Abstract
Bridge monitoring systems provide a huge number of stress data used for reliability prediction. In this article, the dynamic measure of structural stress over time is considered as a time series, and considering the limitation of the existing Bayesian dynamic linear models only applied for short-term performance prediction, Bayesian dynamic nonlinear models are introduced. With the monitored stress data, the quadratic function is used to build the Bayesian dynamic nonlinear model. And two methods are proposed to handle with the built Bayesian dynamic nonlinear model and the corresponding probability recursion processes. One method is to transform the built Bayesian dynamic nonlinear model into Bayesian dynamic linear model with Taylor series expansion technique; then the corresponding probability recursion processes are completed based on the transformed Bayesian dynamic linear model. The other one is to directly handle with the built Bayesian dynamic nonlinear model and the corresponding probability recursion processes with Markov chain Monte Carlo simulation method. Based on the predicted stress information (means and variances) of the above two methods, first-order second moment method is adopted to predict the structural reliability indices. Finally, an actual engineering is provided to illustrate the application and feasibility of the above two methods.
Highlights
Bridges subjected to time-dependent loading and strength deterioration processes will experience the changes due to internal and external factors
Bridge monitoring systems provide a huge amount of the monitored data, such as stress, strain, and deflection
A sound number of studies about structural health monitoring (SHM) information are mainly focused on the modal parameter identification, structural damage detection technology, data modeling, and so on.[5,6,7]
Summary
Bridges subjected to time-dependent loading and strength deterioration processes will experience the changes due to internal and external factors. Based on section ‘‘The transformed state equation based on quadratic function,’’ the built BDNMs in this article are as follows: The monitored equation is yt + 1 = ut + 1 + nt + 1, nt + 1;N1⁄20, Vt + 1, t = 1, 2, . With equations (13)–(18), the updating relationship between the monitored data and state parameters can be obtained as (yt + 1jut + 1);N1⁄2ut + 1, Vt + 1, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. It can be seen from equation (19) that the modeling processes of BDNM can be divided into two key steps. The fitted quadratic function can be transformed into linear state equation with Taylor series expansion technique: 1.
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