# Seismic fragility curves for structures using non-parametric representations

## TL;DR

This paper introduces non-parametric methods, binned Monte Carlo simulation and kernel density estimation, to develop seismic fragility curves without assuming a lognormal distribution, improving accuracy in vulnerability assessments.

## Contribution

The paper presents two novel non-parametric approaches for seismic fragility curve estimation, avoiding the traditional lognormal assumption and enhancing accuracy with synthetic and recorded ground motion data.

## Key findings

- Non-parametric methods provide more accurate fragility curves than lognormal assumptions.
- Curve accuracy depends on ground motion intensity measure and failure criterion.
- Non-parametric approaches perform well with limited recorded ground motion data.

## Abstract

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g. the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g. peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.