Faire le lien entre la morphologie d'un signal sonore et certains de ses attributs perceptifs est une étape capitale dans l'élaboration d'un synthétiseur proposant un contrôle intuitif. Certains aspects de cette morphologie peuvent être caractérisés au moyen de "descripteurs acoustiques". Lorsqu'ils sont choisis judicieusement, ces descripteurs permettent de classer des signaux dans des catégories ayant un sens perceptif ; ceci permet d'établir un lien entre morphologie et perception. Dans le travail présenté ici, on s'intéresse en particulier à la catégorisation perceptive de sons d'impact.La plupart des descripteurs considérés ici se construisent à partir d'une modélisation paramétrique du signal. Dans notre cas, la modélisation la plus appropriée semble être la décomposition en somme de sinusoïdes amorties. Une estimation stable et rigoureuse des paramètres du modèle étant essentielle au calcul des descripteurs, on se penche sur la comparaison de plusieurs méthodes de décomposition. Il ressort que la méthode à haute résolution ESPRIT semble la plus indiquée, mais qu'elle ne peut pas être utilisée sous sa forme classique. On propose donc différentes adaptations. En particulier, on s'intéresse à l'application d'ESPRIT dans des repères de Gabor. En outre, on propose des méthodes pour maximiser le caractère parcimonieux de la décomposition.On étudie finalement un cas d'application concret : à partir d'une banque de sons enregistrés en chambre anéchoïque résultant d'impacts sur divers objets du quotidien, on évalue la pertinence d'un ensemble de descripteurs pour la catégorisation en fonction du matériau perçu. / Linking an audio signal morphology with some of its perceptual attributes is a key step when elaborating a intuitively controlled synthesizer. Some of these morphology aspects can be characterized using "acoustical descriptors". When chosen wisely, descriptors can allow a classification of audio signals in categories which are perceptually relevant ; in such cases, this approach establishes a link between morphology and perception. The present work focuses on the perceptual categorization of impact sounds.Most of the descriptors proposed here are computed using a parametrized description of the signal. Here, the most appropriate parametrization seems to be a decomposition in exponentially damped sinusoids. A robust and stable estimation of the model parameters being essential to the computation of relevant descriptors, different parametrization methods are described and compared. From these comparisons, it appears that the high-resolution method ESPRIT is the most appropriate, but that it cannot be applied in its classical form. Several adaptations are therefore investigated. In particular, the application of ESPRIT in Gabor frames is considered. Besides, a method is proposed in order to minimize the number of components necessary for a satisfactory decomposition.Finally, a concrete application is addressed : from an impact sounds bank recorded in an anechoic chamber, elaborated with a wide range of everyday-life objects, the relevance of several acoustical descriptors for the perceptual categorization of the perceived material is investigated.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho analisamos as soluÃÃes para a equaÃÃo de movimento para os osciladores de Lane-Emden, onde a massa à dada por m(t)=t^α, onde α>0. Os osciladores de Lane-Emden sÃo osciladores harmÃnicos amortecidos, onde o fator de amortecimento depende do tempo, γ(t)=α/t. Obtivemos as expressÃes analÃticas de q(t), dq(t)/dt, and p(t)=m(t)(dq(t)/dt) para α=2 e α=4. Discutimos as diferenÃas entre as expressÃes da hamiltoniana e da energia para sistemas dependentes do tempo. TambÃm, comparamos nossos resultados com aqueles do oscilador de Caldirola-Kanai. Usamos o mÃtodo dos invariantes quÃnticos e uma transformaÃÃo unitÃria para obter a funÃÃo de onda exata de SchrÃdinger, ψn (q,t), e calcular para n=0 a entropia conjunta (entropia de Leipnik) dependente do tempo e as informaÃÃes Fisher para posiÃÃo (Fq) e para o momento (Fp) para duas classes de osciladores harmÃnicos quÃnticos amortecidos. Observamos que a entropia de Leipnik nÃo varia no tempo para o oscilador Caldirola-Kanai, enquanto diminui e tende a um valor constante (ln(e/2)) para tempos assintÃticos para o oscilador de Lane-Emden. Isto à devido ao fato de que, para este Ãltimo, o fator de amortecimento diminui à medida que o tempo aumenta. Os resultados mostram que a dependÃncia do tempo da entropia de Leipnik à bastante complexa e nÃo obedece a uma tendÃncia geral de aumento monotonicamente com o tempo e que Fq aumenta enquanto Fp diminui com o aumento do tempo. AlÃm disso, FqFp aumenta e tende a um valor constante (4/ℏ^2 ) no limite em que t->∞. NÃs comparamos os resultados com os do bem conhecido oscilador de Caldirola-Kanai. / In this work we analyze the solutions of the equations of motions for two Lane-Emden-type Caldirola-Kanai oscillators. For these oscillators the mass varies as m(t)=t^α, where α>0.We obtain the analytical expression of q(t), dq(t)/dt, and p(t)=m(t)(dq(t)/dt) for α=2 and α=4. These are damped-like harmonic oscillators with a time-dependent damping factor given by γ(t)=α/t. We discuss the differences between the expressions for the hamiltonian and the mechanical energy for time-dependent systems. We also compared our results to those of the well-known Caldirola-Kanai oscillators. We use the quantum invariant method and a unitary transformation to obtain the exact SchrÃdinger wave function, ψn (q,t), and calculate for n=0 the time-dependent joint entropy (LeipnikÂs entropy) and the position (Fq) and momentum (Fp) Fisher information for two classes of quantum damped harmonic oscillators. We observe that the joint entropy does not vary in time for the Caldirola-Kanai oscillator, while it decreases and tends to a constant value (ln(e/2)) for asymptotic times for the Lane-Emden ones. This is due to the fact that for the latter, the damping factor decreases as time increases. The results show that the time dependence of the joint entropy is quite complex and does not obey a general trend of monotonously increase with time and that F_q increases while F_p decreases with increasing time. Also, FqFp increases and tends to a constant value (4/ℏ^2 ) in the limit t->∞.We compare the results with those of the well-known Caldirola-Kanai oscillator.

