Robust Parameter Identification of Nonlinear Frictional Systems from Noisy Response Data

This study proposes SINDy-PI-SWR, a parameter identification framework for nonlinear frictional systems that integrates Parallel Implicit Sparse Identification (SINDy-PI) with sliding window resampling (SWR). To our knowledge, this is the first application of an implicit sparse identification framework combined with SWR for frictional dynamics. The proposed framework employs a hybrid regularisation strategy, incorporating L0 regularisation to promote sparsity and L2 regularisation to suppress parameter outliers, thereby improving robustness against measurement noise. The identification performance of the proposed method is benchmarked against numerical integration results. Results demonstrate the SWR technique effectively overcomes the original SINDyPI method's challenge with high noise. Beyond conventional root mean square error (RMSE), this study introduces a coefficient offset as the critical evaluation criterion. For instance, in single degree-of-freedom (SDOF) systems at a noise level of 0.3, SWR reduces the Coulomb model RMSE by 93.78% and suppresses the Stribeck model coefficient offset by 87.3% at a noise level of 0.2. For Stribeck and steady-state Dieterich-Ruina models, the method prioritizes minimizing coefficient offsets over RMSE, enhancing model identifiability. The effectiveness of this SINDy-PI-SWR method is experimentally verified. For the tested cases with excitations at 15, 17, 19 and 25 Hz, it is found that the Coulomb friction provided the best agreement in the tested cases up to 19 Hz, whereas the steady-state Dieterich-Ruina law gave a comparatively better empirical fit in the tested 25 Hz case within the candidate model library. The proposed SINDy-PI framework significantly improves parameter identification performance in frictional systems, offering a novel paradigm for constructing precise nonlinear dynamic models in engineering applications.