Research Article A Generalized ANN Model for Analyzing and...

Hindawi Publishing CorporationChinese Journal of EngineeringVolume 2013 Article ID 647191 9 pageshttpdxdoiorg1011552013647191

Research ArticleA Generalized ANN Model for Analyzing and SynthesizingRectangular Circular and Triangular Microstrip Antennas

Taimoor Khan and Asok De

Department of Electronics Engineering Delhi Technological University Delhi 110 042 India

Correspondence should be addressed to Taimoor Khan ktaimoorgmailcom

Received 1 September 2013 Accepted 23 September 2013

Academic Editors H H-C Iu and L Li

Copyright copy 2013 T Khan and A De This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Since last one decade artificial neural network (ANN) models have been used as fast computational technique for differentperformance parameters of microstrip antennas Recently the concept of creating a generalized neural approach for differentperformance parameters has been motivated in microstrip antennas This paper illustrates a generalized neural approach foranalyzing and synthesizing the rectangular circular and triangular MSAs simultaneously Such approach is very much requiredfor the antenna designers for getting instant answer for the required parameters Here total seven performance parameters of threedifferent MSAs are computed using generalized neural approach as such a method is rarely available in the open literature even forcomputing more than three performance parameters simultaneously The results thus obtained are in very good agreement withthe measured results available in the referenced literature for all seven cases

1 Introduction

Microstrip antennas are being widely used for different appli-cations in wireless communication due to several attractivefeatures low profile conformable to planar and nonplanarsurfaces most economical mechanically robust light weighteasy mount-ability and so forth [1] Since the microstripantenna (MSA) operates only in the vicinity of resonancefrequency it needs to be calculated accurately for analyz-ing the microstrip antennas Similarly for designing theMSAs the physical dimensions must also be calculatedprecisely Several classical methods [2ndash14] have been usedfor computing the resonance frequency of rectangular MSAs[2ndash5] resonance frequency of circular MSAs [6ndash12] andresonance frequency of triangular MSAs [13 14] Thesemethods can broadly be categorized as analytical methodsand numerical methods The analytical methods provide agood spontaneous explanation for the operation of MSAsThese methods are based on the physical assumptions forsimplifying the radiation mechanism of the MSAs and arenot suitable for many structures where the thickness of thesubstrate is not very thin On the other hand the numericalmethods provide accurate results but only at the cost ofhuge mathematical burden in the form of complex integral

equations The choice of test function and path integrationappears to be more critical without initial assumptions inthe final stage of the numerical results Also these methodsrequire a new solution even for a minor alteration in thegeometryThus the requirement for having a new solution forevery minor change in the geometry as well as the problemsassociated with the thickness of the substrates in analyticalmethods leads to complexities and processing cost

In recent years the artificial neural network (ANN)models have acquired tremendous utilization in microwavecommunications [24ndash27] and especially in analyzing andsynthesizing the MSAs [18ndash23 28 29] due to their ability andadaptability to learning generalization smaller informationrequirement fast real-time operation and ease of imple-mentation features [24] The ANN model is trained usingmeasured calculated andor simulated patterns The aim ofthe training process is to minimize error between referenceand actual outputs of the ANN model Once the model istrained for a specified error it returns the results very fastFor analyzing theMSAs several neural models [18 23 28 29]have been reported for calculating the resonance frequency ofrectangular MSAs [18] the resonance frequency of circularMSAs [23] and the resonance frequency of triangular MSAs[28] respectively For synthesizing the equilateral triangular

2 Chinese Journal of Engineering

MSA its side length has also been computed using neuralnetwork by Gopalakrishnan andGunasekaran [29]Thus theneural methods [18 23 28 29] have been used for computinga single parameter (ie the resonance frequency or physicaldimension) of the same MSAs respectively

Recently the concept for creating generalized neuralmodels has gained popularity for computing different per-formance parameters simultaneously [19ndash22] Firstly it hasbeen introduced by Guney et al [19] for computing theresonance frequencies of rectangular circular and triangularMSAs simultaneously Guney and Sarikaya [20 21] havecomputed the resonance frequencies of rectangular circularand triangular MSAs simultaneously by introducing twodifferent generalized methods one is based on adaptive neu-ral network-based fuzzy inference system (ANFIS) method[20] and another based on concurrent neurofuzzy system(CNFS) method [21] Turker et al [22] have proposed ageneralized neural model for analyzing and synthesizingthe rectangular MSAs simultaneously The synthesis of theproblem has been defined as the forward-side and analysisas the reverse-side [21] Thus three different parameters thatis resonance frequency width and length of rectangularMSAs have been computed simultaneously in this modelwhereas in ANFIS and CNFS methods the three computedparameters have been mentioned as the resonance frequencyof rectangular MSAs resonance frequency of circular MSAsand the resonance frequency of triangular MSAs Furtherthe neural models [19ndash21] are based on the approach forcalculating the equivalent area whereas the model [22] isbased on making switching between forward- and reverse-side prior to calculating the desired parameter For com-puting different parameters simultaneously in a commonneural approach sometimes it becomes undesirable and timeconsuming to the antenna designer when instant answeris required In the proposed work authors have proposeda simple and more accurate generalized neural approachfor analyzing and synthesizing the rectangular circular andtriangular MSAs simultaneously as such an approach israrely available in the referenced literature The proposedapproach is based in making equal dimensionality in theinput patterns before applying training which has recentlybeen applied in computing different performance parametersof triangular MSAs [30] and of circular MSAs [31]

2 Geometries for Patterns Generation

Themicrostrip antenna in its simplest configuration consistsof a radiating conductive patch on one side of a dielectricsubstrate of relative permittivity ldquo120576

119903rdquo and of thickness ldquoℎrdquo

having a ground plane on the other side [1] The side-viewof the proposed geometry with different radiating patchesis shown in Figure 1 In Figure 1(b) RMSA corresponds toa rectangular MSA of physical dimensions ldquo119882

119903rdquo and ldquo119871

119903rdquo

CMSA to a circular MSA of radius ldquo119877119888rdquo and TMSA to an

equilateral triangular MSA of side length ldquo119878119905rdquo

From the discussion made in conventional approaches[2ndash14] it is concluded that if the geometric dimensions rela-tive permittivity dielectric thickness and mode of propaga-tion are given then the resonance frequency can be calculated

Ground plane

Radiating patch

SMA connector

Substrate (120576r and h)

(a) Side view

RMSA CMSA TMSA

(b) Different radiating patches

Figure 1 Geometry of microstrip antenna

easily Keeping this concept in mind total 81-patterns (46 forresonance frequency of rectangular MSAs 20 for resonancefrequency of circular MSAs and 15-for resonance frequencyof triangularMSAs) are arranged 46-patterns for rectangularMSAs are obtained from the works of Chang et al [2] Carver[3] and Kara [4 5] 20-patterns for circular MSAs from theworks ofDahele and Lee [6 7] Carver [8] Antoszkiewicz andShafai [9] Howell [10] Itoh andMittra [11] and Abboud et al[12] and 15-patterns for triangular MSAs are obtained fromthe works of Chen et al [13] and Dahele and Lee [14] Thesepatterns are shown in Table 1

As the microstrip antenna (MSA) has narrow bandwidthand operates only in the vicinity of the resonance frequencythe choice of geometric dimensions giving specific resonanceis also important The rectangular circular and triangularshapes of MSAs are the most popular shapes Hence for syn-thesizing the rectangular MSAs the geometric dimensions(ldquo119882119903rdquo and ldquo119871

119903rdquo) can be computed from the given five input

parameters ldquo119891119903rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo and ldquo119899rdquo For synthesizing the

circularMSAs its radius ldquo119877119888rdquo can be estimated from the given

five input parameters ldquo119891119888rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo and ldquo119899rdquo Similarly

for synthesizing the triangularMSAs the side length can alsobe computed if the five input parameters ldquo119891

119905rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo

and ldquo119899rdquo are given This concept is applied for creating thepatterns required for synthesizing these three MSAs Total127 patterns (46 each for width and length of rectangularMSAs 20 for radius of circularMSAs and 15 for side length oftriangular MSAs) are created and are shown in Table 2Thus208 generated patterns (81 analysis patterns + 127 synthesispatterns) are used for training and testing of the ANNmodelto be discussed in Section 3

