Dynamic prediction of bridge reliability indices and load effects based on monitoring data and Bayesian updating of generalized probability density evolution equations

To address the challenge of achieving accurate real-time prediction for reliability indices and load effects of the existing bridge based on the extensive data collected through bridge health monitoring systems, a dynamic reliability analysis method for the existing bridges has been given with the Bayesian updated generalized density evolution filtering algorithm and first order second moment method. Firstly, a Bayesian updated generalized density evolution filtering prediction algorithm for load effects was proposed through the fusion of dynamic linear models, probability density evolution theory and particle filtering algorithm, facilitating the dynamic prediction processes. To leverage the benefits of Bayesian recursion for uncertainty analysis, the study derives generalized probability density evolution equations for both the system state and observed variables. The analytical solution is obtained through integration with the established dynamic linear model, to estimate the a priori distribution of the system state. Subsequently, employing the theory of particle filtering, the study estimates the posterior distribution of the system state, enabling the recursive realization of the dynamic prediction process. Then, based on resistance information and predicted load effect information, dynamic reliability indices of the existing bridges were analyzed with first order second moment method. Finally, through the actual engineering verification, the proposed method has higher prediction accuracy compared with particle filtering algorithm, LSTM neural network algorithm and ARIMA model.