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Yes / In the equivalent frequency-based model, the antenna array gain is utilised to characterise the frequency response of the beam squint effect generated by the antenna array. This impact is considered for a wide range of uniform linear array (ULA) and uniform planar array (UPA) designs, including those with and without tapering configurations. For a closer look at how the frequency response of the array adapts to the variations in the incidence angle of the signal, the bandwidth of the spectrum is varied and investigated. To study this effect, we have considered using the gain array response as an equivalent channel model in our approach. Beam squinting caused by distortion in the frequency response gain can be verified by one of two equalisers: a zero-forcing (ZF) equaliser or a minimum mean square error (MMSE) equaliser. Different cases with their analysis and results are studied and compared in terms of coded and uncoded modulations. / This work was supported in part by the Satellite Network of Experts V under Contract 4000130962/20/NL/NL/FE, and in part by the Innovation Program under Grant H2020-MSCA-ITN-2016 SECRET-722424.

In this work, the random vibration of higher-order nonlinear beams and composite plates subjected to stochastic loading is studied. The fourth-order nonlinear beam equation is examined to study the effect of rotary inertia and shear deformation on the root mean square values of displacement response. A new linearly coupled equivalent linearization method is proposed and compared with the widely used traditional equivalent linearization method. The new method is proven to yield closer predictions to the numerical simulation results of the nonlinear beam vibration. A systematical investigation of the nonlinear random vibration of composite plates is conducted in which effects of nonlinearity, choices of different plate theories (the first order shear deformation plate theory and the classical plate theory), and temperature gradient on the plate statistical transverse response are addressed. Attention is paid to calculate the R.M.S. values of stress components since they directly affect the fatigue life of the structure. A statistical data reconstruction technique named ARMA modeling and its applications in random vibration data analysis are discussed. The model is applied to the simulation data of nonlinear beams. It is shown that good estimations of both the nonlinear frequencies and the power spectral densities are given by the technique. / Ph. D.

Self-excited systems are open loop unstable plants having a nonlinearity that prevents an exponentially increasing time response. The resulting limit cycle is induced by any slight disturbance that causes the response of the system to grow to the saturation level of the nonlinearity. Because there is no external disturbance, control of these self-excited systems requires that the open loop system dynamics are altered so that any unstable open loop poles are stabilized in the closed loop. This work examines a variety of adaptive control approaches for controlling a thermoacoustic instability, a physical self-excited system. Initially, a static feedback controller loopshaping design and associated system identification method is presented. This design approach is shown to effectively stabilize an unstable Rijke tube combustor while preventing the creation of additional controller induced instabilities. The loopshaping design method is then used in conjunction with a trained artificial neural network to demonstrate stabilizing control in the presence of changing plant dynamics over a wide variety of operating conditions. However, because the ANN is designed specifically for a single combustor/actuator arrangement, its limited portability is a distinct disadvantage. Filtered-X least mean squares (LMS) adaptive feedback control approaches are examined when applied to both stable and unstable plants. An identification method for approximating the relevant plant dynamics to be modeled is proposed and shown to effectively stabilize the self-excited system in simulations and experiments. The adaptive feedback controller is further analyzed for robust performance when applied to the stable, disturbance rejection control problem. It is shown that robust stability cannot be guaranteed because arbitrarily small errors in the plant model can generate gradient divergence and unstable feedback loops. Finally, a time-averaged-gradient (TAG) algorithm is investigated for use in controlling self-excited systems such as the thermoacoustic instability. The TAG algorithm is shown to be very effective in stabilizing the unstable dynamics using a variety of controller parameterizations, without the need for plant estimation information from the system to be controlled. / Ph. D.

L’objectif principal de cette thèse est de décliner et d’analyser l’algorithme kernel-LMS à noyau Gaussien dans trois cadres différents: celui des noyaux uniques et multiples, à valeurs réelles et à valeurs complexes, dans un contexte d’apprentissage distributé et coopératif dans les réseaux de capteurs. Plus précisement, ce travail s’intéresse à l’analyse du comportement en moyenne et en erreur quadratique de cas différents types d’algorithmes LMS à noyau. Les modèles analytiques de convergence obtenus sont validés par des simulations numérique. Tout d’abord, nous introduisons l’algorithme LMS, les espaces de Hilbert à noyau reproduisants, ainsi que les algorithmes de filtrage adaptatif à noyau existants. Puis, nous étudions analytiquement le comportement de l’algorithme LMS à noyau Gaussien dans le cas où les statistiques des éléments du dictionnaire ne répondent que partiellement aux statistiques des données d’entrée. Nous introduisons ensuite un algorithme LMS modifié à noyau basé sur une approche proximale. La stabilité de l’algorithme est également discutée. Ensuite, nous introduisons deux types d’algorithmes LMS à noyaux multiples. Nous nous concentrons en particulier sur l’analyse de convergence de l’un d’eux. Plus généralement, les caractéristiques des deux algorithmes LMS à noyaux multiples sont analysées théoriquement et confirmées par les simulations. L’algorithme LMS à noyau complexe augmenté est présenté et ses performances analysées. Enfin, nous proposons des stratégies de diffusion fonctionnelles dans les espaces de Hilbert à noyau reproduisant. La stabilité́ de cas de l’algorithme est étudiée. / The main objective of this thesis is to derive and analyze the Gaussian kernel least-mean-square (LMS) algorithm within three frameworks involving single and multiple kernels, real-valued and complex-valued, non-cooperative and cooperative distributed learning over networks. This work focuses on the stochastic behavior analysis of these kernel LMS algorithms in the mean and mean-square error sense. All the analyses are validated by numerical simulations. First, we review the basic LMS algorithm, reproducing kernel Hilbert space (RKHS), framework and state-of-the-art kernel adaptive filtering algorithms. Then, we study the convergence behavior of the Gaussian kernel LMS in the case where the statistics of the elements of the so-called dictionary only partially match the statistics of the input data. We introduced a modified kernel LMS algorithm based on forward-backward splitting to deal with $\ell_1$-norm regularization. The stability of the proposed algorithm is then discussed. After a review of two families of multikernel LMS algorithms, we focus on the convergence behavior of the multiple-input multikernel LMS algorithm. More generally, the characteristics of multikernel LMS algorithms are analyzed theoretically and confirmed by simulation results. Next, the augmented complex kernel LMS algorithm is introduced based on the framework of complex multikernel adaptive filtering. Then, we analyze the convergence behavior of algorithm in the mean-square error sense. Finally, in order to cope with the distributed estimation problems over networks, we derive functional diffusion strategies in RKHS. The stability of the algorithm in the mean sense is analyzed.