3 Proposed ANN Modeling

In todayrsquos highly integrated world when solutions to prob-lems are cross-disciplinary in nature ANNs promise tobecome powerful techniques for obtaining solutions toproblems quickly and accurately The ANNs are massivelydistributed parallel processors that have a natural propensityfor storing experiential knowledge andmaking it available for

Chinese Journal of Engineering 3

Table 1 Training and testing patterns [2ndash14] for analysis of MSAs(a)

Analysis of rectangular MSAs [2ndash5]Input parameters (6-dimensional)

119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

57000 38000 03175 23300 1 0 2310045500 30500 03175 23300 1 0 2890029500 19500 03175 23300 1 0 4240019500 13000 03175 23300 1 0 5840017000 11000 03175 23300 1 0 68000998771

14000 09000 03175 23300 1 0 7700012000 08000 03175 23300 1 0 8270010500 07000 03175 23300 1 0 9140017000 11000 09525 23300 1 0 4730017000 11000 01524 23300 1 0 7870041000 41400 01524 25000 1 0 2228068580 41400 01524 25000 1 0 22000998771

10800 41400 01524 25000 1 0 2181008500 12900 00170 22200 1 0 7740007900 11850 00170 22200 1 0 84500998771

20000 25000 00790 22200 1 0 3970010630 11830 00790 25500 1 0 7730009100 10000 01270 10200 1 0 4600017200 18600 01570 23300 1 0 5060018100 19600 01570 23300 1 0 48050998771

12700 13500 01630 25500 1 0 6560015000 16210 01630 25500 1 0 5600013370 14120 02000 25500 1 0 62000998771

11200 12000 02420 25500 1 0 7050014030 14850 02520 25500 1 0 5800015300 16300 03000 25000 1 0 5270009050 10180 03000 25000 1 0 7990011700 12800 03000 25000 1 0 6570013750 15800 04760 25500 1 0 51000998771

07760 10800 03300 25500 1 0 8000007900 12550 04000 25500 1 0 7134009870 14500 04500 25500 1 0 6070010000 15200 04760 25500 1 0 58200998771

08140 14400 04760 25500 1 0 6380007900 16200 05500 25500 1 0 5990012000 19700 06260 25500 1 0 4660007830 23000 08540 25500 1 0 4600012560 27560 09520 25500 1 0 35800998771

09740 26200 09520 25500 1 0 3980010200 26400 09520 25500 1 0 3900008830 26760 10000 25500 1 0 3980007770 28350 11000 25500 1 0 3900009200 31300 12000 25500 1 0 34700

(a) Continued


119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

10300 33800 12810 25500 1 0 32000998771

12650 35000 12810 25500 1 0 2980010800 34000 12810 25500 1 0 31500

(b)

Analysis of circular MSAs [6ndash12]Input parameters (5-dimensional)

119891119888(GHz)

119877119888(cm) h (cm) 120576

119903m n

07400 01588 26500 1 1 6634007700 02350 45500 1 1 4945008200 01588 26500 1 1 6074009600 01588 26500 1 1 52240998771

10400 02350 45500 1 1 3750010700 01588 26500 1 1 4723011500 01588 26500 1 1 4425012700 00794 25900 1 1 4070020000 02350 45500 1 1 2003029900 02350 45500 1 1 13600998771

34930 01588 25000 1 1 1570034930 03175 25000 1 1 1510038000 01524 24900 1 1 1443039750 02350 45500 1 1 1030048500 03180 25200 1 1 1099049500 02350 45500 1 1 0825050000 01590 23200 1 1 1128068000 00800 23200 1 1 0835068000 01590 23200 1 1 08290998771

68000 03180 23200 1 1 08150(c)

Analysis of triangular MSAs [13 14]Input parameters (5-dimensional)

119891119905(GHz)

119878119905(cm) h (cm) 120576

119903m n

41000 00700 105000 1 0 15190998771

41000 00700 105000 1 1 2637041000 00700 105000 2 0 2995041000 00700 105000 2 1 3973041000 00700 105000 3 0 4439087000 00780 23200 1 0 1489087000 00780 23200 1 1 2596087000 00780 23200 2 0 2969087000 00780 23200 2 1 39680998771

87000 00780 23200 3 0 44430100000 01590 23200 1 0 12800100000 01590 23200 1 1 22420100000 01590 23200 2 0 25500100000 01590 23200 2 1 34000100000 01590 23200 3 0 38240998771998771

Testing patterns


Table 2 Training and testing patterns [2ndash14] for synthesis of MSAs(a)

Synthesis of rectangular MSAs [2ndash5]Input parameters (5-dimensional)

119882119903(cm) 119871

119903(cm)

119891119903 (GHz) ℎ (cm) 120576119903

m n23100 03175 23300 1 0 57000 3800028900 03175 23300 1 0 45500 3050042400 03175 23300 1 0 29500 1950058400 03175 23300 1 0 19500 1300068000 03175 23300 1 0 17000998771 11000998771

77000 03175 23300 1 0 14000 0900082700 03175 23300 1 0 12000 0800091400 03175 23300 1 0 10500 0700047300 09525 23300 1 0 17000 1100078700 01524 23300 1 0 17000 1100022280 01524 25000 1 0 41000 4140022000 01524 25000 1 0 68580998771 41400998771

21810 01524 25000 1 0 10800 4140077400 00170 22200 1 0 08500 1290084500 00170 22200 1 0 07900998771 11850998771

39700 00790 22200 1 0 20000 2500077300 00790 25500 1 0 10630 1183046000 01270 10200 1 0 09100 1000050600 01570 23300 1 0 17200 1860048050 01570 23300 1 0 18100998771 19600998771

65600 01630 25500 1 0 12700 1350056000 01630 25500 1 0 15000 1621062000 02000 25500 1 0 13370998771 14120998771

70500 02420 25500 1 0 11200 1200058000 02520 25500 1 0 14030 1485052700 03000 25000 1 0 15300 1630079900 03000 25000 1 0 09050 1018065700 03000 25000 1 0 11700 1280051000 04760 25500 1 0 13750998771 15800998771

80000 03300 25500 1 0 07760 1080071340 04000 25500 1 0 07900 1255060700 04500 25500 1 0 09870 1450058200 04760 25500 1 0 10000998771 15200998771

63800 04760 25500 1 0 08140 1440059900 05500 25500 1 0 07900 1620046600 06260 25500 1 0 12000 1970046000 08540 25500 1 0 07830 2300035800 09520 25500 1 0 12560998771 27560998771

39800 09520 25500 1 0 09740 2620039000 09520 25500 1 0 10200 2640039800 10000 25500 1 0 08830 2676039000 11000 25500 1 0 07770 2835034700 12000 25500 1 0 09200 3130032000 12810 25500 1 0 10300998771 33800998771

29800 12810 25500 1 0 12650 3500031500 12810 25500 1 0 10800 34000

(b)

Synthesis of circular MSAs [6ndash12]Input parameters (5-dimensional)

119877119888(cm)

119891119888(GHz) h (cm) 120576

119903m n

66340 01588 26500 1 1 0740049450 02350 45500 1 1 0770060740 01588 26500 1 1 0820052240 01588 26500 1 1 09600998771

37500 02350 45500 1 1 1040047230 01588 26500 1 1 1070044250 01588 26500 1 1 1150040700 00794 25900 1 1 1270020030 02350 45500 1 1 2000013600 02350 45500 1 1 29900998771

15700 01588 25000 1 1 3493015100 03175 25000 1 1 3493014430 01524 24900 1 1 3800010300 02350 45500 1 1 3975010990 03180 25200 1 1 4850008250 02350 45500 1 1 4950011280 01590 23200 1 1 5000008350 00800 23200 1 1 6800008290 01590 23200 1 1 68000998771

08150 03180 23200 1 1 68000(c)

Synthesis of triangular MSAs [13 14]Input parameters (5-dimensional)

119878119905(cm)

119891119905(GHz) h (cm) 120576

119903m n

15190 00700 105000 1 0 41000998771

26370 00700 105000 1 1 4100029950 00700 105000 2 0 4100039730 00700 105000 2 1 4100044390 00700 105000 3 0 4100014890 00780 23200 1 0 8700025960 00780 23200 1 1 8700029690 00780 23200 2 0 8700039680 00780 23200 2 1 87000998771

