Bayesian dynamic noise model for online bridge deflection prediction considering stochastic modeling error

Predicting bridge deflection is crucial for identifying potential structural issues, as sustained deviations from the expected range may indicate stiffness degradation. To address the stochastic modeling errors often overlooked by existing methods, this paper proposes a Bayesian Dynamic Noise Model (BDNM) for predicting the daily average deflection of bridge structures. The dynamic noise equations are formulated based on measured deflection data and incorporate modeling errors. Using Bayes' theorem, a recursive BDNM process for bridge deflection prediction is established. Within a Bayesian forecasting framework, key parameters, particularly the coefficient and variance of modeling errors, are estimated using the method of moments, while the Bayesian discount factor is determined using Bayesian optimization. In addition, a novel prediction interval formula is developed, considering both modeling errors and monitoring uncertainties, based on the additivity of the normal distribution. This prediction interval is used as an anomaly detection threshold, and the estimated modeling errors from within the model are employed as damage indicators. The model is validated using monitoring data from an in-service bridge and compared with several common methods. Results demonstrate that the proposed method achieves high prediction accuracy and provides reasonable prediction intervals. Simulated scenarios of increased response variability due to stiffness degradation further illustrate the model's sensitivity to structural behavior anomalies. This method lays a theoretical foundation for developing real-time warning systems for in-service bridges.