Choudhury, Swati

Pal, Sankar K

Sushmita, Mitra

IACS Institutional Repository

InJuviJ.Phys 75B (3), 247-249 (2001)U P  Ban iniemational journalModes of radiowave propagation : neural learningS w ati C h o u d h u ry , S u sh m ila  M itra  and  S an k ar K  Pal* M achine Intelligence Unit, Indian Statistical Institute, KoHcala-700 035, India U-mail snnkan^ jsica l ac inA b strac t M odes o l'rad io w av c  p ropagation  depends upon the radiorcfractivity  gradient o f  the m edium  through w hich it is propagating. Radiosonde data  collected  from  D um -D um  A irport, K olkata is analysed to calculate the radiorcfractivity gradient. The estim ated value can be divided into four categories nam ely  siib refraction , norm al refraction , supcrrefraction and ducting  In this paper, we have used a m ultilayer pciceptron (M L P) to learn the relationship  betw een atm ospheric param eters (7', P. e etc) and the output classes w hich helps in predicting  the m ode ol radiow ave p ropagation  Studies have been m ade using dilTcrent network topologies The results are p icscnted  for various num ber o f  hidden lin ers and nodes, using  d ifferent size o f  tra in ing  sets The trained network is used for subsequent rule generation.K eyw ords E lcctrom agncticw ave propagation, radiorcfractivity , m ultilayer perceptron (M LP)PAC S N o s . 4 L 2 0 J b ,  84 35 +11. I n t r o d u c t io nI rop()spheric ra d io w a v e  p ro p a g a tio n  is o n e  o f  th e  im p o rtan t aieas in the  fie ld  o f  e le c tro n ic  c o m m u n ic a tio n  sc ien ces. R ad io refractiv ity  N(T, P, e, h) an d  the  ra d io rc fra c tiv ity  L’radicnt AN a re  th e  k ey  p a ra m e te rs  to  e s tim a te  th e  m o d e  o f  radiowave p ro p a g a tio n , w h e re  T, P, e an d  h d e n o te  the  tem perature, p re s su re , v a p o u r p re s su re  an d  h e ig h t re sp ec tiv e ly  (of the tro p o sp h e r ic  re g io n ) . T h e  ra d io rc fra c tiv ity  g ra d ie n t can be d iv id e d  in to  fo u r  b a s ic  in te rv a ls  d e fin ed  as (I) 0 > AA  ^> -40, ( i i)  - 4 0  ^  A/V >  7 5 , ( i ii)  - 7 5  > AiV ;> 157 and (iv) AN < -  157.If  th e  e s tim a te d  AN is ly in g  in in te rv a l I th e  m o d e  o f  radiow ave p ro p a g a tio n  is sa id  to  be  suhre/racted. U n d e r th is  mode o f  p ro p a g a tio n  th e  s ig n a l level a t th e  re c e iv e r  site  experiences a  g re a te r  lo ss  a n d  so m e tim e s  it b eco m e s  loo  small to u se . T h e  m o d e  o f  ra d io w a v e  p ro p a g a tio n  is sa id  to  be normal i f  AN lie s  in in te rv a l 2 . In th e  p re se n c e  o f  n o rm al refractive c o n d it io n  ra d io w a v e  tra v e ls  b e tw een  a  p a ir  o f  liansm itting  an d  re c e iv in g  a n te n n a s  w ith  m o d e ra te  p a th  loss. On the o th e r  h a n d , i f  AN lies  in th e  in te rv a l 3 o r  4 th e  m o d e  of rad io w av e  p ro p a g a tio n  is te rm e d  as  superrefraction o r  l^uain^  re s p e c tiv e ly . O n  th e  o c c u rre n c e  o f  su p c re fra c tio n  and d