A probabilistic framework with recurrent mixture density network for reliability analysis of bridge expansion joint under thermal loading

Expansion joints (EJs) are critical components of a bridge to accommodate the temperature-induced movements and prevent structural damage. Predicting the EJ displacements and providing early warnings are crucial to the maintenance and safety of bridges. This paper presents a novel probabilistic framework to predict the EJ displacements, integrating a recurrent mixture density network and Bayesian linear regression. This approach addresses the inherent uncertainties of the measured structural temperatures and linear regression parameters through robust simulations. The Monte Carlo simulation can effectively evaluate the marginal posterior distribution of the EJ displacements. This framework not only derives the critical parameters from the simulations, but also provides the probability distributions associated with the random forecasting errors under significant temperature variations. The recurrent mixture density network, Bayesian linear regression and the combined models, upon examination with different evaluation indicators, prove that the models work well in predicting the probability distributions. The reliability and anomaly indices obtained show that this innovative methodology can provide precise and probabilistic estimation of the factors governing the EJ displacements for steering the early warning systems.