On efficiency and accuracy of sparse identification of bistable nonlinear energy sink chains

Bistable nonlinear energy sinks have been widely studied in energy harvesting and vibration absorption systems. The precise identification of local bistable nonlinear stiffness force is of significance to predicting and controlling the dynamic responses. Sparse identification is a very popular data-driven method that has been widely used in nonlinear dynamics identification. However, the accuracy and efficiency of sparse identification of multi-degree-of-freedom bistable systems are still not yet investigated. Besides, the significance of physical information of basis functions in sparse identification has not been numerically validated. This paper established the model of Bistable Nonlinear Energy Sink Chains (BENSC) and the vibration absorption characteristic is numerically analyzed. The Sparse Identification of Nonlinear Dynamics Systems (SINDy) and physics-informed SINDy are conducted on two-degree-of-freedom to ten-degree-of-freedom BENSC systems. The results show that with the increase in noise levels, the identification accuracy will be greatly decreased using SINDy with third-order polynomial basis functions. Besides, the computing time is exponentially increased when the number of degrees of freedom increases. However, the physics-informed sparse identification with basis functions a prior still keeps an accuracy of around 0.5% even under the noise level of 20 dB. The identification efficiency greatly improved compared with SINDy using third-order polynomial basis functions. The results give new insights into the accuracy and efficiency issues of sparse identification applied to BNESC systems under noise.