Uncertainty Specification and Propagation for Loss Estimation Using FOSM Methods

Estimation of repair costs in future earthquakes is one component of loss estimation currently being developed for use in performance based engineering. An important component of this calculation is the estimation of total uncertainty in the result, as a result of the many sources of uncertainty in the calculation. Monte Carlo simulation is a simple approach for estimation of this uncertainty, but it is computationally expensive. The procedure proposed in this report uses the First-Order Second Moment (FOSM) method to collapse several conditional random variables into a single conditional random variable, total repair cost given IM (where IM is a measure of the ground motion intensity). Numerical integration is then used to incorporate the ground motion hazard. The ground motion hazard is treated accurately because it is the dominant contributor to total uncertainty. Quantities that can be computed are expected annual loss, variance in annual loss, and the mean annual rate (or probability) of exceeding a given loss.

A general discussion of element-based loss estimation is presented, and a framework for loss estimation is outlined. The method works within the framework proposed by the Pacific Earthquake Engineering Research Center (PEER).

The report makes suggestions for representation of correlation among the random variables, such as repair costs, where data and information are very limited. Guidelines for the estimation of uncertainty in peak interstory drift given IM are also presented. This includes using structural analysis to estimate aleatory uncertainty and correlations for an example structure. Several studies attempting to characterize epistemic uncertainty are referenced as an aid.

A simple numerical calculation is presented to illustrate the mechanics of the procedure. The results of the example are also used to illustrate the effect of uncertainty on the rate of exceeding a given total cost. This illustrates that uncertainty in total repair cost given IM may or may not have a significant effect on the annual rate of exceeding a given cost.