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Improved probabilistic seismic demand-intensity relationship: heteroskedastic approachs

As an integral part of assessing the seismic performance of structures, the probabilistic seismic demand-intensity relationship has been widely studied. In this study, the phenomenon of heteroscedasticity in probabilistic seismic demand models was systematically investigated. A brief review of the definition, diagnosis, and conventional treatment of heteroscedasticity is presented herein, and based on that, two more generalized methods for both univariate and multivariate cases are proposed. For a typical four-span simply supported girder bridge, a series of nonlinear time history analyses were performed through multiple stripe analysis to determine its seismic demand-intensity that can be employed as a sample set. For both univariate and multivariate cases, probabilistic seismic demand models were developed based on the two aforementioned methods under the Bayesian regression framework, and the fitted results were compared and analyzed with the conventional models using linear regression approaches. In the presence of probabilistic seismic demand considering heteroscedasticity, the patterns of non-constant variance or covariance can be characterized effectively, and a better-calibrated prediction region than that of homoscedastic models can be provided. The causes of the heteroscedasticity phenomenon and subsequent solutions are thoroughly discussed. The analysis procedures can be further embedded in seismic fragility and risk assessment, thus providing a more accurate basis for aseismic decision-making.