Bayesian multi-task learning methodology for reconstruction of structural health monitoring data

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.