Most existing computational methods for inverting material properties of multilayer systems have focused primarily on elastic properties of materials or a static approach. Typically, they are based on a two-stage approach: (I) modeling structural responses with a computer program, and (II) estimating layer properties mathematically using the response outputs determined in stage I without interactions with the governing state partial-differential-equation (PDE) of stage I. This two-stage approach may not be accurate and efficient enough for inverting larger scale model parameters. The objective of this research was to develop a computational method to invert dynamic moduli of multilayer systems with applications to flexible pavements under falling weight deflectometer (FWD) tests, thereby advancing existing methods and fostering understanding of material behaviors. This research first developed a finite-element and Newton-Raphson method to invert layer elastic moduli using FWD data. The model improved the moduli seeds estimation and achieved a satisfactory accuracy based on Monte Carlo simulations, addressing the common back-calculation issue of no unique solutions. Consequently, a time-domain finite-element method was developed to simulate dynamic-viscoelastic responses of the multilayer systems under loading pulses. Simulation results demonstrated that the dynamic-viscoelastic-damping-coupled model could emulate structural responses more accurately, thereby advancing existing simulation approaches. By using the dynamic-viscoelastic-response model as one computation module, this research led to the development of a PDE-constrained Lagrangian optimization method to invert dynamic moduli and viscoelastic properties of multilayer systems. The Lagrangian function was used as an objective function, with a regularization term and governing-state PDE constraint. Both the first-order (gradient) and second-order variation (Hessian matrix) of the Lagrangian were computed to satisfy necessary and sufficient optimality conditions, and Armijo rule was modified to determine a stable step length. The developed method improved computation speed significantly, and it is superior for large-scale inverse problems. The model was implemented for evaluating flexible pavements under FWD tests and for inverting the master curve of dynamic moduli of the asphalt layer. Independent computer coding was developed for all numerical methods. The computational methods developed may also be applied to other multilayer systems, such as tissues and sandwich structures at different time and length scales. / text

nÃo hà / Quando se pretende simular o comportamento de uma rede hidrÃulica, à necessÃrio conhecer todos os parÃmetros fÃsicos desta rede. Com o tempo, alguns desses parÃmetros vÃo se alterando naturalmente devido ao desgaste e ao prÃprio uso, isso ocorre, por exemplo, com as rugosidades das tubulaÃÃes. A estimativa desses parÃmetros nÃo se dà por mÃtodos diretos, necessita-se conhecer algumas respostas hidrÃulicas, como vazÃo e pressÃo, para que se possa estimar esses parÃmetros atravÃs de mÃtodos inversos. O processo de busca ocorre atravÃs da comparaÃÃo entre medidas de pressÃo observadas em campo e medidas de pressÃo obtidas por esses mÃtodos. A busca pelo melhor conjunto resposta que represente esses parÃmetros desconhecidos recebe o nome de calibraÃÃo. Desenvolve-se um mÃtodo para estimar a rugosidade das tubulaÃÃes de uma rede hidrÃulica a partir de dados observados de cargas hidrÃulicas transientes durante um evento transitÃrio. O MÃtodo Iterativo do Gradiente HidrÃulico Alternativo (MIGHA) à utilizado como mÃtodo inverso neste trabalho. O transiente à provocado por manobras em uma vÃlvula de controle. Ensaios sÃo realizados em diferentes cenÃrios e sob diferentes condiÃÃes e os resultados mostram um mÃtodo simples, com resultados satisfatÃrios. / The real behavior of a Water distribution System depends on precise knowledge of physical parameters such as diameter, roughness, flow consumption (demands), etc. These parameters commonly change with time. For instance, one of the main parameters, the real roughness, tend to increase with time due to degradation of the specific pipe material. One can not precisely determine the real roughness of a pipe by using direct measurement methods. In order to achieve the objective of estimating roughness with some precision, two parameters of the water distribution network should be measured in the field, these parameters are pipe flow and pressure. Once known these parameters for a reasonable amount of points, equally distributed along the network of pipes, the real roughness may be determined by inverse methods. This process is called calibration. This study proposes a methodology to determine pipe roughness using transient pressure data which occurs during the Water Hammer Analysis phenomena. The Iterative Hydraulic Gradient Method is used as the inverse method in this study. The transient pressure data is produced by changes in the flow caused by opening and closing of Control Valves. According to results presented in this study the new methodology proposed appears to be simple and which produces reliable results.

