Reliability analysis of structural systems using imprecise probability models

The use of the theory of imprecise probabilities in structural reliability analysis has gained momentum in recent years. This is due to the fact that classical probability theory has been found insufficient for modeling problems in which the limited amount of information makes the construction of precise reliability models impossible. Limiting an exact evaluation of the failure probability in mechanical and structural systems. Random set theory allows for the estimation of the probability interval when there is random and epistemic uncertainty. With this theory, it is possible to model basic variables, such as CDFs, probability boxes, and intervals, among other representation of uncertainty. Additionally, it allows for representation of input variable dependence, by means of copulas. In this thesis, a number of formulations are presented, in order to estimate the failure probability interval. The first is based on the random sets theory, which uses the Dempster-Shafer evidence theory with an infinite number of focal elements. The second approach proposes calculation of the interval as a design optimization problem, based on reliability. It was proven theoretically, and via numerical experiments, that the second formulation provides tighter bounds for the failure interval than others estimated by the random sets theory. Additionally, two other methodologies for obtaining the failure interval, based on random set theory and on properties of visualization and representation, are proposed. These are provided by the transformation in polar coordinates proposed by Hurtado (2012). Both methodologies perform a polar analysis of the focal elements. The first does so with each focal element in its entirety, while the second takes samples from within each focal element. These methodologies avoid the costly optimization procedure used by the extension principle. Various practical applications are presented, which contribute to the state of the art, regarding uncertainty management. On the other hand, the properties of the forementioned transformation in polar coordinates are also used to create applications in the analysis of structural systems, in which it is considered more than a limit state function; it also provides a visual tool for sensitivity analysis in structural systems. All of these applications and methodologies are illustrated with practical examples present in the literature. To conclude, obtained results show a significant advance in the management of uncertainty and dependencies for input variables in a system, in addition to providing the necessary tools, with simple, but effective theoretical and practical developments, in order to obtain a reliable evaluation of the failure interval for mechanical and structural systems that are consistent with the formulation and characteristics of the problem

• Autores: Ramírez Candamil, Juliana
• Tipo de recurso: Doctoral thesis
• Fecha de publicación: 2017
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/62303
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/62303; http://bdigital.unal.edu.co/61334/
• Palabra clave: 51 Matemáticas / Mathematics; 6 Tecnología (ciencias aplicadas) / Technology; 62 Ingeniería y operaciones afines / Engineering; Structural reliability analysis; Imprecise probability theory; Failure probability interval; Random sets theory; FORM method; Linear regression; Polar transformation; Reliability plot; Monte Carlo simulation; Monte Carlo method; Análisis de confiabilidad de estructuras; Teoría de probabilidades imprecisas; Intervalo de probabilidad de falla; Teoría de conjuntos aleatorios; Método FORM; regresión lineal; Transformación polar; Gráfica de confiabilidad; Simulación de Monte Carlo; Método de Montecarlo
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional