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Gömülü iletken cisimlerin elektromagnetik dalgalar yardımı ile zaman domeninde algılanması

Başlık çevirisi mevcut değil.

  1. Tez No: 75056
  2. Yazar: SELÇUK PAKER
  3. Danışmanlar: PROF. DR. BİNGÜL YAZGAN
  4. Tez Türü: Doktora
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1998
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Elektrik-Elektronik Mühendisliği Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 73

Özet

ÖZET GÖMÜLÜ İLETKEN CİSİMLERİN ELEKTROMAGNETİK DALGALAR YARDIMI İLE ZAMAN DOMENİNDE ALGILANMASI Geniş bandlı yüksek güçlü RF işaret kaynaklan ve yine geniş bandlı hassas alıcılardaki yapısal teknolojik gelişmeler gömülü cisimlerin algılanması için yeni yöntem ve uygulamaların geliştirilmesini kaçınılmaz kılmaktadır, ister sivil ister askeri amaçlar için olsun yeni algoritmalara gereksinim duyul maktadır. Yakın geçmişe kadar elektromagnetik dalgalar kullanılarak cisimlerin görüntülenmesi çoğunluk ile simetrik cisimler için frekans domeninde gerçekleştirilmiştir. Düşük kontrasta sahip cisimler için geliştirilen yöntemler sınırlı uygulama alanı bulmuşlardır. Diğer bir grup çalışmada ise radar temeline dayanan gecikme hesaplanmıştır. Elektromagnetik kaynakların gelişimi ile radar prensibi gömülü cisimlerin deteksiyonuna uygulanabilmiştir. Tezin birinci bölümünde konu açıklanarak problemin geometrik yapısı tanıtılmış, çözüm için izlenecek yol ve uygulanacak kısıtlamalar belirtilmiştir. Gerçekleştirilmiş çalışmalar kısaca özetlenmiştir, ikinci bölümde zaman domeninde gömülü cisimden saçılan dalganın hesap edilmesi için kul lanılacak sayısal hesaplama yöntemi özetlenerek bu yöntemde problemle ilgili yapılması gerekli iyileştirmeler belirtilmiştir. Tezin üçüncü bölümünde cisimden alınan cevabın ön işlenmesi açıklanarak güç yoğunluk vektörünün cismin algılanmasındaki rolü belirtilmiştir. Üçüncü bölümde problem geometrisine ait Green fonksiyonunun analitik olarak elde edilmesi açıklanmıştır. Cisim kesitinin integral denklem ile elde edilmesi yine bu bölümde yer almak tadır. Dördüncü bölümde seçilen değişik problem parametreleri için elde edilen sonuçlar sunulmuştur. Son bölümde ise önerilen yöntem ile ilgili sonuçlar ver ilmiş ve yapılması düşünülen çalışmalar belirtilmiştir. Bu tez çalışmasında elektromagnetik dalga kullanılarak gömülü cisimlerin zaman domeninde algılanması hedeflenmiştir. Cismi uyaran dalga şeklinin zaman domeninde geniş bandlı bir darbe olduğu düşünülmüştür. Gömülü cismin silindirik rastgele kesitli ve mükemmel iletken kuvvetli saçıcı olduğu kabul edilmiştir. Önerilen algılama yönteminin, cismi uyaran kaynak işaretinin davranışı, gözlem bölgesi, cisim boyutları, ortam paremetrelerinin pratik uygulanabilir değerleri için kabul edilebilir sonuçlar vermesi hedeflenmiştir. Zaman domeni cevabından elde edilen güç yoğunluk vektörünün cismin belirlenmesinde kullanılması ve probleme ait Green fonksiyonu kullanılarak hiç bir yaklaşıldık yapılmaksızın analitik olarak cismin algılanması ilk kez bu tezde işlenmiştir.

Özet (Çeviri)