Les phénomènes de contact entre les corps, déformables ou non, sont omniprésents dans la vie courante. Leurs modélisations requièrent des outils mathématiques faisant appel à des systèmes d'équations aux dérivées partielles incluant des conditions aux limites non triviales pour décrire le contact. Si les aspects physiques de la mécanique du contact sont connus depuis longtemps, la théorie mathématique qui lui est dédiée reste relativement récente laissant ainsi place à de nombreux problèmes à investiguer. Ce travail porte sur la modélisation, l'analyse et la simulation numérique de tels problèmes. Il se situe à mi-chemin entre la mécanique du contact et les aspects mathématiques inhérents au type de problème qui en découle. L'objectif est ici d'étudier certaines catégories de problèmes faisant intervenir des conditions originales de contact (avec et sans frottement) à la fois d'un point de vue mathématique et numérique, afin d'apporter une contribution à la théorie mathématique, puis de mettre en avant quelques méthodes numériques adaptées à leur résolution dans un cadre spécifique. / Contact phenomena between bodies, whether they are deformable or not, abound in everyday life. Their modellings require mathematical tools using systems of partial differential equations and involving complex boundary conditions, in order to describe the contact. While the physical aspects of such phenomena have been known for a long time, the mathematical theory remains relatively recent which leaves room for numerous problems. This work focuses on the modelling, the analysis and the numerical simulations of such problems. It is located halfway between contact mechanics and the mathematical aspects inherent to the mechanical questions involved. Our aim is to study several groups of problems that include original contact conditions (with or without friction), both from a mathematical and numerical point of view, in order to contribute to the theory, and also to highlight several numerical methods used to solve specific contact problems.

