Investigation of multivariate seismic surrogate demand modeling for multi-response structural systems

Probabilistic seismic risk assessment of complex multi-response structural systems requires accurate estimations of multiple engineering demand parameters (EDPs) that are related to different failure modes. One conventional way is developing multiple separate univariate seismic demand models for each of the EDPs. However, such an approach lacks sufficient consideration of the correlations among different EDPs and also requires repetitive model tuning and training. Another alternative, which has not yet been extensively studied, is to develop a single multivariate surrogate demand model (MvSDM) that is able to jointly provide the estimates for all the EDPs. To facilitate more accurate and realistic seismic demand modeling of multi-response structural systems, the present study conducts a comprehensive investigation of different MvSDMs, which are constituted by a systematic trend model that characterizes the mean response hypersurface, and a covariance model that quantifies the correlated model errors. Three types of systematic trend models including multivariate linear regression (MvLR), partial least squares regression (PLSR) and artificial neural network (ANN); along with three model error covariance estimation methods including joint probabilistic demand model (JPSDM) method, sample regression residual covariance (SCOV) method and multi-output Gaussian process regression (MOGP), are considered. The influence of trend model and error covariance model selection on seismic demand and fragility modeling is then studied based on a typical three-span concrete-girder highway bridge structure in the Central and Southeastern US. The results suggest that kernel PLSR and ANN as the systematic trend models, and the SCOV method as the error covariance model are promising alternatives that can contribute to accurate and reliable multivariate surrogate demand modeling yet with good computational efficiency.