Development of an adaptive model class for considering spatiotemporal correlation in Bayesian model updating and system identification

For system identification problems, modeling the prediction errors is non-trivial, especially in time-domain analysis, which may involve responses over many measured degrees-of-freedom and time steps. The conventional approach assumes independent and identically distributed (i.i.d.) prediction errors of data points. This simplified assumption is often flawed in real applications. The i.i.d. assumption is jeopardized by low signal-to-noise ratios; large differences in noise intensities from different channels; correlation among data channels; system peculiarities, such as damping level, material nonlinearity and fine finite element mesh that causes response interaction at close regions; consideration of more than one quantity of interest, etc. In this paper, a novel model class, devoid of this assumption, is developed for adaptively modeling the spatiotemporal correlation in time history structural responses (and their prediction errors) with few parameters and easy computational operability, especially in the determinants and inverse. The adaptive model class ensures that the spatiotemporal correlation is simultaneously optimized with other uncertain parameters by the Bayesian system identification framework. Aside the development of the adaptive spatiotemporal model class, another major contribution in this paper is the analytical evaluations of the posterior PDF and relative entropy to show the significance of considering the correlation in identification problems. For verification purposes, several spatiotemporal correlation model classes are constructed based on typical functions, and their performances against the proposed adaptive model class as well as the uncorrelated model class was assessed based on the Bayesian model class selection method. The verification consists of a simulated cantilever beam and a real engineering case study of a ballasted railway track system. The results demonstrated superior performances of the proposed adaptive model class when compared to other typical correlation model classes. It is also demonstrated that the model updating results are misleading if the prediction error correlation is not considered. © 2025 Elsevier Ltd.