Ce mémoire porte sur l'étude et l’optimisation du fonctionnement des extensomètres à corde vibrante pour la surveillance des constructions stratégiques. Ce travail se décompose en trois étapes.Premièrement, le fonctionnement du capteur en mode amorti et en mode entretenu est décrit. Un dispositif électronique de lecture à base de microcontrôleur est réalisé pour valider les développements. Deuxième, le comportement du capteur est étudié en établissant des modèles représentant les couplages magnéto-mécaniques entre la corde vibrante, la bobine d'excitation et la bobine de mesure. Les influences du mode d'excitation et des paramètres parasites sur la réponse du capteur sont analysées. Enfin, l'effet de la foudre est simulé en utilisant un simulateur de décharge électrostatique. La réponse du capteur est mesurée avant, pendant et après la décharge. Les résultats de ce travail peuvent se résumer en quatre points essentiels. Premièrement, le mode entretenu est préférable au mode amorti. Deuxièmement, la position d'excitation optimale est au centre de la corde. De plus, une excitation continue ou une excitation pulsée d'un grand nombre de cycles est préférable à une excitation pulsée d'un petit nombre de cycles. Troisièmement, la fréquence de résonance mesurée en mode entretenu diffère de celle mesurée en mode amorti à cause de deux paramètres : la force magnétique moyenne et le couplage mutuel entre les bobines. Quatrièmement, sous l'action des décharges, le champ magnétique résiduel est modifié, conduisant ainsi à une modification de la fréquence de résonance mesurée par le capteur. / This thesis focuses on the study and the optimization of the operation of vibrating wire sensors for strategic construction monitoring. This work is divided into three stages.Firstly, the sensor operation in damped mode and in sustained mode is described. To validate the developments, an electronic microcontroller-based reading device is realized. Secondly, the sensor behavior is investigated by establishing models representing the magneto-mechanical coupling between the vibrating wire, the excitation coil and the measurement coil. The influences of excitation mode and spurious parameters on the sensor response are analyzed. Finally, the effect of lightning is simulated using electrostatic discharge simulator. The sensor response is measured before, during and after discharge.The results of this work can be summarized in four main points. Firstly, the sustained mode is preferable to the damped mode. Secondly, the optimal excitation position is at the center of the wire. Furthermore, a continuous excitation or a pulsed excitation of a large number of cycles is preferable to a pulsed excitation of a small number of cycles. Thirdly, the resonant frequency measured in sustained mode differs from that measured in damped mode due to two parameters: average magnetic force and mutual coupling between coils. Fourthly, under the action of discharges, the remaining magnetic field is modified, thus leading to a variation in the resonant frequency measured by the sensor.

Negative-imaginary systems are broadly speaking stable and square (equal number of inputs and outputs) systems whose Nyquist plot lies underneath (never touches for strictly negative-imaginary systems) the real axis when the frequency varies in the open interval 0 to ∞. This class of systems appear quite often in engineering applications, for example, in lightly damped flexible structures with collocated position sensors and force actuators, multi-link robots, DC machines, active filters, etc. In this thesis, robustness analysis and controller synthesis methods for uncertain negative-imaginary systems are explored. Two new reformulation techniques are proposed that facilitate both the robustness analysis and controller synthesis for uncertain negative-imaginary systems. These reformulations are based on the transformation from negative-imaginary systems to a bounded-real framework via the positive-real property. In the presence of strictly negative-imaginary uncertainty, the robust stabilization problem is posed in an equivalent H∞ control framework; similarly, a negative-imaginary robust performance analysis problem is cast into an equivalent μ-framework. The latter framework also allows robust stability analysis when the perturbations are a mixture of bounded-real and negative-imaginary uncertainties. The proposed two techniques pave the way for existing H∞ control and μ theory to be applied to robustness analysis and controller synthesis for negative-imaginary systems. In addition, a static state-feedback synthesis method is proposed to achieve robust stability of a system in the presence of strictly negative-imaginary uncertainties. The method is developed in the LMI framework, which can be solved efficiently using convex optimization techniques. The controller synthesis method is based on the negative-imaginary stability theorem: a positive feedback interconnection of two negative-imaginary systems is internally stable if and only if the DC loop gain is contractive and at least one of the systems in the interconnected loop is strictly negative-imaginary. Also, in order to handle non-strict negative-imaginary uncertainties, a strongly strictly negative-imaginary lemma is proposed that helps to ensure the strictly negative-imaginary property of the nominal closed-loop system for robustness. To this end, a state-space characterization for strictly negative-imaginary property is given for non-minimal systems where the conditions are convex and hence numerically attractive. The results in this thesis hence facilitate both the robustness analysis and controller synthesis for negative-imaginary systems that quite often arise in practical scenarios. In addition, they can be applied to quantify the worse-case performance for this class of systems. Therefore, the proposed results have important implications in controller synthesis for uncertain negative-imaginary systems that achieve not only robust stabilization but also robust performance.

This work deals with the power supply of wireless sensors. When using a wireless sensor is desirable application of alternative energy sources, because the primary cells or batteries may reduce the extent or length of service of the sensor itself. Ambient energy can be used as a suitable alternative source. This energy must be in an appropriate form, which allows its conversion to electric energy. These appropriate, already used types include: solar en., temperature gradient en., en. of flowing liquids, vibration, etc. The advantage of vibrations is its presence in almost all mechanical systems. One of the possibilities for using the vibration of machine systems for power supply wireless sensors is using the vibration power generator with oscillating component. The generator must be designed so that its resonance frequency coincides with the frequency of vibration in the machine system. This method can be used only if the machinery system vibrations at least partially constant. Another option is to use the vibrations caused by, for example, transit transport, or different step acting factor. In this case, it is desirable that the generator is designed with variable resonant frequency, which can partly be achieved, for example, integrating several oscillating component in the body of generator. After the general analysis of the problem, graduation theses will be concerned with the possibility of use of energy from the short damped oscillation and step impulse. Focusing on a proposal of multi-element structures.

