Bayesian emulation for forecasting modal frequencies under multivariate environmental variability with data association metric and incremental updating

Accommodating the influence of Environmental and Operational Variability (EOV) on modal parameters has been a critical issue in Structural Health Monitoring (SHM). In this study, a Bayesian predictive model incorporating data association metric and incremental updating scheme is proposed to forecast the variability of modal frequencies under EOV. Fast Bayesian Operational Modal Analysis (FBOMA) is firstly employed to identify the modal properties. Based on the training data set of identified modal frequencies and multivariate Environmental and Operational Parameters (EOPs), Maximal Information Coefficient (MIC) as an efficient data association metric capable of capturing a wide range of associations is employed to measure their dependence, thereby screening out the factors with the largest correlation. Subsequently, Bayesian emulator providing a nonlinear surrogate mapping between the probability spaces of the modal frequencies and multivariate EOPs is established as a predictive model to forecast the Most Probable Values (MPVs) and associated uncertainties of modal frequencies due to arbitrary EOV. The approach constantly adapts the new field measurements to incrementally update the predictive model and improve the prediction accuracy. The case study using long-term monitoring of the Z24-Bridge demonstrates the superior prediction accuracy of the proposed scheme. Also, the proposed probabilistic input-output modelling scheme has the potential of distinguishing the variations of frequencies due to damage and EOV. This work provides a new possibility for simultaneously accommodating coupling effect of multivariate factors, nonlinear relationship, and multiple uncertainties.