The objective of the thesis is to formulate a strategy that gives a robust identification of constitutive law from full-field measurements taking into account 3D effects. Model validation from global response of samples or structures has shortcomings that can be overcome by the use of full-field measurement techniques. Full-field measurement techniques offer the opportunity to acquire large amount of experimental data that might be useful in the context of identification of constitutive law parameters. Among the full field measurement techniques the most popular is digital and stereo image correlation. The existing strategies to make use of full-field data like the Virtual Field Method, the Equilibrium Gap Method, the Constitutive Equation Gap Method and the Reciprocity Method were limited to 2D applications. However, for a specimen with finite thickness 3D effects must be included. Most importantly, for the case of plasticity, stress triaxiality plays an important role. Its effect must therefore be accounted for in the modelling of the constitutive behaviour of the material. Thus in this thesis we propose a method to identify the parameters of an elasto-plastic constitutive law in which the mechanical model can have 3D kinematics. The strategy has been shown to be noise robust, almost independent of initial parameter guess and mesh refinement and allows differentiating between constitutive models with same global response on the basis of mean correlation error. The identification is shown to be good for both single and multiple cameras. The strategy validation is done for stainless steel. The global identified load displacement response of the strategy for mono and stereo mechanical image correlation is very close to the experiments. Lastly, the material parameters have been identified with very different initial guess but all converge to the same final values which show the robustness of the proposed strategy.

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Nesta pesquisa, estudamos e comparamos duas maneiras de se construir redes. O principal objetivo do nosso estudo é encontrar uma forma efetiva de se construir redes, especialmente quando temos menos observações do que variáveis. A construção das redes é realizada através da estimação do coeficiente de correlação parcial com base na estatística clássica (inverse method) e na Bayesiana (priori conjugada Normal - Wishart invertida). No presente trabalho, para resolver o problema de se ter menos observações do que variáveis, propomos uma nova metodologia, a qual chamamos correlação parcial local, que consiste em selecionar, para cada par de variáveis, as demais variáveis que apresentam maior coeficiente de correlação com o par. Aplicamos essas metodologias em dados simulados e as comparamos traçando curvas ROC. O resultado mais atrativo foi que, mesmo com custo computacional alto, usar inferência Bayesiana é melhor quando temos menos observações do que variáveis. Em outros casos, ambas abordagens apresentam resultados satisfatórios. / This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Invese Wishart conjugate prior). In this current work, in order to solve the problem of having less observations than variables, we propose a new methodology called local partial correlation, which consists of selecting, for each pair of variables, the other variables most correlated to the pair. We applied these methods on simulated data and compared them through ROC curves. The most atractive result is that, even though it has high computational costs, to use Bayesian inference is better when we have less observations than variables. In other cases, both approaches present satisfactory results.

Nesta pesquisa, estudamos e comparamos duas maneiras de se construir redes. O principal objetivo do nosso estudo é encontrar uma forma efetiva de se construir redes, especialmente quando temos menos observações do que variáveis. A construção das redes é realizada através da estimação do coeficiente de correlação parcial com base na estatística clássica (inverse method) e na Bayesiana (priori conjugada Normal - Wishart invertida). No presente trabalho, para resolver o problema de se ter menos observações do que variáveis, propomos uma nova metodologia, a qual chamamos correlação parcial local, que consiste em selecionar, para cada par de variáveis, as demais variáveis que apresentam maior coeficiente de correlação com o par. Aplicamos essas metodologias em dados simulados e as comparamos traçando curvas ROC. O resultado mais atrativo foi que, mesmo com custo computacional alto, usar inferência Bayesiana é melhor quando temos menos observações do que variáveis. Em outros casos, ambas abordagens apresentam resultados satisfatórios. / This research is about studying and comparing two different ways of building complex networks. The main goal of our study is to find an effective way to build networks, particularly when we have fewer observations than variables. We construct networks estimating the partial correlation coefficient on Classic Statistics (Inverse Method) and on Bayesian Statistics (Normal - Invese Wishart conjugate prior). In this current work, in order to solve the problem of having less observations than variables, we propose a new methodology called local partial correlation, which consists of selecting, for each pair of variables, the other variables most correlated to the pair. We applied these methods on simulated data and compared them through ROC curves. The most atractive result is that, even though it has high computational costs, to use Bayesian inference is better when we have less observations than variables. In other cases, both approaches present satisfactory results.

