Modeling nonlinear behavior of piezoelectric actuators using improved WT-GRU neural network

The coupling of hysteresis and low damping vibration in a piezoelectric actuator results in low modeling accuracy and adversely affects output motion precision. To mitigate this problem, this paper proposes an improved wavelet transform gated recurrent unit (WT-GRU) model. This model integrates a convolutional layer with WT-GRU to enhance its capability to express complex relationships. Firstly, the input voltage sequence undergoes wavelet transform to decompose it into a set of frequency subsequences. Then, using the feature extraction and representation ability of the convolutional layer, significant features are extracted from subsequences to construct a time series feature vector. Finally, a gated recurrent unit is trained to predict the output displacement sequence accurately. Statistical metrics such as mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination ( R ² ) were utilized to evaluate the model performance. Additionally, experimental tests were conducted with frequency excitation signals at 80–120 Hz. Experimental results show that the proposed model achieves a MAE of 0.0102 mm, an RMSE of 0.0148 mm, and an R ² value of 0.9478. This model exhibits a significant advantage in accurately predicting the output displacement of piezoelectric actuators, thereby providing a reliable foundation for designing piezoelectric actuator control systems.