Seismic hazards can pose devastating regional impacts and lead to significant structural damages, economic losses and casualties, as observed in the past major earthquake events. Moreover, with rapid urbanization and population growth, especially in earthquake-prone zones, exposures to seismic threats are also heightening. In the future, seismic hazards will continue existing as major threats to the human built environment. Therefore, confident probabilistic seismic risk assessment (PSRA) of the built environment, is critical to informing decision-making such as retrofit prioritization, pre-event planning and risk mitigation, post-event response, as well as insurance underwriting or risk financing. However, the current PSRA framework largely relies on scalar conditioning metrics with an underlying conditional independence assumption, which is often times violated in reality. As a result, different conditioning metric selection can lead to drastically different seismic risk estimates. In this regard, the overarching goal of this thesis is to facilitate more robust and confident PSRA of general multi-response structural systems, with particular focus on intensity measure (IM) selection and uncertainty propagation.

First of all, this thesis addresses a long standing question in PSRA, which is the lack of multivariate hazard consistent ground motion selection for use in probabilistic seismic demand estimation of structures. Specifically, a novel multivariate return period (MRP)-based ground motion selection methodology is proposed. MRP generalizes the return period concept by incorporating the joint rate of exceedance of a vector of IMs, thereby providing more holistic characterization of the seismic hazard. By leveraging MRP in linking the level of seismic hazard to a vector of IMs, the proposed MRP-based methodology for the first time achieves multivariate hazard consistency over a vector of IMs, and outperforms all the state-of-the-art ground motion selection alternatives.

This thesis also proposes new approaches for surrogate demand modeling of complex multi-response structural systems under earthquake excitation. By leveraging advanced multivariate statistical and machine learning techniques, multivariate surrogate demand models (MvSDMs) are developed to facilitate more unified and joint demand estimation and uncertainty propagation. The formulation of the MvSDMs consists of two major components including a systematic trend model to characterize the mean response hypersurface, and an error covariance model to quantify the correlated model errors. The efficacy of different MvSDMs is thoroughly examined in terms of both predictive performance and system fragility curves, and promising MvSDM alternatives are identified.

A preliminary general IM comparative study is then carried out to examine the explanatory power potential and the applicability of different IM formulations, including those conventional IMs, recently proposed advanced IMs, and other potential IM candidates not yet studied. The IM comparative study is based on general hysteretic single-degree-of-freedom (SDOF) systems with a wide range of structural parameters. The underlying mechanisms of different IM formulations are explored and promising IM formulations are identified.

Finally, enabled by the above-mentioned study and information theory, an entropy-based IM selection methodology is proposed. This is the first IM selection approach able to holistically consider multiple sources of uncertainties, all the way from seismic hazards to demand modeling. Practical heuristics and workflow are developed to enable entropy-based IM selection in both site-specific and regional-level PSRA. The efficacy of the proposed IM selection method and the influence of IM selection on PSRA of individual structures as well as spatially distributed structural portfolios is thoroughly evaluated. Moreover, the influence of vector-IM record updating on uncertainty reduction of spatial ground motion random field as well as on risk estimates in post-event regional-level PSRA is examined.

Overall, this thesis provides powerful tools and methodologies for ground motion selection, multivariate surrogate demand modeling, and IM selection in PSRA, which collectively contribute to more confident seismic risk estimates of general multi-response structural systems, and better inform decision making under earthquake hazards.