Indian Jounal of Radio & Space Physics Vol. 38, August 009, pp 33-37 PSO diven RBF fo design of equilateal tiangula micostip patch antenna Vidya Saga Chintakindi,$, Shyam Sunda Pattnaik,#,*, O P Bajpai & S Devi Dept of ETV&ECE, ITTTR, Chandigah 60 09, India Diecto, UIET, Kuuksheta Univesity, Kuuksheta E-mail: # headetv@yahoo.co.in, $ chvidya66@gmail.com Received 6 ovembe 008; evised eceived and accepted May 009 Recent advances in compute aided design packages fo electomagnetic applications have helped antenna enginees to design, simulate and synthesize antennas efficiently. The PSO diven RBF has been developed to calculate the esonant fequency of equilateal tiangula micostip patch antenna (ETMPA). The pesent pape highlights the simplicity, computational efficiency and accuacy of the poposed method. The achieved esults have been compaed with published expeimental and theoetical findings to validate the pesented appoach, which seems to be in vey good ageements. Keywods: Paticle swam optimization (PSO), Radial basis neual netwok (RBF), Atificial neual netwok (A), PSO dven RBF, Equilateal tiangula micostip patch antenna (ETMPA) PACS o.: 84.40.Ba Intoduction Micostip antennas ae finding gowing inteest in space, ada, wieless and bio-medical applications due to thei attactive featues like ease of fabication, light weight and compatibility. These featues make the planne antenna moe attactive in the pesent emeging scenaio like MIMO systems -3. As the demand is gowing day by day fo miniatuization and efficiency, the challenge fo development of accuate and efficient tools fo pecision design is also gowing. In the pesent pape, a paticle swam optimization 4 diven adial basis neual netwok 5-6 (PSO diven RBF) is poposed to calculate accuately and efficiently esonant fequency of equilateal tiangula micostip patch antenna (ETMPA). The pesented hybid tool of PSO and RBF seems to be a good compute aided design (CAD) tool fo planna antenna design. Fomulation of PSO-RBF system PSO has been successfully applied in many aeas, like function-optimization in electomagnetic field, atificial neual netwok taining, fuzzy system contol and othe aeas whee genetic algoithm (GA) ae geneally applied 5-6. The PSO optimization pocess finds local best (lbest) and global best (gbest) by mechanism of displacement and velocity of paticles 7-8. The paticle displacement and the paticle velocity ae expessed as 7 S(t)=S(t-)+V(t) () V(t)=W*V(t-)+C (lbest- S(t-))+ C (gbest- S(t-))... () whee, V(t), is paticle velocity; S(t), paticle displacement; lbest, local best; gbest, global best; W, inetial weight; C and C, acceleation constants; and, andom values; and t, cuent iteation. To get the solution (gbest), initially the paticles ae allowed to move andomly in -dimensional coodinate space. The evolutions of paticles ae guided only by the best solution and tend to be egulated by behavio of the neighbos. In the simplest fom, this evolutionay pocedue can be epesented by position and velocity of paticles expessed in Eqs () and (), espectively. RBF as in Fig. ae applied fo vaious modeling puposes 5. In RBF, the inputs x, the total input to the i th hidden neuon (h i ) is expessed as 6 : n x j c ij h i =, i =,,..., j = λ ij (3) whee,, is numbe of hidden neuons; z ij = σ(h i ), output value of the i th hidden neuon; σ, a adial basis function. The paametes c ij and λ ij ae centes and
34 IDIA J RADIO & SPACE PHYS, AUGUST 009 standad deviations of adial basis activation functions. Finally, the outputs of the RBF netwok ae computed fom hidden neuons as: yk WkiZki i= 0 = (4) whee, W ki, is the weight of the link between the i th neuon of the hidden laye and the k th neuon of the output laye. Taining paametes W of the RBF netwok include W k0, W ki, c ij, λ ij, k =,... m; i =,,...; j =,... n. In the poposed method, the weight of neual netwok is eplaced by paticle position equation and the ate of change, i.e. E( t) W ( t) of the neual netwok is eplaced with paticle velocity expession. PSO diven RBF is poposed to calculate esonant fequency of equilateal tiangula micostip patch antenna. The mean squae eo (MSE) is used as the fitness function 8 which is epesented