The research presented in this thesis addresses the problem of updating an analytical model using a parametric Reference Basis approach. In this method, some parameters are assumed to be accurate (e.g. natural frequencies, mode shapes and mass matrix), while others are adjusted so that the eigenvalue equation is satisfied. Updating is done with the use of principal submatrices, and the method seeks the best parameters multiplying these matrices. This is a departure from classical model reference, and is closer to the formulation of sensitivity methods. The submatrices allow updating of the stiffness matrix with certain freedom while preserving connectivity. Closed form solution can be achieved through multiple ways; two different approaches, denoted as the Quadratic Compression Method (QCM) and the Full Vector Method (FVM), are described in this paper. It is shown that the QCM possesses superior robustness properties with respect to noise in the data. This fact, as well as the simplicity offered by QCM, is demonstrated theoretically and experimentally. The experiments are presented to show the advantage of the QCM in the updating process. / Master of Science

We address the problem of identifying the neighborhood structure of an undirected graph, whose nodes are labeled with the elements of a multivariate normal (MVN) random vector. A semi-definite program is given for estimating the information matrix under arbitrary constraints on its elements. More importantly, a closed-form expression is given for the maximum likelihood (ML) estimator of the information matrix, under the constraint that the information matrix has pre-specified elements in a given pattern (e.g., in a principal submatrix). The results apply to the identification of dependency labels in a graphical model with neighborhood constraints. This neighborhood structure excludes nodes which are conditionally independent of a given node and the graph is determined by the non- zero elements in the information matrix for the random vector. A cross-validation principle is given for determining whether the constrained information matrix returned from this procedure is an acceptable model for the information matrix, and as a consequence for the neighborhood structure of the Markov Random Field (MRF) that is identified with the MVN random vector.

For target location and tracking in wireless communication systems, mobile target positioning and tracking play an important role. Since multi-sensor system can be used as an efficient solution to target positioning process, more accurate target location estimation and tracking results can be obtained. However, both the deployment of designed multi-sensor and location algorithm may affect the overall performance of position location. In this thesis, based on the time difference of arrival (TDOA), two closed-form least-square location methods, spherical-interpolation (SI) method and spherical-intersection (SX) method are used to estimate the target location. The two location methods are different from the usual process of iterative and nonlinear minimization. The locations of the target and the designed multiple sensors may yield geometric effects on location performance. The constraints and performance of the two location methods will first be introduced. To achieve real-time target tracking, the Kalman filtering structures are used to combine the SI and SX methods. Because these two positioning and tracking systems have different and complementary performance inside and outside the multi-sensor array, we consider using data fusion to improve location estimation results by using interacting multiple model (IMM) based estimator, in which internal filters running in parallel are designed as the SX-KF1 and the SI-KF2. However, due to the time-varying characteristics of measurement noises, we propose an adjusting scheme for measurement noise variance assignment in the Kalman filters to obtain improved location estimation results. Simulation results are obtained by running Matlab program. In three-dimensional multi-sensor array scenarios, the results of moving target location estimation shows that the IMM-based estimators effectively improve the position performance.

The world-wide development of new high-speed rail lines has led to more stringent design requirements for railway bridges, mainly because high-speed trains can cause resonance in the bridge superstructure. Dynamic simulations, often utilising time-consuming finite element analysis (FEA), have become essential for avoiding such problems. Therefore, guidelines and tools to assist structural engineers in the design process are needed. Considerable effort was spent at the beginning of the project, to develop simplified models based on two-dimensional (2D) Bernoulli-Euler beam theory. First, a closed-form solution for proportionally damped multi-span beam, subjected to moving loads was derived (Paper I). The model was later used to develop design charts (Paper II) and study bridges on existing railway lines (Paper III). The model was then extended to non-proportionally damped beams (Paper IV) in order to include the effects of soil-structure interactions. Finally, the importance of the interaction between the surrounding soil and the bridge was verified by calibrating a finite element (FE) model by means of forced vibration tests of an end-frame bridge (Paper V). Recommendations on how to use the models in practical applications are discussed throughout the work. These recommendations include the effects of shear deformation, shear lag, train-bridge and soil-structure interactions, for which illustrative examples are provided. The recommendations are based on the assumption that the modes are well separated, so that the response at resonance is governed by a single mode. The results of the work show that short span bridges, often referred to as `simple´ bridges, are the most problematic with respect to dynamic effects. These systems are typically, non-proportionally damped systems that require detailed analyses to capture the `true´ behaviour. Studying this class of dynamic system showed that they tend to contain non-classical modes that are important for the structure response. For example, the bending mode is found to attain maximum damping when its undamped natural frequency is similar to that of a non-classical mode. / <p>QC 20170213</p>

