Stochastic Ground Motion Models for Uncertainty Quantification in Earthquake Engineering

Earthquakes are among the most destructive natural hazards, causing significant loss of life and economic damage. Traditionally, seismic risk is computed by combining three conditionally independent components: hazard, vulnerability, and exposure. However, recent advancements in computational power and data availability are shifting this paradigm toward an integrated framework: Uncertainty Quantification in Earthquake Engineering (UQEE). UQEE merges the three components into a consistent probabilistic framework, enabling more informed and reliable decision-making in seismic design and risk management for civil infrastructures. An Uncertainty Quantification (UQ) framework is typically characterized by a probabilistic input, a computational model and quantities of interest used for decision-making. In the context of Earthquake Engineering, UQ aims to identify, model, and analyze uncertainties among seismic hazard inputs, structural models (e.g., finite element models), structural responses, and the resulting performance metrics. This thesis primarily focuses on the probabilistic modeling of seismic inputs, specifically constructing stochastic ground motion models (GMMs) that accurately capture the characteristics and variability of recorded ground motions (GMs). Our core technique employs stochastic process modeling for a suite of recorded GM time series. This modeling accounts for two layers of uncertainty: intrinsic uncertainty within individual GMs and record-to-record variability within specific or across various earthquake scenarios. Intrinsic uncertainty is embedded in a modulated filtered white noise model (MFWNM), while record-to-record variability is represented by a joint probability density function (PDF) for the MFWNM parameters. The first part of this thesis explores the “optimal” model structure for the stochastic GMMs. Specifically, we propose fitting an often-overlooked parameter in MFWNM: the high-pass filter’s corner frequency, which controls the low-frequency content of simulated motions. Additionally, we explore proper MFWNM configurations, including different frequency filters (single- and multi-mode) and trend functions (constant, linear, and non-parametric) to represent these filters’ time-varying properties. Finally, we explore two dependence structures to build joint PDFs for the GMM parameters: Gaussian copula and R-Vine copula. These investigations are critical for developing the GMM simulators. Next, this thesis develops two stochastic GM simulators as toolboxes for engineers and researchers. The first, a data-driven stochastic GM simulator, generates a synthetic GM dataset that is statistically compatible with a target GM dataset. This target dataset can be selected under the ergodicity assumption, that is long-term temporal variability at a specific site can be represented by spatial variability from similar seismological sites. The second toolbox, a site-based stochastic GM simulator, generates a synthetic GM dataset for specific earthquake and site scenarios, especially where records are insufficient. This method involves building vectorized ground motion prediction equations (GMPEs) to estimate the MFWNM parameters, including their mean, variability, and correlation. Finally, to enable efficient forward UQ, the thesis also investigates using surrogate models as substitutes for computationally intensive models in UQEE. Specifically, active-learning-based surrogate models are explored for forward UQ analysis, with a focus on computing full distribution functions. A comprehensive study is conducted on this approach by investigating desirable surrogate configurations, including surrogate model types, enrichment methods for experimental design, and stopping criteria.