Data features-based Bayesian learning for time-domain model updating and robust predictions in structural dynamics

Bayesian inference has been demonstrated as a rigorous tool for updating models and predicting responses in structural dynamics. Most often, the likelihood function within the Bayesian framework is formulated based on a point-to-point probabilistic description of the discrepancy between the measurements and model predictions. This description results in an underestimation of uncertainties due to the inherent reduction of the parameter uncertainty as the number of data points increases. In this paper, the problem of estimating the uncertainty of parameters is revisited using time-domain responses. Specifically, spatially and temporally uncorrelated/correlated prediction models are developed to re-formulate the likelihood function based on data features between the measurements and model predictions. The relation between the proposed probabilistic technique and the likelihood-free approximate Bayesian computation (ABC) strategy is investigated, analytically demonstrating that the proposed data features-based models can offer consistent uncertainties for the model parameters. Linear and nonlinear models with time histories data of building systems are utilized to demonstrate the effectiveness of the proposed framework. Results show that the proposed models yield consistent parameter uncertainties and realistic uncertainty bounds for quantities of interest (QoI). These uncertainty bounds are independent of the sampling rate used for the time history response. In contrast, the classical Bayesian formulation tends to underestimate parameter uncertainties and produces overly narrow, unrealistic bounds for response predictions.