Reconstruction of the roadway coverage parameters from radar probing measurements

Transcription

1 Surface Effects and Contact Mechancs X 37 Reconstructon of the roadway coverage parameters from radar probng measurements A. Kranyukov Faculty of Computer Scence and Electroncs, Transport and Telecommuncaton Insttute, Latva Abstract Ths work has focused on the development of an approach to the soluton of the structural nverse problem of radar subsurface probng of roadway coverage. To solve the nverse problem n the frequency doman by the method of comparson, teratve procedure s used for the am of functon mnmzaton. The drect problem of radar subsurface probng s based on the lnear system response functons for the radar antenna system and on the equatons for wave propagaton n horzontally multlayered roadway coverage. The nverse problem has been nvestgated numercally. A genetc algorthm s used to nvestgate the global mnmum of the am functon. Statstcal assessment of the reconstructon accuracy under varous condtons has been done. The am functon of the nverse problem of radar probng of roadway coverage was nvestgated. Keywords: radar probng measurements, reconstructon of the roadway coverage, nverse problem of radar probng, genetc algorthm. 1 Introducton Radar subsurface probng s wdely used for performng scentfc and practcal research. It allows one to fnd the hdden objects. Roadway coverage s a complex mult-layered constructon. It s well known that n dfferent seasons of the year and n dfferent envronmental condtons the preservaton of road cover depends not only on usage but also on dfferent clmate-related factors. As a result dfferent processes take place wthn roadway coverage: the appearance of vods, changes n dampness of the sol, changes n the ablty of the sol to flter water, etc. Tmely dentfcaton of these processes allows one to make a tmely WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne) do: /secm110041

2 38 Surface Effects and Contact Mechancs X decson about the necessary actons for optmzaton of explotaton, upkeep and reconstructon of the road cover [1]. Nowadays to research the nner structure of roadways subsurface radar probng methods are wdely used [2, 3]. In spte of substantal achevements n research and development of the radar probng methods for roadway coverage, there are some problems to mprove the nterpretaton of radar probng data. The effcency of the radar probng heavly depends on the algorthms and the methods of sgnal processng, reflected from the roadway coverage. Tradtonal nterpretaton methods of the roadways subsurface radar probng results do not provde the requred precson and effectveness of roadway montorng. Subsurface radar profles provde only a qualtatve pcture of the roadway condton. Only an experenced specalst can restore the approxmate structure of the roadway coverage under nvestgaton. Ths s not enough for radar montorng of roadway coverage, snce the radar probng of roadways has specfc features. Ensurng hgh relablty and effcency of roadway coverage radar montorng s a challenge. It s necessary to perform reconstructon of electro-physcal parameters of roadway coverage wth detecton and dentfcaton of nner zones and objects. 2 Inverse problem of roadway coverage radar probng Reconstructon of the geometrcal and electrcal parameters can be performed by usng the secondary processng of radar probng sgnals, dentfcaton and object recognton. These problems can be solved by usng varous computatonal methods and algorthms. However, the appled computatonal methods and algorthms have to provde the requred accuracy of the results of radar probng nterpretaton of the roadway coverage and the dagnoss of the nternal structural elements condton. Reconstructon of the geometrcal and electro-physcal characterstcs of the object under exploraton based on the radar measurements results s an nverse problem of radar probng, whch s, n general, ll-posed and not unque. To solve ths problem, dfferent methods of comparng the drect soluton of an assumed subsurface structure wth the measured data of radar probng are usually appled. The soluton of the nverse problem by the comparson method can be found both n the tme and the frequency doman. An nverse problem for the radar probng of roadway coverage s usually a structural nverse problem. Pror nformaton s used n order to solve structural nverse problem. Pror nformaton can be obtaned from the approprate road documentaton. Pror nformaton allows us to defne the roadway coverage structure and to create ts electrcal model, whch s then used for solvng the drect problem of the radar probng. In ths work the nverse problem of roadway coverage radar probng s solved n the frequency doman usng the vector of parameters P p1, p2,..., pn, p - electro-physcal parameters of the model - layer. Electro-physcal parameters of each layer are: thckness h, where n - the number of model layers and WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

