Piezoelectric actuators are widely used in precision positioning systems. However, their inherent nonlinear behaviors, particularly hysteresis and output saturation, degrade modeling accuracy and limit control performance. Existing studies have generally used either black-box models or traditional physical models. The former typically lack physical interpretability, while the latter can exhibit limited accuracy when the actuator response includes coupled nonlinear effects. To address this issue, this paper proposes a hybrid physics-informed neural network (Hybrid-PINN) framework. An equivalent attenuation model, with a calibrated attenuation coefficient, is first established to describe output saturation and provide a nominal physical reference. A parallel neural network is then introduced to compensate for higher-order residuals not accounted for by the nominal physical model. By incorporating a physically constrained loss function, the proposed framework combines information from the physical mechanism with experimental data. A series of experiments was conducted on a stacked lever-amplified piezoelectric actuator. The results show that the proposed model captures the main hysteresis and saturation tendencies of the tested actuator, and that prediction accuracy is improved by more than 20% compared with the traditional physical model. A detailed comparison with a multilayer perceptron, a standard physics-informed neural network, and LSTM models was also performed. The proposed model achieves lower prediction errors in most of the tested cases and exhibits improved convergence under current experimental conditions. Overall, this work provides a physically interpretable modeling framework at the actuator level for piezoelectric actuators within their calibrated operating range.

Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.