Grid-search-based neural network modeling of piezoelectric hysteresis for gravitational wave inertial sensor

The inertial sensor serves as the core payload for space-based gravitational wave detection, providing a stable inertial reference for observing mid-frequency and low-frequency gravitational waves in the universe and black holes. This paper designs a novel three-stage release mechanism for precisely releasing the test mass, namely the physical carrier of the inertial sensor. Due to the nonlinear hysteresis properties, modeling piezoelectric actuators plays an important role in ensuring low residual momentum. A neural network algorithm based on grid search-optimized multilayer perceptrons (MLP) is designed for the piezoelectric actuators used in the third-stage release mechanism. Meanwhile, an experimental setup is developed to acquire input and output data. The improved generalized Bouc-Wen (GB-W) and MLP models are used for parameter identification and model training. Experimental results indicate that the improved GB-W model achieves an error rate within 4%, while the MLP model optimized via grid search achieves a prediction error within 1%, demonstrating superior modeling performance. The MLP model offers a simpler yet more accurate approach, and its effective performance is verified through experiments with triangular and square wave signals across multiple frequencies.