A GENERIC RELIABILITY ANALYSIS AND DESIGN FRAMEWORK WITH RANDOM PARAMETER, FIELD, AND PROCESS VARIABLES

This dissertation aims at developing a generic reliability analysis and design framework that enables reliability prediction and design improvement with random parameter, field, and process variables. The capability of this framework is further improved by predicting and managing reliability even with a dearth of data that can be used to characterize random variables. To accomplish the research goal, three research thrusts are set forth. First, advanced techniques are developed to characterize the random field or process. The fundamental idea of these techniques is to model the random field or process with a set of important field signatures and random variables. These techniques enable the use of random parameter, field, and process variables for reliability analysis and design even with a dearth of data. Second, a generic reliability analysis framework is proposed to accurately assess system reliability in the presence of random parameter, field, and process variables. An advanced probability analysis technique, the Eigenvector Dimension Reduction (EDR) method, is developed by integrating the Dimension Reduction (DR) method with three proposed improvements: 1) an eigenvector sampling approach to obtain statistically independent samples over a random space; 2) a Stepwise Moving Least Square (SMLS) method to accurately approximate system responses over a random space; and 3) a Probability Density Function (PDF) generation method to accurately approximate the PDF of system responses for reliability analysis. Third, a generic Reliability-Based Design Optimization (RBDO) framework is developed to solve engineering design problems with random parameter, field, and process variables. This design framework incorporates the EDR method into RBDO. To illustrate the effectiveness of the developed framework, many numerical and engineering examples are employed to conduct the reliability analysis and RBDO with random parameter, field, and process variables. This dissertation demonstrates that the developed framework is very accurate and efficient for the reliability analysis and RBDO of engineering products and processes