Les travaux de thèse gravitent autour de la thématique des matériaux poreux en aéronautique, et de la prise en compte de l'incertitude sur les caractérisations réalisées. Est envisagé l'ajout de matériaux poreux au sein des cavités de liners acoustiques, matériaux constitués d'une plaque perforée et d'une cavité fonctionnant sur le principe du résonateur de Helmholtz et majoritairement utilisés dans l'industrie aéronautique. Cet ajout est réalisé avec pour objectif d'augmenter l'étendue spectrale de l'absorption acoustique de tels matériaux et d'en améliorer le fonctionnement en présence d'un fort niveau sonore et d'un écoulement rasant.Pour répondre à cette problématique générale, deux grandes pistes sont suivies. Plusieurs études sont d'abord menées sur des matériaux poreux seuls, afin de déterminer les propriétés intrinsèques de leur micro-géométrie, nécessaires à l'utilisation des modèles semi-phénoménologiques de fluide équivalent adoptés par la suite. Pour cela, un outil statistique d'inférence Bayésienne est utilisé afin d'extraire l'information sur ces propriétés, contenue dans les signaux réfléchis ou transmis par un matériau poreux, et ce dans trois régimes fréquentiels distincts. De plus, une extension de la modélisation des matériaux poreux rigides est proposée, par l'ajout de deux paramètres intrinsèques reliés au comportement visco-inertiel du fluide intra-pores dans le régime des basses fréquences.Dans un second temps, l'impédance d'un liner, une propriété globale représentant le comportement acoustique de matériaux, est identifiée par inférence Bayésienne. Des données issues d'un benchmark de la NASA sont utilisées pour valider l'outil d'inférence développé, lorsque le matériau est en présence d'un écoulement rasant. Une extension des résultats au cas du banc B2A de l'ONERA est également réalisée, avec des mesures des champs de vitesses au dessus du liner, obtenues par LDV. Cette technique d'identification est par la suite utilisée sur un cas issu du B2A où un matériau poreux est présent au sein des cavités du liner, afin de mettre à jour l'influence du matériau poreux sur la réponse acoustique du liner en présence d'un écoulement rasant. Des mesures complémentaires en tube à impédance, sans écoulement et en incidence normale, sont également réalisées à différents niveaux sonores et pour diverses combinaisons de plaques perforées et de matériaux poreux, de façon à mettre en évidence l'influence de la présence d'un matériau poreux sur le comportement acoustique d'un liner soumis à de forts niveaux sonores. / The present work focuses on porous materials in aeronautics and the uncertainty considerations on the performed identifications. Porous materials are added inside the cavities of acoustic liners, materials formed with perforated plates and cavities, behaving as Helmholtz resonators, which are widely used in the industry. The aim is to increase the frequency range of the absorption spectrum, while improving the behaviour of liners to grazing flow and high sound intensity.This general topic is addressed by following two different leads.Porous materials were first considered in order to identify the intrinsic properties of their micro-geometry, necessary to the equivalent fluid semi-phenomenological models used later on. To achieve this, a statistical Bayesian inference tool is used to extract information on these properties, contained in reflected or transmitted signals, in three distinct frequency regimes. Furthermore, a modelling extension of rigid porous media is introduced, by adding two new intrinsic parameters related to the pore micro-structure and linked to the visco-inertial behaviour of the intra-pore fluid, at low frequencies.Then, the liner impedance, a global property representing the acoustic behaviour of materials, is identified through a Bayesian inference process. Data from a NASA benchmark are used to validate the developed tool, when the liner is subject to a shear grazing flow. An extension of these results to ONERA's B2A aeroacoustic bench is also performed, with measurements of the velocity profiles above the liner, obtained with a Laser Doppler Velocimetry technique. This identification technique is then further used for liner materials filled with porous media, to highlight the eventual influence of such a porous media on the acoustic response of the liner, when subject to a shear grazing flow. Additional measurements are permed without flow, at normal incidence, in a classical impedance tube. Different combinations of perforated plates and porous materials are tested at different sound pressure level, to evaluate the influence of the presence of porous media on the non-linear behaviour of liners when high sound pressure levels are present.

