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In order to study the hysteresis nonlinear characteristics of piezoelectric actuators, a novel hybrid modeling method based on Long-Short-Term Memory (LSTM) and Nonlinear autoregressive with external input (NARX) neural networks is proposed. First, the input–output curve between the applied voltage and the produced angle of a piezoelectric tip/tilt mirror is measured. Second, two hysteresis models named LSTM and NARX neural networks were, respectively, established mathematically, and then were tested and verified experimentally. Third, a novel adaptive weighted hybrid hysteresis model which combines LSTM and NARX neural networks was proposed through analyzing and comparing the unique characteristics of the above two hysteresis models. The proposed hybrid model combines LSTM’s ability to approximate nonlinear static hysteresis and NARX’s high dynamic-fitting ability. Experimental results show that the RMS errors of the hybrid model are smaller than those of LSTM model and NARX model. That is to say, the proposed hybrid model has a relatively high accuracy. Compared with the traditional differential equation-based and operator-based hysteresis models, the presented hybrid neural network method has higher flexibility and accuracy in modeling performance, and is a more promising method for modeling piezoelectric hysteresis.

The widely used Bouc–Wen hysteresis model can be utilized to accurately simulate the voltage–displacement curves of piezoelectric actuators. In order to identify the unknown parameters of the Bouc–Wen model, an improved artificial bee colony (IABC) algorithm is proposed in this paper. A guiding strategy for searching the current optimal position of the food source is proposed in the method, which can help balance the local search ability and global exploitation capability. And the formula for the scout bees to search for the food source is modified to increase the convergence speed. Some experiments were conducted to verify the effectiveness of the IABC algorithm. The results show that the identified hysteresis model agreed well with the actual actuator response. Moreover, the identification results were compared with the standard particle swarm optimization (PSO) method, and it can be seen that the search performance in convergence rate of the IABC algorithm is better than that of the standard PSO method.

This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.

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