3 Surface Effects and Contact Mechancs X 39 conductvty and relatve delectrc constant, and the range of possble values of these parameters [4]. When solvng the nverse problem of subsurface probng t s very mportant to ratonally select the type of nformatve characterstcs, the quantty and the area of the orgnal data n order to calculate the am functon. Whle solvng the nverse problem of radar probng n the frequency doman by the method of comparson, the am functon looks the followng way: B e, P - B t, PM 1 nmax nmax 0 2, (1) where nmax s ndex of the spectral component wth frequency fmax; Be, P s value of nformatve characterstcs, t s derved from the sgnal reflected by roadway coverage, whch s characterzed by vector P ; Bt, PM s calculated theoretcal value of the nformatve characterstcs for solvng the drect problem of subsurface radar probng. To calculate Bt, P the vector M of parameters PM s chosen, t belongs to the set of allowed values of parameters PPOS. The soluton of the nverse problem s the vector of parameters PM. In order to fnd vector PM, one has to fnd the global mnmum of the am functon. Modular or complex values of the reflected sgnal s spectral densty or coeffcent of medum reflecton can be used as an nformatve characterstc. In ths work the reflected sgnal s complex spectral densty S e, P and modular spectral densty S e, P are used as nformatve characterstc Be. The am functon depends on nformatve characterstc and a great number of ts arguments n a complcated way. Along wth a global mnmum am functon has a great number of local mnmums. Inverse problem has been nvestgated numercally by usng electromagnetc model of roadway coverage and drect problem model of subsurface radar probng. Iteratve procedure was chosen for the search of global mnmum of am functon by usng genetc algorthm [4]. 3 Models and condtons for nverse problem solvng 3.1 Drect problem model of subsurface radar probng A typcal subsurface radar system has three man components: a transmtter and a recever are drectly connected to ther antennas, and a control unt wth a dsplay [3]. The transmttng antenna radates a short hgh-frequency WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

4 40 Surface Effects and Contact Mechancs X electromagnetc (EM) pulse nto the nspected medum, where t s refracted, dffracted and reflected prmarly as t encounters changes n delectrc permttvty and electrc conductvty. Waves that are reflected back by the probed medum nduce sgnals n the recevng antenna, and are recorded as dgtzed sgnals for dsplay and further analyss. Accordng to that, the sgnal formng channel for subsurface radar probng n frequency doman may be presented as t s shown n fg. 1 [4]. S ex ( ) K ANT ( ) R refl ( ) S L ( ) K FW ( ) Fgure 1: Sgnal formng channel for subsurface radar probng n frequency doman. K ANT ( ) s a complex transfer functon of the antenna system, R refl ( ) s a reflecton coeffcent of the object under nspecton, and K FW ( ) There s a complex transfer functon of the antennas drectly coupled n the EM feld; S ex ( ) s the spectrum of the sgnal, whch s used for mpact exctaton of the transmttng antenna, U L ( ) s the spectrum of the sgnal across the load resstance of the recevng antenna. As a result, complex transfer functon of radar subsurface probng model may be represented n the followng way: K RAD ( ) S L ( ) S ex ( ) K FW ( ) K ANT ( ) R refl ( ). (2) It depends on the condtons of the subsurface radar probng, as well as on the geometry of the antennas locaton. To get the expresson K RAD ( ) the followng features of the subsurface radar probng were taken nto account: both radar antennas are lnear vbrators; the radar antennas are located n the ar and are parallel to each other; the heght of antennas locaton H over upper medum boundary s suffcently small ( H 0 ). WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

