The topic of this dissertation is the derivation, development, and evaluation of novel hybrid algorithms for process control that use a limited number of measurements and that are suitable to operate in the presence of large amounts of process noise. As an initial step, affine and neural network statistical process models are developed in order to simulate the steady-state system behavior. Such models are vitally important in the evaluation, testing, and improvement of all other process controllers referred to in this work. Afterwards, fuzzy logic controller rules are assimilated into a mathematical characterization of a model that includes the modes and mode transition rules that define a hybrid hierarchical process control. The main processing entity in such framework is a closed-loop control algorithm that performs global and then local optimizations in order to asymptotically reach minimum bias error; this is done while requiring a minimum number of iterations in order to promptly reach a desired operational window. The results of this research are applied to surface mount technology manufacturing-lines yield optimization. This work achieves a practical degree of control over the solder-paste volume deposition in the Stencil Printing Process (SPP). Results show that it is possible to change the operating point of the process by modifying certain machine parameters and even compensate for the difference in height due to change in print direction.

La complexité de la forme de la surface est une caractéristique morphologique des surfaces pliées. Dans cette thèse, nous visons à développer des méthodes spectrales pour quantifier cette caractéristique du cortex cérébral humain reconstruit à partir d'images MR structurales. Tout d'abord, nous suggérons certaines propriétés qu'une mesure standard de la complexité de surface devrait posséder. Ensuite, nous proposons deux définitions claires de la complexité de la surface en fonction des propriétés de flexion de surface. Pour quantifier ces définitions, nous avons étendu la transformée de Fourier à fenêtres illustrée récemment pour transformer en maillage des surfaces. Grâce à certaines expériences sur les surfaces synthétiques, nous montrons que nos mesures basées sur la courbure permettent de surmonter les surfaces classiques basées sur la surface, ce qui ne distingue pas les plis profonds des oscillants ayant une surface égale. La méthode proposée est appliquée à une base de données de 124 sujets adultes en bonne santé. Nous définissons également la complexité de la surface par la régularité de Hölder des mouvements browniens fractionnés définis sur les collecteurs. Ensuite, pour la première fois, nous développons un algorithme de régression spectrale pour quantifier la régularité de Hölder d'une surface brownienne fractionnée donnée en estimant son paramètre Hurst H. La méthode proposée est évaluée sur un ensemble de sphères browniennes fractionnées simulées. En outre, en supposant que le cortex cérébral est une surface brownienne fractionnée, l'algorithme proposé est appliqué pour estimer les paramètres Hurst d'un ensemble de 14 corticus cérébraux fœtaux. / Surface shape complexity is a morphological characteristic of folded surfaces. In this thesis, we aim at developing some spectral methods to quantify this feature of the human cerebral cortex reconstructed from structural MR images. First, we suggest some properties that a standard measure of surface complexity should possess. Then, we propose two clear definitions of surface complexity based on surface bending properties. To quantify these definitions, we extended the recently introduced graph windowed Fourier transform to mesh model of surfaces. Through some experiments on synthetic surfaces, we show that our curvature-based measurements overcome the classic surface area-based ones which may not distinguish deep folds from oscillating ones with equal area. The proposed method is applied to a database of 124 healthy adult subjects. We also define the surface complexity by the Hölder regularity of fractional Brownian motions defined on manifolds. Then, for the first time, we develop a spectral-regression algorithm to quantify the Hölder regularity of a given fractional Brownian surface by estimating its Hurst parameter H. The proposed method is evaluated on a set of simulated fractional Brownian spheres. Moreover, assuming the cerebral cortex is a fractional Brownian surface, the proposed algorithm is applied to estimate the Hurst parameters of a set of 14 fetal cerebral cortices.

The quadratic class of time-frequency distributions (TFDs) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different TFDs' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare TFDs, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about TFDs are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for TFDs' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of TFDs' properties desirable for practical applications, we define an objective measure to quantify the quality of TFDs. This local measure of TFDs' resolution performance combines all important signal time-varying parameters, along with TFDs' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of TFDs, by modifying their kernel filter parameters to enhance the TFDs' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the TFDs. The resolution performance measure and the accompanying TFDs' comparison criteria allow to improve procedures for designing high-resolution quadratic TFDs for practical time-frequency analysis. The separable kernel TFDs, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.