Bayesian Cloud Analysis: efficient structural fragility assessment using linear regression

Abstract

Cloud Analysis is based on simple regression in the logarithmic space of structural response versus seismic intensity for a set of registered records. A Bayesian take on the Cloud Analysis, presented herein, manages to take into account both record-to-record variability and other sources of uncertainty related to structural modelling. First, the structural response to a suite of ground motions, applied to different realizations of the structural model generated through a standard Monte Carlo, is obtained. The resulting suite of structural response is going to be used as “data” in order to update the joint probability distribution function for the two regression parameters and the conditional logarithmic standard deviation. In the next stage, large-sample MC simulation based on the updated joint probability distribution is used to generate a set of plausible fragility curves. The robust fragility is estimated as the average of the generated fragility curves. The dispersion in the robust fragility is estimated as the variance of the plausible fragility curves generated. The plus/minus one standard deviation confidence interval for the robust fragility depends on the size of the sample of “data” employed. Application of the Bayesian Cloud procedure for an existing RC frame designed only for gravity-loading demonstrates the effect of structural modelling uncertainties, such as the uncertainties in component capacities and those related to construction details. Moreover, a comparison of the resulting robust fragility curves with fragility curves obtained based on the Incremental Dynamic Analysis shows a significant dependence on both the structural performance measure adopted and the selection of the records

RC infilled building performance against the evidence of the 2016 EEFIT Central Italy post-earthquake reconnaissance mission: empirical fragilities and comparison with the FAST method

“…This assumption reflects also the case of obsolete seismic design for residential buildings since their ductility is often limited by the occurrence of brittle failures Verderame 2013, 2015;Jalayer et al 2015). The other parameters are defined as follows:…”

Simulation-Based Probabilistic Tsunami Hazard Analysis: Empirical and Robust Hazard Predictions

“…The evidence-based assessment facilitates the calculation of robust hazard curves (Jalayer et al 2015). Once the most suitable model T i is identified, the posterior distribution of its parameters p(h i |D,T i ) can be used to build the robust predictive probability density function of future response X through total probability theorem:…”

An earthquake-source-based metric for seismic fragility analysis

“…They describe the relationship between earthquake hazard and the structural response expressed as engineer design parameters (e.g., maximum inter-story drift, maximum displacement). Peak ground acceleration (PGA) (Shinozuka et al 2000;Sasani et al 2002;Choun and Elnashai 2010;Garcia and Soong 2003;Banerjee and Shinozuka 2008) and pseudo-spectral acceleration (PSA) (Gardoni and Rosowski 2009;Liel et al 2009;Ellingwood et al 2007;Lin et al 2013a;Jalayer et al 2015) are among the most widely used intensity measures in fragility analysis. Two major issues regarding fragility are discussed in this paper and solutions to overcome them are sought.…”

“…This model is also adopted by the Federal Emergency Management Agency (FEMA) through ATC-58 (Porter et al 2006;FEMA 2012). Various methods have been proposed to estimate the parameters of the log-normal distribution from data (Koutsourelakis 2010;Baker 2015;Jalayer et al 2015).…”