A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science. 2014. / No abstract provided.

Le Contrôle Non Destructif (CND) de matériaux composites multicouches pour des problèmes de qualité, viabilité, sécurité et disponibilité des systèmes qui impliquent des pièces fabriquées dans les industries aéronautiques et de l’automobile est devenu une tâche essentielle aujourd’hui. L'objectif visé par cette thèse est l’imagerie électromagnétique de structures complexes multicouches anisotropes, de plus en plus utilisées dans des applications, et encore source de sérieux défis à l'étape de leur modélisation et encore plus à l'étape souvent en enfance de leur imagerie. En utilisant une vaste gamme de fréquences, qui va des courants de Foucault jusqu’aux micro-ondes, il y a un fort besoin de rendre disponibles des procédures de modélisation et d'imagerie qui sont robustes, rapides, précises et utiles à la décision des utilisateurs finaux sur des défauts potentiels, tant donc en basse fréquence (BF) (matériaux conducteurs, type fibre de carbone) qu’en haute fréquence (HF) (matériaux diélectriques, type fibre de verre). De plus, il est important d'obtenir des résultats en des temps brefs. Cependant, cela nécessite la connaissance d’une réponse précise à des sources externes aux multicouches, en considérant les couches des composites comme non endommagées ou endommagées : on parle donc de solution du problème direct, avec le cas particulier de sources élémentaires conduisant aux dyades de Green (DGF). La modélisation et la simulation numérique du problème direct sont gérés principalement via une solution au premier ordre de la formulation intégrale de contraste de source impliquant le tenseur de dépolarisation des défauts, quand ceux-ci sont assez petits vis-à-vis de l’épaisseur de peau locale (cas BF) ou de la longueur d'onde locale (cas HF). La précision des DGF doit nécessairement être assurée alors, même si les sources se situent loin de l'origine, ce qui donne un spectre de dyades qui oscille très rapidement. La technique d'interpolation-intégration dite de Padua-Domínguez est ainsi introduite dans le but d'évaluer de façon efficace des intégrales fortement oscillantes.Néanmoins, les matériaux composites peuvent souffrir de divers défauts, lors du processus de fabrication ou pendant leurs utilisations. Vides d’air, cavités remplies de liquide, fissures, etc., peuvent affecter le fonctionnement correct des structures composites. Il est donc indispensable de pouvoir détecter la présence des défauts. Ici, l’insistance est sur la méthode bien connue d’imagerie dite MUltiple SIgnal Classification (MUSIC), qui est basée sur la décomposition en valeurs singulières (SVD) des DGF ; celle-ci est développée afin de localiser les positions de multiples petits défauts volumiques en interaction faible enfouis dans des milieux anisotropes uniaxiaux. Le principal inconvénient de la méthode MUSIC est cependant sa sensibilité par rapport au bruit. Par conséquent, des méthodes MUSIC avec une résolution améliorée et la Recursively Applied and Projected (RAP) MUSIC sont introduites afin de surmonter un tel inconvénient de l'algorithme standard et de fournir des résultats de qualité avec une meilleure résolution. De nombreuses simulations numériques illustrent ces investigations. / Non-Destructive Testing/Evaluation (NdT/E) of multi-layered composite materials for problems of quality, viability, safety and availability of systems involving manufactured parts (in aeronautics and in automotive industry, as a good example) has become an interesting and challenging task nowadays. The focus of the PhD thesis is on the electromagnetic (EM) imaging of complex anisotropic multi-slab composite panels as increasingly encountered in applications, yet source of strong challenges at modeling stage and even more at often-in-infancy imaging stage. From eddy-currents to microwaves, there is a strong need to make available modeling and imaging procedures that are robust, fast, accurate and useful to potential end-users’ decision about potential defects both at low-frequency (LF) (conductive materials, carbon-fiber like) and high-frequency (HF) (dielectric materials, glass-fiber like). Moreover, it is important to get the results in close-to-real-time. However, this requires an accurate response to external sources of the multilayers, considering the layers which these composite structures are made of as undamaged or damaged. The modeling at forward stage is managed via a first-order solution involving the dyadic Green’s functions (DGF) of the layers along with the depolarization tensor of the assumed defects when they are small enough vis-à-vis the skin depth (LF case) or the wavelength (HF case). The accuracy of the DGF has to be ensured even if the sources lie far away from the origin, which yields a fast-oscillating spectrum of the dyads. The Padua-Domínguez interpolation-integration technique is introduced herein in order to evaluate in an effective fashion fast-oscillating integrals.Damages or disorders, which these composite structures may suffer from, are of many kinds. One could mention voids, fluid-filled cavities or uniaxial defects with obvious impacts on the electromagnetic and geometric parameters of the multilayers. That is, the task to make available to end-users imaging algorithms tailored to detect the presence of defects. The well-known standard MUltiple SIgnal Classification (MUSIC) algorithm, which is based on the Singular Value Decomposition (SVD) of such DGF, is here applied to localize the positions of small multiple defects with weak interaction embedded in anisotropic uniaxial media. The main drawback of MUSIC is its sensitivity with respect to the noise. Therefore, MUSIC with enhanced resolution and Recursively Applied and Projected (RAP) MUSIC are introduced to overcome such a drawback of the standard algorithm and to provide quality results with better resolution.

