Publication: CUANTIFICACIÓN DE LA INCERTIDUMBRE EN SISTEMAS ESTRUCTURALES APLICANDO TÉCNICAS DE REDUCCIÓN DE MODELOS, REMUESTREO Y REDUCCIÓN DE VARIANZA
Date
2019
Authors
GONZÁLEZ BUSTOS, IVÁN VLADIMIR
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Abstract
La predicción del desempeño de una estructura puede ser llevada a cabo mediante modelos
computacionales de diversa complejidad. Estos modelos evalúan la respuesta de la estructura para
una determinada con guración de los parámetros de entrada. En ciertas aplicaciones, existirá incertidumbre
en estos parámetros, por lo que sus valores precisos podrían ser difíciles de establecer.
Dicha incertidumbre afectará la respuesta del modelo, generando incerteza en ella. La incertidumbre
presente puede ser modelada mediante la teoría de probabilidad y ser incorporada al modelo
mediante variables aleatorias. De esta forma, la respuesta del modelo se convierte en una variable
aleatoria, aumentando considerablemente la complejidad del problema. Existen diferentes técnicas
para abordar el problema de cuanti cación de incertidumbre. En particular, dos serán estudiadas
en este trabajo: estadísticas de segundo orden y análisis de sensibilidad global mediante índices
de Sobol'. Las estadísticas de segundo orden permiten, por ejemplo, caracterizar la forma de una
distribución de probabilidad, cuanti cando su variabilidad. Por su parte, los índices de Sobol' cuantifi can el impacto de cada parámetro sobre la variabilidad de la respuesta; indicando cuáles de ellos
son más importantes y cuáles no. La aplicación de estas técnicas puede entregar información valiosa
respecto del comportamiento del modelo que puede ser de utilidad en, por ejemplo, la toma
de decisiones, el análisis de riesgos y la evaluación económica. No obstante, en aplicaciones de interés práctico, en general, el costo computacional asociado es muy elevado pues habitualmente es
necesario recurrir a técnicas de simulación para la estimación de estas cantidades.
El trabajo presente tiene por objetivo desarrollar y aplicar herramientas que permitan cuantifi car
de manera e ciente la incertidumbre asociada a la respuesta de sistemas estructurales. En este
contexto, se desarrollan técnicas basadas en conceptos de remuestreo, reducción de modelos y
reducción de varianza para estimar estadísticas de segundo orden e índices de Sobol'. Las técnicas
desarrolladas permiten una reducción sustancial en el costo computacional asociado a la estimación
de estas cantidades.
The prediction of the behavior of a structural system can be carried out resorting to computational models of different complexity. These models evaluate the response of the structure for a certain con guration of its input parameters. In certain applications, there exists uncertainty in these parameters, so their precise values may be difficult to establish. This uncertainty will affect the response of the model, generating uncertainty in it. The existing uncertainty can be modeled by means of probability theory and can eventually be incorporated into the model by means of random variables. Thus, the response of the model becomes a random variable, increasing the complexity of the problem. There are several techniques to address the issue of quantifying uncertainty. In particular, two will be studied in this work: second order statistics and global sensitivity analysis using Sobol' indeces. Second-order statistics allow, for example, to characterize the shape of a probability distribution, quantifying its variability. On the other hand, the Sobol' indeces quantify the impact of each random variable on the variability of the response; indicating which of them are more important and which are not. The application of these techniques can provide valuable information regarding the behavior of the model that may result useful in, for example, decision making, risk analysis and economic evaluation. However, in applications of practical interest, in general, the associated computational cost may be very high since it is usually necessary to resort to simulation techniques to estimate these quantities. The objective of this work is to develop and apply tools to efficiently quantify the uncertainty associated with the response of structural systems. In this context, techniques based on concepts of resampling, model reduction and variance reduction to estimate second-order statistics and Sobol' indeces are developed. These techniques allow a substantial reduction in the computational cost associated with the estimation of these quantities.
The prediction of the behavior of a structural system can be carried out resorting to computational models of different complexity. These models evaluate the response of the structure for a certain con guration of its input parameters. In certain applications, there exists uncertainty in these parameters, so their precise values may be difficult to establish. This uncertainty will affect the response of the model, generating uncertainty in it. The existing uncertainty can be modeled by means of probability theory and can eventually be incorporated into the model by means of random variables. Thus, the response of the model becomes a random variable, increasing the complexity of the problem. There are several techniques to address the issue of quantifying uncertainty. In particular, two will be studied in this work: second order statistics and global sensitivity analysis using Sobol' indeces. Second-order statistics allow, for example, to characterize the shape of a probability distribution, quantifying its variability. On the other hand, the Sobol' indeces quantify the impact of each random variable on the variability of the response; indicating which of them are more important and which are not. The application of these techniques can provide valuable information regarding the behavior of the model that may result useful in, for example, decision making, risk analysis and economic evaluation. However, in applications of practical interest, in general, the associated computational cost may be very high since it is usually necessary to resort to simulation techniques to estimate these quantities. The objective of this work is to develop and apply tools to efficiently quantify the uncertainty associated with the response of structural systems. In this context, techniques based on concepts of resampling, model reduction and variance reduction to estimate second-order statistics and Sobol' indeces are developed. These techniques allow a substantial reduction in the computational cost associated with the estimation of these quantities.
Description
Keywords
SISTEMAS ESTRUCTURALES , REDUCCION DE VARIANZA , INDICES DE SOBOL'