Optimazation of marine sediments characterization via statistical analysis

The task of geotechnical site characterization includes defining the layout of ground units and establishing their relevant engineering properties. This is an activity in which uncertainties of different nature (inherent, experimental, of interpretation…) are always present and in which the amount and characteristics of available data are highly variable. Probabilistic methodologies are applied to assess and manage uncertainties. A Bayesian perspective of probability, that roots probability on belief, is well suited for geotechnical characterization problems, as it has flexibility to handle different kind of uncertainties and highly variable datasets –in quality and quantity. This thesis addresses different topics of geotechnical site characterization from a probabilistic perspective, with emphasis on offshore investigation, on the Cone Penetration Test (CPTu) and on Bayesian methodologies.The first topic addresses soil layer delineation based on CPT(u) data. The starting point is the recognition that layer delineation is problem-oriented and has a strong subjective component. We propose a novel CPTu record analysis methodology which aims to: a) elicit the heuristics that intervene in layer delineation, facilitating communication and coherence in interpretation b) facilitate probabilistic characterization of the identified layers c) is simple and intuitive to use. The method is based on sequential distribution fitting in conventionally accepted classification spaces (Soil Behavior Type charts). The proposed technique is applied at different sites, illustrating how it can be related to borehole observations, how it compares with alternative methodologies and how it can be extended to create cross-site profiles. The second topic addresses strain-rate corrections of dynamic CPTu data. Dynamic CPTu impact on the seafloor and are very agile characterization tools. However, they require transformation to equivalent quasi-static results that can be conventionally interpreted. Up to now the necessary corrections are either too vague or require the acquisition of paired dynamic and quasi-static CPTu records (i.e., same location’s acquisition). A Bayesian methodology is applied to derive strain-rate coefficients in a more general setting, one in which some quasi-static CPTu records are available in the study area, but they need not be paired to any converted dynamic CPTu. Application to a case study offshore Nice shows that the results match those obtained using paired tests. Furthermore, strain rate correction coefficients and transformed quasi-static profiles are expressed in probabilistic terms.The third topic addressed is the optimization of soil unit weight prediction from CPTu readings. A Bayesian Mixture Analysis is applied to a global database to identify hidden soil classes within it. The goal is to improve the accuracy of regressions between geotechnical parameters obtained by exploiting the database. The method is applied to predict soil unit weight from CPTu data, a problem that has intrinsic practical interest but it is also representative of difficulties faced by a larger class of problems in geotechnical regression. Results highlight a decrease of systematic transformation uncertainty and an improve of accuracy of soil unit weight prediction from CPTu at new sites. In a final application we present a probabilistic earthquake-induced landslide susceptibility map of the South-West Iberian margin. A simplified geotechnical pixel-based slope stability model is considered to whole study area within which the key stability model parameters are treated as random variables. Site characterization at the regional scale combines a global database with available geotechnical data through a Bayesian scheme. Outputs (landslide susceptibility maps) are derived from a reliability-based design procedure (Montecarlo simulations) providing a robust landslide susceptibility prediction at the site according to Receiver Operating Curve (ROC).La caracterización geotécnica de un emplazamiento incluye la definición de la disposición de las unidades de suelo y el establecimiento de sus propiedades de ingeniería relevantes. Es una actividad en la que siempre están presentes incertidumbres y en la que la cantidad y las caracteristicas de los datos disponibles son muy variables. Para evaluar y gestionar las incertidumbres se aplican metodologías probabilísticas. Una perspectiva bayesiana de la probabilidad es muy adecuada para la caracterización geotécnica, ya que tiene flexibilidad para manejar incertidumbres y datos muy variables. Esta tesis aborda diferentes temas de caracterización geotécnica desde una perspectiva probabilística, con énfasis en la investigación en alta mar, en el ensayo de penetración de cono (CPTu) y en las metodologías bayesianas El primer tema aborda la delineación de la capa de suelo basada en los datos CPT(u). El punto de partida es el reconocimiento de que la delineación de capas tiene un fuerte componente subjetivo. Proponemos una novedosa metodología de análisis de registros CPTu que tiene como objetivo: a) expresar la heurística que interviene en la delineación de capas, facilitando la comunicación en la su interpretación b) facilitar la caracterización probabilística de las capas identificadas c) uso sencillo e intuitivo. El método se basa en el ajuste de distribuciones secuenciales en espacios de clasificación (tablas de comportamiento del suelo). La técnica propuesta se aplica en diferentes emplazamientos, ilustrando cómo puede relacionarse con sondeos, cómo se compara con metodologías alternativas y cómo puede ampliarse para crear perfiles entre emplazamientos. El segundo tema aborda las correcciones de la velocidad de deformación de los datos del CPTu dinámico (que impactan en el fondo marino y son herramientas de caracterización muy ágiles). Sin embargo, requieren una transformación a resultados equivalentes que puedan ser interpretados convencionalmente. Hasta ahora las correcciones necesarias son vagas o requieren la adquisición de CPTu dinámicos y cuasi-estáticos emparejados. Se aplica una metodologia bayesiana para derivar los coeficientes de velocidad de deformación en un entorno más general, en el que se dispone de algunos registros de CPTu cuasi­estáticos en la zona de estudio, pero no es necesario emparejarlos con ningún CPTu dinámico convertido. La aplicación a un estudio de caso en el mar de Niza muestra que los resultados coinciden con los obtenidos mediante pruebas emparejadas. El tercer tema abordado es la optimización de la predicción del peso unitario del suelo a partir de las lecturas del CPTu. Se aplica un análisis de mezclas bayesiano a una base de datos global para identificar las clases de suelo ocultas en ella. El objetivo es mejorar la precisión de las regresiones entre los parámetros geotécnicos obtenidos explotando la base de datos. El método se aplica a la predicción del peso unitario del suelo a partir de los datos del CPTu. Los resultados destacan una disminución de la incertidumbre sistemática de la transformación y una mejora de la precisión de la predicción del peso unitario del suelo a partir de CPTu en nuevos sitios. En una aplicación final presentamos un mapa probabilistico de susceptibilidad a los deslizamientos de tierra inducidos por terremotos en el margen suroeste de la Península Ibérica. Se considera un modelo geotécnico simplificado de estabilidad de laderas basado en píxeles para toda el área de estudio, dentro del cual los parámetros clave del modelo de estabilidad se tratan como variables aleatorias. La caracterización a escala regional combina una base de datos global con los datos geotécnicos disponibles mediante un esquema bayesiano. Mapas de susceptibilidad a los corrimientos de tierra se derivan de un procedimiento de diseño basado en la fiabilidad que proporciona una predicción robusta de la susceptibilidad a deslizamientos de tierra en el sitio de acuerdo con la curva operativa del receptor (ROC).Postprint (published version

