SHM-based condition assessment of bridges using gaussian process regression

Abstract

The structural health monitoring (SHM) technology enables to gain information about the in-service performance of bridges. By integrating the monitoring data from online SHM systems, the structural condition of the monitored structure can be evaluated and the health status can be evolutionarily traced. The advancement in SHM technology has been evolving from the monitoring-based diagnosis to the monitoring-based prognosis. Conventional analytical methods process the monitoring data with deterministic parameters and coefficients and have difficulties in determining the uncertainties stemming from the measurement noises, modeling errors, time-varying environmental effects, and etc. In recent years, the Bayesian modeling approach with Gaussian process (GP) has earned attention because of its characteristic which allows for the probabilistic processing and has great capability of flexibility in modeling different kinds of relationships as well. The covariance function in GP can determine the distribution of target function, and should be carefully chosen in order to fit the real covariance distribution of the data regression relationship. Usually the squared exponential (SE) covariance is chosen in GP because it corresponds to a linear combination of infinite number of basis functions and has the largest flexibility. But when the relationship characteristic is known a priori, the explicitly defined covariance function may perform better than the general-purposed SE one. The work described in this thesis is devoted to exploring the flexibility of GP in modeling different relationships by explicitly modifying the model, for the purpose of structural health condition assessment using the monitoring data. A Gaussian process regression (GPR) model is first formulated to establish the relationship between the temperature and expansion joint displacement for the Ting Kau Bridge (TKB). Apart from a general-purposed GPR model defined with SE covariance function (SE-GPR), the explicit covariance function is derived for a linear GPR (L-GPR) model based on the observed linear relationship. The log marginal likelihood maximization method is used to optimize the hyperparameters in GPR models. The performance of the optimized L-GPR model and SE-GPR model are evaluated and compared using the same sample data set. The results show that the L-GPR model with explicit linear covariance function which fits the linear relationship performs better in linear regression and prediction. The outperformed L-GPR model is further used to predict the expansion joint displacement under extreme design temperature. By comparing with the designed allowable maximum and minimum values, the structural health condition of the TKB is examined. In practice, a simple linear relationship may not be adequate, therefore a generalized model is needed. The L-GPR model is further extended to generalized linear model. Before applying simple linear model on the inputs, the inputs are first projected into some high dimensional space using a set of basis functions. The covariance function for a generalized linear relationship is then derived and applied to a polynomial relationship. An explicit polynomial GPR model (P-GPR) is formulated to establish the relationship between the lateral displacement and wind data for the Tsing Ma Bridge. Among the first three order polynomial relationships considered in this study, the P-GPR with second order polynomial (P-GPR2) is selected as the optimal GPR model with the largest log marginal likelihood and smallest root mean square error. The outperformed P-GPR2 model is further used to predict the lateral displacement under extreme design wind speed at 53.3 m/s. The wind direction for maximum displacement prediction is considered in two cases: most probable direction and most unfavorable direction. The predicted total displacement is compared with the designed allowable value to check the structural health condition.