Reconstruction of structural health monitoring data is a challenging task, since it involves time series data forecasting especially in the case with a large block of missing data. In this study, we propose a novel methodology for structural health monitoring data recovery in the context of Bayesian multi-task learning with multi-dimensional Gaussian process prior. The proposed methodology stands to model a series of tasks simultaneously rather than modeling each task independently while explicitly encoding the correlations among tasks that can be learnt efficiently from data. The primary advantage of Bayesian multi-task learning for data reconstruction is that it makes more efficient use of the data available and gives rise to enhanced reconstruction capability by making use of the underlying task relatedness. Since the modeling performance of the Gaussian process–based Bayesian approach heavily relies on the selected covariance function, particular focus has been laid on the influences of various kinds of covariance functions including the unblended and composite (hybrid) ones on reconstruction performance. The instrumented Canton Tower of 600 m high is used as a test bed to illustrate the effectiveness of the proposed method in reconstruction of structural health monitoring data. The traditional Bayesian single-task learning approach is also implemented for comparison purpose. The reconstruction results of the structural health monitoring data show that the proposed Bayesian multi-task learning methodology affords an excellent performance, while the Bayesian single-task learning method is unreliable in certain cases; yet, the selection of covariance function has a significant impact on the reconstruction performance of the proposed methodology. The work presented in this study also gains insight into how to choose an appropriate covariance function for reconstruction of missing structural health monitoring data.

The advancement in structural health monitoring (SHM) technology has been evolving from monitoring-based diagnosis to monitoring-based prognosis. The structural stress response derived by the measured strain data is increasingly used for structural condition diagnosis and prognosis because it can be directly used to indicate the safety reserve of a structural component or provide information regarding the load-carrying capacity of the whole structure. Therefore, accurate forecasting of structural stress responses is an essential step for the reliable diagnosis and prognosis of structural condition. For a large-scale, complex structure subjected to multisource effects such as live loads and environmental loads, its stress evolution is a typically nonlinear dynamic process. Moreover, the online monitoring-derived stress data extracted from an SHM system are extremely massive. This arouses a strong demand for developing a computationally efficient and accurate method for forecasting structural stress responses. In this work, we propose the use of a Bayesian modeling approach with Gaussian processes (GPs), which allows for probabilistic forecasts of structural stress responses and has great capability of modeling the underlying nonlinear dynamic process. Although powerful for characterizing dynamic nonlinearity of structural stress responses, the conventional GP-based Bayesian modeling approach remains computationally intensive because of the massive stress data increasingly gathered by the monitoring system. We propose a moving window strategy to substantially shrink the size of training data, thus leading to a reduced-order GP model and effectively alleviating the high computational cost. The feasibility of the reduced-order GP-based Bayesian modeling approach is illustrated by using the real-time monitoring-derived stress data acquired from a supertall structure. Its performance is compared with the full GP-based Bayesian approach, and the comparison results indicate that the proposed approach holds higher computational accuracy and efficiency for stress response forecasts than the traditional method.

Enormous data are continuously collected by the structural health monitoring system of civil infrastructures. The structural health monitoring data inevitably involve anomalies caused by sensors, transmission errors, or abnormal structural behaviors. It is important to identify the anomalies and find their origin (e.g. sensor fault or structural damage) to make correct interventions. Moreover, online anomaly identification of the structural health monitoring data is critical for timely structural condition assessment and decision-making. This study proposes an online approach for detecting anomalies of the structural health monitoring data based on the Bayesian dynamic linear model. In particular, Bayesian dynamic linear model, consisting of various components, is implemented to characterize the feature of real-time measurements. Expectation maximization algorithm and Kalman smoother are combined to estimate the Bayesian dynamic linear model parameters and generate log-likelihood functions. The subspace identification method is introduced to overcome the initialization issue of the expectation maximization algorithm. The log-likelihood difference of consecutive time steps is then used to determine thresholds without introducing extra anomaly detectors. The proposed Bayesian dynamic linear model-based approach is first illustrated by the simulation data and then applied to the structural health monitoring data collected from two long-span bridges. The results indicate that the proposed method exhibits good accuracy and high computational efficiency and also allows for reconstructing the strain measurements to replace anomalies.