Both empirical and process-simulation models are useful for evaluating the effects of management practices on environmental quality and crop yield. The use of these models is limited, however, because they need many soil property values as input. The first step towards modelling is the collection of input data. Soil properties can be highly variable spatially and temporally, and measuring them is time-consuming and expensive. Efficient methods, which consider the uncertainty and cost of measurements, for estimating soil hydraulic properties form the main thrust of this study. Hydraulic properties are affected by other soil physical, and chemical properties, therefore it is possible to develop empirical relations to predict them. This idea quantified is called a pedotransfer function. Such functions may be global or restricted to a country or region. The different classification of particle-size fractions used in Australia compared with other countries presents a problem for the immediate adoption of exotic pedotransfer functions. A database of Australian soil hydraulic properties has been compiled. Pedotransfer functions for estimating water-retention and saturated hydraulic conductivity from particle size and bulk density for Australian soil are presented. Different approaches for deriving hydraulic transfer functions have been presented and compared. Published pedotransfer functions were also evaluated, generally they provide a satisfactory estimation of water retention and saturated hydraulic conductivity depending on the spatial scale and accuracy of prediction. Several pedotransfer functions were developed in this study to predict water retention and hydraulic conductivity. The pedotransfer functions developed here may predict adequately in large areas but for site-specific applications local calibration is needed. There is much uncertainty in the input data, and consequently the transfer functions can produce varied outputs. Uncertainty analysis is therefore needed. A general approach to quantifying uncertainty is to use Monte Carlo methods. By sampling repeatedly from the assumed probability distributions of the input variables and evaluating the response of the model the statistical distribution of the outputs can be estimated. A modified Latin hypercube method is presented for sampling joint multivariate probability distributions. This method is applied to quantify the uncertainties in pedotransfer functions of soil hydraulic properties. Hydraulic properties predicted using pedotransfer functions developed in this study are also used in a field soil-water model to analyze the uncertainties in the prediction of dynamic soil-water regimes. The use of the disc permeameter in the field conventionally requires the placement of a layer of sand in order to provide good contact between the soil surface and disc supply membrane. The effect of sand on water infiltration into the soil and on the estimate of sorptivity was investigated. A numerical study and a field experiment on heavy clay were conducted. Placement of sand significantly increased the cumulative infiltration but showed small differences in the infiltration rate. Estimation of sorptivity based on the Philip's two term algebraic model using different methods was also examined. The field experiment revealed that the error in infiltration measurement was proportional to the cumulative infiltration curve. Infiltration without placement of sand was considerably smaller because of the poor contact between the disc and soil surface. An inverse method for predicting soil hydraulic parameters from disc permeameter data has been developed. A numerical study showed that the inverse method is quite robust in identifying the hydraulic parameters. However application to field data showed that the estimated water retention curve is generally smaller than the one obtained in laboratory measurements. Nevertheless the estimated near-saturated hydraulic conductivity matched the analytical solution quite well. Th author believes that the inverse method can give a reasonable estimate of soil hydraulic parameters. Some experimental and theoretical problems were identified and discussed. A formal analysis was carried out to evaluate the efficiency of the different methods in predicting water retention and hydraulic conductivity. The analysis identified the contribution of individual source of measurement errors to the overall uncertainty. For single measurements, the inverse disc-permeameter analysis is economically more efficient than using pedotransfer functions or measuring hydraulic properties in the laboratory. However, given the large amount of spatial variation of soil hydraulic properties it is perhaps not surprising that lots of cheap and imprecise measurements, e.g. by hand texturing, are more efficient than a few expensive precise ones.

Both empirical and process-simulation models are useful for evaluating the effects of management practices on environmental quality and crop yield. The use of these models is limited, however, because they need many soil property values as input. The first step towards modelling is the collection of input data. Soil properties can be highly variable spatially and temporally, and measuring them is time-consuming and expensive. Efficient methods, which consider the uncertainty and cost of measurements, for estimating soil hydraulic properties form the main thrust of this study. Hydraulic properties are affected by other soil physical, and chemical properties, therefore it is possible to develop empirical relations to predict them. This idea quantified is called a pedotransfer function. Such functions may be global or restricted to a country or region. The different classification of particle-size fractions used in Australia compared with other countries presents a problem for the immediate adoption of exotic pedotransfer functions. A database of Australian soil hydraulic properties has been compiled. Pedotransfer functions for estimating water-retention and saturated hydraulic conductivity from particle size and bulk density for Australian soil are presented. Different approaches for deriving hydraulic transfer functions have been presented and compared. Published pedotransfer functions were also evaluated, generally they provide a satisfactory estimation of water retention and saturated hydraulic conductivity depending on the spatial scale and accuracy of prediction. Several pedotransfer functions were developed in this study to predict water retention and hydraulic conductivity. The pedotransfer functions developed here may predict adequately in large areas but for site-specific