An Adaptive Neuro-Fuzzy Inference System for Calculation Resonant Frequency of Microstrip Dipole Antenna

Transcription

1 An Adaptve Neuo-Fuzzy Ineence System o Calculaton Resonant Fequency o Mcostp Dpole Antenna S. Cumhu Başaan İ. Bucu Topak Ahmet Yadımcı e-mal: cbasaan@akdenz.edu.t e-mal: bmutlu@akdenz.edu.t e-mal: yadmc@akdenz.edu.t Akdenz Unvesty, The Hghe School o Techncal Vocatonal Educaton, Antalya, Tukey Key wods: Mcostp dpole antenna, ANFIS, esonant equency ABSTRACT The accuate computaton o the esonant equency o mcostp antennas s an mpotant acto to guaantee the coect behavou. To ths am, Hgh Fequency Stuctue Smulato (HFSS) s commonly used. In ths pape, we pesented an adaptve neuo-uzzy neence system (ANFIS) that calculates esonant equency o the mcostp dpole antennas (MSDAs). ANFIS uses dpole s length and wdth, the antenna substate s pemttvty value and ts sze as nputs to calculate esonant equency. s obtaned by usng ANFIS agee qute well wth the HFSS esults. I. INTRODUCTION Techncal lteatue has boadly nvestgated Mcostp patch antennas (MSPAs). These antennas ae lghtweght, aeodynamcally conomable to acat and mssle suaces, compatble wth sold-state devces, and smple and nexpensve to constuct. Futhemoe, by addng loads between the patch and the gound plane (.e. pns and vaacto dodes), one can desgn adaptve elements contanng vaable esonant equency, mpedance, polazaton, and adaton patten []. Nevetheless, naow bandwdth s one majo dawback o the mcostp antennas. Consequently, pnted antennas wok ecently by closely matchng the esonant equency. Theeoe, ths paamete s accuate evaluaton s undamental n the mcostp antenna desgn pocess. A coect evaluaton o the esonant equency eques a goous ull-wave model []. The Fnte Element Method (FEM), the Method o Moments (MoM), and Fnte Deence Method (FDM) etc. have poved useul o analyss o such antennas by povdng goous solutons to the pesent poblem. Howeve, ths technque eques sgncant computaton and s tme-consumng. Recently, studes developed altenatve methods o esonant equency detemnaton usng uzzy logc (FL), neual netwoks (NNs), and combned adaptve neuo-uzzy neence systems (ANFIS) [-,6]. We developed an adaptve neuo-uzzy neence system that calculates esonant equency o the mcostp dpole antennas (MSDAs). Although the MSDAs esonant equency geatly depends on the dpole s length, t also depends on the dpole s wdth, the antenna substate s pemttvty value, and ts sze (whch aects esonant equency). The past two decades have wtnessed sgncant advances n FL and NNs. Some have unsuccessully used FL and NN sepaately to nd the MSDA s esonant equency. The FL system s dculty stems om consttutng coect membeshp unctons and ule base. Insucent tanng sets esulted n NNs poducng unstable esults. The synegsm o FL systems and NN poduced a system capable o leanng, hgh-level thnkng, and easonng. Ths tool detemnes the mpecsely-dened complex system s behavou. The neuon-uzzy system s pupose s to apply neual leanng technques to denty and tune the neuo-uzzy system s paametes and stuctue. These neuo-uzzy systems combne the benets o these two poweul paadgms nto a sngle capsule. The mult-unctonalty makes them sutable o a wde ange o scentc applcatons. The stengths nclude ast and accuate leanng, good genealzaton capabltes, excellent explanaton acltes (omed by semantcally meanngul uzzy ules), and can accommodate both data and exstng knowledge about any pesent poblem. ANFIS can nd a model that closely matches the nputs wth the taget. Fuzzy nteace system (FIS) s a knowledge epesentatve whee each uzzy ule descbes the system s local behavou. Vewng FIS as a eed owad netwok stuctue whee the pmay nputs and ntemedate esults ae sent to compute the output allows us to apply the same back-popagaton pncple n the neual netwoks. The netwok stuctue that mplements FIS s called ANFIS and employs hybd leanng ules to tan a Sugeno-style FIS wth lnea ule outputs. Among the vaous methodology combnatons n sot computng, uzzy logc and neuo-computng ae the most