44430 00780 23200 3 0 8700012800 01590 23200 1 0 10000022420 01590 23200 1 1 10000025500 01590 23200 2 0 10000034000 01590 23200 2 1 10000038240 01590 23200 3 0 100000998771998771

Testing patterns

use It resembles the brain since knowledge is acquired by theneural networks through learning process and interneuronconnection strengths are used to store this knowledge Neuralnetworks learn by known examples of a problem to acquireknowledge about it Once the ANN trains successfully it canbe put to effective use in solving ldquounknownrdquo or ldquountrainedrdquo


instances of the problem [24] Multilayered perceptron(MLP) and radial basis function (RBF) neural networks haveprimarily been used in computing different parameters of theMSAs [18ndash23 28 29] A radial basis function (RBF) neuralnetworks consists of three layers in which each layer is havingentirely different roles The input layer is made up of sourcenodes which connect the networks to the outside environ-ment The input layer does not accomplish any process butsimply buffers the data The hidden layer applies a Gaussiantransformation from the input space to the hidden space[32] The output layer is linear supplying the response of thenetworks to the patterns applied at the input layer As far astraining of the neural networks is concerned the RBF neuralnetworks are much faster than the multilayers perceptron(MLP) neural networks It is so because the learning processin RBF neural networks has two stages and both stages aremademore efficient by using appropriate learning algorithms[32] This is the prime reason of using RBF neural networksinstead of MLP neural networks in present work Thereare three common steps followed in applying RBF neuralnetworks on the proposed problem Firstly the trainingpatterns are generated then the structural configuration ofhidden layer neurons is selected in the second step andfinally in the third step the weights are optimized by usingtraining algorithm The trained neural model is then testedon the remaining arbitrary sets of samples not included in thetraining samples These steps are being discussed here

31 Patterns Generation andTheir Dimensionality The theo-reticalexperimental patterns mentioned in Tables 1 and 2 areused for training and testing the proposed neural model It isclear from these tables that the dimensionality of input pat-tern is symmetrical in six different cases except for analyzingthe rectangular MSAs It means that the resonance frequencyof the rectangular MSAs is the function of six dimensionalinput patterns that is [119882

119903119871119903120576119903ℎ 119898 119899] whereas the

dimensionality of the input pattern is five in all six remainingcases Hence if the dimensionality of input pattern for theanalysis of rectangular MSAs reduces from six to five then itbecomes compatible to the remaining six cases

For the fundamental mode (ie 119898 = 1 and 119899 = 0)of rectangular MSAs the resonance frequency depends onfour parameters that is width and length of the patch andthickness and relative permittivity of the substrateThese fourparameters dependency is represented by variables ldquo119909

1rdquo ldquo1199092rdquo

ldquo1199093rdquo and ldquo119909

4rdquo respectively The fundamental mode used here

is not varying hence it can be represented by single integerldquo1199095rdquo instead of integers ldquo119898rdquo and ldquo119899rdquo where 119909

5= 1means119898 =

1 and 119899 = 0 Thus the resonance frequency has become thefunction of five variables ldquo119909

1rdquo ldquo1199092rdquo ldquo1199093rdquo ldquo1199094rdquo and ldquo119909

5rdquo The

five-dimensional input patterns each for width and lengthcalculation of the rectangular MSAs are mentioned as theresonance frequency (119909

1) dielectric thickness (119909

2) relative

permittivity (1199093) and modes of propagation (119909

4and 119909

5) The

five-dimensional input patterns each for circular MSAs andtriangular MSAs analysis as well as synthesis are also createdusing the same approach and represented by the variables1199091 1199092 1199093 1199094 and 119909

5 respectively To distinguish these seven

different cases an additional variable ldquo119872rdquo that is a modecontrol is also included in five-dimensional input patternsThe mode control 119872 is selected as 119872 = 1 119872 = 2 and119872 = 3 for computing the resonance frequency width andlength of rectangular MSAs respectively119872 = 4 and119872 = 5for the resonance frequency and radius of circularMSAs andfinally 119872 = 6 and 119872 = 7 for calculating the resonancefrequency and side length of the triangular MSAs respec-tively This six-dimensional input pattern that is [119909] rarr[11990911199092119909311990941199095119872] is used as the training and

testing pattern for computing seven different parameters ofthree different MSAs simultaneouslyThus the input-outputpatterns with their original andmodified dimensionalities forall seven different cases are also mentioned in Table 3

32 Structural Configuration and Training Strategy To builda successful neural-networks application training stage is oneof themost critical phases Training the neural networks basi-cally consists of adjustingweights of the neural networks withthe help of a training algorithm Before doing training of theRBFmodel all 208 patterns are normalized between +01 and+09 usingMATLAB software [33]The training performanceof the proposed neural networks is observed by varying thenumber of neurons in the hidden layer and after many trialsit is optimized as forty-five neurons for the best performanceFurther the training performance of the neural model is alsoobserved with seven different training algorithms [15ndash17]BFGS quasi-Newton (BFG) Bayesian regulation (BR) scaledconjugate-gradient (SCG) Powell-Beale conjugate gradient(CGP) conjugate gradient with Fletcher-Peeves (CGF) one-step secant (OSS) and Levenberg-Marquardt (LM)

A RBF neural model proposed for computing sevendifferent parameters is illustrated in Figure 2 in which theweight matrix is designated by [w] and the bias value by119887 respectively Initially some random values are assignedfor the weights which are then optimized using trainingalgorithm and coding for this implementation is createdin MATLAB software [33] In Figure 2 the input matrixdesignated as [119909] rarr [119909

11199092119909311990941199095119872] is of six-

dimensional The structural configuration of the proposedmodel is optimized as [6-45-1] It means that there are 6neurons in the input layer 45 neurons in the hidden layerand single neuron in the output layer For the applied inputpattern some random numbers between 0 and 1 are assignedto the weights and the output of the model is computedcorresponding to that input pattern Some parameters likemean square error (MSE) learning rate momentum coeffi-cient and spread value required during training of the neuralmodel are taken as 5 times 10-7 01 05 and 05 respectivelyThe MSE between the calculated and referenced results isthen computed for 169 training patterns and all the weightsare updated accordingly This updating process is carried outafter presenting each set of input pattern until the calculatedaccuracy of the model is estimated satisfactory Once it isachieved the second phase that is testing algorithm iscreated with the help of these updated weights for remaining39 samples in the MATLAB software [33] The arbitrary setout of total 39 testing sets is now applied on the model and itscorresponding result is obtained respectively


Table 3 Dimensionality of input parameters for training and testing of ANN model

Case-I (119872 = 1) resonance frequency of RMSAs Case-II (119872 = 2) width of RMSAsInput parameters (x) Output parameter (119910) Input parameters (x) Output parameter (119910)1199091rarrWidth of the patch (119882

119903)

Resonance frequency (MHz) ofrectangular MSAs(Total 46 patterns)

1199091rarrResonance frequency (119891

119903)

Width (cm) of rectangularMSAs

(Total 46 patterns)

1199092rarr Length of the patch (119871

119903) 119909

2rarrDielectric thickness (h)

1199093rarrDielectric thickness (h) 119909

3rarrRelative permittivity (120576

119903)


119903) 119909

4rarrMode of propagation (m)

1199095rarrMode of propagation (m and

n) 1199095rarrMode of propagation (n)

Case-III (119872 = 3) length of RMSAs Case-IV (119872 = 4) resonance frequency of CMSAsInput parameters (x) Output parameter (119910) Input parameters (x) Output parameter (y)1199091rarrResonance frequency (119891

119903)

Length (cm) of rectangularMSAs

(Total 46 patterns)

1199091rarrRadius (119877

119888)

Resonance frequency (MHz)of Circular MSAs(Total 20 patterns)




119903) 119909


119903)

1199094rarrMode of propagation (m) 119909


1199095rarrMode of propagation (n) 119909

5rarrMode of propagation (n)

Case-V (119872 = 5) radius of CMSAs Case-VI (119872 = 6) resonance frequency of TMSAsInput parameters (x) Output parameter (y) Input parameters (x) Output parameter (y)1199091rarrResonance frequency (119891