Multiple Signal Classification (MUSIC) Algorithm based and Wigner Distribution-Principal Component Analysis (WD-PCA) based classification techniques are very recently suggested resonance region approaches for electromagnetic target classification. In this thesis, performances of these two techniques will be compared concerning their robustness for noise and their capacity to handle large number of candidate targets. In this context, classifier design simulations will be demonstrated for target libraries containing conducting and dielectric spheres and for dielectric coated conducting spheres. Small scale aircraft targets modeled by thin conducting wires will also be used in classifier design demonstrations.

For successful identification of structural defects in plates and pipes, it is essential to understand structural wave propagation characteristics such as dispersion relations. Analytical approaches to identify the dispersion relations of homogeneous, simple plates and circular pipes have been investigated by many researchers. However, for plates or pipes with irregular cross-sectional configurations or multi-layered composite structures, it is almost impossible to obtain the analytical dispersion relations and associated mode shapes. In addition, full numerical modeling approaches such as finite element (FE) methods are not economically feasible for high (e.g., ultrasonic) frequency analyses where an extremely large number of discretized meshes are required, resulting in significantly expensive computation. In order to address these limitations, Hybrid Analytical/Finite Element Methods (HAFEMs) are developed to model composite plates and pipes in a computationally-efficient manner. When a pipe system is used to transport a fluid, the dispersion curves obtained from a “hollow” pipe model can mislead non-destructive evaluation (NDE) results of the pipe system. In this study, the HAFEM procedure with solid elements is extended by developing fluid elements and solid-fluid boundary conditions, resulting in the dispersion curves of fluid-filled pipes. In addition, a HAFEM-based acoustic transfer function approach is suggested to consider a long pipe system assembled with multiple pipe sections with different cross-sections. For the validation of the proposed methods, experimental and full FE modeling results are compared to the results obtained from the HAFEM models. In order to detect structural defect locations in shell structures from defect-induced, subtle wave reflection signals and eliminate direct-excitation-induced and boundary-reflected, relatively-strong wave signals, a time-frequency MUSIC algorithm is applied to ultrasonic wave data measured by using an array of piezoelectric transducers. A normalized, structurally-damped, cylindrical 2-D steering vector is proposed to increase the spatial resolution of time-frequency MUSIC power results. A cross-shaped array is selected over a circular or linear array to further improve the spatial resolution and to avoid the mirrored virtual image effects of a linear array. Here, it is experimentally demonstrated that the proposed time-frequency MUSIC beamforming procedure can be used to identify structural defect locations on an aluminum plate by distinguishing the defect-induced waves from both the excitation-generated and boundary-reflected waves.

