Updating uncertainty of rare event occurrence probability based on Bayesian approach

摘要

Bayesian method and information criteria (information entropy and logarithmic likelihood) are applied to the seismic fragility evaluation and updating process. Those are informative and effective in the fragility update and the uncertainty reduction. Expected information entropy with respect to our belief on the seismic capacity is a useful figure-of-merit for estimating the importance or usefulness of performing a seismic qualification test before the results are obtained. Expected logarithmic likelihood is an appropriate measure and can be used to estimate the importance of the evidence which we have already known. Furthermore, it is meaningful that the expected entropy and logarithmic likelihood be weighted by the seismic hazard curves. It tells us the most effective way of the fragility update because the most risk-contributive PGA level depends on the subjective judgment on the hazard. It is recommended to perform additional vibration test is to be designed according to the expected entropy which suggests a reasonable guideline for the fragility update. The most contributive part of the fragility curve to the seismic failure frequency is the fragility tail in most cases and a test at the tail PGA level is more useful.