5 Surface Effects and Contact Mechancs X Then complex transfer functon of the antenna system 41 K ANT ( ) may be presented as: K ANT ( ) j 30 k0 L 2eff ( ) RL d 2 (2h2 ) 2 [ RL Z n ( )]2 2 ( ) cos 0 2 ( ) sn ( ) cos 0 where: j 1 s mage unty; (3), l s half length of lnear antennas; d s the dstance between the radar antennas; k0 c s the wave number for free space; 2 f s the angular frequency of monochromatc wave wth lner f ; 0 arctg (d / 2h2 ) s the ncdent angle; h2 and 2 are thckness and complex permttvty of the nspected layer; Z n ( ) s nput mpedance of radar antennas; RL s load resstor of the recevng antenna; L eff ( ) s effectve frequency antennas length. L eff ( ) s expressed as 2 1 cos k L l, L eff ( ) sn k l k L (4) L where: l s half length of lnear antennas; k L s the complex wave s number[5], whch depends on antennas dameter a, antennas hgh H over upper boundary of nspected medum, and complex refracton coeffcent n 2. In accordance wth [4], complex transfer functon of the antennas drectly coupled feld s expressed as K FW ( ) j 30k0 L 2eff ( ) RL ( 2 ( ) 1)d [ RL Z n ( )]2 jk 2 ( )e 0 2 ( )d (5) e jk0d. Reflecton coeffcent R refl ( ) s expressed as a complex reflecton coeffcent for oblque ncdence of plane wave on the upper boundary of the nspected medum. Equatons (2), (3) and (5) have been used for further drect problem soluton of roadway coverage radar subsurface probng n the frequency doman n order to calculate S L ( ). WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

6 42 Surface Effects and Contact Mechancs X 3.2 Electromagnetc propertes modellng of roadway coverage The electro-physcal parameters of the roadway coverage layers were modeled takng nto account that the roadway coverage layers are composed of such materals as asphalt, concrete, crushed stone, crushed slag, sand and others. The number of the layers can vary but the electro-physcal characterstcs of some layers can be very smlar or even equal. Roadway coverage layers are placed between two sem-nfnte spaces where the upper sem-nfnte space s ar and the lower one s subgrade. Two models of the roadway were used n carryng out ths research: double-layer and three-layer models. Electro-physcal parameters of partal double-layer model medum are presented n table 1. Table 1: Electro-physcal parameters of partal model medum. Partal medum of model Ar Frst layer Second layer Lower sem-nfnte space (subgrade) Electro-physcal parameters of partal model medum, s/m h, m The characterstc features of solvng the nverse problem by usng the genetc algorthm Searchng for the global mnmum by means of the genetc algorthm takes a lot of tme and may even turn out to be mpossble. It has been suggested, that genetc algorthm s used to study such value of the am functon, whch s not more the value of threshold. Therefore, value of threshold has a substantal nfluence on the nverse problem soluton whle usng genetc algorthm. Use of great value of threshold does not allow one to reconstruct the electro-physcal parameters of roadway coverage wth enough accuracy. Dmnshng threshold ncreases the tme of nverse problem decson substantally. The am functon s a power parameter, because value of threshold may be calculated by usng mean power of spectral consttuents of S e, P, used for the calculaton of am functon. If the number of spectral components s nmax the average mean power of those spectral components S e, P s expected to be as follows: Pav 1 nmax S, P nmax 0 e 2, WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne) (6)