Through-the-wall Imaging (TWI) is crucial for various applications such as law enforcement, rescue missions and defense. TWI methods aim to provide detailed information of spaces that cannot be seen directly. Current state-of-the-art TWI systems utilise ultra-wideband (UWB) signals to simultaneously achieve wall penetration and high resolution. These TWI systems transmit signals and mathematically back-project the reflected signals received to image the scenario of interest. However, these systems are diffraction-limited and encounter problems due to multipath signals in the presence of multiple scatterers. Time reversal (TR) methods have become popular for remote sensing because they can take advantage of multipath signals to achieve superresolution (resolution that beats the diffraction limit). The Decomposition Of the Time-Reversal Operator (DORT in its French acronym) and MUltiple SIgnal Classification (MUSIC) methods are both TR techniques which involve taking the Singular Value Decomposition (SVD) of the Multistatic Data Matrix (MDM) which contains the signals received from the target(s) to be located. The DORT and MUSIC imaging methods have generated a lot of interests due to their robustness and ability to locate multiple targets. However these TR-based methods encounter problems when the targets are behind an obstruction, particularly when the properties of the obstruction is unknown as is often the case in TWI applications. This dissertation introduces a novel total sub-MDM algorithm that uses the highly acclaimed MUSIC method to image targets hidden behind an obstruction and achieve superresolution. The algorithm utilises spatio-temporal windows to divide the full-MDM into sub-MDMs. The summation of all images obtained from each sub-MDM give a clearer image of a scenario than we can obtain using the full-MDM. Furthermore, we propose a total sub-differential MDM algorithm that uses the MUSIC method to obtain images of moving targets that are hiddenbehind an obstructing material.

The angle of arrival estimation of multiple sources plays a vital role in the field of array signal processing as MIMO systems can be employed at both the transmitter and the receiver end and the system capacity, reliability and throughput can be significantly increased by using array signal processing. Almost all applications require accurate direction of arrival (DOA) estimation to localize the sources of the signals. Another important parameter of localization systems is the array geometry and sensor design which can be application specific and is used to estimate the DOA. In this work, various array geometries and arrival estimation algorithms are studied and then a new scheme for multiple source estimation is proposed and evaluated based on the performance of subspace and non-subspace decomposition methods. The proposed scheme has shown to outperform the conventional Multiple Signal Classification (MUSIC) estimation and Bartlett estimation techniques. The new scheme has a better performance advantage at low and high signal to noise ratio values (SNRs). The research work also studies different array geometries for both single and multiple incident sources and proposes a geometry which is cost effective and efficient for 3, 4, and 5 antenna array elements. This research also considers the shape of the ground plane and its effects on the angle of arrival estimation and in addition it shows how the mutual couplings between the elements effect the overall estimation and how this error can be minimised by using a decoupling matrix. At the end, a novel miniaturised multi element reconfigurable antenna to represent the receiver base station is designed and tested. The antenna radiation patterns in the azimuth angle are almost omni-directional with linear polarisation. The antenna geometry is uniplanar printed logspiral with striplines feeding network and biased components to improve the impedance bandwidth. The antenna provides the benefit of small size, and re-configurability and is very well suited for the asset tracking applications.

L'objet de la thèse est la détection électromagnétique non-itérative de petits objets enfouis. Le problème direct de diffraction est abordé en utilisant une formule asymptotique rigoureuse du champ diffracté par des inclusions dont la taille caractéristique est petite devant la longueur d'onde de leur illumination dans le milieu d'enfouissement. La prise en compte de la diffraction multiple dans le cas de deux inclusions sphériques est abordée grâce à un tenseur de polarisation spécifique qui est calculé dans un système approprié de coordonnées bisphériques. Le modèle de Foldy-Lax est aussi utilisé afin de prendre en compte le couplage entre plusieurs inclusions. Les simulations numériques montrent que cet effet de couplage ne peut être ressenti qu'en leurs voisinages immédiats. Une configuration d'enfouissement en demi-espace est aussi étudiée en détail. Les dyades de Green alors nécessaires sont calculées de manière exacte par "force brutale" numérique. Puis trois méthodes approchées de calcul des intégrales de Sommerfeld qui sont impliquées sont proposées, les simulations montrant qu'elles font gagner un temps de calcul significatif dans le calcul de ces dyades, tout en étant de précision convenable. La prise en compte du couplage entre une sphère et l'interface est aussi investiguée grâce à un tenseur de polarisation adéquat en coordonnées bisphériques (de facto, une des deux sphères dégénère en cette interface). A chaque fois, les champs diffractés simulés par la méthode asymptotique sont comparés à des champs obtenus par la méthode dite des dipôles couplés (CDM). Les résultats montrent que la méthode asymptotique fournit des valeurs du champ diffracté satisfaisantes tant que les tailles des inclusions restent assez petites devant la longueur d'onde. L'algorithme d'imagerie MUSIC est quant à lui utilisé pour détecter ces inclusions à partir de leur matrice de réponse multistatique (MSR) collectée via un réseau plan d'extension limitée de dipôles émetteurs-récepteurs idéaux. L'analyse des valeurs et des vecteurs singuliers de la matrice MSR montre qu'il existe une différence entre les données calculées par la méthode asymptotique et celles calculées par la méthode CDM. Mais cette différence ne persiste pas si l'on considère des données bruitées, même à relativement faible niveau de bruit. Dans les deux cas, MUSIC permet une estimation fiable de la position des inclusions, la notion de "super-localisation" étant en particulier discutée. Une méthode est par ailleurs proposée afin de détecter l'angle d'inclinaison d'un ellipsoïde incliné enfoui.

