  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.

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