Publication: ESTRATEGIAS PARA LA ESTIMACIÓN DE LA SENSIBILIDAD DE LA CONFIABILIDAD ESTRUCTURAL APLICANDO LA TÉCNICA DE SIMULACIÓN LINE SAMPLING
Date
2018
Authors
HERNÁNDEZ FARÍAS, HERMAN BASTIÁN
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Abstract
El diseño estructural utiliza modelos de cálculo numérico basados en los métodos de elementos fi nitos. Tales modelos dependen de propiedades estructurales (v.gr. módulo de Young, coefi ciente de Poisson, dimensiones de elementos) y de solicitaciones ambientales (v.gr. cargas de viento, sismos, empujes de suelo). Estas variables, que de nen el modelo estructural, presentan un nivelde incertidumbre que afecta al comportamiento del sistema. Es por este motivo, que se busca una cuanti cación del nivel de incertidumbre, recurriendo a distintas herramientas, como a la teoría de probabilidad con el fin de estimar la confi abilidad estructural.La confi abilidad es una medida que puede ser cuanti cada a través de la probabilidad de falla.Esta última cantidad, mide la probabilidad de que una (o más) respuestas estructurales superen un umbral aceptable que asegure condiciones de servicio o integridad. Este criterio de falla puede ser impuesto por una normativa o una limitante de diseño, como el desplazamiento máximo de techo.Además, para poder estimar la probabilidad de falla, las variables del modelo, ya sea propiedades estructurales o solicitaciones, se representan como variables aleatorias asociadas con algún tipo de distribución de probabilidad. Este tipo de caracterización, implica la selección de parámetros de distribución de probabilidad tales como el valor esperado o la desviación estándar. Dicha selecciónes clave y puede afectar la magnitud de la probabilidad de falla. Por tal motivo, resulta de interés cuanti car la sensibilidad de la probabilidad de falla respecto de los parámetros de distribución.Lo anterior, permite identi car los parámetros más influyentes y tomar precauciones de diseño adecuadas.En el contexto descrito anteriormente, esta tesis propone estrategias para cuanti ficar la sensibilidad de la probabilidad de falla, reutilizando la información adquirida del análisis de con fiabilidad. La sensibilidad se evalúa utilizando dos estrategias distintas: integración sobre el contorno o integrando sobre el volumen de la región de falla. Las estrategias son aplicadas utilizando la técnica desimulación Line Sampling y se contrasta su e ciencia numérica con el método de Monte Carlo.Cabe señalar que en la literatura se ha estudiado anteriormente la sensibilidad con Line Sampling.Sin embargo, las estrategias propuestas generalizan resultados anteriores y son aplicadas a campos aleatorios.
The structural design usually uses numerical models based on nite element methods. Such modelsdepend on structural properties (i.e. Young's modulus, Poisson's coeficient, element dimensions)and environmental stresses (i.e. wind loads, earthquakes, soil thrusts). These variables, which de nethe structural model, present a level of uncertainty that affects the behavior of the system. It is forthis reason that a quanti cation of the level of uncertainty is sought, using different tools, such asprobability theory in order to estimate structural reliability.Reliability is a measure that can be quanti ed through the probability of failure. This last quantitymeasures the probability that one (or more) structural responses will exceed an acceptable thresholdthat ensures service or integrity conditions. This failure criterion can be imposed by a regulationor a design constraint, such as maximum ceiling displacement. It is clear that determining theprobability of failure is crucial to make a desition, whether for design or maintenance, for example.Besides, in order to estimate the probability of failure, the model variables, whether structuralproperties or stresses, are represented as random variables associated with some kind of probabilitydistribution. This type of characterization involves the selection of probability distribution parameterssuch as the expected value or the standard deviation. This selection is key and can affect themagnitude of the failure probability. For this reason, it is interesting to quantify the sensitivity ofthe failure probability with respect to the distribution parameters. The sensitivity analysis allowsto identify the most inuential parameters and take appropriate design precautions.In the context described above, this thesis proposes strategies to quantify the sensitivity of thefailure probability, reusing the information acquired from the reliability analysis. The sensitivity isevaluated using two different approaches: integration on the contour or integrating on the volumeof the fault region. The approaches are applied using the Line Sampling simulation technique andits numerical efficiency is contrasted with the Monte Carlo method. It is important to mentionthat in the literature the sensitivity with Line Sampling has been previously studied. However, theproposed strategies generalize previous results and are applied to random fi elds.
The structural design usually uses numerical models based on nite element methods. Such modelsdepend on structural properties (i.e. Young's modulus, Poisson's coeficient, element dimensions)and environmental stresses (i.e. wind loads, earthquakes, soil thrusts). These variables, which de nethe structural model, present a level of uncertainty that affects the behavior of the system. It is forthis reason that a quanti cation of the level of uncertainty is sought, using different tools, such asprobability theory in order to estimate structural reliability.Reliability is a measure that can be quanti ed through the probability of failure. This last quantitymeasures the probability that one (or more) structural responses will exceed an acceptable thresholdthat ensures service or integrity conditions. This failure criterion can be imposed by a regulationor a design constraint, such as maximum ceiling displacement. It is clear that determining theprobability of failure is crucial to make a desition, whether for design or maintenance, for example.Besides, in order to estimate the probability of failure, the model variables, whether structuralproperties or stresses, are represented as random variables associated with some kind of probabilitydistribution. This type of characterization involves the selection of probability distribution parameterssuch as the expected value or the standard deviation. This selection is key and can affect themagnitude of the failure probability. For this reason, it is interesting to quantify the sensitivity ofthe failure probability with respect to the distribution parameters. The sensitivity analysis allowsto identify the most inuential parameters and take appropriate design precautions.In the context described above, this thesis proposes strategies to quantify the sensitivity of thefailure probability, reusing the information acquired from the reliability analysis. The sensitivity isevaluated using two different approaches: integration on the contour or integrating on the volumeof the fault region. The approaches are applied using the Line Sampling simulation technique andits numerical efficiency is contrasted with the Monte Carlo method. It is important to mentionthat in the literature the sensitivity with Line Sampling has been previously studied. However, theproposed strategies generalize previous results and are applied to random fi elds.
Description
Catalogado desde la version PDF de la tesis.
Keywords
ANALISIS DE CONFIABILIDAD , CAMPO ALEATORIO , ESTRATEGIAS DE INTEGRACION , LINE SAMPLING , SENSIBILIDAD DE LA PROBABILIDAD DE FALLA , VARIABLE ALEATORIA