Abstract The focus of this thesis is to study direction of arrival (DoA) estimation algorithms for reconfigurable leaky-wave antennas and advanced antenna arrays. Directional antennas can greatly improve the spectrum reuse, interference avoidance, and object and people localization. DoA estimation algorithms have also been shown to be useful for applications such as positioning for user tracking and location-based services in wireless local area networks (WLANs). The main goal is to develop novel DoA estimation algorithms for both advanced antenna arrays and composite right/left-handed (CRLH) leaky-wave antennas (LWAs). The thesis introduces novel modifications to existing DoA estimation algorithms and shows how these can be modified for real-time DoA estimation using both antenna types. Three modified DoA estimation algorithms for CRLH-LWAs are presented: 1) modified multiple signal classification (MUSIC), 2) power pattern cross-correlation (PPCC), and 3) adjacent power pattern ratio (APPR). Additionally, the APPR algorithm is also applied to advanced antenna arrays. The thesis also presents improvements to the modified MUSIC and APPR algorithms. The complexity of the algorithms is reduced by selecting a smaller number of received signals from different directions. The results show that the selection of the radiation patterns is very important and that the proposed algorithms can successfully estimate the DoA, even in a real-world environment. Based on the results, this thesis provides a good starting point for future research of DoA estimation algorithms to enhance the performance of future-generation wireless networks and the accuracy of localization. / Tiivistelmä Tässä väitöskirjassa tutkitaan suunnanestimointialgoritmeja uudelleen konfiguroituville vuotoaaltoantenneille (LWA, leaky wave antenna) ja kehittyneille antenniryhmille. Suuntaavilla antenneilla voidaan parantaa huomattavasti spektrin uudelleen käyttöä ja esineiden ja ihmisten sijaintipaikannusta sekä pienentää häiriöitä. Suunnanestimointialgoritmit ovat myös osoittautuneet hyödylliseksi esimerkiksi seuranta- ja sijaintipaikannuspalvelusovelluksille langattomissa lähiverkoissa. Työn päätavoite on kehittää uusia suunnanestimointialgoritmeja sekä kehittyneille antenniryhmille että vuotoaaltoantenneille (composite right/left-handed (CRLH) LWA). Työssä osoitetaan, miten olemassa olevia suunnanestimointialgoritmeja voidaan muokata uudella tavalla, jotta ne soveltuisivat molemmille antennityypeille reaaliaikaiseen suunnanestimointiin. Vuotoaaltoantennille on kehitetty kolme erilaista suunnanestimointialgoritmia: 1) muunneltu MUSIC- (multiple signal classification), 2) säteilykyvioiden tehojen ristikorrelaatio- (PPCC, power pattern cross correlation) ja 3) vierekkäisten säteilykuvioiden tehosuhdealgoritmi (APPR, adjacent power pattern ratio). APPR-algoritmia on myös käytetty kehittyneelle antenniryhmälle. Työssä esitetään myös parannuksia muunnelluille MUSIC- ja APPR-algoritmeille. Algoritmien kompleksisuutta voidaan pienentää valitsemalla vähemmän vastaanotettuja signaaleja. Tulokset osoittavat, että signaalien valinta on hyvin tärkeää ja ehdotetut algoritmit estimoivat onnistuneesti saapuvan signaalin suunnan todellisessa mittausympäristössä. Yhteenvetona voidaan sanoa, että tämä väitöstyö on hyvä lähtökohta suunnanestimointialgoritmitutkimukselle, jonka tavoitteena on parantaa tulevien sukupolvien langattomien verkkojen suorituskykyä ja paikannuksen tarkkuutta.