u c t c o n d it io n  th e  ra d io w a v e  b e tw e e n  a p a ir  o f  transm itting a n d  re c e iv in g  a n te n n a s  p ro p a g a te  w ith  leas tp a th  loss w h ich , in tu rn , im p ro v es the  re lia b ility  an d  th e  p e rfo m ia n c c  o f  the system .A rtific ia l n eu ra l n e tw o rk s  (A N M s) a tte m p t to  re p lic a te  th e  computational p o w er (lo w -lev e l a rith m e tic  p ro c e s s in g  ab ility )  o f  b io lo g ica l n eu ra l n e tw o rk s  and , th e reb y , h o p efu lly  en d o w  m ach in es w ith  some* o f  th e  (h ig h e r-le v e l)  cognitive abilities th a t b io lo g ica l o rg an ism s p o sse ss  (d u e  in p a rt, p e rh ap s , to  th e ir low -level co m p u ta tio n a l p ro w ess) . H o w ev er, an  im p ed im en t to  a m ore  w id esp read  a c c e p ta n c e  o f  A N N s is th e  ab sen ce  o f  a cap ab ility  to  e x p la in  to  th e  u se r, in a  hum : n -co m p reh en sib le  fo rm , h o w  the  n e tw o rk  a rr iv e s  a t a p a rtic u la r  d ec is io n . R ecen tly  th e re  h a s  b een  w id e sp re a d  ac tiv ity  a im ed  at re d re ss in g  th is  s itu a tio n , b y  e x tra c tin g  th e  e m b e d d e d  k n o w led g e  in tra in e d  A N N s in th e  fo rm  o f  sy m b o lic  ru les  [ 1,2]. T h is  se rv es  to  id en tify  th e  a ttr ib u te s  th a t c ith e r ind iv id u ally  o r in a co m b in a tio n , a re  th e  m o s t s ig n ifican t d e te rm in an ts  o f  th e  d ec is io n  o r  c la s s if ic a tio n .In o u r  p re sen t in v es tig a tio n , w e h av e  used  a  m u lti la y e r p e rc e p tro n  (M L P ) an d  its fu zzy  v e rs io n  (fu z z y  M L P ) to  le a m  the  re la tio n sh ip  b e tw een  th e  inpu t p a ra m e te rs  T, P, e, h, Tx, e,, hs, N and  th e  o u tp u t c la ss  AN. T h e  fo u r in te rv a ls  fo r AN a re  m ap p ed  to  th ree  o u tp u t c la s se s , c lu b b in g  in te rv a ls  3 , 4 to  c lass  3 on ly . T h is  h e lp s  us in p re d ic tin g  th e  m o d e  o f  rad io w av e  p ro p ag a tio n  from  th e  m easu re  o f  T, P , e o f  th e‘^)m.-iponding Author © 2001 lACS248 Swati Choudhury, Sushmita Miira and Sankar K Paltro p o sp h e r ic  re g io n  a t a  p a r t ic u la r  h e ig h t h. S tu d ie s  hav e  b e e n  m a d e  u s in g  d if fe re n t n e tw o rk  to p o lo g ie s . T h e  lea rn in g  ra te  is g ra d u a lly  d e c re a se d . E x te n s iv e  re su lts  a re  p re se n te d  fo r  v a rio u s  n u m b e rs  o f  h id d e n  lay ers  and  n o d es , u s in g  d if fe re n t s iz e s  o f  tr a in in g  se ts. T h e  tra in e d  n e tw o rk  is u sed  fo r  su b s e q u e n t ru le  g e n e ra tio n .2 . R tt le  g e n e r a t io n  a n d  fu z z y  IM LP In g e n e ra l, th e  p rim a ry  inp u t to  a c o n n e c tio n is t ru le  g en e ra tio n  a lg o r ith m  is a re p re se n ta tio n  o f  th e  tra in e d  A N N , in  te rm s o f  its n o d e s  an d  links, an d  so m e tim e s  th e  d a ta  se t. O n e  in te rp re ts  o n e  o r  m o re  h id d e n  an d  o