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The nanopositioning stage with a piezoelectric driver usually compensates for the nonlinear outer-loop hysteresis characteristic of the piezoelectric effect using the Prandtl–Ishlinskii (PI) model under a single-ring linear voltage, but cannot accurately describe the characteristics of the inner-loop hysteresis under the reciprocating linear voltage. In order to improve the accuracy of the nanopositioning, this study designs a nanopositioning stage with a double-parallel guiding mechanism. On the basis of the classical PI model, the study firstly identifies the hysteresis rate tangent slope mark points, then segments and finally proposes a phenomenological model—the mark-segmented Prandtl–Ishlinskii (MSPI) model. The MSPI model, which is fitted together by each segment, can further improve the fitting accuracy of the outer-loop hysteresis nonlinearity, while describing the inner-loop hysteresis nonlinearity perfectly. The experimental results of the inverse model compensation control show that the MSPI model can achieve 99.6% reciprocating linear voltage inner-loop characteristic accuracy. Compared with the classical PI model, the 81.6% accuracy of the hysteresis loop outer loop is improved.

In order to monitor the rail base, the dispersion characteristics and propagation properties of the guided wave are studied. Firstly, two modes named as Modes V1 and V2 are selected by the semianalytical finite element method (SAFE). The region at the bottom edge can be monitored by Mode V1, while the junction of the base edge and the flange can be detected by Mode V2. Then, the characteristics in the propagation process are analyzed using the finite element method (FEM). The two modes can be separated about 0.6 ms after they are excited. Thirdly, a wave attenuation algorithm based on mean is proposed to quantify the wave attenuation. Both waves can have weak attenuation and be detected within 5 m. Finally, a mode-identified experiment is performed to validate the aforementioned analysis. And a defect detection experiment is performed to demonstrate the excellent monitoring characteristics using Mode V2. These results can be used to monitor the rail base in practice engineering.