Le but de ce travail est de développer un outil d'aide à l'analyse de mission pour un satellite artificiel autour de la Lune. Nous développons tout d'abord une théorie analytique qui décrit suffisamment bien la dynamique du satellite lunaire : nous considérons les quatre perturbations majeures de natures différentes qui l'influencent, ainsi que leurs différents couplages. Les résultats sont obtenus sous forme fermée, sans aucun développement en série de l'excentricité ni de l'inclinaison de l'orbite du satellite : la solution s'applique donc à une large gamme de valeurs. Nous utilisons la méthode des Transformées de Lie pour moyenniser deux fois l'Hamiltonien du problème, dans des variables canoniques, ce qui permet d'intégrer des orbites avec un temps de calcul réduit d'un facteur environ 200 000. Grâce à cela, nous produisons des cartes inédites d'espaces de phase (a,i) qui permettent de sélectionner les paramètres orbitaux selon les besoins de la mission lunaire. De nombreuses vérifications analytiques par rapport à la littérature ont été réalisées, et se sont avérées concluantes; la qualité des deux moyennisations a également été vérifiée. Le logiciel développé est souple et permet un traitement automatisé; les intégrations sont automatiquement vérifiées. Nous avons aussi apporté quelques améliorations significatives au manipulateur algébrique des FUNDP, comme l'ajout de fractions symboliques. Par ailleurs, nous résolvons le problème zonal complet du satellite artificiel, étudions l'effet de C22 sur l'inclinaison critique ainsi que l'effet de la Terre sur les durées de vie orbitales limitées de certains satellites lunaires. The aim of this work is to develop a tool helpful to mission analysis of a lunar artificial satellite. We first develop an analytical theory which sufficiently well describes the dynamics of the lunar satellite : we consider the four main perturbations of various kind which influence it, together with their several coupling. The results are obtained in closed form, without any series expansion in eccentricity nor inclination of the orbit of the satellite : so the solution applies for a wide range of values. We use the Lie Transform method for averaging twice the Hamiltonian of the problem, in canonical variables, which allows to integrate orbits with a CPU time reduced by a factor of about 200 000. Thanks to that, we produce unpublished (a,i) phase space maps from which the orbital parameters can be selected on the basis of the needs of the lunar mission. Many conclusive analytical checks with the literature have been performed, and both averaging processes have been checked. The software developed is flexible and allows an automated treatment; the integrations are automatically checked. We also improved significantly the algebraic manipulator of the FUNDP, like the inclusion of symbolic fractions. Moreover, we solve the complete zonal problem of the artificial satellite, we study the effect of C22 on the critical inclination, and also the effect of the Earth on the limited orbital lifetimes of some lunar satellites.

The steady state response of thin-walled members subjected to harmonic forces is investigated in the present study. The governing differential equations of motion and associated boundary conditions are derived from the Hamilton variational principle. The harmonic form of the applied forces is exploited to eliminate the need to discretize the problem in the time domain, resulting in computational efficiency. The formulation is based on a generalization of the Timoshenko-Vlasov beam theory and accounts for warping effects, shear deformation effects due to bending and non-uniform warping, translational and rotary inertial effects and captures flexural-torsional coupling arising in asymmetric cross-sections. Six of the resulting seven field equations are observed to be fully coupled for asymmetric cross-sections while the equation of longitudinal motion is observed to be uncoupled. Separate closed form solutions are provided for the cases of (i) doubly symmetric cross sections, (ii) monosymmetric cross-sections, and (iii) asymmetric cross-sections. The closed-form solutions are provided for cantilever and simply-supported boundary conditions. A family of shape functions is then developed based on the exact solution of the homogeneous field equations and then used to formulate a series of super-convergent finite beam elements. The resulting two-noded beam elements are shown to successfully capture the static and dynamic responses of thin-walled members. The finite elements developed involve no special discretization errors normally encountered in other finite element formulations and provide results in excellent agreement with those based on other established finite elements with a minimal number of degrees of freedom. The formulation is also capable to predict the natural frequencies and mode-shapes of the structural members. Comparisons with non-shear deformable beam solutions demonstrate the importance of shear deformation effects within short-span members subjected to harmonic loads with higher exciting frequencies. Comparisons with shell element solution results demonstrate that distortional effects are more pronounced in cantilevers with short spans. A generalized stress extraction scheme from the finite element formulation is then developed. Also, a generalization of the analysis procedure to accommodate multiple loads with distinct exciting frequencies is established. The study is concluded with design examples which illustrate the applicability of the formulation, in conjunction with established principles of fatigue design, in determining the fatigue life of steel members subjected to multiple harmonic forces.

