy Means Clusterng and Its Applcaton n System Identfcaton," n Informaton Technology Convergence, 007. ISITC 007. Internatonal Symposum on, Joenju, 007, pp [5] Vadm Tmonn and Elena Saveleva, "Spatal Predcton of Radoactvty Usng General Regresson Neural Network," Monash Unversty EPRESS, Australa, Appled GIS Vol No, 005. Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton Lcense whch permts any use, dstrbuton, and reproducton n any medum, provded the orgnal author(s) and the source are credted. Alvn Sahron receved hs bachelor s degree from Unverstas Islam Indonesa Yogyakarta, Indonesa, and master s degree from jont program n system engneerng between Gadjah Mada Unversty (UGM) -Insttut Teknolog Bandung (ITB)-Karlsruhe Insttute Tech (KIT, Germany). Now he s currently a full lecturer, researcher, and consultant engneerng at Unverstas Islam Indonesa Yogyakarta. Hs current research s n control system, ntellgent system, machne learnng, and artfcal ntellgence. Hs current research s related to the development of neural network and ts hybrd system fundamental and applcatons n several applcatons. Hs also plannng take hs doctoral degree n artfcal ntellgence system applcaton. [] B. Kosko, Neural Network and Fuzzy Systems. USA: Prentce Hall, 99. [3] Pao YH, SM Phllps, and Sobajc D.J, "Neural-net computng and the