Abstract
Bridge structures in service are subjected to long-term ambient environments and continuously increasing traffic demands; therefore, the physical quantities of the existing bridge structures are subjected to changes in both time and space. Through health monitoring for bridges, the data of the load effects of bridge structures, including strain, stress, deflection, and so on, of the specified structural components or structures, can be obtained. The novel monitoring systems installed in bridge structures contain sensors providing a large amount of monitored data. Proper processing of the continuously provided monitored data is one of the main difficulties in the field of structural health monitoring for time-dependent reliability prediction of structural components and/or structures. Under the actions of the common random sources of the time-dependent input load data, the time-dependent nonlinear correlation will exist among the time-dependent output load effect data. The Bayesian dynamic linear models are introduced to predict the time-dependent output variables and model the time-dependent nonlinear correlation coefficients between them. Then, the Gaussian copula–Bayesian dynamic linear models are built based on the Gaussian copula theory and the time-dependent correlation coefficients. The models can better and more feasibly predict the future reliability of bridge structures. Finally, an actual application example is provided to illustrate the feasibility and application of the built Gaussian copula–Bayesian dynamic linear models for structural reliability prediction.
Highlights
The time-dependent structural reliability formula is often expressed in terms of a vector of basic random variables characterizing uncertainties in quantities such as time-variant resistances and timedependent load effects which are usually correlated with each other
This article takes the two-dimensional random variables as the example, based on the Bayesian dynamic linear models (BDLMs), the timevariant correlation parameters of Gaussian copula function is computed through Pearson linear correlation coefficients: 1. Time-variant correlation parameters of Gaussian copula function based on Pearson linear correlation coefficients: For the corresponding BDLMs to two different monitored variables y1, t + 1 and y2, t + 1, the Pearson linear correlation coefficients between the two predicted random variables can be approximately expressed as rt + 1ð1, 2Þ =
Failure probability of multiple-dimensional series system can be solved based on equation [43], by computing the time-variant correlation parameter matrix and the marginal distributions of all the predicted random variables based on BDLMs
Summary
The time-dependent structural reliability formula is often expressed in terms of a vector of basic random variables characterizing uncertainties in quantities such as time-variant resistances (time-variant allowed load effect caused by structure degradation) and timedependent load effects which are usually correlated with each other. Equation [4] reveals how to construct the copula function of a multivariate distribution with given marginal distributions It follows from the probability integral transform that the random variables Ui[FXi (Xi), i = 1, 2, . According to equations [10] and [11], if the marginal distributions of x1 and x2 are both normal distributions, combining the concept of Gaussian copula function, the correlation parameters r can be obtained r rÀFÀ1 rÀFÀ1. In order to reasonably assess the structural time-variant reliability, the dynamic Gaussian copula function with time-dependent correlation parameters, namely, Gaussian copulaBDLMs, is built in this article, which can analyze the time-variant nonlinear correlation between different time series. The probability recursion processes of BDLMs based on AR[1] model
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