119888)

Radius (cm) of circular MSAs(Total 20 patterns)

1199091rarr Side-length of patch (119878

119905)

Resonance frequency (MHz)of triangular MSAs(Total 20 patterns)




119903) 119909


119903)





Case-VII (119872 = 7) side length of TMSAsInput parameters (x) Output parameter (y)


119905)

1199092rarrDielectric thickness (h) Side-length (cm) of triangular MSAs1199093rarrRelative permittivity (120576

119903) (Total 20 patterns)

1199094rarrMode of propagation (m)1199095rarrMode of propagation (n)

Table 4 Comparison of average absolute error versus training algorithm

Trainingalgorithm[15ndash17]

Average absolute error in analysis and synthesisNumber of

iteration requiredRectangular MSAs Circular MSAs Triangular MSAsAnalysis Synthesis Analysis Synthesis Analysis Synthesis

BFG 1135MHz 11500 cm 3410MHz 18020 cm 1320MHz 14110 cm 13049BR 3133MHz 21300 cm 2720MHz 10290 cm 2270MHz 11620 cm 12046SCG 2553MHz 06800 cm 2580MHz 10310 cm 2450MHz 10110 cm 19602CGB 5100MHz 10900 cm 1510MHz 12310 cm 3540MHz 00150 cm 14021CGF 1450MHz 10300 cm 1430MHz 09160 cm 1850MHz 10130 cm 11302OSS 2180MHz 17600 cm 1020MHz 21060 cm 2370MHz 12040 cm 14803LM 3200MHz 00037 cm 0700MHz 00045 cm 1600MHz 00051 cm 1476

4 Calculated Results and Discussion

The training performance of the proposed generalized modelis observed with seven different training algorithms BFGBR SCG CGP CGF OSS and LM backpropagation algo-rithms respectively but only the Levenberg-Marquardt (LM)back propagation is proved to be the fastest convergingtraining algorithm and produced the results with least mean

square error (MSE) as mentioned in Table 4 To determinethe most suitable implication given in the literature [2ndash14] the computed results are compared with the theo-reticalexperimental results reported in the literature Foranalysis and synthesis of rectangular MSAs this comparisonis made with the experimental results of Chang et al [2]Carver [3] and Kara [4 5] For circular MSAs analysisand synthesis it is made with the experimental results of


y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times

minusx minus 1205831

2

212059021


2

212059022

minusx minus 120583Mminus1

2

21205902Mminus1

minusx minus 120583i

2

21205902i

minusx minus 120583M2

21205902M

sum

Figure 2 Proposed ANNmodel

2 6 10 14 18 22 26 30 34 38 42 46Number of patterns

Abso

lute

erro

r

656

555

454

353

252

151

050

Comparison of absolute error during analysis of MSAs

Absolute error (MHz) in analysis of rectangular MSAsAbsolute error (MHz) in analysis of circular MSAsAbsolute error (MHz) in analysis of triangular MSAs

Figure 3 Absolute errors during analysis of rectangular circularand triangular MSAs

Dahele and Lee [6 7] Carver [8] Antoszkiewicz and Shafai[9] Howell [10] Itoh and Mittra [11] and Abboud et al[12] whereas for equilateral triangular MSAs a comparisonis made with the results of Chen et al [13] and Daheleand Lee [14] The absolute errors between the theoreti-calexperimental results and the computed results via ANNmodeling are also calculated for analysis and synthesis ofrectangular circular and triangular MSAs respectively Thisabsolute error is plotted in Figure 3 for analysis of rectangular


Abso

lute

erro

r

Comparison of absolute error during synthesis of MSAs

Absolute error (cm) in synthesis of rectangular MSAsAbsolute error (cm) in synthesis of circular MSAsAbsolute error (cm) in synthesis of triangular MSAs

000900080007000600050004000300020001

Figure 4 absolute errors during synthesis of rectangular circularand triangular MSAs

circular and triangular MSAs respectively and for synthesisof rectangular circular and triangular MSAs it is plotted inFigure 4 respectively

A comparison between the present method results andthe results computed in previous neural models [18ndash23 2829] is also given in Table 5This table shows that in the neuralmodels [18ndash22] the average absolute error for analyzingthe rectangular MSAs has been calculated as 1633MHz7188MHz 617MHz 1688MHz and 500MHz whereas inthe present model it is only 32MHz In case of synthesizingthe rectangular MSAs the model [22] is having the averageabsolute error of 00041 cm whereas in present model it iscalculated as 0037 cm In case of analyzing the circularMSAsthe proposed method is having the average absolute errorof only 030MHz whereas in the methods [19ndash21 23] ithas been calculated as 055MHz 231MHz 455MHz and035MHz respectively For synthesizing the circular MSAsthe present model is having the average absolute error of00045 cm whereas there is no neural model proposed forsynthesizing the circular MSAs in the open literature [18ndash23 28 29] For analyzing the equilateral triangular MSAsthe models [19ndash21 28] are having average absolute errors as153MHz 1833MHz 180MHz and 187MHz respectivelywhereas in the present model it is calculated as 1373MHzand in case of synthesizing triangular MSAs the averageabsolute error in testing patterns of the presentmethod is only00051 cm whereas in the model [29] it has been mentionedas 00090 cm It is clear from the comparison given in Table 5that the computed results by the proposed neural model aremore accurate than the neural results of other scientists [18ndash23 28 29]

5 Conclusion

In this paper authors have proposed a simple and accurategeneralized neural approach for computing seven differentparameters of three different microstrip antennas as thereis no such neural approach suggested in the referencedliterature even for computing more than three parameters


Table 5 Comparison of the present method and previous neural methods

Absolute error during analysis of rectangular MSAsProposed method [18] [19] [20] [21] [22]320MHz 1633MHz 7188MHz 617MHz 1688MHz 500MHz

Absolute error during synthesis of rectangular MSAsProposed method [22] mdash mdash mdash mdash00037 cm 00041 cm mdash mdash mdash mdash

Absolute error during analysis of CMSAsProposed method [23] [19] [20] [21] mdash030MHz 055MHz 231MHz 455MHz 035MHz mdash

Absolute error during synthesis of CMSAsProposed method [18ndash29]00045 cm No neural model is available in the literature [18ndash29]

Absolute error during analysis of TMSAsProposed method [28] [19] [20] [21] mdash1373MHz 153MHz 1833MHz 180MHz 187MHz mdash

Absolute error during synthesis of TMSAsProposed method [29] mdash mdash mdash mdash00051 cm 00090 cm mdash mdash mdash mdash

simultaneously A neuralmodel is rarely proposed in the liter-ature for synthesizing the rectangular circular and triangularMSAs simultaneously or synthesizing the circular MSAsThe proposed generalized model has refined the requirementof these two synthesis models As the proposed model hasproduced more encouraging results for all seven differ-ent cases simultaneously without having any complicatedstructure andor training strategy it can be recommendedto include in antenna CAD (computer-aided design) algo-rithms The concept of the proposed approach is so simpleand accurate that it can be generalized for large numberof computing parameters depending upon the number ofhidden nodes and the distribution of the input-output pat-terns The approach can be very useful to antenna designersto accurately predict any desired parameter (ie resonancefrequency of rectangular MSAs width of rectangular MSAslength of rectangular MSAs resonance frequency of circularMSAs radius of circular MSAs resonance frequency of tri-angular MSAs or side length of equilateral triangular MSAs)of the microstrip antennas by inputting its correspondingparameters within a friction of a second after doing trainingof proposed generalized neural method successfully

In general computing 7 different performance param-eters may require 7 different neural networks moduleswhereas in the present work only one module is fulfilling therequirement of 7 independent modules Hence the presentapproach has been consideredmore generalized in this sense

References

[1] I J Bahl and P Bhartia Microstrip Antennas Artech HouseDedham Mass USA 1980

[2] E Chang S A Long and W F Richards ldquoAn experimentalinvestigation of electrically thick rectangular microstrip anten-nasrdquo IEEE Transactions on Antennas and Propagation vol 34no 6 pp 767ndash772 1986

[3] K R Carver ldquoPractical analytical techniques for the microstripantennasrdquo in Proceedings of Workshop on Printed CircuitAntenna Technology pp 71ndash720 New Mexico State UniversityLas Cruces Mexico 1979

