Propagating uncertainties for loss estimation in performance-based earthquake engineering using moment matching

A new methodology, called moment matching, to efficiently estimate repair costs of a building due to future earthquake excitation is presented. As well as excitation uncertainties, other uncertainties considered include those in the structural model and those in the capacity to resist damage and the unit repair costs of structural and non-structural components. Given the first few moments of the basic uncertain variables, moment matching uses specially selected point estimates to propagate the uncertainties in order to more accurately estimate the first few moments of the repair costs. Two buildings are chosen as illustrative examples to demonstrate the use of moment matching: one hypothetical three-degree-of-freedom shear building, and a real seven-storey hotel building. It is shown that the moment matching technique is much more accurate than the First-Order Second-Moment approach when propagating the first two moments, whilst the computational cost is of the same order. The repair cost moments estimated by the moment matching technique are also compared to those obtained by the more computationally demanding Monte Carlo simulation, and it is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Last, but not least, a procedure for sensitivity analysis is discussed and it is concluded that the most important uncertainties for the real building example are those that correspond to spectral acceleration, component capacity, ground motion details and unit repair costs.