Development of empirical and analytical fragility functions using kernel smoothing methods

Fragility functions that define the probabilistic relationship between structural damage and ground motion intensity are an integral part of performance-based earthquake engineering or seismic risk analysis. This paper introduces three approaches based on kernel smoothing methods for developing analytical and empirical fragility functions. A kernel assigns a weight to each data that is inversely related to the distance between the data value and the input of the fragility function of interest. The kernel smoothing methods are, therefore, non-parametric forms of data interpolation. These methods enable the implicit treatment of uncertainty in either or both of ground motion intensity and structural damage without making any assumption about the shape of the resulting fragility functions. They are particularly beneficial for sparse, noisy, or non-homogeneous data sets. For illustration purposes, two types of data are considered. The first is a set of numerically simulated responses for a four-story steel moment-resisting frame, and the second is a set of field observations collected after the 2010 Haiti earthquake. The results demonstrate that these methods can develop continuous representations of fragility functions without specifying their functional forms and treat sparse data sets more efficiently than conventional data binning and parametric curve fitting methods. Moreover, various uncertainty analyses are conducted to address the issues of over-fitting, bias, and confidence intervals. Copyright (c) 2014 John Wiley & Sons, Ltd.