Modern statistics typically deals with complex data, in particular where the ambient dimension of the problem p may be of the same order as, or even substantially larger than, the sample size n. It has now become well understood that even in this type of high-dimensional scaling, statistically consistent estimators can be achieved provided one imposes structural constraints on the statistical models. In spite of great success over the last few decades, we are still experiencing bottlenecks of two distinct kinds: (I) in multivariate modeling, data modeling assumption is typically limited to instances such as Gaussian or Ising models, and hence handling varied types of random variables is still restricted, and (II) in terms of computation, learning or estimation process is not efficient especially when p is extremely large, since in the current paradigm for high-dimensional statistics, regularization terms induce non-differentiable optimization problems, which do not have closed-form solutions in general. The thesis addresses these two distinct but highly complementary problems: (I) statistical model specification beyond the standard Gaussian or Ising models for data of varied types, and (II) computationally efficient elementary estimators for high-dimensional statistical models. / text

This work analytically solves the governing equations of the laminar film condensation from pure vapors in vertical tubes to find the condensate film thickness. The solution is then extended to turbulent flow conditions for steam. All other relevant quantities are derived from the film thickness solution. For laminar film condensation of quiescent vapors, an exact explicit solution and an approximate closed-form solution were found by using a new definition of the dimensionless film thickness, the Lambert W-function, and a logarithmic function approximation. For laminar mixed-convection film condensation with interfacial shear stress, an approximate closed-form solution was found by using a new definition of the pressure gradient. For turbulent film condensation of steam, correlations of the turbulent vapor and liquid viscosities were formed by asymptotically comparing this approximate laminar closed-form solution to a turbulent flow numerical solution. The present solutions compared very well to published numerical and experimental data.

The steady state response of thin-walled members subjected to harmonic forces is investigated in the present study. The governing differential equations of motion and associated boundary conditions are derived from the Hamilton variational principle. The harmonic form of the applied forces is exploited to eliminate the need to discretize the problem in the time domain, resulting in computational efficiency. The formulation is based on a generalization of the Timoshenko-Vlasov beam theory and accounts for warping effects, shear deformation effects due to bending and non-uniform warping, translational and rotary inertial effects and captures flexural-torsional coupling arising in asymmetric cross-sections. Six of the resulting seven field equations are observed to be fully coupled for asymmetric cross-sections while the equation of longitudinal motion is observed to be uncoupled. Separate closed form solutions are provided for the cases of (i) doubly symmetric cross sections, (ii) monosymmetric cross-sections, and (iii) asymmetric cross-sections. The closed-form solutions are provided for cantilever and simply-supported boundary conditions. A family of shape functions is then developed based on the exact solution of the homogeneous field equations and then used to formulate a series of super-convergent finite beam elements. The resulting two-noded beam elements are shown to successfully capture the static and dynamic responses of thin-walled members. The finite elements developed involve no special discretization errors normally encountered in other finite element formulations and provide results in excellent agreement with those based on other established finite elements with a minimal number of degrees of freedom. The formulation is also capable to predict the natural frequencies and mode-shapes of the structural members. Comparisons with non-shear deformable beam solutions demonstrate the importance of shear deformation effects within short-span members subjected to harmonic loads with higher exciting frequencies. Comparisons with shell element solution results demonstrate that distortional effects are more pronounced in cantilevers with short spans. A generalized stress extraction scheme from the finite element formulation is then developed. Also, a generalization of the analysis procedure to accommodate multiple loads with distinct exciting frequencies is established. The study is concluded with design examples which illustrate the applicability of the formulation, in conjunction with established principles of fatigue design, in determining the fatigue life of steel members subjected to multiple harmonic forces.

This work analytically solves the governing equations of the laminar film condensation from pure vapors in vertical tubes to find the condensate film thickness. The solution is then extended to turbulent flow conditions for steam. All other relevant quantities are derived from the film thickness solution. For laminar film condensation of quiescent vapors, an exact explicit solution and an approximate closed-form solution were found by using a new definition of the dimensionless film thickness, the Lambert W-function, and a logarithmic function approximation. For laminar mixed-convection film condensation with interfacial shear stress, an approximate closed-form solution was found by using a new definition of the pressure gradient. For turbulent film condensation of steam, correlations of the turbulent vapor and liquid viscosities were formed by asymptotically comparing this approximate laminar closed-form solution to a turbulent flow numerical solution. The present solutions compared very well to published numerical and experimental data.