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.
With increasing train speed, it is necessary to study the relation between slab track vibration and travelling speed. In this paper, a wireless sensor network system is deployed on a typical ballastless slab track in China, which uses acceleration nodes to collect vibration information when the train is passing by at different constant speeds. Then, after comparing the denoising effects of a hard threshold method, a soft threshold method and a Bayes wavelet method, the Bayes wavelet denoising method is used to remove the noise, while the spatial variability characteristics of the signal are preserved. Finally, the wavelet energy spectrum is adopted to obtain the duration and energy of the non-stationary vibration data. The time-frequency function curve is obtained to further analyse the physical behaviour of the vehicletrack system. A hammering experiment is conducted to show the importance of the results. This work facilitates a better understanding of the track vibration characteristics for monitoring the status of the track.
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.
To e®ectively study vibration characteristics of tracks under di®erent track structures, wavelet transforms of the vibration data are used for pattern classi¯cation of vibration feature. First, acceleration data of the track are collected with running speed of 150 km/h at 26 positions respectively on a slab tangent track, ballast tangent track and ballast curve track by a wireless sensor network (WSN). Then they are analyzed using the power spectral densities (PSDs) and wavelet-based energy spectrum analysis. The paper elaborates on the reasons for the di®erences of vibration energy and excitation frequencies due to the mechanism of di®erent frequency bands and the corresponding track structures. Based on these, the instantaneous frequencies, vibration energies and durations in the low, medium, and high frequency bands are selected as the features for three track structures. A function curve representing the features is proposed to detect the abnormal track structure by a correlation analysis. Finally, the proposed method of pattern classi¯cation has been validated by experimental testings.
In this paper, a Stewart’s positive solution optimization model is proposed, for obtaining the complex solution to a Stewart’s forward kinematics problem, considering the existence of multiple solutions. The model converts the positive kinematics problem into an optimization problem, in which the value of the objective function is used to represent the precision of Stewart’s positive solution. A self-aggregating moth–flame optimization algorithm (SMFO) is used to improve the accuracy of Stewart’s forward kinematics solution. Two features were added to the conventional MFO algorithm to obtain a more stable balance between global and local explorations. First, Gaussian distribution was used for the flame population to select suitable individuals for Levy Flight operation, increase the diversity of the population, and enhance the algorithm’s ability to jump out of a local optimum. Second, in the middle and late iterations, the positions of the flames were periodically adjusted using the light intensity-attraction characteristic (LIAC) to strengthen the connection between individual flames and enhance the local exploration ability of the algorithm. The proposed SMFO algorithm is compared with three classic meta-heuristic algorithms for eight benchmark functions. Experimental results indicate that the SMFO algorithm is significantly better than the other three algorithms in terms of solution quality and convergence rate. To verify the effectiveness of the SMFO algorithm in solving the Stewart positive kinematics optimization model, values of eight sets of conventional position and posture parameters as well as limiting position and posture parameters were randomly obtained, and values of 16 sets of position and posture parameters were obtained using four algorithms. The results indicate that the SMFO algorithm can improve the accuracy of the forward kinematics solution to 4.05E-09 mm.
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