# Hierarchical bayesian fusion of inspection and monitoring data for probabilistic bridge deterioration assessment

## TL;DR

This paper introduces a Bayesian framework that combines inspection and monitoring data to better predict bridge deterioration and failure risks.

## Contribution

A novel hierarchical Bayesian model that integrates discrete inspection and continuous monitoring data for probabilistic bridge deterioration assessment.

## Key findings

- The Bayesian AFT model with Weibull distribution effectively captures failure risks using covariates like crack number and bridge span.
- The Metropolis–Hastings regression model successfully estimates incremental crack growth and tracks environmental impacts.
- The integrated hierarchical framework outperforms traditional methods in predicting crack failure and long-term deterioration trends.

## Abstract

Bridges are susceptible to long-term deterioration due to environmental exposure and cyclic loading, making the accurate evaluation of crack evolution crucial for predictive maintenance and structural safety management. Traditional deterioration models that rely solely on periodic inspection data often fail to capture the dynamic and stochastic nature of crack propagation. To address this limitation, this study proposes a hierarchical Bayesian inference framework that integrates discrete inspection data with continuous crack monitoring data to achieve a unified probabilistic characterization of bridge deterioration. First, a Bayesian Accelerated Failure Time (AFT) model based on the Weibull distribution is developed to model the failure risk of bridge deck slabs. The model robustly handles right-censored data through sampling and incorporates multiple covariates, including crack number, type, damage category, bridge span, and geometric parameters. Posterior distributions of the shape and scale parameters, together with hazard ratio analysis, quantitatively reveal the influence of each factor on structural failure risk. Second, within the dynamic state layer of the proposed hierarchical framework, a Metropolis–Hastings-based regression model is constructed to estimate incremental crack growth, which is then aggregated monthly to form a continuous degradation trend series. This method effectively captures the response of crack development to environmental fluctuations and supports predictive analysis for on-site maintenance planning. Finally, the failure risk model and the crack evolution model are coupled within a hierarchical Bayesian framework to enable joint risk estimation. The proposed model integrates multi-source information with varying temporal resolutions and uncertainty levels and employs a Bayesian posterior updating mechanism to adaptively refine parameters as new monitoring data become available. Validation using real bridge monitoring datasets demonstrates that the posterior-updated model significantly outperforms traditional inspection-based approaches in capturing crack failure behavior and long-term deterioration trends.