as: MSE = (taget-output) p (5) whee, p, is the numbe of pattens. The PSO is used to minimize the eo between input and output of RBF by updating the weight between input to hidden laye and hidden to output laye neuons. The adial basis function is used as activation function at hidden laye. The pefomance Fig. RBF neual netwok stuctue of PSO diven RBF is evaluated by taking taining, testing and evaluating pattens of vaious design antennas. The paametes of PSO diven RBF ae as follows: umbe of input nodes = 5; umbe of hidden nodes = 0; umbe of output nodes = ; umbe of weights between input and hidden laye = 50; umbe of weights between hidden and output laye = 0; Activation function at hidden laye output is adial basis function; Activation function at output laye output is linea activation function; Fitness function is mean squae eo; C = C = ; & = andom [0 ]; W = 0.9 to 0.4; umbe paticles = 5; Maximum paticle velocity = 5; umbe of iteations of PSO = 50; umbe of epochs of A = 450. The pseudo code of PSO diven RBF is pesented as follows: Step : Initialize paticle position and velocity at andom. Step : Evaluate fitness function. Step 3: Update the weights, lbest and gbest. Step 4: If the eo is 0.00 go to Step else continue. Step 5: Update gbest. Step 6: If no. of paticles is equal to 5 go to Step else continue. Step 7: If numbe of iteations is not equal to zeo then go to Step else continue. Step 8: End. Step 9: Afte the evolutionay pocess, tain the best netwok futhe with PSO algoithm on the combined taining and validation set until it conveges. Step 0: Repeat next iteation. 3 Implementation of the model In the pape, the esonant fequency (f) of equilateal tiangula micostip patch antenna is calculated using its paametes like patch length (a), pemittivity of the substate (ε ), height (h) of the
CHITAKIDI et al.: PSO DRIVE RBF FOR DESIG OF ETMPA 35 substate and modes TM m,n,l (efs 7-8) as shown in the geometic of equilateal tiangula micostip patch antenna (Fig. ). The esonant fequency of equilateal tiangula micostip patch antenna is expessed as 9 : C f = m + mn + n (6) m,n,l 3α ( ) eff ε whee, a eff ( ) h π a = a + ln ( ) +.776 πε a h (7) f m,n,l, is esonant fequency; C, velocity of light in fee space; a and a eff, physical and effective length of the tiangula patch; h, substate thickness; ε, pemittivity of the substate. Eo minimization function of PSO is given as: E [ ] min = fmes f (8) eo = 00% f f mes (9) Fo feed fowad neual netwok, esonant fequency (f m,n,l ), pemittivity of the substate (ε ), height (h) of the substate and modes TM m,n,l ae taken as inputs whee esonant fequency of ETMPA is taken as output in RBF neual netwok of 5-0- (Fig. 3). Twenty-nine pattens fom efs (0-3) ae taken fo taining the netwoks and est fou pattens ae used fo testing the netwoks. Table shows the compaison between expeimental esults with GA and PSO-RBF. Table pesents compaison of PSO, atificial neual netwok (A) (ef. 4) and PSO-RBF methods. As seen fom Table, the PSO-RBF fused soft computing tool is computationally efficient and povides bette accuacy and hence can be suitable soft computing tools fo the situation like whole body simulation, aay of antenna embedded on the body of missiles, etc. The algoithm was applied fo pesent wok fo micostip antenna on thick substate, i.e. h/λ 0 > 0.085 fo which the standad fomula available in liteatue fails to povide accuate esults. The pape aims at dawing the attentions to the pocess of infomation fusion and thei applications to efficient antenna design. Simple antenna stuctue is consideed to test the success of the poposed method. The developed code is being used to analyze and optimize the paamete of paasitically coupled stacked micostip patch antenna and lage unifom and non-unifom aay. The simulated esults will be compaed with expeimental finding and published in futue. Fo multilaye stuctue like stacked patches, poposed algoithm is found to be quite efficient. umbe of layes, Fig. Geometic of equilateal tiangula micostip patch antenna Fig. 3 RBF neual netwok of 5-0-
