Statistical Analysis of Fragility Curves

TLDR

Both empirical and analytical fragility curves are considered. This paper presents a statistical analysis of structural fragility curves and methods for testing goodness of fit and estimating confidence intervals of the median and log‑standard deviation. The empirical fragility curves are derived from bridge damage data from the 1995 Kobe earthquake, the analytical curves from nonlinear dynamic analysis, and both are modeled with two‑parameter lognormal distributions whose parameters are estimated by maximum likelihood, with additional procedures for goodness‑of‑fit testing and confidence‑interval estimation. An analytical interpretation of randomness and uncertainty associated with the median is provided.

Abstract

This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.