2 common (hence the tem neuo-uzzy systems). Such systems play an mpotant ole n the ntaton o ules om obsevatons. It s a poweul tool o quckly and ecently dealng wth mpecson and nonlneaty wheeve t occus. Neuo-adaptve leanng technques wok smlaly to neual netwoks. These technques allow the uzzy modelng pocedue to lean nomaton about a data set that computes the membeshp uncton paametes, allowng the assocated uzzy neence system to tack the gven nput/output data. A neual-type stuctue smla to a neual netwok that maps nputs though nput and output membeshp unctons and assocated paametes can be used to ntepet the nput/output map. Ths elmnates the nomal eed owad multlaye netwok s dsadvantages (dcult to undestand o mody). We explan MSDAs and how to use ANFIS to tan a uzzy neence system that calculates the esonant equency. II. MICROSTRIP DIPOLE ANTENNAS Fgue shows the mcostp pnted dpole antenna contanng a conventonal hal-wave dpole loaded wth two open-ccuted stubs. The antenna, pnted on a PCB substate, s ed ethe by cable, suace mount connecto, o pnted tansmsson lne. Whee L epesents length, W s dpole wdeness, Ds s dstance between the dpole edges and substate edges, h' s the substate thckness and ε s the substate s delectc s constant value. III. ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM ANFIS s a multlaye neual netwok-based uzzy system [5]. Its topology s shown n Fgue, and the system has a total o ve layes. In ths connectonst stuctue, the nput and output nodes epesent the descptos and the actvty, espectvely and n the hdden layes, thee ae nodes unctonng as membeshp uncton (MFs) and ules. Ths elmnates the dsadvantage o a nomal eed owad multlaye netwok, whch s dcult o an obseve to undestand o to mody. Fo smplcty, we assume that the examned uzzy neence system has two nputs x and y and one output, the actvty. To pesent the ANFIS achtectue, two uzzy -then ules based on st ode Sugeno model ae consdeed: Rule : I (xs A ) and (ys B ) then ( = p x+ q y+ ) Rule : I (xs A ) and (ys B ) then ( = p x+ q y+ ) Fgue. The achtectue o ANFIS Whee x and y ae the nputs, A and B ae the uzzy sets, ae the outputs wthn the uzzy egon speced by the uzzy ule, p, q and ae the desgn paametes that ae detemned dung the tanng pocess. In the st laye, all the nodes ae adaptve nodes wth anode uncton: o = μ ( x), o=, () A Fgue.. Geomety o the mcostp dpole antenna. We xed the space between the symmetcal metal patches on the substate at mm and the antenna s ed om ths space. By changng the antenna paametes L, W, h, ε and Ds, we obtaned 6 antenna conguatons, usng 5 o tanng and the est o testng. Table shows system tanng and Table shows test data. We used mateals used o antenna desgn such as FR-, RT/duod and Roges TMM. We obtaned the antenna substate s thckness and pemttvty values om poduce ms catalogs. We used Ansot Hgh Fequency Stuctue Smulato (HFFS) sotwae, based on FEM, to compute and test the data set. Whee x s the nput to node, and A s the lngustc label (low, hgh, etc.) assocated wth ths node uncton. In othe wods, o s the membeshp uncton o A, and t speces the degee to whch the gven x satses the quante A. Usually we chose μ A (x) to be bellshaped wth maxmum equal to and mnmum equal to 0. As the values o paametes { a, b, c} change, the bell-shaped unctons vay accodngly, thus exhbtng vaous om o membeshp unctons on lngustc label A. Paametes n ths laye ae eeed to as pemse paametes.

