Bayesian empirical vulnerability modelling for hierarchical levels of damage and loss: Applications to Tsunami Risk Modelling

Abstract

Empirical fragility and vulnerability curves express the probabilities of exceeding certain damage and loss levels respectively for given values of intensity measures for specific classes of building or infrastructure. These empirical curves are derived based on observed pairs of intensity versus damage and loss data. It is usually convenient to define the damage and/or loss levels in a hierarchical manner, implying discrete, mutually exclusive, and collectively exhaustive (MECE) states. This means that the fragility/vulnerability curves for consecutive hierarchical damage/loss levels will not cross.

The present work proposes a fully simulation-based Bayesian workflow for inference and model class selection to perform ensemble modelling of the tsunami fragility/vulnerability curves for MECE damage/loss states and the related uncertainties for a given class of buildings. Instead of commonly used bootstrap resampling for estimating the uncertainty in the resulting empirical fragility curves, the workflow employs adaptive Markov Chain Monte Carlo Simulation (MCMC), based on likelihood estimation using point-wise intensity values. This will lead to consistent model parameter estimation and confidence intervals (uncertainties) for MECE the damage/loss states. The empirical fragility/vulnerability curves are constructed using three generalized linear regression models by adopting probit, logit, and complementary loglog link functions. Among the set of viable models considered, Bayesian model class selection is used to identify the simplest model among the three viable models that fits the data best. The proposed workflow is quite general and can be applied to any type of risk expressed by a set of MECE damage or loss states, where the exceedance of a damage or loss level is expressed as a Bernoulli variable. This work presents case-study applications in tsunami risk modelling. In these applications, existing datasets from various past tsunamis are implemented including the central South Pacific tsunami on September 29, 2009, the Sulawesi Tsunami (Indonesia) on September 28, 2018, and the historical 1755 Lisbon Tsunami. The proposed workflow is provided as open-source software on the site of the European Tsunami Risk Service (https://eurotsunamirisk.org/tsunamirisktoolkit/).