u tp u t un its  in to  ru les , w h ich  m ay  la te r  be c o m b in e d  an d  s im p lif ie d  to  a rr iv e  a t a  m o re  c o m p re h e n s ib le  ru le  set. T h e se  ru le s  can  a lso  p ro v id e  n ew  in s ig h ts  in to  th e  a p p lic a tio n  d o m ain . T h e  use o f  A N N  h e lp s  in ( i)  in c o rp o ra t in g  p a ra l le l ism  an d  (ii)  ta c k lin g  o p tim iz a tio n  p ro b le m s  in the  d a ta  d o m a in . F u zzy  n eu ra l n e tw o rk s  [ I ] can  be u sed  fo r the  sam e  p u rp o se , an d  can  a lso  h a n d le  u n c e rta in ty  at v a rio u s  s tag es .The fu z z y  M L P  [1] in c o rp o ra te s  fu zz in ess  at th e  in p u t a n d  o u tp u t lev e ls  o f  th e  M LF^ an d  is c a p a b le  o f  h a n d lin g  e x a c t (n u m e r ic a l)  a n d /o r  in e x a c t ( lin g u is tic )  fo rm s o f  in p u t d a ta . A n y  in p u t fea tu re  v a lu e  is d e sc r ib e d  in te rm s  o f  so m e  c o m b in a tio n  o f  m e m b e rsh ip  v a lu es  in th e  lin g u is tic  p ro p e r ty  se ts  low (L), medium (A /) an d  hi^h {H). D u rin g  tra in in g , th e  w e ig h ts  a re  u p d a te d  by  b a c k p ro p a g a tin g  e rro rs .A n rt-d im en sio n a l p a tte rn  F\ ^  |F , i ,  F,2, . ., F,„] is re p re se n te d  as  a  3A ?-dim ensional v e c to r-  l//low(/",l) {F ,) ....... (/^m) ( ^ ) l ,  ( 1 )Table I. Recognition score for Ml.P with J0"/o Irjiming setw h ere  th e  / /  v a lu es  in d ic a te  th e  m e m b e rsh ip  fu n c lio n s o f the c o rre sp o n d in g  lin g u is tic  ;r-sets /ow , medium a n d  high along each  fe a tu re  ax is .T h e  n e tw o rk  is tra in e d  u s in g  b a c k p ro p a g a tio n  and the c o n n e c tio n  w e ig h ts  p ru n e d  w ith  w e ig h t d e cay . T h e  trained n e tw o rk  is n e x t a n a ly z e d  fo r ru le  g e n e ra tio n . T h e  strong p a th s  fro m  th e  o u tp u t n o d e s  (c la s se s )  to  th e  in p u t (features)i.e ., th o se  p a th s  h a v in g  la rg e  m a g n itu d e , a re  ex trac ted . We c o n s id e r  b o th  p o s itiv e  an d  n e g a tiv e  lin k  w e ig h ts  in the p ro c e ss . T h e  a n te c e d e n ts  o f  th e  ru le s  a re  in te rm s o f the lin g u is tic  v a lu es  a t  th e  in p u t to  w h ich  th e  p a th  can be traced .3. ResultsT h e  a lg o rith m  w as im p le m e n te d  on  th e  rad io so n d e  data o f  th e  p r e - m o n s o o n  s e a s o n  c o l l e c t e d  f r o m  Indian M e te o ro lo g ic a l D e p a rtm e n t, K o lk a ta  an d  c o n s is te d  o f 360 p a tte rn s  p o in ts . T h e re  w ere  e ig h t fe a tu re s  co rresp o n d in g  to te m p e ra tu re  (7 ) , p re s su re  (P ) , v a p o u r  p re s su re  (e ) , height (/;), su rfa c e  te m p e ra tu re  (T^), su rfa c e  v a p o u r  p re s su re  height a t 1000 m b  p re s su re  level (/j.v) an d  ra d io re fra c tiv ity  (A )^ The th ree  o u tp u t c la s se s  re fe r  to  su b -re fra c tio n , n o rm a l refraction a n d  su p e r-re fra c tio n  an d  d u c tin g . T h e  in