An algorithm is presented which computes a state feedback for a standard linear system which not only stabilizes, but also dampens the closed-loop system dynamics. In other words, a feedback gain vector is computed such that the eigenvalues of the closed-loop state matrix are within the region of the left half-plane where the magnitude of the real part of each eigenvalue is greater than the imaginary part. This may be accomplished by solving one periodic algebraic Riccati equation and one degenerate Riccati equation. The solution to these equations are computed using numerically robust algorithms. Finally, the periodic Riccati equation is unusual in that it produces one symmetric and one skew symmetric solution, and as a result two different state feedbacks. Both feedbacks dampen the system dynamics, but produce different closed-loop eigenvalues, giving the controller designer greater freedom in choosing a desired feedback.

In this thesis the path integral formalism is applied to the calculation of the dynamics of dissipative quantum systems. The time evolution of a system of bilinearly coupled bosonic modes is treated using the real-time path integral technique in coherent-state representation. This method is applied to a damped harmonic oscillator within the Caldeira-Leggett model. In order to get the stationary trajectories the corresponding Lagrangian function is diagonalized and then the path integrals are evaluated by means of the stationary-phase method. The time evolution of the reduced density matrix in the basis of coherent states is given in simple analytic form for weak system-bath coupling, i.e. the so-called rotating-wave terms can be evaluated exactly but the non-rotating-wave terms only in a perturbative manner. The validity range of the rotating-wave approximation is discussed from the viewpoint of spectral equations. In addition, it is shown that systems without initial system-bath correlations can exhibit initial jumps in the population dynamics even for rather weak dissipation. Only with initial correlations the classical trajectories for the system coordinate can be recovered. The path integral formalism in a combined phase-space and coherent-state representation is applied to the problem of curve-crossing dynamics. The system of interest is described by two coupled one-dimensional harmonic potential energy surfaces interacting with a heat bath. The mapping approach is used to rewrite the Lagrangian function of the electronic part of the system. Using the Feynman-Vernon influence-functional method the bath is eliminated whereas the non-Gaussian part of the path integral is treated using the perturbation theory in the small coordinate shift between potential energy surfaces. The vibrational and the population dynamics is considered in a lowest order of the perturbation. The dynamics of a Gaussian wave packet is analyzed along a one-dimensional reaction coordinate. Also the damping rate of coherence in the electronic part of the relevant system is evaluated within the ordinary and variational perturbation theory. The analytic expressions for the rate functions are obtained in the low and high temperature regimes.

The thesis consists of two parts, a theoretical part and an applied part, and in addition an Appendix. Except for a very short chapter in the applied part and the appendix we only present previously unknown results leading to a very concise style. In the theoretical part we study rates of decay for vector-valued functions and semigroups of operators depending on a real and positive variable. Under boundedness assumptions on the function/semigroup itself and under analytic extendability assumptions of its Laplace transform/resolvent across the imaginary axis we provide (almost) sharp rates of decay. Our results improve known results in this very active area of research. In the second part of the thesis we apply our results to specific examples (from the field of PDEs): local energy decay for wave equations on exterior domains, energy decay for damped wave equations on bounded domains and decay for a viscoelastic boundary damping model for sound waves. Many more examples can be found in the vast literature.:Part 1 Quantified Tauberian theorems and decay of C0-semigroups 1 Decay of vector-valued functions 2 Optimal decay for C0-semigroups on Hilbert spaces Part 2 Applications: decay of waves 3 Local decay for waves in exterior domains 4 Waves on a square with constant damping on a strip 5 A viscoelastic boundary damping model

In this thesis we study the global existence of small data solutions to the Cauchy problem for semilinear damped wave equations with an effective dissipation term, where the data are supposed to belong to different classes of regularity. We apply these results to the Cauchy problem for weakly coupled systems of semilinear effectively damped waves with respect to the defined classes of regularity for different power nonlinearities. We also presented blow-up results for semi-linear systems with weakly coupled damped waves.