SUMMARY DETECTION OF THE BURIED CONDUCTED OBJECTS USING ELECTROMAGNETIC WAVES IN TIME-DOMAIN Historically, most electromagnetic wave propagation problems have been an alyzed in the frequency domain with the assumption of steady state. The main reason is that most electromagnetic sources have been built to operate in the time-harmonic regime (single frequency). However, new technological advances have made it possible to generate high-power, wide-band electromag netic signals such as short-duration pulses. Together with wide-band receivers, these impulsive sources provide for a gathering of data over a large frequency range at a high rate. At the same time, interest has emerged to study and understand various transient wave phenomena. The analysis of electromagnetic pulse propagation through high-speed inte grated circuits, the study of wide-band antenna and radar systems, subsurface detection, geophysical exploration, and target identification are among the areas which relie on the transient wave propagation in inhomogeneous me- dia.In some applications, it is required to deduce the physical properties of the medium or object under study, such as the size, shape and electrical char acteristics, from the transient scattered field measured at a set of receivers outside the scatterer due to a collection of transmitters. This kind of prob lems are known as the inverse scattering problems whose solution is inherently non-unique. In this thesis, first an efficient method of solving transient electromagnetic scattering problem in an arbitrary two-dimensional inhomogeneous, isotropic medium is introduced. The method is then applied to model the ground pen etrating radar. Then, obtained transient response of the object is analyzed. Two dimensional detection algorithm is developed by using the frequency do main Green's function. Some results are given, and comparisons are made between different physical configurations. Several excellent and flexible methods have been developed in recent years for the solution of time-domain wave propagation problems in inhomogeneous media in one, two or three dimensions. Three include the finite difference time domain FDTD method [1], the transmission line matrix method TLM, and some integral equation methods [2]. Almost all wave propagation takes place in three spatial dimensions. However, if three-dimensional models are used in Vlly=b observation path 1 £j.g ground 2 A~x Figure 1 Typical experimental configuration of the problem the numerical solution of wave propagation in inhomogeneous media, one finds that even the largest and most powerful present-day computers are quickly swamped with relatively small-sized problems. Hence, even if the available theoretical models are valid for three dimensions, our computational capabili ties are not prepared for them. This is why in many cases, a two-dimensional model is used to approximate three-dimensional media and objects. This is, in fact, a sufficient approximation in several situations, e.g., in modeling the geophysical formations parallel to the surface of the Earth, reinforcement bars in construction. In Chapter 2, an efficient solution to forward scattering problem is introduced based on the finite difference time domain (FDTD) method. This solution is then applied to model the subsurface interface radar geometry. The geometry consist of two isotropic half-spaces characterized by constitutive parameters {?0,fj,0,cr = 0) and (er. e0,fj,0,a ^ 0). Region 1 is a homogeneous half-space and corresponds to free space. Region 2, representing the ground, is an inhomogeneous half-space. An arbitrary shaped perfectly conducting (PEC) object of finite size is located in region 2. This could, for example, represent a vertical cross section of the earth, xy plane, consisting of several inhomogeneities that run parallel to the ground, z direction as shown in Fig.l. The object is illuminated by a linearly polarized impulsive plane wave from the region 1. The refracted pulse is the source of the scattered response. The reconstruction process requires successive solutions to a forward scatter ing problem. For this investigation, the FDTD technique is used for the for- vmward scattering problem by making some geometry depending improvements. Since FDTD is a time domain technique, the desired frequency components are obtained via a discrete Fourier transform. Time-dependent source free two dimensional Maxwell's equations in Cartesian coordinates are dEz = -p- dHx dEz /*- dHv dHv dH._ x dEz = e-^- + oEz dy ^ dt dx ' dt dx dy“ dt We are able to discritize these three differential equation as SSihJ) = H^-%J) ~ J^Erll\h3) - ET^iiJ - 1)] J3J(i, j) = JBÇ-%3) + ^Er1/2(iJ) ~ K~l/2(i ~ 1, J)] -n/a,,,x _ t'ET^İiJ), At.[fly(»,j)-fly(i-l,j)] z {,J) {e + o At) ^ Ax(e + aAt) At-[H2(i,j)-H2(i,j-l)\ Ay(e + a At) (1) (2) (3) (4) The superscripts refer the time steps. Here, At is the unit time step, Ax, Ay is the distance between adjacent nodes as shown in Fig.2. For the iterative finite difference schemes, the stability criterion needs to be specified. ©__£__Ö._-^._.q__ A-O- id, j+D - - _ 4> _ _ A i -£ - -A- T $- - A- - $ - Ay * T * * (i,j> ©- -A - -© - -A- 4 ¦©- - A- - (i+l,j> ©- o E, * H, A H, Figure 2 Typical node configuration 2D finite-difference grid. For the two dimensional problem, the required Courant-Lewy-Friedrichs sta bility condition is At< 1 CsJ{l/AxY + (i/Ayy (5) where c is the speed of light in the free-space. The quantities Ax and Ay are chosen according to the highest frequency content of the source excitation. These discretized Maxwell's equations (2)- (4) can be written for the scattered wave components in the lossy media as IX3.5 4 Time [ran} Figure 3 Shifted first derivative Gaussian pulse - Incident Field. HSiiJ) = K~\h3) ~ KH{Erl/2(iJ) ~ Erl/2(i,j - 1)) H%(i, j) = H%-'(i,j) + KH(E?