Learning model discrepancy using sparse Bayesian polynomial NARX: case study for Bouc-Wen hysteresis model

Overview & Synopsis

Comparing experimental data with numerical simulation results may reveal discrepancies that cannot be di- rectly explained by the underlying physical model. This issue is particularly pronounced in nonlinear regimes, where the system behavior is not fully understood or where the sources of nonlinearity remain unclear. The aim of this study is to model these discrepancy errors through a data-driven framework. The proposed approach combines the NARX (Nonlinear AutoRegressive with eXogenous inputs) model with the SINDy (Sparse Identification of Nonlinear Dynamical Systems) methodology. In this framework, NARX is employed to represent the discrepancy dynamics, while the nonlinear basis functions are identified using a Bayesian formulation of SINDy, which enables the quantification of uncertainty. The methodology is validated through a numerical application involving one of the nonlinear benchmarks, the Bouc-Wen hysteresis model. The approach learns an interpretable model that corresponds to the hidden hysteresis force from a noisy data and demonstrates the ability to derive an interpretable time-domain model that remains robust in the presence of measurement noise.