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

TL;DR

This paper presents a Bayesian two-stage framework that integrates physics-based fragility models with real-time observations to improve spatial vulnerability estimates during natural hazard events.

Contribution

It introduces a novel Probit-Normal representation for fragility functions and combines local Bayesian updates with Gaussian Process modeling for spatial information propagation.

Findings

Corrects biased priors in vulnerability estimates

Propagates damage information spatially across regions

Produces uncertainty-aware exceedance probabilities for real-time decision-making

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.