Vibration signal prediction of straddle-type monorail train gearboxes based on topological data analysis

Straddle-type monorail train gearboxes operate in complex environments where vibration signals exhibit strong non-stationarity, nonlinearity, and high noise levels. In practical operating conditions, gearbox fault samples are difficult to obtain, and critical features are often obscured by noise, leading to overfitting and poor generalization of existing deep learning models for time series prediction. To address these challenges, this paper proposes a topology-guided time-series prediction model designed for small-sample conditions. First, an adaptive period detection mechanism is constructed using the Hilbert-Huang transform and the Teager energy operator to overcome the limitations of traditional methods in extracting features from non-stationary signals. Second, a topological attention mechanism is introduced by mapping vibration signals into a topological point cloud and quantifying multi-scale structural features via persistent homology, thereby generating an attention map with physical interpretability. Finally, a topology attention-guided convolutional neural network is constructed to achieve high-precision vibration signal prediction. Experimental results show that the proposed model achieves a coefficient of determination (R²) approximately 61% higher than that of the TimesNet model, verifying its robustness and efficient predictive performance under small sample conditions.