applications local calibration is needed. There is much uncertainty in the input data, and consequently the transfer functions can produce varied outputs. Uncertainty analysis is therefore needed. A general approach to quantifying uncertainty is to use Monte Carlo methods. By sampling repeatedly from the assumed probability distributions of the input variables and evaluating the response of the model the statistical distribution of the outputs can be estimated. A modified Latin hypercube method is presented for sampling joint multivariate probability distributions. This method is applied to quantify the uncertainties in pedotransfer functions of soil hydraulic properties. Hydraulic properties predicted using pedotransfer functions developed in this study are also used in a field soil-water model to analyze the uncertainties in the prediction of dynamic soil-water regimes. The use of the disc permeameter in the field conventionally requires the placement of a layer of sand in order to provide good contact between the soil surface and disc supply membrane. The effect of sand on water infiltration into the soil and on the estimate of sorptivity was investigated. A numerical study and a field experiment on heavy clay were conducted. Placement of sand significantly increased the cumulative infiltration but showed small differences in the infiltration rate. Estimation of sorptivity based on the Philip's two term algebraic model using different methods was also examined. The field experiment revealed that the error in infiltration measurement was proportional to the cumulative infiltration curve. Infiltration without placement of sand was considerably smaller because of the poor contact between the disc and soil surface. An inverse method for predicting soil hydraulic parameters from disc permeameter data has been developed. A numerical study showed that the inverse method is quite robust in identifying the hydraulic parameters. However application to field data showed that the estimated water retention curve is generally smaller than the one obtained in laboratory measurements. Nevertheless the estimated near-saturated hydraulic conductivity matched the analytical solution quite well. Th author believes that the inverse method can give a reasonable estimate of soil hydraulic parameters. Some experimental and theoretical problems were identified and discussed. A formal analysis was carried out to evaluate the efficiency of the different methods in predicting water retention and hydraulic conductivity. The analysis identified the contribution of individual source of measurement errors to the overall uncertainty. For single measurements, the inverse disc-permeameter analysis is economically more efficient than using pedotransfer functions or measuring hydraulic properties in the laboratory. However, given the large amount of spatial variation of soil hydraulic properties it is perhaps not surprising that lots of cheap and imprecise measurements, e.g. by hand texturing, are more efficient than a few expensive precise ones.

Les méthodologies de conception des grappes de fonderie reposent fondamentalement sur l’analyse de l’énergie dégagée par le métal au cours de sa solidification. En effet, l’interprétation de ces transferts thermiques permet de calculer localement le temps de solidification et donc d’identifier les points chauds d’une pièce de fonderie. Dans le cas du moulage en sable, ces échanges thermiques sont bien connus et depuis longtemps modélisés (Chvorinov). Leur modélisation correspond à un moule thermiquement infini, c’est à dire que toute l’énergie dégagée par le métal lors de sa solidification est absorbée par le moule. En revanche, dans le cas d’une carapace ou d’une coquille, une partie de cette énergie est transmise à l’environnement via le moule ; ainsi la modélisation la plus adaptée sera donc celle considérant le moule comme un milieu thermiquement fini. Des manipulations de référence ont permis d’acquérir une bonne compréhension des mécanismes thermiques intervenant dans ce procédé de fonderie et mettent en évidence toute la complexité des échanges, à la fois internes et externes au moule (qui se produisent en simultané pendant la phase de solidification du métal). Ces manipulations ont permis par ailleurs, à l’aide de modèles statistiques, d’estimer les paramètres physiques qui sont difficilement accessibles du fait de leurs dépendances et des conditions de travail expérimentales (les échanges avec le milieu ambiant, le coefficient d’échange et le flux entre le métal et le moule). Ces valeurs issues d'expérimentations réalisées en condition réelles serviront à alimenter les bases de données matériaux utilisées en fonderie et dans les simulations numériques. La démarche et les modèles développés dans le cadre de ce travail de thèse permettent un calcul plus fiable qui servira au dimensionnement des masselottes dans le cas du procédé à cire perdue. A plus long terme, cette démarche pourrait être étendue à d’autres procédés de fonderie puisque la méthodologie développée sur du moulage à cire perdue sera transposable aux cas des moules à noyau, des moules métalliques ou autres procédés similaires. / Design casting methodologies are based on the analysis of the energy released by the metal during its solidification. Indeed, the knowledge of this heat transfer permits to faithfully predict local solidification time and to identify last solidified zones. In the case of sand casting, heat exchanges are well known and have been modeled for a long time (Chvorinov). The last, modelize "thermally infinite mold" so in this case whole metal energy threw solidification phase is absorbed by the mold. In contrary, for a shell, a portion of metal energy is transmitted to environment threw the shell, so in this case, the most appropriate model is "a thermally finished mold". Reference experimentations gives a good understanding of energy / thermal mechanisms involved in the casting process and highlight both internal and external shell thermal exchanges complexity (which occur simultaneously during solidification metal). These manipulations allow to use inverse method to estimate hardly measured parameters (such as external heat transfer coefficient or metal-mold interfacial heat transfer), and therefore to build reliable thermal parameters databases used in numerical simulations. Methodology and models developed in this study allow a reliable sizing feed calculation for investment casting. On the long-range, this knowledge could be applied to other foundry processes since the methodology developed on investment casting will be transposed to core molds, die-casting or other molds.