PSO driven RBF NN to calculate Microstrip patch Antenna parameter

Transcription

1 90 PSO diven RBF to calculate Micostip patc Antenna paamete Vidya Saga Cintakindi *, D. Syam Sunda Pattnaik *, D.O.P.Bajpai **, S.Devi *, P.K.Pata *, K.M.Bakwad * * Dept. of ETV&ECE, ITTTR, Secto-6, Candiga , India Tel: ; Fax: ; eadetv@yaoo.co.in\ ** Diecto, UIET, Kuusekta Univesity, Kuusekta, India; VOL.4, O., MARCH 009 Abstact- In tis pape, we pesent paticle swam optimization diven adial basis neual netwok to calculate te adius of cicula micostip patc antenna. Te poposed algoitm is tested wit te aleady publised antenna stuctues and te esults ae compaed. Te esults ae in good ageement and ae wit bette accuacy. Index Tems- CMSA, PSO, A, RBF, Radius. I. ITRODUCTIO In Bio-Medical applications, Rada, and wieless communication systems, te micostip antennas ae extensively used due to tei low-pofile featue and ease of fabication [1]. Wit ecent advances in electomagnetic compute-aided design (CAD), te design of micostip antenna as been benefited fom te utilization of accuate numeical metods [1]. In yea 004, Paticle swam optimization (PSO) was intoduced to te electomagnetic (EM) community to calculate micostip patc antenna paametes []. umbe of soft computing tecniques tat exist i.e., Atificial neual netwoks (A), Genetic Algoitm, Fuzzy logic etc.,[-3] ae also used to calculate diffeent paametes of Micostip antenna [1]. But a igoous seac fo faste algoitm simplicity, empasizing speed and accuacy esulted in Paticle Swam Optimization (PSO) [4]. Teefoe, te autos pesent a simple and accuate compute aided design (CAD) appoac fo micostip antenna design by ybidizing PSO wit adial basis neual netwok (RBF). A. Paticle Swam Optimization Paticle Swam Optimization is an evolutionay optimization tecnique, wic is a local to global seac metod based on paticle seac. It follows te optimization pocess by means of local best (lbest), global best (gbest), paticle displacement and velocity. In PSO te social aspect of mind and intelligence comes into play[5].te paticles ae consideed to move toug coodinates of -dimensional space. Wen paticle moves, it sends its co-odinates to a function and measues its fitness value, close to a best solution fo te poblem. Te evolution of paticles, guided only by te best solution, tend to be egulated by beavio of te neigbos. In te simplest fom, te position S and velocity V of eac paticle ae epesented by te following equations consideing lbest ate tan gbest as te best position of te paticle efeed to te neigbos. B. Basic PSO Equations Te paticle velocity is expessed as [6] V ( t) = W V( t 1) + C1 1 ( lbest S( t 1) ) (1) + C ( gbest S( t 1)) and te paticle displacement is expessed as [6] S( t) = S( t 1) + V ( t) () Wee, V=PaticleVelocity, S=Paticle displacement lbest = local best and gbest =global best IJMOT ISRAMT

