Covariance Structure Modeling of Engineering Demand Parameters in Cloud‐Based Seismic Analysis

ABSTRACT Probabilistic seismic demand modeling aims to estimate structural demand as a function of ground motion intensity—a critical stage in seismic risk assessment. Although many models exist to describe the structural demand, few consider the covariance among engineering demand parameters, potentially overlooking a key factor in improving the accuracy of these models. This study aims to investigate the impact of heteroscedastic covariance models on seismic demand hazard and loss estimates, using an illustrative example of a mid‐rise steel structure, a hypothetical seismic source model, and a non‐stationary stochastic ground‐motion model. Cloud analysis is performed to establish median demand estimates using a linear model, a bilinear model, and a Gaussian process regression (GPR) model. Various seismic demand and loss estimates are produced from combinations of four variance and four correlation models, which consider both homoscedasticity and heteroscedasticity. Heteroscedastic models include a step‐model, a linear regression‐based model, and a model using another GPR. Earth mover's distance is used as a metric to assess the accuracy of each estimate against a benchmark solution obtained via an unconditional approach (i.e., empirically estimating demand exceedance frequencies from simulated ground motion time‐histories). The study shows that using more complex, heteroscedastic variance models improves risk and loss estimate accuracy, with the GPR‐based variance model proving the most accurate. Although the method used to account for correlation has a smaller impact on model accuracy, considering correlation is also important for covariance formulation, as models that ignore correlation yield the least accurate seismic demand and loss estimates.