-l'*(i,j) - EZ~lf2{i ~ 1, 3)) -ür«(flrı/a(i,i)-flrı/2(i,i-i)) Kex = eT + a At Ke2 = At/A, er + a At xy KH = At VoA, (6) (7) (8) 0) xy Since the spatial domain of the considered scheme is inevitably finite, appro priate boundary conditions are employed to eliminate reflections from the walls of the computational domain. In this thesis, the second order MUR absorbing boundary condition is applied [3]. This boundary condition is imposed for only electrical field component. The source of excitation in scattered field is a known incident field that is injected into the grid via the PEC object nodes. The time variation of the incident field (waveform) can be arbitrary, but the first derivative of the Gaus sian pulse shape is used in thesis. For the PEC boundary condition on the object only electric incident field is needed for these PEC nodes. E?(i,j) = -Er(i,r,n) (10) For the Ax = Ay = Axj, = 1cm spatial distance, Courant stability criteria requires the 23.6psn time step. To obtain the better result, 16.Qpsn time steps is used to time domain calculations. Usually, Axy is taken to be one-tenth of the smallest wavelength included in the spectrum of ElT{i, j;n). For the2 3 Frequency [GHz] Figure 4 Normalized amplitude spectrum of the incident wave form. calculations Xmin = 10.0 x A^ which corresponds the \min = 10.0cm and max imum spectral frequency is fmax = 3GHz. Incident field wave form is taken as -11.4 109(i -r)e”2-466 I(jl9(*-T)2 shown in Fig.3. Frequency transformation of this pulse shape can be seen in Fig.4. The receiver moves horizontally along the interface (y = 6) and records the scattered wave. Instantenous power density of this response can be calculated as Pt(x;i) = E(x;t) x H(x;t) total scattered power density would be oo P{x) = J Pt(x;t)dt (11) (12) which shows the amount and direction of the power that is leaved away the object at the observation locations. These directions can be continued to the medium interface and can be transformed back to the region 2 by using the Snell's refraction rule. Graphical representation of this continuation is show in Fig. 5 with the correct shape and location of the object. For the Fig.5, host medium is the lossy ground half space with the parameters er = 8, a = 0.001 S/m, and incident plane wave direction is 0jnc=45° in region 1, PEC object is consist two distributed part, one of them is the cylinder which is centered at the (x = 100cm; y = -60cm) and radius is a = 10cm, the second part of the object is the rectangular prism with the dimension 20cm x 5cm which is located (a; = 155cm; -42.5cm). The object is illuminated by the first derivative of the Gaussian pulse shape which is shown in Fig.3. 1500A* time step FDTD calculation is performed. The normalized amplitude and direction XIr-r- 30 :':iit ' * /' 100 1» 200 300 Figure 5 Amplitude and direction of the power density function. of the cumulative power density function is calculated on the observation path. For the recognition of the object, frequency domain response is obtained by us ing the discrete Fourier transformation of the measured electrical field Ez(x; tn) At N ^ 71=1 (13) where N is the number of the observation time samples. For the reconstruction of the cross section of the object, analytical system function (Green's function) is expressed. Unit amplitude line filament's electrical field can be expressed as the Green's function in the free space [4] G2(a;,y;£,77) = ^ J 00 ei(z-Ç)a+iV*l=«%-'?)l ^ da (14) a£ where (x, y) is the observation location and (£, rj) is the source point and k2 is the complex wave number of the host media w.a «2 = -i/?r + t C V W?0 (15) The plane wave term in the integral equation (14) can be refracted to the region 1 and can be expressed as [5] a 21 i °? eJa(x-Ç)+V*?-a2î.-V*?-"2* da (16) az xuE < Figure 6 Normalized cross section of the reconstructed object. In general, the observed frequency domain response of the buried object can be thought as the superposition of the surface currents. To obtain current distribution, transformed response is integrated observation path by using the system Green's function as I(Ç,T,) = JEz(x)f)'G*2l(x;Ç,r])dx (17) where L corresponds the observation path, for the above example, L = 300cm and b = 25cm, obtained horizantal cross section (solid line) and object (dashed line) is shown in Fig. 6. To demonstrate the performance of the detection method many different type of object and illimunation configuration are used in chapter four. Presented method does not require any priory knowledge of object. Time domain pulse response of the buried strong object is considered for the measured data. Re alistic media and physical sizes are used. The usage of the power density direction for the detection is introduced. System Green's function is used to obtain the object cross section distribution by using the integral equation formulation. xni

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