7 Surface Effects and Contact Mechancs X 43 but the value of α s set as Pav, K (7) where К s a dmensonless coeffcent, set by the user. Nevertheless, the value of К must be chosen so that the specfed reconstructon accuracy of roadway coverage parameters s taken nto account. Values of the electro-physcal parameters of the layers of the road coverage can vary n the lmts of up to 1.5 tmes. Therefore for the formaton of chromosome populaton of genetc algorthm the possble values range of every electro-physcal parameter s from 0,75v to 1,25v, where v s the value of each specfc parameter (see table 1). The range of search for each parameter was 50% of ts model value. 4 Results of roadway coverage parameters reconstructon For the nvestgaton of the nverse problem algorthm that had been consdered above, software applcaton has been developed, whch s able: to model the structure and the electro-physcal parameters of the road coverage; to fnd the soluton of the drect problem of the radar probng; to fnd the soluton of the nverse problem of the radar probng by usng the genetc algorthm; to nvestgate the am functons, etc. All the results mentoned below have been obtaned after applyng ths software. The model sgnal on the output of the recevng antenna, whch was obtaned wth the help of equatons (2)-(5) and parameters, s presented n table 1. The probng sgnal was generated by the mpact exctaton of the transmttng antenna for H=0,01m, l=0,5m and d=0,5m and was a decayng harmonc oscllaton wth the central frequency 100 MHz. Impact exctaton pulse of the transmttng antenna was trangular pulse, duraton of whch was equal to 2 ns. Almost the whole energy (99.9%) of the sgnal, reflected from the model medum, s located wthn the band MHz. The soluton of the nverse problem s vector PM, t was further used to fnd the relatve error of reconstructon for each of roadway coverage parameters. In order to defne the optmal condtons for the generc algorthm to be used to solve the nverse problem of radar subsurface probng we tred to fnd out how these values were nfluenced by the followng factors: the coeffcent K, defnng the threshold of the acceptable soluton ; frequency range of the reflected sgnal spectrum used, lmted by ts maxmal frequency fmax. To obtan statstcal assessment solutons of the nverse problem about 100 examples were used. The value of K n our calculatons was changed wthn the range of 100 to 5000 wth fxed fmax = 500 MHz. WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

8 44 Surface Effects and Contact Mechancs X Fgures 2 and 3 show nfluence coeffcent K on the relatve error (upper fgure) and the relatve root-mean-square (RMS) error (lower fgure) of reconstructon of electro-physcal parameters of the frst layer. Fgure 2: Fgure 3: Influence of value K on accuracy reconstructon of the frst layer parameters by usng S e, P. Influence of value K on accuracy reconstructon of the frst layer parameters by usng S e, P. When usng S e than when usng, P the relatve errors of reconstructon and h are less S, P, and are, n fact, close to 0. When K 1000 the e 1 1 relatve errors of reconstructon 1 and h1 slghtly decrease. Dependences of relatve RMS error for the frst layer parameters show that the ncrease of K wll result n a smaller range of possble values of 1 and h1. The range of possble values of 1 remans unchanged wth the ncrease of К; therefore the values of relatve RMS error for 1 are stable and sgnfcant. For ths reason dependences of 1 have a chaotc character. WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

9 Surface Effects and Contact Mechancs X 45 Influence of value K on relatve RMS errors of the second layer parameters reconstructon s smlar to those of the frst layer. The dfference s n hgher values of relatve RMS errors for 2 and h2. Correspondngly the relatve error for 2 and h2 s hgher, as t s shown on fgures 4 and 5, although they decrease wth the ncrease of K when usng S e, P (fg. 5). When usng S e, P the relatve errors for 2 and h2 are less than 1% already when К = 1000 (fg. 4). Dependence of 2 has also chaotc character as RMS error for 2 s ndependent of К. Fgure 4: Influence of value K on accuracy reconstructon of secondary layer parameters by usng S e Fgure 5:, P. Influence of value K on accuracy reconstructon of second layer parameters by usng S e, P. Influence of value K on accuracy reconstructon of lower sem-nfnte space (subgrade) parameters s shown on fgures 6 and 7. Increase of value К leads to decrease of RMS errors for 3 and 3 and therefore to decrease of relatve errors of reconstructon. When К s more than 1000 the relatve errors hardly change. Values of 3 and h3 are reconstructed wth relatve error less than 1% already when К = The dependence of the am functon on electro-physcal parameters of the roadway coverage has been nvestgated. In order to demonstrate the dependence of the am functon on electro-physcal parameters n a three-dmensonal form two partal electro-physcal parameters have been selected for calculatons of the am functon. To calculate the value of the theoretcal spectral densty S t, PM the values of two of the electro-physcal parameters of one of the roadway coverage layers have been changed, whle keepng the remanng 6 constant and equal to the model ones. The range of changes of the chosen WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

