Novel deep learning solutions with layered recurrent neural networks for nonlinear stiff Dahl hysteresis model in piezoelectric actuator.

Abstract

Piezoelectric Actuators (PEAs) are vital for precision positioning in various applications, including scrupulous machinery and Nano/micro manufacturing. However, their performance is often compromised by complex Nonlinear Hysteresis effects. Current techniques for PEAs' hysteresis either rely on nonconvex, calibration-rich formulations, which are subpar in response to drive-amplitude and frequency variations, or on machine-learning schemes, needing enormous task-specific datasets and offering low training stability and interpretability. To address this, we employ artificial intelligence, specifically using neurocomputing feed-forward and back-propagation networks with the Levenberg-Marquardt (LM) optimization technique, to analyze the behavior of the Dahl Hysteresis Model (DHM) that represents these hysteresis effects. The synthetically generated data are formulated through the numerical integration of the stiff DHM equations, using an Adams time-integration scheme applied to four different excitation inputs: Unit-Amplitude Sinusoid, Sinusoid with Direct Current Offset, Damped Transient, and Damped Harmonic. The excitable and system parameters are varied in a systematic manner in order to generate resultant displacement time series, themselves utilized as input sequences during the training phase of a Recurrent Neural Network (RNNs). This approach enables us to approximate solutions and optimize values through Back-Propagative Recurrent Neural Networks (BP-RNNs) with the assistance of the LM local search optimizer algorithm. Our analysis of BP-LRNNs and LM performance in modeling the DHM for piezoelectric actuators involves various metrics, such as convergence-based learning curves, assessment of adaptive control factors, checks on gradients and validations, and accuracy measures contingent upon Mean Squared Error (MSE), Histogram Analysis, and Regression Analysis. This research deepens our understanding of piezoelectric actuator behavior, ultimately enhancing their potential for high-performance precision positioning applications.