Adaptive importance sampling for seismic fragility curve estimation

As part of Probabilistic Risk Assessment studies, it is necessary to study the fragility of mechanical and civil engineered structures when subjected to seismic loads. This risk can be measured with fragility curves, which express the probability of failure of the structure conditionally to a seismic intensity measure. The estimation of fragility curves relies on time-consuming numerical simulations, so that careful experimental design is required in order to gain the maximum information on the structure's fragility with a limited number of code evaluations. We propose and implement an active learning methodology based on adaptive importance sampling in order to reduce the variance of the training loss. The efficiency of the proposed method in terms of bias, standard deviation and prediction interval coverage are theoretically and numerically characterized. Keywords: Computer experiments, probabilistic risk assessment, importance sampling, statistical learning 1. Introduction The notion of fragility curve was developed in the early 80s in the context of seismic probabilistic risk assesment (SPRA) [1, 2] or performance based earthquake engineering (PBEE) [3]. Fully documented templates are available in the elsarticle package on CTAN. Fragility curves are used in several domains: nuclear safety evaluation [4], estimation of the collapse risk of structures in seismic regions [5], design checking process [6]. Nonetheless, the use of fragility curves is not limited to seismic load but is extended to other loading sources such as wind and waves 10 [7]. For complex structures, fragility curve estimation requires a large number of numerical mechanical simulations, involving in most cases non linear computationally expensive calculations. Moreover, they should account for both the uncertainties due to the seismic demand and due to the lack of knowledge on the system itself, respectively called random and epistemic uncertainties [8, 9]. As 15 failure for a typical and reliable mechanical structure is a rare event, the crude Monte Carlo method cannot be applied because it would require too many numerical simulations to produce a sufficiently large number of failed states [10, p.27].