An Active Learning Kriging-based Bayesian Framework for Probabilistic Structural Model Exploration

The Bayesian framework in structural health monitoring includes both modal identification and model exploration. Probabilistic model exploration, also named as model updating, can effectively estimate the structural parameters and quantify their uncertainties. However, it can be computationally intensive on application to real-world large-scale structures. Meta-models, e.g. Kriging models, can help tackle this challenge but they also introduce more uncertainties. In this paper, a novel Bayesian framework combining the active learning Kriging approach is proposed. The framework comprises three major components: the improved fast Bayesian spectral density approach for modal identification, the active learning Kriging method for meta-modelling, and the Bayesian structural model exploration. The Transitional Markov Chain Monte Carlo algorithm is implemented throughout the framework to sample the posterior distributions. The uncertainties from three aspects, i.e., (1) measurements, (2) meta-model construction and (3) finite element modelling, are considered in definition of the likelihood function adopted in both the active learning and model exploration processes. Compared with the ordinary Kriging model and adaptive Kriging approach using U function, the proposed active learning method significantly reduces the uncertainties of the Kriging predictor and improves its local prediction performance with fewer samples. The proposed framework is validated by a continuous test beam in the laboratory and applied to a real-world cable-stayed bridge using structural health monitoring data. A mode-matching criterion is used to overcome the difficulty of closely spaced modes in model exploration of the cable-stayed bridge. As the proposed framework is data-driven, no weighting hyperparameters are required. The active learning Kriging-based Bayesian framework can directly process structural dynamic time history response and conduct probabilistic model exploration with multiple uncertainties included, and therefore is promising in application to major structures.