p u t fea tu res  were sp lit in to  2 4  c o m p o n e n ts  in th e  lin g u is tic  sp a c e  o f  eq. (1)V a rio u s  th re e - la y e re d  n e tw o rk s  (M L P  an d  fu zzy  MLP) w ere  used  w ith  d if fe re n t n u m b e rs  o f  h id d e n  nodes ami tra in in g  se ts. T a b le s  1 an d  2 p ro v id e  sa m p le  classification re su lts  u s in g  th e  M L P  w ith  3 0 %  tra in in g  se t an d  the fuzzv M L P  w ith  4 0 %  tra in in g  se t re sp e c tiv e ly .N o o f  h idden  nodesT rain ing  set Testing set M eansquareerrorNoo fIterations( 'la ssnetC lassnet1 2 3 1 2 32 96 77 86 21 84 34 88 79 89 61 76.71 65 45 80 56 0 0701 23013 100,00 85 71 98 72 86.92 85 71 74 66 66 82 77 46 0 0654 22514 93 33 85 71 98 72 90 65 90 91 70 55 63 64 78 31 0 0561 23015 100 00 92 86 98 72 93 46 87 01 73 29 60 00 77 18 0 0439 22516 100 00 100 00 98 72 97 20 87 66 69 86 61 82 76 34 0 0324 2251T a b le  2. R ecognition  score for fiii^/v M LP with 40%  tra in ing  setN o o f T rain ing  set Tc.sting set M ean Nohidden C lass C lass _ square o fnodes 1 2 3 net 1 2 3 net erro r Iterations2 93 55 91 38 86.36 91 55 75.97 60.27 50 91 65 63 0 .0630 19013 96 77 87 93 81 82 90 85 80 52 63 01 54 55 69,30 0 0753 19514 100 00 100 00 86 36 97 89 83 12 71 23 52 73 73 52 0 .0417 19515 100 00 98 28 90 91 97 89 85 06 67 81 50 91 72 68 0.0314 19516 100 00 100 00 90 91 98.59 78 57 66 44 54 55 69 86 0 0246 19517 100 00 100 00 90 91 98,59 80.52 71 23 58 18 73 24 0 0231 19518 100 00 100.00 95 45 99 30 77.92 69 18 52 73 70.42 0 0238 19519 100 00 100 00 95 50 99 30 81 17 70.55 49  09 71 83 0 0202 195110 100 00 100 00 90.91 98 59 77 92 74 66 50.91 72 39 0 0 1 7 7 1951II 100 00 100 00 90,91 98 59 81 17 71.92 54 55 73 .24 0.0190 195112 100 00 100 00 90 91 98,59 84 92 70 55 52.73 73 80 0.0195 1951Modes o f radiowave propagation : neural learning 249Sample rules extracted from a pruned fuzzy MLP, with four hidden nodes, for class I (sub-refractive) are as follows.Positive : If c is high, H im  is high or medium, T is low, T, is low,Negative : H  is not high.4. ConclusionsWe have demonstrated classification and rule generation for radio-sonde data using an MLP and fuzzy MLP. The networks learnt the relationship between the input parameters T /J, e, h and the output class AA^ . Studies have been madeusing different network topologies. It is expected that this type of neural network based model will be advantageous to the scientists and engineers working in the area of remote sensing, atmospheric science, radio communication and various other related fields.References[I] S K Pal and S Mitra Neuro^fuzzy Pattern Recognition Methods in Soft Computing (New York . John Wiley) (1999)f2| A B Tickle, R Andrews, M Goica and J Dicderich IEEE Transactions on Neural Networks 9 1057 (1998)

Modes of Radiowave Propagation: Neural Learning

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/6313/1/Modes%20of%20Radiowave%20Propagation%20Neural%20Learning_Swati%20Choudhury.pdf

Modes of Radiowave Propagation: Neural Learning

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