36 IDIA J RADIO & SPACE PHYS, AUGUST 009 Table Compaison of PSO, A and PSO-RBF Paamete PSO (ef. 8) A (ef. 4) Pesent Method (PSO RBF) Maximum leaning 000 0000 50 steps Eo pecision e-5 e-3 e-7 Convegence ate 80% 85% 96% umbe of layes - 5 3 Activation - 5 functions Taining eos 0.0085 0.089 0.0003 Testing eos 0.0096 0.0978 0.0009 Mean squae eo (MSE) 38.43e-7 5.77e-7 0.65e-7 Table Compaison of esults fo testing antennas Patch o. Mode ε a, cm h, cm Theoy f (ef. 9) Measued f (efs 0-) GA f (ef. ) Pesent Method (PSO-RBF) f. TM 0.3 0.00 0.59.85.80*.8.8. TM 0.3 0.00 0.59.570.550*.56.554 3. TM 0.5 0.4 0.04.66.637^.60.635 4. TM 30 0.5 0.4 0.04 4.548 4.504^ 4.504 4.504 *Measued by Dahele & Lee 0 ; ^ measued by Chen et al. using PSO-RBF technique is developed and pesented. The poposed method could achieve bette accuacy and with educed computational time. The poposed method may be used as an altenate CAD simulation tool fo micostip antenna design due to its simple and genealization chaacteistics. The pesented method can be used in the design of miniatuized antenna with and without loading. The poposed method can be used fo multi-stacked patch antenna and fo lage antenna aay design. Acknowledgment One of the authos (Vidya Saga Chintakindi) thanks Diecto, Dept. of Technical Education, Andha Padesh fo sponsoing the eseach unde AICTE-QIP (POLY) scheme. Thanks ae also due to D. S C Laoiya, Diecto, ITTTR, Chandigah fo poviding necessay facilities fo caying out the eseach wok. Fig. 4 Compaison of convegence substate thickness, gap spacing between substate and ove all dimension of diffeent substate layes ae included as pat of the input paametes to PSO- RBF. The esonant fequencies ae obtained fo tiangula and ectangula micostip antenna. An eo of 4.6% is obseved and the effots ae being made to educe it. Figue 4 depicts the compaison of convegence. As seen fom Table, the eo in the poposed method is less than 0.0%. 4 Conclusion A novel appoach to detemine esonant fequency of equilateal tiangula micostip patch antenna Refeences Pata P K, Pattnaik S S & Devi S, ew bandwidth enhancement technique fo micostip patch, Int J Micow Opt Technol (USA), 3 () (008) pp -5. Pata P K, Pattnaik S S, Devi S, Vidyasaga C, Sasty G V R S & Bakwad K M, ew bandwidth enhancement and multi-esonance technique fo micostip patch antenna, Micow Opt Technol Lett (USA), 50 (5) (008) pp 6-65. 3 Bahl I J & Batia P, Micostip antennas, (Atech House, Dedham, MA), 980. 4 Robinson J & Rahmat-Samii Y, Paticle swam optimization in electomagnetics, IEEE Tans Antennas Popag (USA), 5 () (004) pp 397-407. 5 eog D K, Pattnaik S S, Panda D C, Devi S, Khuntia B & Dutta M, Design of a wide band micostip antenna and use of atificial neual netwoks in the paamete calculation, IEEE Antennas Popag Mag (USA), 47 (3) (005) pp 60-65. 6 Patnaik A, Choudhuy B, Padhan P, Misha R K & Chistodoulou C, An A application fo fault finding in antenna aays, IEEE Tans Antennas Popag (USA), 55 (3) (007), pp 775-777. 7 Kennedy J & Ebehat R C, Paticle swam optimization, Poc IEEE Int Conf. on neual netwoks IV (Piscataway, J, USA), 995, pp 94-948.
CHITAKIDI et al.: PSO DRIVE RBF FOR DESIG OF ETMPA 37 8 Chintakindi V S, Pattnaik S S, Devi S, Pata P K & Sasty G V R S, Calculate patch adius of cicula micostip patch antenna using paticle swam optimization technique, Poc IEEE Int Conf Advances in Compute Vision and Infomation Technology (Auangabad, India), 007, pp 36-39. 9 Suzuki Y & Chiba T, Compute analysis method fo abitaily shaped micostip antenna with multi teminals, IEEE Tans Antennas Popag (USA), AP-3 (984) pp 585-590. 0 Dahele J S & Lee K F, On the esonant fequencies of the tiangula patch antenna, IEEE Tans Antennas Popag (USA), AP-35 (987) pp 00-0. Chen W, Lee K F & Dahele J, Theoetical and expeimental studies of the esonant fequencies of equilateal tiangula micostip antenna, IEEE Tans Antennas Popag (USA), 40 (99) pp 53-56. Kaaboga D, Guney K, Kaaboga & Kaplan A, Simple and accuate effective side expession obtained by using a modified genetic algoithm fo the esonant fequency of an equilateal tiangula micostip antenna, Int J Electon (UK), 83 (997) pp 99-08. 3 Guha D & Siddiqui J Y, Resonant fequency of equilateal tiangula micostip antenna with and without ai gap, IEEE Tans Antennas Popag (USA), 5 (8) (004) pp 74-77.