Dynamic Modeling and Measurement Uncertainty Evaluation of the Nonlinear Piezoelectric Impulse Drive System With Small Samples

Evaluating measurement uncertainty is crucial for ensuring the reliability of piezoelectric drive systems. However, existing international standards are insufficient for dynamic measurement uncertainty evaluation, primarily due to the complexity of dynamic systems and the challenges of establishing uncertainty propagation models with limited samples. To address this issue, we propose a temporal evidential regression network (T-ENet) for developing dynamic models and evaluating uncertainty in piezoelectric impulse drive systems with small-sample nonlinear characteristics. We combine an evidential regression model with gated recurrent units (GRUs) to create a robust modeling framework. This framework integrates gradient-updated meta-learning algorithms, allowing it to perform effectively with minimal training data and gradient updates, accurately capturing the temporal features of dynamic systems and estimating and predicting the distribution parameters of system dynamic uncertainty. Experimental results validate the effectiveness of our method, and comparisons with traditional long short-term memory (LSTM) and GRU networks demonstrate its superiority in dynamic prediction. The correlation between prediction uncertainty and actual error confirms the effectiveness of our method in estimating uncertainty in dynamic measurements and provides a key reference for analyzing the reliability of actual measurement results.