[4] M Kara ldquoThe resonant frequency of rectangular microstripantenna elements with various substrate thicknessesrdquoMicrowave and Optical Technology Letters vol 11 no 2pp 55ndash59 1996

[5] M Kara ldquoClosed-form expressions for the resonant frequencyof rectangular microstrip antenna elements with thick sub-stratesrdquo Microwave and Optical Technology Letters vol 12 no3 pp 131ndash136 1996

[6] J S Dahele and K F Lee ldquoEffect of substrate thickness onthe performance of a circular-disk microstrip antennasrdquo IEEETransactions on Antennas and Propagation vol 31 no 2 pp358ndash360 1983

[7] J SDahele andK F Lee ldquoTheory and experiment onmicrostripantennas with air-gapsrdquo in Proceedings of IEE Conference vol132 pp 455ndash460 1985

[8] K R Carver ldquoPractical analytical techniques for the microstripantennasrdquo in Proceedings of Workshop on Printed Circuit Anten-nas New Mexico State University 1979

[9] K Antoskiewicz and L Shafai ldquoImpedance characteristics ofcircular microstrip patchesrdquo IEEE Transactions on Antennasand Propagation vol 38 no 6 pp 942ndash946 1990

[10] J Q Howell ldquoMicrostrip antennasrdquo IEEE Transactions onAntennas and Propagation vol 23 no 1 pp 90ndash93 1975

[11] T Itoh and R Mittra ldquoAnalysis of a microstrip disk resonatorrdquoArchiv fur Elektronik undUbertragungstechnik vol 27 no 11 pp456ndash458 1973

[12] F Abboud J P Damiano and A Papiernik ldquoNew determina-tion of resonant frequency of circular disc microstrip antennaapplication to thick substraterdquo Electronics Letters vol 24 no 17pp 1104ndash1106 1988

[13] W Chen K F Lee and J S Dahele ldquoTheoretical and exper-imental studies of the resonant frequencies of the equilateraltriangularmicrostrip antennasrdquo IEEE Transactions on Antennasand Propagation vol 40 pp 1253ndash1256 1992


[14] J S Dahele and K F Lee ldquoOn the resonant frequencies of thetriangular patch antennasrdquo IEEE Transactions on Antennas andPropagation vol 35 no 1 pp 100ndash101 1987

[15] P E Gill W Murray andM HWright Practical OptimizationAcademic Press New York NY USA 1981

[16] L E Scales Introduction to Non-Linear Optimization SpringerNew York NY USA 1985

[17] M THagan andM BMenhaj ldquoTraining feedforward networkswith the Marquardt algorithmrdquo IEEE Transactions on NeuralNetworks vol 5 no 6 pp 989ndash993 1994

[18] D Karaboga K Guney S Sagiroglu and M Erler ldquoNeuralcomputation of resonant frequency of electrically thin and thickrectangular microstrip antennasrdquo IEE Proceedings vol 146 no2 pp 155ndash159 1999

[19] K Guney S Sagiroglu and M Erler ldquoGeneralized neuralmethod to determine resonant frequencies of various micro-strip antennasrdquo International Journal of RF and MicrowaveComputer-Aided Engineering vol 12 no 1 pp 131ndash139 2002

[20] K Guney and N Sarikaya ldquoA hybrid method based on com-bining artificial neural network and fuzzy inference systemfor simultaneous computation of resonant frequencies of rect-angular circular and triangular microstrip antennasrdquo IEEETransactions on Antennas and Propagation vol 55 no 3 pp659ndash668 2007

[21] KGuney andN Sarikaya ldquoConcurrent neuro-fuzzy systems forresonant frequency computation of rectangular circular andtriangular microstrip antennasrdquo Progress in ElectromagneticsResearch vol 84 pp 253ndash277 2008

[22] N Turker F Gunes and T Yildirim ldquoArtificial neural design ofmicrostrip antennasrdquo Turkish Journal of Electrical Engineeringand Computer Sciences vol 14 no 3 pp 445ndash453 2006

[23] S Sagiroglu K Guney and M Erler ldquoResonant frequencycalculation for circular microstrip antennas using artificialneural networksrdquo International Journal of RF and MicrowaveComputer-Aided Engineering vol 8 no 3 pp 270ndash277 1998

[24] Q J Zhang and K C Gupta Neural Networks for RF andMicrowave Design Artech House 2000

[25] PMWatson andK CGupta ldquoEM-ANNmodels formicrostripvias and interconnects in dataset circuitsrdquo IEEE Transactionson Microwave Theory and Techniques vol 44 no 12 pp 2495ndash2503 1996

[26] P M Watson and K C Gupta ldquoDesign and optimization ofcpw circuits using em-ann models for cpw componentsrdquo IEEETransactions on Microwave Theory and Techniques vol 45 no12 pp 2515ndash2523 1997

[27] P M Watson K C Gupta and R L Mahajan ldquoDevelop-ment of knowledge based artificial neural network models formicrowave componentsrdquo IEEE International Microwave Digestvol 1 pp 9ndash12 1998

[28] S Sagiroglu and K Guney ldquoCalculation of resonant frequencyfor an equilateral triangular microstrip antenna with the use ofartificial neural networksrdquo Microwave and Optical TechnologyLetters vol 14 no 2 pp 89ndash93 1997

[29] R Gopalakrishnan and N Gunasekaran ldquoDesign of equilateraltriangular microstrip antenna using artifical neural networksrdquoin Proceedings of the IEEE International Workshop on AntennaTechnology (IWAT rsquo05) pp 246ndash249 March 2005

[30] T Khan and A De ldquoComputation of different parameters oftriangular patch microstrip antennas using a common neuralmodelrdquo International Journal ofMicrowave andOptical Technol-ogy vol 5 pp 219ndash224 2010

[31] T Khan and A De ldquoA common neural approach for computingdifferent parameters of circular patch microstrip antennasrdquoInternational Journal of Microwave and Optical Technology vol6 no 5 pp 259ndash262 2011

[32] S Chen C F N Cowan and P M Grant ldquoOrthogonal leastsquares learning algorithm for radial basis function networksrdquoIEEETransactions onNeuralNetworks vol 2 no 2 pp 302ndash3091991

[33] H Demuth andM BealeNeural Network Tool Box for Use withMATLAB Userrsquos GuideTheMathWorks Inc 5th edition 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



MSA its side length has also been computed using neuralnetwork by Gopalakrishnan andGunasekaran [29]Thus theneural methods [18 23 28 29] have been used for computinga single parameter (ie the resonance frequency or physicaldimension) of the same MSAs respectively

Recently the concept for creating generalized neuralmodels has gained popularity for computing different per-formance parameters simultaneously [19ndash22] Firstly it hasbeen introduced by Guney et al [19] for computing theresonance frequencies of rectangular circular and triangularMSAs simultaneously Guney and Sarikaya [20 21] havecomputed the resonance frequencies of rectangular circularand triangular MSAs simultaneously by introducing twodifferent generalized methods one is based on adaptive neu-ral network-based fuzzy inference system (ANFIS) method[20] and another based on concurrent neurofuzzy system(CNFS) method [21] Turker et al [22] have proposed ageneralized neural model for analyzing and synthesizingthe rectangular MSAs simultaneously The synthesis of theproblem has been defined as the forward-side and analysisas the reverse-side [21] Thus three different parameters thatis resonance frequency width and length of rectangularMSAs have been computed simultaneously in this modelwhereas in ANFIS and CNFS methods the three computedparameters have been mentioned as the resonance frequencyof rectangular MSAs resonance frequency of circular MSAsand the resonance frequency of triangular MSAs Furtherthe neural models [19ndash21] are based on the approach forcalculating the equivalent area whereas the model [22] isbased on making switching between forward- and reverse-side prior to calculating the desired parameter For com-puting different parameters simultaneously in a commonneural approach sometimes it becomes undesirable and timeconsuming to the antenna designer when instant answeris required In the proposed work authors have proposeda simple and more accurate generalized neural approachfor analyzing and synthesizing the rectangular circular andtriangular MSAs simultaneously as such an approach israrely available in the referenced literature The proposedapproach is based in making equal dimensionality in theinput patterns before applying training which has recentlybeen applied in computing different performance parametersof triangular MSAs [30] and of circular MSAs [31]