2 91 VOL.4, O., MARCH 009 W=Inetial weigt [0.9, 0.4] C 1 & C ae acceleation constants=.0(constant) 1 & ae andom values [0, 1] and t=cuent iteation In tis pape, PSO uses gadient descent tecnique to adjust te synapse weigts between neuons in ode to minimize te RBF eo between te actual output and desied taget output. PSO is to minimize te squaed diffeence between te measued adius value and te calculating adius fo cicula micostip patc antenna is also pesents in tis wok. C. AFIS Adapative neuo - fuzzy infeence system (AFIS) is an explained in ef. [10]. Te AFIS is a class of adaptive netwoks wic ae functionally equivalent to fuzzy infeence systems (FISs). Calculated micostip antenna paametes using AFIS [10] wic is sows complicated netwok and lage taining data. PSO & RBF is a ybid soft computing tecnique is pesent in tis pape to obtain bette pefomance and faste convegence wit simple stuctue. II. DEVELOPMET OF THE PROPOSED A MODEL Atificial neual netwoks ae biologically inspied tat map set of inputs to set of outputs. Eac neuon in eac laye geneates one nomalized output, as a function of its nomalized inputs. Te used netwok acitectue is multi laye i.e., one input laye, one idden laye and one output laye. All layes ae fully connected and of te feed fowad type. Te outputs ae nonlinea functions of te input, and ae contolled by weigts tat ae computed duing leaning pocess. In ou poposed metod, leaning pocess is supevised type. Feed fowad neual netwoks wit a single idden laye tat use adial basis activation functions fo idden neuons ae called adial basis function netwoks. A typical RBF netwok stuctue is given in Fig. 1. Te paametes c ij and λ ij ae centes and standad deviations of adial basis activation functions. Commonly used adial basis activation functions ae Gaussian and multiquadatic. Given te inputs x, te total input to te itidden neuon γ i is given by [9] n x j cij γ i =, i = 1,..., j= 1 λ (3) ij Wee, is te numbe of idden neuons. Te output value of te it idden neuon is z ij = σ(γi), σ(γ) is a adial basis function. Finally, te outputs of te RBF netwok ae computed fom idden neuons as y k = i= 0 w ki z ki Wee, wki is te weigt of te link between te it neuon of te idden laye and te kt neuon of te output laye. Taining paametes w of te RBF netwok include wk0, wki, cij, λ ij, k = 1,,..., m, i = 1,,....,, j = 1,,... n λ ij, c ij W ki Z 1 Z X 1 Fig.1 RBF neual netwok stuctue D.PSO-RBF SYSTEM (4) In tis pape, PSO diven RBF is poposed to calculate patc adius of cicula micostip patc antenna. Fig. sows te netwok aciteue of RBF of 3-9-1wit 36 weigts and 9 biasing weigts and fig3 sows te geomety of cicula micostip antenna. Te mean squae eo (MSE) is used as te fitness function [3] wic is epesented as X n Z IJMOT ISRAMT

3 9 VOL.4, O., MARCH 009 MSE = 1 p ( t ag et output) Wee, p is te numbe of pattens (5) Step9. Afte te evolutionay pocess, tain te best netwok fute wit PSO algoitm on te combined taining and validation set until it conveges. Step10. Repeat next iteation. Te PSO is used to minimize te eo between input and output of RBF wit updating of weigt between inputs to idden laye and idden to output layes neuons. Te adial basis function is used as activation function between idden and output laye. Te pefomance of PSO diven RBF is evaluated by taking taining, testing and evaluate pattens of vaious design antennas. Te algoitm of PSO diven RBF as follows 1. umbe of input nodes =3. umbe of idden nodes=9 3. umbe of output nodes=1 4. umbe of paticles is equal between input and idden laye=7 5. umbe of paticles is equal between idden and output laye =9 6. Activation function at idden laye output is adial basis function 7. Activation function at output laye output is linea activation function 8. Fitness function is mean squae eo. 9. C 1 =; 10. C =; 11. w= 0.9 to umbe of iteations of PSO = umbe of epocs A =450 Step1. Initialize paticle position and velocity at andom Step. Evaluate fitness function Step3. Update te weigts, lbest and gbest Step4. If te eo is go to step else continue Step5. Update gbest Step6. If no. of paticles is equal to 36 go to step else continue Step7. If numbe of iteations is not equal to zeo ten go to step else continue Step8. End E. DEVELOPMET MODEL Te adius of a cicula patc is expessed as [1]. F a = 1 πa (6) 1 + ln πε a Wee, F = f ε Eo minimization function of PSO is given as 1 (7) E min = a mes a a eo = 100 % 1 (8) a mes Fo feed fowad neual netwok, esonant fequency (f), pemittivity of te substate (ε ) and eigt () of te substate ae taken as inputs wee as patc adius of cicula micostip patc antenna, is taken as output as sown in Fig.. Twenty nine pattens fom [7-15] ae taken fo taining te netwoks and est eigt pattens ae used fo testing te netwoks. Te esults obtained wit te pesent tecnique i.e. PSO- RBF wee close to te expeiment esults, compaed to te numeical and analytical esults pesented in Table 1. Fig.4 depicts plot of gbest veses iteations. Te plot of diffeences veses and analytical esults in Fig.5 sows te esults. Table 1 sows te compaison between expeimental esults wit AFIS, PSO & PSO-RBF. Table pesents compaison of metods. As seen fom Table 1, in te poposed metod, te eo is less tan 0.01% wile te computational time is seconds. IJMOT ISRAMT

