Uncertainty propagation in probabilistic seismic loss estimation

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Probabilistic estimation of losses in a building due to earthquake damage is a topic of interest to decision makers and an area of active research. One promising approach to the problem, proposed by the Pacific Earthquake Engineering Research (PEER) Center, involves breaking the analysis into separate components associated with ground motion hazard, structural response, damage to components and repair costs. Each stage of this method has both inherent (aleatory) randomness and (epistemic) model uncertainty, and these two sources of uncertainty must be propagated through the analysis in order to determine the total uncertainty in the resulting loss estimates. In this paper, the PEER framework for seismic loss estimation is reviewed and options for both characterizing and propagating the various sources of uncertainty are proposed. Models for correlations (among, e.g., element repair costs) are proposed that may be useful when empirical data is lacking. Several options are discussed for propagating uncertainty, ranging from flexible but expensive Monte Carlo simulation to closed form solutions requiring specific functional forms for relationships between variables to be assumed. A procedure that falls between these two extremes is proposed, which integrates over the discrete element damage states, and uses the first-order second-oment method to collapse several conditional random variables into a single conditional random variable representing total repair cost given the ground motion intensity. Numerical integration is then used to incorporate the ground motion hazard. Studies attempting to characterize epistemic uncertainty or develop specific elements of the framework are referenced as an aid for users wishing to implement this loss-estimation procedure.