2 Geometries for Patterns Generation

Themicrostrip antenna in its simplest configuration consistsof a radiating conductive patch on one side of a dielectricsubstrate of relative permittivity ldquo120576

119903rdquo and of thickness ldquoℎrdquo

having a ground plane on the other side [1] The side-viewof the proposed geometry with different radiating patchesis shown in Figure 1 In Figure 1(b) RMSA corresponds toa rectangular MSA of physical dimensions ldquo119882

119903rdquo and ldquo119871

119903rdquo

CMSA to a circular MSA of radius ldquo119877119888rdquo and TMSA to an

equilateral triangular MSA of side length ldquo119878119905rdquo

From the discussion made in conventional approaches[2ndash14] it is concluded that if the geometric dimensions rela-tive permittivity dielectric thickness and mode of propaga-tion are given then the resonance frequency can be calculated

Ground plane

Radiating patch

SMA connector

Substrate (120576r and h)

(a) Side view

RMSA CMSA TMSA

(b) Different radiating patches

Figure 1 Geometry of microstrip antenna

easily Keeping this concept in mind total 81-patterns (46 forresonance frequency of rectangular MSAs 20 for resonancefrequency of circular MSAs and 15-for resonance frequencyof triangularMSAs) are arranged 46-patterns for rectangularMSAs are obtained from the works of Chang et al [2] Carver[3] and Kara [4 5] 20-patterns for circular MSAs from theworks ofDahele and Lee [6 7] Carver [8] Antoszkiewicz andShafai [9] Howell [10] Itoh andMittra [11] and Abboud et al[12] and 15-patterns for triangular MSAs are obtained fromthe works of Chen et al [13] and Dahele and Lee [14] Thesepatterns are shown in Table 1

As the microstrip antenna (MSA) has narrow bandwidthand operates only in the vicinity of the resonance frequencythe choice of geometric dimensions giving specific resonanceis also important The rectangular circular and triangularshapes of MSAs are the most popular shapes Hence for syn-thesizing the rectangular MSAs the geometric dimensions(ldquo119882119903rdquo and ldquo119871

119903rdquo) can be computed from the given five input

parameters ldquo119891119903rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo and ldquo119899rdquo For synthesizing the

circularMSAs its radius ldquo119877119888rdquo can be estimated from the given

five input parameters ldquo119891119888rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo and ldquo119899rdquo Similarly

for synthesizing the triangularMSAs the side length can alsobe computed if the five input parameters ldquo119891

119905rdquo ldquo120576119903rdquo ldquoℎrdquo ldquo119898rdquo

and ldquo119899rdquo are given This concept is applied for creating thepatterns required for synthesizing these three MSAs Total127 patterns (46 each for width and length of rectangularMSAs 20 for radius of circularMSAs and 15 for side length oftriangular MSAs) are created and are shown in Table 2Thus208 generated patterns (81 analysis patterns + 127 synthesispatterns) are used for training and testing of the ANNmodelto be discussed in Section 3

3 Proposed ANN Modeling

In todayrsquos highly integrated world when solutions to prob-lems are cross-disciplinary in nature ANNs promise tobecome powerful techniques for obtaining solutions toproblems quickly and accurately The ANNs are massivelydistributed parallel processors that have a natural propensityfor storing experiential knowledge andmaking it available for




119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

57000 38000 03175 23300 1 0 2310045500 30500 03175 23300 1 0 2890029500 19500 03175 23300 1 0 4240019500 13000 03175 23300 1 0 5840017000 11000 03175 23300 1 0 68000998771

14000 09000 03175 23300 1 0 7700012000 08000 03175 23300 1 0 8270010500 07000 03175 23300 1 0 9140017000 11000 09525 23300 1 0 4730017000 11000 01524 23300 1 0 7870041000 41400 01524 25000 1 0 2228068580 41400 01524 25000 1 0 22000998771

10800 41400 01524 25000 1 0 2181008500 12900 00170 22200 1 0 7740007900 11850 00170 22200 1 0 84500998771

20000 25000 00790 22200 1 0 3970010630 11830 00790 25500 1 0 7730009100 10000 01270 10200 1 0 4600017200 18600 01570 23300 1 0 5060018100 19600 01570 23300 1 0 48050998771

12700 13500 01630 25500 1 0 6560015000 16210 01630 25500 1 0 5600013370 14120 02000 25500 1 0 62000998771

11200 12000 02420 25500 1 0 7050014030 14850 02520 25500 1 0 5800015300 16300 03000 25000 1 0 5270009050 10180 03000 25000 1 0 7990011700 12800 03000 25000 1 0 6570013750 15800 04760 25500 1 0 51000998771

07760 10800 03300 25500 1 0 8000007900 12550 04000 25500 1 0 7134009870 14500 04500 25500 1 0 6070010000 15200 04760 25500 1 0 58200998771

08140 14400 04760 25500 1 0 6380007900 16200 05500 25500 1 0 5990012000 19700 06260 25500 1 0 4660007830 23000 08540 25500 1 0 4600012560 27560 09520 25500 1 0 35800998771

09740 26200 09520 25500 1 0 3980010200 26400 09520 25500 1 0 3900008830 26760 10000 25500 1 0 3980007770 28350 11000 25500 1 0 3900009200 31300 12000 25500 1 0 34700

(a) Continued


119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

10300 33800 12810 25500 1 0 32000998771

12650 35000 12810 25500 1 0 2980010800 34000 12810 25500 1 0 31500

(b)


119891119888(GHz)

119877119888(cm) h (cm) 120576

119903m n

07400 01588 26500 1 1 6634007700 02350 45500 1 1 4945008200 01588 26500 1 1 6074009600 01588 26500 1 1 52240998771

10400 02350 45500 1 1 3750010700 01588 26500 1 1 4723011500 01588 26500 1 1 4425012700 00794 25900 1 1 4070020000 02350 45500 1 1 2003029900 02350 45500 1 1 13600998771

34930 01588 25000 1 1 1570034930 03175 25000 1 1 1510038000 01524 24900 1 1 1443039750 02350 45500 1 1 1030048500 03180 25200 1 1 1099049500 02350 45500 1 1 0825050000 01590 23200 1 1 1128068000 00800 23200 1 1 0835068000 01590 23200 1 1 08290998771

68000 03180 23200 1 1 08150(c)


119891119905(GHz)

119878119905(cm) h (cm) 120576

119903m n

41000 00700 105000 1 0 15190998771

41000 00700 105000 1 1 2637041000 00700 105000 2 0 2995041000 00700 105000 2 1 3973041000 00700 105000 3 0 4439087000 00780 23200 1 0 1489087000 00780 23200 1 1 2596087000 00780 23200 2 0 2969087000 00780 23200 2 1 39680998771

87000 00780 23200 3 0 44430100000 01590 23200 1 0 12800100000 01590 23200 1 1 22420100000 01590 23200 2 0 25500100000 01590 23200 2 1 34000100000 01590 23200 3 0 38240998771998771

Testing patterns




119882119903(cm) 119871

119903(cm)

119891119903 (GHz) ℎ (cm) 120576119903

m n23100 03175 23300 1 0 57000 3800028900 03175 23300 1 0 45500 3050042400 03175 23300 1 0 29500 1950058400 03175 23300 1 0 19500 1300068000 03175 23300 1 0 17000998771 11000998771

77000 03175 23300 1 0 14000 0900082700 03175 23300 1 0 12000 0800091400 03175 23300 1 0 10500 0700047300 09525 23300 1 0 17000 1100078700 01524 23300 1 0 17000 1100022280 01524 25000 1 0 41000 4140022000 01524 25000 1 0 68580998771 41400998771

21810 01524 25000 1 0 10800 4140077400 00170 22200 1 0 08500 1290084500 00170 22200 1 0 07900998771 11850998771

39700 00790 22200 1 0 20000 2500077300 00790 25500 1 0 10630 1183046000 01270 10200 1 0 09100 1000050600 01570 23300 1 0 17200 1860048050 01570 23300 1 0 18100998771 19600998771

65600 01630 25500 1 0 12700 1350056000 01630 25500 1 0 15000 1621062000 02000 25500 1 0 13370998771 14120998771

