ANÁLISIS PROBABILÍSTICO MULTIVARIADO DE PELIGRO SÍSMICO USANDO CÓPULAS
DOI:
https://doi.org/10.18867/ris.107.588Palabras clave:
tasa media de excedencia, medida de intensidad vectorial, ? de KendallResumen
El análisis probabilístico multivariado de peligro sísmico permite estimar la tasa de excedencia de medidas de intensidad vectoriales del movimiento sísmico del suelo considerando su distribución de probabilidad conjunta. Dicho análisis se emplea en el análisis probabilista de demanda sísmica de estructuras cuya respuesta está correlacionada con un conjunto de medidas de intensidad. En tales casos, es conveniente calcular la tasa de excedencia de la respuesta utilizando la tasa de excedencia de medidas de intensidad vectoriales, a diferencia de un enfoque univariado donde las tasas de excedencia de un conjunto de medidas de intensidad son calculadas por separado sin tomar en cuenta la dependencia estadística entre ellas. En este trabajo se presenta una formulación multivariada para el análisis probabilístico de peligro sísmico de medidas de intensidad vectoriales usando cópulas. La formulación es de carácter genérico pues expresa la tasa de excedencia en términos de la cópula de una medida de intensidad vectorial, sin suponer para ésta una distribución de probabilidad conjunta en particular. La formulación se empleó en un ejemplo de estimación de la tasa de excedencia de la distorsión de entrepiso máxima de un edificio de acero de 20 niveles usando un modelo de regresión en función de las aceleraciones espectrales asociadas con los dos primeros modos de vibrar. El modelo de cópula de las aceleraciones espectrales se estimó usando datos de registros sísmicos de la zona de transición de la Ciudad de México. Este tipo de excitación genera una contribución importante de la respuesta asociada con el segundo modo de la estructura. La formulación multivariada produjo tasas de excedencia significativamente menores que los obtenidos con un análisis univariado usando la aceleración espectral para el modo fundamental de la estructura como medida de intensidad escalar.
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