Bayesian Updating of Damaged Building Distribution in Post-Earthquake Assessment

Abstract eng:
This paper proposes a method to have a whole picture of earthquake damage rapidly and accurately as a post-earthquake damage assessment. In Japan, strong ground motion observation station networks, such as K-NET and KiK-net are in place across the country. With the networks, the observed records are collected by information and communication technology as soon as they are recorded. Japan Real-time information System for earthquake (J-RISQ) has been developed, which estimates the strong motion distribution by spatial interpolating the collected records in a very short time. Given fragility functions, which relate ground motion intensity and damage probability, and building statistics are prepared, distribution of damaged buildings is able to be estimated immediately. Such estimation will help governments and private sectors to grasp the whole damage situation and to make their disaster management more effective. However, it should be noted that the estimation includes errors those associated with interpolating strong ground motion observation and those in evaluating fragility functions. Meanwhile, actual damage will be gradually informed, although it may be for limited areas, because local governments etc. start to collect and report it as a part of disaster response activities. Then, by using such information on actual damage, it is possible to make the estimation more realistic even for the region where damage information is not reported yet. This paper proposes to apply Bayesian inference for merging information described above. The procedure of the proposed method is summarized as following; the target area, where might be subject to strong ground motion, is divided into geography mesh. In each mesh, safety margin, which is difference between seismic load effect and resistance of building, is evaluated for each category of building and each damage state by use of the estimated strong ground motion distribution, and the parameters of the prepared fragility functions. Here, the categories of building are determined by the types of building structure, seismic design codes etc. Damage states are classified in such as ‘major damage’ or ‘heavy damage’ etc. Then, the errors in evaluating safety margins are modeled as normal distributed random variables. The damage probability is evaluated as the probability that safety margin is negative with consideration of the errors. The parameters of the normal distributed variables are also dealt as random variables, whose prior distributions are supposed by use of the accuracy of the estimated ground motion distribution and the fragility functions. Once, the actual number of buildings in each damage state is available for some parts of the target area, it is used as the ‘observation’ in Bayesian updating protocol to induce the posterior distribution of the parameters. Finally, the updated damage probability is calculated as the weighted expectation of damage probability with respect to the posterior distribution of the parameters. As an illustrative example, a numerical study with past earthquake disaster records is presented so as to examine the effectiveness and characteristics of the presented method.

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