70500 02420 25500 1 0 11200 1200058000 02520 25500 1 0 14030 1485052700 03000 25000 1 0 15300 1630079900 03000 25000 1 0 09050 1018065700 03000 25000 1 0 11700 1280051000 04760 25500 1 0 13750998771 15800998771

80000 03300 25500 1 0 07760 1080071340 04000 25500 1 0 07900 1255060700 04500 25500 1 0 09870 1450058200 04760 25500 1 0 10000998771 15200998771

63800 04760 25500 1 0 08140 1440059900 05500 25500 1 0 07900 1620046600 06260 25500 1 0 12000 1970046000 08540 25500 1 0 07830 2300035800 09520 25500 1 0 12560998771 27560998771

39800 09520 25500 1 0 09740 2620039000 09520 25500 1 0 10200 2640039800 10000 25500 1 0 08830 2676039000 11000 25500 1 0 07770 2835034700 12000 25500 1 0 09200 3130032000 12810 25500 1 0 10300998771 33800998771

29800 12810 25500 1 0 12650 3500031500 12810 25500 1 0 10800 34000

(b)


119877119888(cm)

119891119888(GHz) h (cm) 120576

119903m n

66340 01588 26500 1 1 0740049450 02350 45500 1 1 0770060740 01588 26500 1 1 0820052240 01588 26500 1 1 09600998771

37500 02350 45500 1 1 1040047230 01588 26500 1 1 1070044250 01588 26500 1 1 1150040700 00794 25900 1 1 1270020030 02350 45500 1 1 2000013600 02350 45500 1 1 29900998771

15700 01588 25000 1 1 3493015100 03175 25000 1 1 3493014430 01524 24900 1 1 3800010300 02350 45500 1 1 3975010990 03180 25200 1 1 4850008250 02350 45500 1 1 4950011280 01590 23200 1 1 5000008350 00800 23200 1 1 6800008290 01590 23200 1 1 68000998771

08150 03180 23200 1 1 68000(c)


119878119905(cm)

119891119905(GHz) h (cm) 120576

119903m n

15190 00700 105000 1 0 41000998771

26370 00700 105000 1 1 4100029950 00700 105000 2 0 4100039730 00700 105000 2 1 4100044390 00700 105000 3 0 4100014890 00780 23200 1 0 8700025960 00780 23200 1 1 8700029690 00780 23200 2 0 8700039680 00780 23200 2 1 87000998771

44430 00780 23200 3 0 8700012800 01590 23200 1 0 10000022420 01590 23200 1 1 10000025500 01590 23200 2 0 10000034000 01590 23200 2 1 10000038240 01590 23200 3 0 100000998771998771

Testing patterns





119903119871119903120576119903ℎ 119898 119899] whereas the







5= 1means119898 =



5rdquo The



2) relative


4and 119909

5) The







11199092119909311990941199095119872] is of six-





119903)



119903)


(Total 46 patterns)


119903) 119909




119903)


119903) 119909





119903)


(Total 46 patterns)


119888)





119903) 119909


119903)






119888)



119905)





119903) 119909


119903)







119905)













y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

57000 38000 03175 23300 1 0 2310045500 30500 03175 23300 1 0 2890029500 19500 03175 23300 1 0 4240019500 13000 03175 23300 1 0 5840017000 11000 03175 23300 1 0 68000998771

14000 09000 03175 23300 1 0 7700012000 08000 03175 23300 1 0 8270010500 07000 03175 23300 1 0 9140017000 11000 09525 23300 1 0 4730017000 11000 01524 23300 1 0 7870041000 41400 01524 25000 1 0 2228068580 41400 01524 25000 1 0 22000998771

10800 41400 01524 25000 1 0 2181008500 12900 00170 22200 1 0 7740007900 11850 00170 22200 1 0 84500998771

20000 25000 00790 22200 1 0 3970010630 11830 00790 25500 1 0 7730009100 10000 01270 10200 1 0 4600017200 18600 01570 23300 1 0 5060018100 19600 01570 23300 1 0 48050998771

12700 13500 01630 25500 1 0 6560015000 16210 01630 25500 1 0 5600013370 14120 02000 25500 1 0 62000998771

11200 12000 02420 25500 1 0 7050014030 14850 02520 25500 1 0 5800015300 16300 03000 25000 1 0 5270009050 10180 03000 25000 1 0 7990011700 12800 03000 25000 1 0 6570013750 15800 04760 25500 1 0 51000998771

07760 10800 03300 25500 1 0 8000007900 12550 04000 25500 1 0 7134009870 14500 04500 25500 1 0 6070010000 15200 04760 25500 1 0 58200998771

08140 14400 04760 25500 1 0 6380007900 16200 05500 25500 1 0 5990012000 19700 06260 25500 1 0 4660007830 23000 08540 25500 1 0 4600012560 27560 09520 25500 1 0 35800998771

09740 26200 09520 25500 1 0 3980010200 26400 09520 25500 1 0 3900008830 26760 10000 25500 1 0 3980007770 28350 11000 25500 1 0 3900009200 31300 12000 25500 1 0 34700

(a) Continued


119891119903(GHz)

119882119903(cm) 119871

119903(cm) h (cm) 120576

119903m n

10300 33800 12810 25500 1 0 32000998771

12650 35000 12810 25500 1 0 2980010800 34000 12810 25500 1 0 31500

(b)


119891119888(GHz)

119877119888(cm) h (cm) 120576

119903m n

07400 01588 26500 1 1 6634007700 02350 45500 1 1 4945008200 01588 26500 1 1 6074009600 01588 26500 1 1 52240998771

10400 02350 45500 1 1 3750010700 01588 26500 1 1 4723011500 01588 26500 1 1 4425012700 00794 25900 1 1 4070020000 02350 45500 1 1 2003029900 02350 45500 1 1 13600998771

34930 01588 25000 1 1 1570034930 03175 25000 1 1 1510038000 01524 24900 1 1 1443039750 02350 45500 1 1 1030048500 03180 25200 1 1 1099049500 02350 45500 1 1 0825050000 01590 23200 1 1 1128068000 00800 23200 1 1 0835068000 01590 23200 1 1 08290998771

68000 03180 23200 1 1 08150(c)


119891119905(GHz)

119878119905(cm) h (cm) 120576

119903m n

41000 00700 105000 1 0 15190998771

41000 00700 105000 1 1 2637041000 00700 105000 2 0 2995041000 00700 105000 2 1 3973041000 00700 105000 3 0 4439087000 00780 23200 1 0 1489087000 00780 23200 1 1 2596087000 00780 23200 2 0 2969087000 00780 23200 2 1 39680998771

87000 00780 23200 3 0 44430100000 01590 23200 1 0 12800100000 01590 23200 1 1 22420100000 01590 23200 2 0 25500100000 01590 23200 2 1 34000100000 01590 23200 3 0 38240998771998771

Testing patterns




119882119903(cm) 119871

119903(cm)

119891119903 (GHz) ℎ (cm) 120576119903

m n23100 03175 23300 1 0 57000 3800028900 03175 23300 1 0 45500 3050042400 03175 23300 1 0 29500 1950058400 03175 23300 1 0 19500 1300068000 03175 23300 1 0 17000998771 11000998771

77000 03175 23300 1 0 14000 0900082700 03175 23300 1 0 12000 0800091400 03175 23300 1 0 10500 0700047300 09525 23300 1 0 17000 1100078700 01524 23300 1 0 17000 1100022280 01524 25000 1 0 41000 4140022000 01524 25000 1 0 68580998771 41400998771

21810 01524 25000 1 0 10800 4140077400 00170 22200 1 0 08500 1290084500 00170 22200 1 0 07900998771 11850998771

39700 00790 22200 1 0 20000 2500077300 00790 25500 1 0 10630 1183046000 01270 10200 1 0 09100 1000050600 01570 23300 1 0 17200 1860048050 01570 23300 1 0 18100998771 19600998771

65600 01630 25500 1 0 12700 1350056000 01630 25500 1 0 15000 1621062000 02000 25500 1 0 13370998771 14120998771

70500 02420 25500 1 0 11200 1200058000 02520 25500 1 0 14030 1485052700 03000 25000 1 0 15300 1630079900 03000 25000 1 0 09050 1018065700 03000 25000 1 0 11700 1280051000 04760 25500 1 0 13750998771 15800998771