Electromechanical Dynamics of High Photovoltaic Power Grids

This dissertation study focuses on the impact of high PV penetration on power grid electromechanical dynamics. Several major aspects of power grid electromechanical dynamics are studied under high PV penetration, including frequency response and control, inter-area oscillations, transient rotor angle stability and electromechanical wave propagation.To obtain dynamic models that can reasonably represent future power systems, Chapter One studies the co-optimization of generation and transmission with large-scale wind and solar. The stochastic nature of renewables is considered in the formulation of mixed-integer programming model. Chapter Two presents the development procedures of high PV model and investigates the impact of high PV penetration on frequency responses. Chapter Three studies the impact of PV penetration on inter-area oscillations of the U.S. Eastern Interconnection system. Chapter Four presents the impacts of high PV on other electromechanical dynamic issues, including transient rotor angle stability and electromechanical wave propagation. Chapter Five investigates the frequency response enhancement by conventional resources. Chapter Six explores system frequency response improvement through real power control of wind and PV. For improving situation awareness and frequency control, Chapter Seven studies disturbance location determination based on electromechanical wave propagation. In addition, a new method is developed to generate the electromechanical wave propagation speed map, which is useful to detect system inertia distribution change. Chapter Eight provides a review on power grid data architectures for monitoring and controlling power grids. Challenges and essential elements of data architecture are analyzed to identify various requirements for operating high-renewable power grids and a conceptual data architecture is proposed. Conclusions of this dissertation study are given in Chapter Nine

Efficient Computational Methods for Structural Reliability and Global Sensitivity Analyses

Uncertainty analysis of a system response is an important part of engineering probabilistic analysis. Uncertainty analysis includes: (a) to evaluate moments of the response; (b) to evaluate reliability analysis of the system; (c) to assess the complete probability distribution of the response; (d) to conduct the parametric sensitivity analysis of the output. The actual model of system response is usually a high-dimensional function of input variables. Although Monte Carlo simulation is a quite general approach for this purpose, it may require an inordinate amount of resources to achieve an acceptable level of accuracy. Development of a computationally efficient method, hence, is of great importance. First of all, the study proposed a moment method for uncertainty quantification of structural systems. However, a key departure is the use of fractional moment of response function, as opposed to integer moment used so far in literature. The advantage of using fractional moment over integer moment was illustrated from the relation of one fractional moment with a couple of integer moments. With a small number of samples to compute the fractional moments, a system output distribution was estimated with the principle of maximum entropy (MaxEnt) in conjunction with the constraints specified in terms of fractional moments. Compared to the classical MaxEnt, a novel feature of the proposed method is that fractional exponent of the MaxEnt distribution is determined through the entropy maximization process, instead of assigned by an analyst in prior. To further minimize the computational cost of the simulation-based entropy method, a multiplicative dimensional reduction method (M-DRM) was proposed to compute the fractional (integer) moments of a generic function with multiple input variables. The M-DRM can accurately approximate a high-dimensional function as the product of a series low-dimensional functions. Together with the principle of maximum entropy, a novel computational approach was proposed to assess the complete probability distribution of a system output. Accuracy and efficiency of the proposed method for structural reliability analysis were verified by crude Monte Carlo simulation of several examples. Application of M-DRM was further extended to the variance-based global sensitivity analysis of a system. Compared to the local sensitivity analysis, the variance-based sensitivity index can provide significance information about an input random variable. Since each component variance is defined as a conditional expectation with respect to the system model function, the separable nature of the M-DRM approximation can simplify the high-dimension integrations in sensitivity analysis. Several examples were presented to illustrate the numerical accuracy and efficiency of the proposed method in comparison to the Monte Carlo simulation method. The last contribution of the proposed study is the development of a computationally efficient method for polynomial chaos expansion (PCE) of a system's response. This PCE model can be later used uncertainty analysis. However, evaluation of coefficients of a PCE meta-model is computational demanding task due to the involved high-dimensional integrations. With the proposed M-DRM, the involved computational cost can be remarkably reduced compared to the classical methods in literature (simulation method or tensor Gauss quadrature method). Accuracy and efficiency of the proposed method for polynomial chaos expansion were verified by considering several practical examples.1 yea

Probabilistic Design Optimization of Built-Up Aircraft Structures with Application

This thesis discusses a methodology for probabilistic design optimization of aircraft structures subject to a multidisciplinary set of requirements originating from the desire to minimize structural weight while fulfilling the demands for quality, safety, producibility, and affordability. With this design methodology as the framework, a software is developed, which is capable of performing design optimization of metallic built-up beam structures where the material properties, external load, as well as the structural dimensions are treated as probabilistic random variables. The structural and failure analyses are based on analytical and semi-empirical methods whereas the component reliability analysis is based on advanced first-order second moment method. Metrics-based analytical models are used for the manufacturability analysis of individual parts with the total manufacturing cost estimated using models derived from the manufacturing cost / design guide developed by the Battelle¡¯s Columbus Laboratories. The resulting optimization problem is solved using the method of sequential quadratic programming. A wing spar design optimization problem is used as a demonstrative example including a comparison between non-buckling and buckling web design concepts. A sensitivity analysis is performed and the optimization results are used to highlight the tradeoffs among weight, reliability, and manufacturing cost