Bayesian forecasting of structural bending capacity of aging bridges based on dynamic linear model

The performance degradation of bridge structures is one of worldwide concerned problems in life-cycle civil engineering. Since the deterioration of structural performance is a time-variant process with large amount of aleatory randomness and epistemic uncertainties, it is very important to successively predict structural performance to ensure safety and serviceability. To integrate the past prior information and inspection and/or monitoring data, Bayesian updating techniques are usually used to predict structural performance and condition. However, the traditional prediction functions for processing inspection or monitoring data are normally defined as static polynomial regression functions, which are difficult to realize online, dynamic, and real-time performance prediction. In this paper, the dynamic measure of structural performance with time is treated as a time series, a Bayesian dynamic linear model (DLM) is then introduced. Considering the time-dependent characteristics of structural performance of the considered bridge, a linear growth model is built to predict the short-term variation trends of structural performance. The well-known Kalman filter algorithm is used to estimate and forecast the dynamic performance index for the DLM. The one-step-ahead predictive distribution and the filtering distribution are determined for Bayesian dynamic updating. To allow for the epistemic uncertainty in variance estimation based on monitoring information, use of a discount factor approach is made for specification of unknown variance matrix. Two illustration examples for RC bridge girders are used to demonstrate the applicability of the proposed method.