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

2026-01-19

AI Summary

This study addresses the challenge of integrating physics-informed vulnerability functions with real-time post-disaster observations in natural hazard modeling. To enable dynamic updating of regional vulnerability fields, the authors propose a two-stage Bayesian framework that innovatively reformulates physical vulnerability functions into a Probit-Normal representation. This formulation facilitates reliability-weighted fusion of multi-source heterogeneous observations through a fidelity-weighting mechanism, leveraging Beta-Bernoulli conjugate updating and heteroscedastic Gaussian processes for spatial information propagation. Applied to the 2011 Joplin tornado event, the method effectively corrects prior biases and generates exceedance probabilities with quantified uncertainties, significantly enhancing real-time situational awareness and decision support in post-disaster response.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: State Estimation

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systemsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• multi-fidelity
• spatial fragility fields
• Bayesian updating
• natural hazard modeling
• real-time observations

Innovation

• Bayesian updating
• multi-fidelity data
• Probit-Normal representation
• heteroscedastic fragility
• Gaussian Process