Variational Bayesian system identification for nonlinear seismic response estimation

This work presents a Bayesian system identification method for single degree of freedom (SDOF) systems with nonlinear hysteretic behaviour under earthquake excitation. The method is a parametric modeling technique based on variational inference, known as variational identification of nonlinear dynamics (VINDy). Building on the work of Conti et al. (2024), we include basis functions that enable identification of strong nonlinearity and hysteresis behaviour. The proposed framework is capable of discovering the underlying governing equations of the system of interest from input-output data. The feasibility of the proposed framework is demonstrated on SDOF systems with different hysteresis models. The results show that the proposed approach enables accurate estimation and rigorous uncertainty quantification of the displacement responses including the residual components. Furthermore, three-dimensional shake table experiment data on middle-scale reinforced concrete bridge columns at E-Defense are employed to demonstrate the approach's capability for practical engineering applications.