In most applications, the structure components have to be tested under different loading conditions before being placed in operation. A reliable and low cost measuring technique is desirable. However, most currently employed measuring approaches can only provide the structural response at several discrete locations. The accuracy of the measurements varies with the location and orientation of the sensors. Practically, it is not possible to place sensors at all the critical locations for different excitations. Therefore, an approach that derives the full field response using a limited set of measured data is desirable. In contrast to experimental full field measurement techniques, the expansion approach involves analytically expanding the limited measurements to all the degrees of freedom of the structure. Among all the analytical methods, the modal expansion method is computationally efficient and thus more suitable for real time expansion of measured data. In this method, the full-field response is approximated by the linear combination of mode shapes. In previous studies, the modal expansion method is limited by errors from mode aliasing, inaccuracy of the calculated mode shapes and the noise in measurements. In order to overcome these limitations, the modal expansion method is enhanced by mode selection and error compensation in this study. First, the key parameters used in modal expansion method were analyzed using a cantilever beam model and a method for optimal placement of sensors was developed. A mode selection method and error compensation method based on operation modal analysis and adaptive compressed sensing techniques were then developed to reduce the effects of mode aliasing, mode shape inaccuracy and measurement noise. The developed approach was further tested virtually using a numerical model of rotor 67. The numerical model was created using a two-way coupled fluid structure interaction technique. By developing these methods, the enhanced modal expansion approach can provide full field response for structures under different load conditions. Compared to the traditional modal expansion method, it can expand the data with high noise and under general dynamic loading. / Doctor of Philosophy / Accurate knowledge of the strain and stress at critical locations of a given structure is crucial when assessing its integrity. However, currently employed measuring approaches can only provide the structural response at several discrete locations. Practically, it is not possible to place sensors at all the critical locations for different excitations. Therefore, an approach that derives the full field response using a limited set of measured data is desirable. Compared to experimental full field measurement techniques, the expansion approach is focused on analytically expanding the limited measurements to all the degrees of freedom of the structure. Among all the analytical methods, the modal expansion method is computationally efficient and thus more suitable for real-time expansion of measured data. The current modal expansion method is limited by errors from mode aliasing, inaccuracy of the mode shapes, and the noise in measurements. Therefore, an enhanced method is proposed to overcome these shortcomings of the modal expansion. The following objectives are accomplished in this study: 1) Develop a method for optimal placement of sensors for modal expansion; 2) Eliminate the mode aliasing effects by determining the significance of participated modes using operational modal analysis techniques; 3) Compensate for the noise in measurements and computational model by implementing the compressed sensing approach. After accomplishing these goals, the developed approach is able to provide full field response for structures under different load conditions. Compared to the traditional modal expansion method, it can expand the data under dynamic loading; it also shows promise in reducing the effects of noise and errors. The developed approach is numerically tested using fluid-structure interaction model of rotor 67 fan blade.

Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects -- metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual `square' to a novel `hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects -- metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual `square' to a novel `hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Les microphones capacitifs sont des transducteurs réciproques dont les qualités (sensibilité, bande passante et tenue dans le temps) en font des instruments de mesure performants. Couramment utilisés jusqu’à présent en récepteurs dans l’air à pression atmosphérique et à température ambiante, dans la gamme de fréquences audibles, ils sont correctement caractérisés dans ce cadre depuis près de trente ans. Mais aujourd’hui, leur miniaturisation (par procédé MEMS) et leur usage nouveau en métrologie fine (en récepteurs comme en émetteurs) - qui exigent une connaissance précise de leur comportement dans des domaines de fréquences élevées (jusqu’à 100 kHz), dans des mélanges gazeux aux propriétés différentes de celles de l’air et dans des conditions de pression et de température beaucoup plus élevées ou beaucoup plus basses que les conditions standards - nécessitent une caractérisation beaucoup plus approfondie, aussi bien en terme de modélisation qu’en terme de résultats expérimentaux. C’est ainsi que ici -i/ les effets des couches limites thermiques (seules les couches limites visqueuses sont habituellement retenues) sont introduits dans le modèle, ce qui amène dans le chapitre premier à une étude analytique de la diffusion thermique en parois minces (dont la portée dépasse le cadre strict du transducteur), -ii/ l’influence des orifices de l’électrode arrière sur la déformée de la membrane est traitée au départ par une méthode analytique originale, qui permet de traduire les conditions en frontière non uniformes sur la surface de l’électrode sous forme de sources locales virtuelles, associées à des conditions de frontière rendues uniformes (chapitre second), -iii/ des solutions analytiques nouvelles, dépendant à la fois des coordonnées radiales et azimutales, sont obtenues pour le champ de déplacement de la membrane et pour les champs de pression dans les cavités du microphone par usage de théories modales compatibles avec les couplages multiples qui y prennent place (troisième chapitre), -iv/ un modèle de « circuit à constantes localisées » (reporté pour l’essentiel en annexe) est proposé, à des degrés divers de précision, qui permet en particulier d’accéder de façon simple à la sensibilité et au bruit thermique du microphone (fin du quatrième chapitre), -v/ une étude au vibromètre laser à balayage a été réalisée (début du quatrième chapitre), qui permet non seulement de mettre en évidence pour la première fois les déformées de membrane complexes qui apparaissent en hautes fréquences, mais encore de les quantifier et par-delà de valider les résultats théoriques obtenus et donc les modèles proposés (même s’ils restent perfectibles comme indiqué dans la conclusion). / Condenser microphones are reciprocal transducers whose properties (sensitivity, bandwidth and reliability) make them powerful measurement tools. So far, they have been commonly used as receivers in the audible frequency range, in air at atmospheric pressure and ambient temperature, they have been appropriately characterised in this context for nearly thirty years. But nowadays, their miniaturisation (using MEMS processes) and their new use for metrological purposes (as receivers as well as transmitters) require much deeper theoretical and experimental characterisations because they require an accurate knowledge of their behaviour in high frequency ranges (up to 100 kHz), in gas mixtures, whose properties differ from those of air, and under pressure and temperature conditions much higher or much lower than standard conditions. Thus, here, -i/ the effects of the thermal boundary layers are introduced in the model (only viscous boundary layers are usually accounted for), leading, in the first chapter, to an analysis of the thermal diffusion of thin bodies (whose scope is beyond the strict frame of capacitive transducers), ii/ the influence of the holes in the backing electrode on the dynamic behaviour of the membrane is initially handled with an original analytical method which allows expressing the non-uniform boundary conditions at the surface of the backing electrode as fictitious localised sources associated to uniform boundary conditions (second chapter), -iii/ new analytical solutions, depending both on the radial and azimuthal coordinates, for the pressure field and for the displacement field inside the cavities behind the membrane are expressed using modal theories in agreement with the strong couplings which occur between the different parts of the transducer (chapter three), -iv/ "lumped element circuits", which are more or less approximated (presented in the Appendix), more particularly result in expressing and assessing the sensitivity and the thermal noise (end of chapter three), -v/ experimental results, obtained from measurements of the displacement field of the membrane using a laser scanning vibrometer, both highlight and quantify for the first time the complex behaviour of the membrane in the highest frequency range, and finally lead to the validation of the theoretical results and therefore, the models presented here (even if the latter may still be improved as outlined in the conclusion).