A Two-Stage Bayesian Framework for Multi-Fidelity Online Updating of Spatial Fragility Fields

Abstract: This paper addresses a long-standing gap in natural hazard modeling by unifying physics-based fragility functions with real-time post-disaster observations. It introduces a Bayesian framework that continuously refines regional vulnerability estimates as new data emerges. The framework reformulates physics-informed fragility estimates into a Probit-Normal (PN) representation that captures aleatory variability and epistemic uncertainty in an analytically tractable form. Stage 1 performs local Bayesian updating by moment-matching PN marginals to Beta surrogates that preserve their probability shapes, enabling conjugate Beta-Bernoulli updates with soft, multi-fidelity observations. Fidelity weights encode source reliability, and the resulting Beta posteriors are re-projected into PN form, producing heteroscedastic fragility estimates whose variances reflect data quality and coverage. Stage 2 assimilates these heteroscedastic observations within a probit-warped Gaussian Process (GP), which propagates information from high-fidelity sites to low-fidelity and unobserved regions through a composite kernel that links space, archetypes, and correlated damage states. The framework is applied to the 2011 Joplin tornado, where wind-field priors and computer-vision damage assessments are fused under varying assumptions about tornado width, sampling strategy, and observation completeness. Results show that the method corrects biased priors, propagates information spatially, and produces uncertainty-aware exceedance probabilities that support real-time situational awareness.