Accuracy of approximate methods of uncertainty propagation in seismic loss estimation

Abstract

In this paper the efficacy of an approximate method of uncertainty propagation, known as the first-order second-moment (FOSM) method, for use in seismic loss estimation is investigated. The governing probabilistic equations which define the Pacific Earthquake Engineering Research (PEER)-based loss estimation methodology used are discussed, and the proposed locations to use the FOSM approximations identified. The justification for the use of these approximations is based on a significant reduction in computational time by not requiring direct numerical integration, and the fact that only the first two moments of the distribution are known. Via various examples it is shown that great care should be taken in the use of such approximations, particularly considering the large uncertainties that must be propagated in a seismic loss assessment. Finally, a complete loss assessment of a structure is considered to investigate in detail the location where significant approximation errors are incurred, where caution must be taken in the interpretation of the results, and the computational demand of the various alternatives. KEYWORDSPerformance-based earthquake engineering (PBEE); aleatory uncertainty; epistemic uncertainty; first-order second-moment (FOSM) method; loss estimation; loss deaggregation.2

Prediction of spatially distributed seismic demands in specific structures: Structural response to loss estimation

“…While Figure 7c illustrates that corrected expected loss is reduced for small exceedance probabilities, Figure 7d illustrates that the corrected dispersion in the loss increases. This observation is due to the reduction in the collapse probability at these small exceedance probabilities, which increases the contribution of the uncertainty due to non-collapse (see Bradley and Lee [23] for further details). While predictability of an IM appears to be the dominant effect from the preceding paragraphs, the efficiency of the various IMs, however, affects on distribution of the loss for a given intensity.…”

Component correlations in structure‐specific seismic loss estimation

“…The previous sections address correlations which appear in the structure-specific seismic loss estimation framework given by Equations (1)- (10). There are however additional, potentially important, correlations which are not considered because of the assumptions made in the framework.…”

“…Table 1 presents the computational times required when in performing the seismic loss assessment on a Pentium 4 processor with 3.0 GHz CPU and 512 MB RAM using the seismic loss assessment tool (SLAT) [40], which utilizes the magnitude-oriented adaptive quadrature algorithm [41]. As discussed by Bradley and Lee [10], and evident in Table 1, the effect of nonzero correlations drastically increases the computational demand to perform the analysis. Table 1 illustrates that the loss hazard involves approximately 20 times more computational time than the L|IM relationships, and it can be seen that the using perfect and partial correlations requires approximately 50-times and 3200-times more computational time, respectively, than the assumption of no-correlations.…”

“…The small difference in computational times for correlation assumptions (iv) and (v) illustrate that the additional computational demand due to the DS|EDP and L|DS correlations is minimal compared to considering EDP|IM correlations. By assuming perfect EDP|IM correlations the double-integral in Equation (9) reduces to a single integral as discussed by Bradley and Lee [10], which significantly reduces the computational time. Since correlation approximation (v) uses perfect EDP|IM correlations and partial DS|EDP and L|DS correlations then it will always give a larger value for the lognormal , than using all partial correlations.…”

“…Aslani [3] and Baker and Cornell [9] both use the first-order second-moment (FOSM) approximation when computing the covariance terms in the total loss because of the perceived computational demand of direct numerical integration. The FOSM approximation has been shown to be of limited accuracy in computing such covariance terms compared to direct evaluation via numerical integration [10]. As far as the author is aware only Aslani [3] has briefly investigated the effect of correlation assumptions on the standard deviation in the total loss given intensity.…”