10 46 Surface Effects and Contact Mechancs X parameters has been symmetrcal to the model values and equal to them. Dependences of am functon on delectrc permttvty and ther thckness h1 are shown on fgures 8 and 9. Fgure 6: Fgure 7: 1 of the frst layers Influence of value K on accuracy reconstructon of lower subgrade parameters by usng S e, P. Influence of value K on accuracy reconstructon of lower sub grade parameters by usng S e, P. Fgure 8: Influence of delectrc permttvty 1 and thckness h1 of the frst layer on the am functon by usng S e, P. WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

11 Surface Effects and Contact Mechancs X 47 In the upper part of each fgure there s a three-dmensonal vew of the dependence of the am functon on two parameters calculated for f max =300 MHz, and levels of am functons are shown n the lower part of the fgures for three values of maxmal frequency f max =100, 300 and 500 MHz. The threshold value was used for the mnmal level. In all these dagrams the value was used for am functons, and was calculated usng K = Fgure 9: Influence of delectrc permttvty 1 and thckness h1 of the frst layer on the am functon by usng S e, P. The geometrc forms of the whte areas are ellpses (fg. 8 and fg. 9), but of dfferent szes. Comparatve analyss of these areas allows us to make the followng concluson: a. delectrc permttvty and thckness of layers heavly affect the values of am functons; b. calculaton of the am functons for f max 300 МHz ncreases the sze and compresson of the ellpses, whch means that n order to calculate am functons t s crucal, that c. f max s less than 300 МHz; am functon wth a complex spectral densty s more nformatve, because areas takng values less than are smaller n sze,.e. correspondng ranges of h1 and 1 on the dagrams for usng S e, P are less than those for usng S e, P ; d. e. values of am functon less than, are obtanable under multdrectonal changes of delectrc permttvty and thckness of the layers aganst the modelled values of the parameters of the layers, whch can lead to errors n parameters reconstructon of the probed medum; nfluence of the electrcal conductvty of the layers on the values of the am functons s neglgble. WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)

12 48 Surface Effects and Contact Mechancs X Optmal values of parameters and condtons of genetc algorthm use for searchng of global mnmum of аm functon are as follows: bnary codng alphabet of an estmated parameter; number of bt per parameter s 8; probablty of crossng over s 0,9; probablty of mutaton s 0,05; method of selecton s roulette; admtted number of populaton nto generaton wth the am of functonal means mprovement s 500. The coeffcent K should be equal to several thousands to reduce the relatve error of parameter reconstructon and the tme of solvng the nverse problem. However, the ncrease of coeffcent K ncreases the duraton of the nverse problem soluton. 5 Conclusons The man results are as follows: the relatve errors of parameter reconstructon do not exceed a few percent usng complex values of the reflected sgnal spectral consttuents; optmal parameters and condtons of genetc algorthm applcaton for solvng the nverse problem have been obtaned; results of the work can be used for detecton and dentfcaton of nner zones and objects of roadway coverage. Acknowledgements The paper s wrtten wth the fnancal assstance of European Socal Fund. Project Nr. 2009/0159/1DP/ /09/IPIA/VIAA/006 (The Support n Realsaton of the Doctoral Programme Telematcs and Logstcs of the Transport and Telecommuncaton Insttute) References [1] Haas R., Pavement Desgn and Management Gude, Transportaton Assocaton of Canada, Ottawa, Ontaro, , [2] Rexford M. Morey., Ground Penetratng Radar for Evaluatng Subsurface Condtons for Transportaton Facltes (Synthess of Hghway Practce). Natonal Academy Press, Washngton D.C, [3] Ground penetratng radar: theory and applcatons. Edtor Harry M. Jol. Elsever Scence, [4] Kranyukov A., Kutev V. Model-based results of nverse problem soluton for radar montorng of roadway coverage. Proc. of the Int. Conf. Modellng of Busness, Industral and Transport Systems, Rga, Latva. Rga: Transport and Telecommuncaton Insttute, pp , [5] Kng R.W.P., Smth G.S. Antennas n Matter. Fundamentals, Theory, and Applcatons. The MIT Press, WIT Transactons on Engneerng Scences, Vol 71, 2011 WIT Press ISSN (on-lne)