A Gaussian-process assisted model-form error estimation in multiple-degrees-of-freedom systems

In many applications involving modelling of complex structural dynamical systems, the mathematical models employed are often simplified abstractions of a real -world phenomenon. This presents a challenge in accurately depicting and simulating physical reality. In this study, we focus on locally nonlinear shear -storey -type MDOF systems, which are simplistically assumed as linear dynamic models. The disparity between the presumed linear model and the true nonlinear data -generating phenomenon introduces what we term as model -form error (MFE). The essence of MFEs lies in the mismatch between the governing equations of motion of the assumed mathematical model and the true data -generating model. To tackle these MFEs, we treat the MFEs as externally applied latent forces (LFs) and employ stationary Gaussian processes to model them. Through a Bayesian state estimation process, encompassing both the Kalman filter and smoother, we derive estimates of not only the structural state variables but also the MFEs themselves. The two main novelties of our study lie in (a) the extension of the GPLFMbased MFE identification to MDOF systems, and (b) the exploration of the GPLFM's ability to detect and localise the MFEs within the assumed mathematical model without the need for prior knowledge regarding the nature and/or the locations of these MFEs. Furthermore, the study delves into various scenarios of inference dealing with incomplete measurements and highlights identifiability issues encountered in different incomplete measurement scenarios.