Enhancing sparse regression modeling of hysteresis with optimized PIO algorithm in piezo actuator

The extensive application of piezo actuators is attributed to their high responsiveness and ability to achieve nanoscale steps. However, the accuracy and stability of motion are seriously affected by hysteresis caused by nonlinear characteristics. In this paper, a pigeon-inspired optimization (PIO) algorithm based on dynamic opposite learning (DOL) is proposed to address the issue of nonlinear modeling accuracy in piezo actuators by integrating the sparse identification of nonlinear dynamics (SINDy) method. Firstly, the DOL strategy is employed to introduce reverse pigeon flock into the PIO algorithm, thereby enhancing population diversity and optimization performance. Secondly, through combining the DOLPIO algorithm with the SINDy algorithm, sparse optimization for the penalty process in SINDy algorithm is conducted and the sparse coefficient is optimized based on modeling accuracy. Thirdly, the DOLPIO algorithm is utilized again to optimize the framework of optimized sparse penalty model in order to improve overall modeling accuracy. Finally, experiments are conducted on an established platform to validate the effectiveness of this algorithm.