High temperature superconducting (HTS) bulk YBa $_2$ Cu3O $_{7-x}$ (YBCO) can achieve self-stable magnetic levitation (maglev) over a permanent magnet (PM) for its inherent flux pinning effect, which has considerable potential for engineering applications. The complicated vibration response, however, is lack of enough research for the nonlinearity of the interaction force between the HTS bulks and PMs. This article mainly focuses on the subharmonic resonance of the HTS bulks YBCO levitating above the PMs in Halbach array, which are in reciprocating motion, by numerical simulations. In general, the motion of HTS bulks is approximately harmonic under limited excitation. When the amplitude and frequency of the excitation satisfy certain conditions, the dynamical system undergoes a period-double bifurcation, and then the subharmonic resonance occurs. Moreover, the period-double bifurcation brings the jump phenomenon when the frequency of excitation increases and decreases at the double of eigenfrequency nearby. Simulations show that a suitable damping is able to reduce the vibration markedly. The subharmonic resonance region in amplitude-frequency plane is presented in this paper finally. In a word, the subharmonic resonance would occur in HTS maglev system under certain conditions and its prediction is numerically studied here with a nonlinear mathematics model of levitation force.

Aircraft fuselage corrosion inspection requires both image-domain recognition and metric physical-surface localization for maintenance execution. This study develops a camera-calibrated vision measurement framework that combines PWDE-YOLOv8n-based corrosion perception, original-image coordinate restoration, lens-distortion compensation, ray-based surface mapping, and detector-center bias correction. The perception dataset comprised 2143 images and 5941 corrosion annotations and was partitioned at the physical-specimen, acquisition-session, or source-group level into 1500 training images, 429 validation images, and 214 independent detector-test images. Detailed physical localization was evaluated on a six-image metrology cohort acquired in six sessions, containing 21 corrosion boxes and 84 axial coordinates. A six-fold leave-one-image-out procedure was adopted; in each fold, the center-shift parameters were estimated from the other five images and applied unchanged to the held-out image. The proposed method achieved a mean absolute axial error of 0.641 mm (95% image-cluster bootstrap confidence interval: 0.571–0.708 mm), an RMSE of 0.809 mm, a maximum error of 3.262 mm, and a projected physical-plane bounding-box IoU of 87.12%. The expanded uncertainty of the manually established reference coordinates was 0.374 mm at k = 2, and Monte Carlo propagation produced a mean absolute error of 0.656 mm with a 95% interval of 0.618–0.693 mm. The proposed method reduced the MAE by 97.91% relative to local pixel-to-millimeter scaling and by 70.58% relative to conventional calibrated camera mapping, while producing accuracy comparable to planar homography mapping. Within ρ ≥ 1500 mm, W ≤ 150 mm, and θ ≤ 20°, the estimated curvature-induced additional axial error did not exceed 0.683 mm. A separate ten-image deployment evaluation produced a mean axial error of 2.448 mm and an average processing time of 53.35 ms/image.