Some practical regards on the application of the physics-informed sparse identification for strongly NESs

Strongly Nonlinear Energy Sink structures (NESs) have been widely developed to achieve better performance of vibration suppression recently. Utilizing nonlinear stiffness designs poses great challenges to the system's restoring force measurement and parameter identification. The SINDy (sparse identification of nonlinear dynamics) method has significantly enhanced the efficacy of parameter identification in the past decade. However, the practical considerations regarding model selection, anti-noise capability, synchronized variable retrieval, etc., still pose challenges in strongly nonlinear structure identification. The primary contribution of this study is to conduct thorough investigations on the SINDy identification of strongly NESs encompassing: 1) characterizing the types of strong nonlinearities; 2) exploring numerical techniques for integration and differentiation; 3) selecting appropriate free and forced vibration responses; 4) assessing robustness against noise interference; and 5) considering other equally important aspects. Numerical simulations are conducted on four typical NES structures including piecewise linear, hysteretic, softening-hardening and tristable types to validate these practical issues. The findings indicate that employing a numerical differentiation approach, utilizing a dataset of forced vibration, and maintaining noise levels below 30 dB can yield enhanced identification outcomes. Finally, some discussions on sparse identification of strongly nonlinear NES structures have been illustrated and potential prospects to improve identification accuracy and efficiency are summarized.