3 Evey nodes n second laye s a xed node labeled Π (gue ), whose output s the poduct o all the ncomng sgnals: o = ω = μ ( x) μ ( y), o =, () A B Each node output epesent the ng stength o a ule. In laye evey node s a xed node labeled N. The th node calculates the ato o the th ule s ng stength to the sum o ules ng stengths: o ω = ϖ =, =, Outputs o ths laye ae called nomalzed ng stengths. Evey node n laye s an adaptve node wth a node uncton () o = ϖ = ϖ ( p x+ q y+ ), =, () whee ϖ s a nomalzed ng stength om laye and { p, q, } s the paamete set o ths node. Paametes n ths laye ae eeed to as consequent paametes. The sngle node n the last laye s a xed node labeled Σ, whch computes te oveall output as the summaton o all ncomng sgnals: ω 5 = oveall output = o = ϖ = = ω+ ω Thus we have constucted an ANFIS system that s unctonally equvalent to st-ode Sugeno uzzy model. HYBRID LEARNING ALGORITHM Fom the poposed ANFIS achtectue the oveall output can be expessed as lnea combnatons o the consequent paametes. The output n gue can be wtten as: ω = ω + = ϖ ( p x + q y + ) + ϖ ( p x + q y + ) = ( ϖ x) p + ( ϖ y) q + ( ϖ ) + ( ϖ x) p + ( ϖ y) q + ( ϖ ) Whch s lnea n the consequent paametes p, q,, p, q and. To tan the above ANFIS system, the ollowng eo measue wll be used: (5) (6) n ^ ( k k) (7) k = E = Whee k and k ae the k th desed and estmated outputs, and n s the total numbe o pas (nputs-outputs) o data n the tanng data set. The leanng algothms o ANFIS consst o the ollowng two pats: (a) the leanng o the pemse paametes by back-popagaton and (b) the leanng o the consequence paametes by least-squaes estmaton [6]. Moe speccally, n the owad pass o the hybd leanng algothm, unctonal sgnals go owad tll laye and the consequent paametes ae dented by the least squaes estmate. In the backwad pass, the eo ates popagate backwad, and the pemse paametes ae updated by the gadent descent. Dung the leanng pocess, the paametes assocated wth the membeshp unctons wll change. The computaton o these paametes s acltated by a gadent vecto, whch povdes a measue o how well the uzzy neence system s modellng the nput/output data o a gven set o paametes. It has been poven that ths hybd algothm s hghly ecent n tanng the ANFIS. Theeoe, n the pesent study the poposed ANFIS model was taned wth the backpopogaton gadent descent method n combnaton wth the least squaes method. IV. RESULTS AND DISCUSSION We pesented a new appoach based on ANFIS to calculate MSDA s esonant equency. Sxty-one deent antenna conguatons wee obtaned by changng the antenna paametes L, W, h, ε, and Ds. All substates wee used o ths study came om poduce ms catalogs. Resonant equences o antenna conguatons calculated by used Ansot-Hgh Fequency Stuctue Smulato (HFFS). The data s dvded n two pats, 5 o tanng and 0 o testng. ANFIS used 5 tanng data sets n 00 tanng peods. We used tangula membeshp unctons o esonant equency calculatons. Eo toleance was 0 and the output membeshp uncton was lnea. We used the tanng data set to tan ANFIS, wheeas the testng data set was used to vey the accuacy and eectveness o taned ANFIS model. L, W, h, ε and Ds ae appled to the nputs o the ANFIS. The output s esonant equency. Ate tanng, 0 testng data sets wee used to valdate the ANFIS model s accuacy o the esonant equency. The testng data conssted o deent types o mateal values and vaed n sze. The ANFIS model s test peomance was dened ate compang the smulaton esults and FIS esults.

4 Table. Pat o the tanng set used o ANFIS No ε h W L Ds Smulated ANFIS No Table.. Test data set o ANFIS and esults ε h W L Ds Smulated ANFIS Relatve Eo (%)

5 8 tanng data:o FIS output:* REFERENCES Fequency data set ndex Fgue..Compason o tanng data set esults and FIS esults o esonant equency Fequency testng data:o FIS output:*. D. Poza, Mcostp antennas, Poc. IEEE, Vol. 80, pp. 79 8, Jan.99.. G. Angull and M. Vesac, Resonant Fequency Evaluaton o Mcostp Antennas Usng a Neual- Fuzzy Appoach, IEEE Tansactons on Magnetcs, Vol. 9, No., pp. -6, May 00.. K. Güney, S. Sagıoğlu, and M. Ele, Genealzed neual method to detemne esonant equences o vaous mcostp antennas, Intenatonal Jounal o RF and Mcowave Compute-Aded Engneeng, Vol., pp. -9, 00.. K. Güney, N. Sakaya, Synthess o electcally thn and thck ectangula mcostp antennas wth the use o adaptve neuo-uzzy neence system, Sgnal Pocessng and Communcatons Applcatons Coneence, Poceedng o the IEEE th, pp , May J.-S.R. Jang, ANFIS: Adaptve-netwok based uzzy neence system, IEEE Tans. Syst. Man Cyben, Vol., pp , J.-S.R. Jang, Sel-leanng uzzy contolles based on tempoal backpopagaton, IEEE Tans. Neual Netwok, Vol., pp. 7-7, data set ndex Fgue..Compason o testng data set esults and FIS esults o esonant equency In table, the smulated esult -labeled column shows the HFSS esults whle the ANFIS esult -labeled column shows the FIS esults. In table, the ANFIS model calculates the esonant equency wth.07%,.8%, 0.8%, 0.%, and.60% wth elatve eo value, espectvely. These esults show the ANFIS s mean accuacy at 98.9%. Whle Fgue compaes the esults between the tanng data set and FIS output, Fgue shows the testng data set and FIS output. V. CONCLUSION As a consequence, a method based on the ANFIS o computng the esonant equency o Mcostp dpole antennas has been pesented. The hybd-leanng algothm s used to denty the ANFIS paametes. The esults o the ANFIS ae n vey good ageement wth the smulated. We hope that the ANFIS wll nd wdespead applcatons n solvng antenna and mcowave ntegatedccut poblems.