Physics-informed sparse identification of bistable structures

The design of bistable structures is a hot topic in the last decade due to its wide application in smart actuators, energy harvesters, flexible robotics, etc. The characterization of the nonlinear restoring force of bistable structures plays a significant role in modeling and enhancing dynamic performance. However, the traditional nonparametric identification methods may have insufficient accuracy or even be invalid because of numerical differentiation procedures and static fitting. Besides, the modern data-driven sparse regression identification methods rely highly on the assumed nonlinear basis functions and lack interpretability. In this paper, a physics-informed sparse identification method is proposed for the nonlinear restoring force identification of bistable structures. The function of the nonlinear restoring force is physically informed by the derived equation of the Hilbert transform and parameter fitting. Furthermore, sparse identification is conducted based on the free vibration responses of the bistable vibrator. The numerical studies verify the effectiveness of the proposed algorithm under the noise level of 30 dB. Experimental measurement is conducted on a magnetic coupled bistable beam to perform the model identification. It has been demonstrated that the reconstructed dynamic response and nonlinear restoring force both keep in good agreement with the measured ones.