80000 03300 25500 1 0 07760 1080071340 04000 25500 1 0 07900 1255060700 04500 25500 1 0 09870 1450058200 04760 25500 1 0 10000998771 15200998771

63800 04760 25500 1 0 08140 1440059900 05500 25500 1 0 07900 1620046600 06260 25500 1 0 12000 1970046000 08540 25500 1 0 07830 2300035800 09520 25500 1 0 12560998771 27560998771

39800 09520 25500 1 0 09740 2620039000 09520 25500 1 0 10200 2640039800 10000 25500 1 0 08830 2676039000 11000 25500 1 0 07770 2835034700 12000 25500 1 0 09200 3130032000 12810 25500 1 0 10300998771 33800998771

29800 12810 25500 1 0 12650 3500031500 12810 25500 1 0 10800 34000

(b)


119877119888(cm)

119891119888(GHz) h (cm) 120576

119903m n

66340 01588 26500 1 1 0740049450 02350 45500 1 1 0770060740 01588 26500 1 1 0820052240 01588 26500 1 1 09600998771

37500 02350 45500 1 1 1040047230 01588 26500 1 1 1070044250 01588 26500 1 1 1150040700 00794 25900 1 1 1270020030 02350 45500 1 1 2000013600 02350 45500 1 1 29900998771

15700 01588 25000 1 1 3493015100 03175 25000 1 1 3493014430 01524 24900 1 1 3800010300 02350 45500 1 1 3975010990 03180 25200 1 1 4850008250 02350 45500 1 1 4950011280 01590 23200 1 1 5000008350 00800 23200 1 1 6800008290 01590 23200 1 1 68000998771

08150 03180 23200 1 1 68000(c)


119878119905(cm)

119891119905(GHz) h (cm) 120576

119903m n

15190 00700 105000 1 0 41000998771

26370 00700 105000 1 1 4100029950 00700 105000 2 0 4100039730 00700 105000 2 1 4100044390 00700 105000 3 0 4100014890 00780 23200 1 0 8700025960 00780 23200 1 1 8700029690 00780 23200 2 0 8700039680 00780 23200 2 1 87000998771

44430 00780 23200 3 0 8700012800 01590 23200 1 0 10000022420 01590 23200 1 1 10000025500 01590 23200 2 0 10000034000 01590 23200 2 1 10000038240 01590 23200 3 0 100000998771998771

Testing patterns





119903119871119903120576119903ℎ 119898 119899] whereas the







5= 1means119898 =



5rdquo The



2) relative


4and 119909

5) The







11199092119909311990941199095119872] is of six-





119903)



119903)


(Total 46 patterns)


119903) 119909




119903)


119903) 119909





119903)


(Total 46 patterns)


119888)





119903) 119909


119903)






119888)



119905)





119903) 119909


119903)







119905)













y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119882119903(cm) 119871

119903(cm)

119891119903 (GHz) ℎ (cm) 120576119903

m n23100 03175 23300 1 0 57000 3800028900 03175 23300 1 0 45500 3050042400 03175 23300 1 0 29500 1950058400 03175 23300 1 0 19500 1300068000 03175 23300 1 0 17000998771 11000998771

77000 03175 23300 1 0 14000 0900082700 03175 23300 1 0 12000 0800091400 03175 23300 1 0 10500 0700047300 09525 23300 1 0 17000 1100078700 01524 23300 1 0 17000 1100022280 01524 25000 1 0 41000 4140022000 01524 25000 1 0 68580998771 41400998771

21810 01524 25000 1 0 10800 4140077400 00170 22200 1 0 08500 1290084500 00170 22200 1 0 07900998771 11850998771

39700 00790 22200 1 0 20000 2500077300 00790 25500 1 0 10630 1183046000 01270 10200 1 0 09100 1000050600 01570 23300 1 0 17200 1860048050 01570 23300 1 0 18100998771 19600998771

65600 01630 25500 1 0 12700 1350056000 01630 25500 1 0 15000 1621062000 02000 25500 1 0 13370998771 14120998771

70500 02420 25500 1 0 11200 1200058000 02520 25500 1 0 14030 1485052700 03000 25000 1 0 15300 1630079900 03000 25000 1 0 09050 1018065700 03000 25000 1 0 11700 1280051000 04760 25500 1 0 13750998771 15800998771

80000 03300 25500 1 0 07760 1080071340 04000 25500 1 0 07900 1255060700 04500 25500 1 0 09870 1450058200 04760 25500 1 0 10000998771 15200998771

63800 04760 25500 1 0 08140 1440059900 05500 25500 1 0 07900 1620046600 06260 25500 1 0 12000 1970046000 08540 25500 1 0 07830 2300035800 09520 25500 1 0 12560998771 27560998771

39800 09520 25500 1 0 09740 2620039000 09520 25500 1 0 10200 2640039800 10000 25500 1 0 08830 2676039000 11000 25500 1 0 07770 2835034700 12000 25500 1 0 09200 3130032000 12810 25500 1 0 10300998771 33800998771

29800 12810 25500 1 0 12650 3500031500 12810 25500 1 0 10800 34000

(b)


119877119888(cm)

119891119888(GHz) h (cm) 120576

119903m n

66340 01588 26500 1 1 0740049450 02350 45500 1 1 0770060740 01588 26500 1 1 0820052240 01588 26500 1 1 09600998771

37500 02350 45500 1 1 1040047230 01588 26500 1 1 1070044250 01588 26500 1 1 1150040700 00794 25900 1 1 1270020030 02350 45500 1 1 2000013600 02350 45500 1 1 29900998771

15700 01588 25000 1 1 3493015100 03175 25000 1 1 3493014430 01524 24900 1 1 3800010300 02350 45500 1 1 3975010990 03180 25200 1 1 4850008250 02350 45500 1 1 4950011280 01590 23200 1 1 5000008350 00800 23200 1 1 6800008290 01590 23200 1 1 68000998771

08150 03180 23200 1 1 68000(c)


119878119905(cm)

119891119905(GHz) h (cm) 120576

119903m n

15190 00700 105000 1 0 41000998771

26370 00700 105000 1 1 4100029950 00700 105000 2 0 4100039730 00700 105000 2 1 4100044390 00700 105000 3 0 4100014890 00780 23200 1 0 8700025960 00780 23200 1 1 8700029690 00780 23200 2 0 8700039680 00780 23200 2 1 87000998771

44430 00780 23200 3 0 8700012800 01590 23200 1 0 10000022420 01590 23200 1 1 10000025500 01590 23200 2 0 10000034000 01590 23200 2 1 10000038240 01590 23200 3 0 100000998771998771

Testing patterns





119903119871119903120576119903ℎ 119898 119899] whereas the







5= 1means119898 =



5rdquo The



2) relative


4and 119909

5) The







11199092119909311990941199095119872] is of six-





119903)



119903)


(Total 46 patterns)


119903) 119909




119903)


119903) 119909





119903)


(Total 46 patterns)


119888)





119903) 119909


119903)






119888)



119905)





119903) 119909


119903)







119905)













y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119903119871119903120576119903ℎ 119898 119899] whereas the







5= 1means119898 =



5rdquo The



2) relative


4and 119909

5) The







11199092119909311990941199095119872] is of six-





119903)



119903)


(Total 46 patterns)


119903) 119909




119903)


119903) 119909





119903)


(Total 46 patterns)


119888)





119903) 119909


119903)






119888)



119905)





119903) 119909


119903)







119905)













y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119903)



119903)


(Total 46 patterns)


119903) 119909




119903)


119903) 119909





119903)


(Total 46 patterns)


119888)





119903) 119909


119903)






119888)



119905)





119903) 119909


119903)







119905)













y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










y

b

Exp

Exp

Exp

Exp

Exp

w1

w2

wi

wMminus1

wM

times


2

212059021


2

212059022


2

21205902Mminus1


2

21205902i


21205902M

sum



Abso

lute

erro

r

656

555

454

353

252

151

050






Abso

lute

erro

r



000900080007000600050004000300020001




5 Conclusion












References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















References





































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article A Generalized ANN Model for Analyzing and...

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Transcript of Research Article A Generalized ANN Model for Analyzing and...