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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.

Strain sensors, especially fiber Bragg grating (FBG) sensors, are of great importance in structural health monitoring, mechanical property analysis, and so on. Their metrological accuracy is typically evaluated by equal strength beams. The traditional strain calibration model using the equal strength beams was built based on an approximation method by small deformation theory. However, its measurement accuracy would be decreased while the beams are under the large deformation condition or under high temperature environments. For this reason, an optimized strain calibration model is developed for equal strength beams based on the deflection method. By combining the structural parameters of a specific equal strength beam and finite element analysis method, a correction coefficient is introduced into the traditional model, and an accurate application-oriented optimization formula is obtained for specific projects. The determination method of optimal deflection measurement position is also presented to further improve the strain calibration accuracy by error analysis of the deflection measurement system. Strain calibration experiments of the equal strength beam were carried out, and the error introduced by the calibration device can be reduced from 10 με to less than 1 με. Experimental results show that the optimized strain calibration model and the optimum deflection measurement position can be employed successfully under large deformation conditions, and the deformation measurement accuracy is improved greatly. This study is helpful to effectively establish metrological traceability for strain sensors and furthermore improve the measurement accuracy of strain sensors in practical engineering scenarious.

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