Interpretable sparse identification of a bistable nonlinear energy sink

Bistable nonlinear energy sinks have received great interest due to their efficient broad-band targeted energy transfer over a wide range of input energy levels. The precise identification of bistable nonlinear stiffness force is of significance to predict and enhance the system performance of the vibration energy absorption. However, the nonlinear stiffness force in nonlinear energy sink structures with local bistability is difficult to measure and identify because of snap-through characteristics. Inspired by physics-informed data-driven regression in machine learning, an interpretable sparse identification method is proposed to determine the stiffness force of a bistable nonlinear energy sink. The restoring force surface is constructed on bistable nonlinear energy sink equations and the nonlinear stiffness force trajectory is intercepted by assuming two quasi-zero velocity planes. Furthermore, the candidate functions in the sparse regression algorithm can be physically informed by conducting the least-squares parameter fitting of the intercepted nonlinear stiffness force trajectories. Numerical investigations demonstrate that the proposed method not only gives physics information but also improves the accuracy by 0.48%, 3.26% and 22.21% under the noise level of 30 dB, 20 dB, and 10 dB, respectively. Moreover, the reconstructed dynamic response has a good agreement with the theory. Experimental measurements are performed on a magnetically coupled bistable nonlinear energy sink. Results show that the accuracy improves by 4.52% and 11.76% compared to restoring force surface and Hilbert transform-based methods, respectively.