4 93 VOL.4, O., MARCH 009 Patc o. Table1. Compaision of Cicula Micostip Patc Radius of Expeimental Mesued Value wit PSO, PSO-RBF & AFIS of Vaious Ticknesses and Relative Pemittivies [10] ε f (GHz) Measued a mes AFIS a AFIS [10] PSO a pso Pesent Metod PSO-RBF a pso Diff. a mes & AFIS % Diff. a mes & PSO- RBF % * * * ^ # $ $ $ *Measued by Daele and Lee [1]: ^ measued by Daele and Lee[13]; #measued by Cave[14]: $measued by Antoszkiewicz and Safai[15] ε a f Fig Feed Fowad eual etwok (3-9-1) Top view Fig: 4 Plot fo epoc veses gbest values Feed point 14 D a=d/ =D/ Radius mes. AFIS PSO PSO-RBF Side view Cicula patc numbes Co-axial Pobe Fig: 3 geomety cicula micostip antenna Fig: 5 Compaison of Patces Radius Between AFIS PSO,PSO-RBF & Measuements IJMOT ISRAMT

5 VOL.4, O., MARCH Table. Compaison of PSO, AFIS & PSO-RBF Paamete PSO AFIS PSO RBF Maximum leaning steps Eo pecision 1e-5 1e-7 1e-9 Convegence ate 86% 89% 98% umbe of layes Activation functions - 3 Taining eos Testing eos Mean squae eo (MSE) e e e-5 III. COCLUSIO In tis pape, a novel appoac to calculate adius of cicula micostip antenna using PSO-RBF tecnique is developed. Te poposed metod could acieve bette accuacy and wit educed computational time. Te poposed metod may be used as an altenate CAD simulation tool fo micostip antenna design due to its simple and genealization caacteistics. ACKOWLEDGMET Te autos ae tankful to eviewes fo tei valuable suggestions. REFERECES [1] P K Pata, D S S Pattnaik and Swapna Devi ew Bandwidt Enancement Tecnique fo Micostip Patc, Intenational Jounal Micowave and Optical Tecnology lettes, USA,3 (1),Januay 008,pp [] Jacob Robinson and Yaya Ramat-Samii, Paticle Swam Optimization in Electomagnetics, IEEE Tansactions on Antennas and Popagation, Vol. 5, O., Febuay 004, pp [3] D. K. eog, S. S. Pattnaik, D. C. Panda, S. Devi, B. Kuntia and M. Dutta, Design of a Wide Band Micostip Antenna and use of Atificial eual etwoks in te Paamete Calculation, IEEE Antenna and Popagation Magazine, 47(3), June 005, [4] Ebeat, R. C. and Si, Y. Paticle swam optimization: developments, applications and esouces, Poc. Congess on Evolutionay Computation, IEEE sevice cente, Piscataway, J., Seoul, Koea.,001. [5] Si Y. and Ebeat, R.CA modified paticle swam optimize, Poceedings of te IEEE Intenational Confeence on Evolutionay Computation., IEEE Pess, Piscataway, J, 1998, [6] Kennedy, J. and Ebeat, R. C. Paticle swam optimization. Poc. IEEE int'l conf. on neual netwoks IV, IEEE sevice cente, Piscataway, J, 1995, [7] Pata Padyumna Kuma, D. S. S. Pattnaik, Swapna Devi, C. Vidyasaga, G. V. R. S. Sasty, K. M. Bakwad, ew bandwidt enancement and multiesonance tecnique fo micostip patc antenna, Micowave and Optical Tecnology lettes, 50(5),mac,008, [8] I.J. Bal and P.Batia, Micostip antennas (Atec House, Dedam: MA, 1980). [9] S.Sagiolu, K.Guney, M.Ele, Resonantfequency calculation fo cicula micostip antennas using atificial neual netwoks,intenational of RF and Micwave Compute- Aided Engineeing, 8(3),1998, [10] Keim Guney and ucan Saikaya, Adapative euo-fuzzy Intefeence System fo computing patc adius of cicula micostip antennas, Micowave and Optical Tecnology Lettes,48(8),August,006, [11] C.A.Balanis, Antenna Teoy (Jon Wiley & Sons, Inc., 1997). [1].J.S.Daele and K.F. Lee, Effect of substate tickness on te pefomance of cicula disk micostip antenna, IEEE Tans.Antennas Popagate AP-9,1981, [13] J.S.Daele and K.F. Lee, Teoy and expeiment on micostip antenna wit ai gaps, IEE Poc.Pt.H.13,1985, [14] K.R.Cave, Pactical analytical tecniques fo te micostip antenna, Poc.Wksp Pinted Cic. Antenna Tecnol, Las Cuces, ew Mexico, 1979, [15] Antoszkiewicz and L. Safai, Impedance caacteistics of cicula micostip patces, IEEE Tans. Antennas Popagat. AP-38,1990, IJMOT ISRAMT