A multidimensional probabilistic seismic demand analysis framework for bridge structures using non-parametric kernel density estimation

Traditional probabilistic seismic demand analysis (PSDA) of bridge structures is typically formulated using a single engineering demand parameter (EDP) and assumes predefined probability distribution forms, which may be insufficient to capture the coupled seismic response of complex bridge systems. To overcome these limitations, this study proposes a multidimensional PSDA framework based on performance limit states and a non-parametric kernel density estimation (KDE) approach. By incorporating bivariate correlation KDE, a joint probabilistic seismic demand model for multiple EDPs is established without prescribing explicit parametric forms for their marginal or joint distributions. A high-pier, large-span continuous steel girder bridge is selected as a case study. Incremental dynamic analysis combined with nonlinear time-history analysis is performed to evaluate the pier curvature ductility factor (PCDF) and bearing relative displacement (BRD). Based on multidimensional performance limit state formulations, the proposed framework is integrated with seismic hazard analysis to estimate the average annual exceedance probability of structural demands. The results indicate that the multidimensional PSDA generally produces higher exceedance probabilities than conventional single-EDP-based methods, suggesting a more conservative and realistic assessment of seismic risk. Furthermore, the correlation coefficient between EDPs is shown to have a significant impact on the estimated exceedance probabilities. Overall, the proposed framework shows good potential for application in seismic performance assessment of complex bridge structures.