Molecular Biology has allowed the characterization and manipulation of the molecules of life in the wet lab. Also the structures of those macromolecules are being continuously elucidated. During the last decades of the past century, there was an increasing interest to study how the different genes are organized into different organisms (‘genomes’) and how those genes are expressed into proteins to achieve their functions. Currently the sequences for many genes over several genomes have been determined. In parallel, the efforts to have the structure of the proteins coded by those genes go on. However it is experimentally much harder to obtain the structure of a protein, rather than just its sequence. For this reason, the number of protein structures available in databases is an order of magnitude or so lower than protein sequences. Furthermore, in order to understand how living organisms work at molecular level we need the information about the interaction of those proteins. Elucidating the structure of protein macromolecular assemblies is still more difficult. To that end, the use of computers to predict the structure of these complexes has gained interest over the last decades. The main subject of this thesis is the evaluation of current available computational methods to predict protein – protein interactions and build an atomic model of the complex. The core of the thesis is the evaluation protocol I have developed at Service de Conformation des Macromolécules Biologiques et de Bioinformatique, Université Libre de Bruxelles, and its computer implementation. This method has been massively used to evaluate the results on blind protein – protein interaction prediction in the context of the world-wide experiment CAPRI, which have been thoroughly reviewed in several publications [1-3]. In this experiment the structure of a protein complex (‘the target’) had to be modeled starting from the coordinates of the isolated molecules, prior to the release of the structure of the complex (this is commonly referred as ‘docking’). The assessment protocol let us compute some parameters to rank docking models according to their quality, into 3 main categories: ‘Highly Accurate’, ‘Medium Accurate’, ‘Acceptable’ and ‘Incorrect’. The efficiency of our evaluation and ranking is clearly shown, even for borderline cases between categories. The correlation of the ranking parameters is analyzed further. In the same section where the evaluation protocol is presented, the ranking participants give to their predictions is also studied, since often, good solutions are not easily recognized among the pool of computer generated decoys. An overview of the CAPRI results made per target structure and per participant regarding the computational method they used and the difficulty of the complex. Also in CAPRI there is a new ongoing experiment about scoring previously and anonymously generated models by other participants (the ‘Scoring’ experiment). Its promising results are also analyzed, in respect of the original CAPRI experiment. The Scoring experiment was a step towards the use of combine methods to predict the structure of protein – protein complexes. We discuss here its possible application to predict the structure of protein complexes, from a clustering study on the different results. In the last chapter of the thesis, I present the preliminary results of an ongoing study on the conformational changes in protein structures upon complexation, as those rearrangements pose serious limitations to current computational methods predicting the structure protein complexes. Protein structures are classified according to the magnitude of its conformational re-arrangement and the involvement of interfaces and particular secondary structure elements is discussed. At the end of the chapter, some guidelines and future work is proposed to complete the survey.

This thesis considers statistical issues in source localization from the received signal strength (RSS) measurements at sensor locations, under the practical assumption of log-normal shadowing. Distance information of source from sensor locations can be estimated from RSS measurements and many algorithms directly use powers of distances to localize the source, even though distance measurements are not directly available. The first part of the thesis considers the statistical analysis of distance estimation from RSS measurments. We show that the underlying problem is inefficient and there is only one unbiased estimator for this problem and its mean square error (MSE) grows exponentially with noise power. Later, we provide the linear minimum mean square error (MMSE) estimator whose bias and MSE are bounded in noise power. The second part of the thesis establishes an isomorphism between estimates of differences between squares of distances and the source location. This is used to completely characterize the class of unbiased estimates of the source location and to show that their MSEs grow exponentially with noise powers. Later, we propose an estimate based on the linear MMSE estimate of distances that has error variance and bias that is bounded in the noise variance.