To address the challenges of drill string vibration monitoring and early warning in drilling engineering, this study proposes a time series classification prediction method for lateral drill string vibrations while drilling. This approach leverages a collaborative surface-downhole vibration monitoring system, integrating a self-developed high-frequency vibration measurement protection joint (with a 1500 Hz sampling rate) and downhole multi-parameter measurement tools to achieve comprehensive capture of vibration signals. By innovatively combining surface vibration data, downhole triaxial acceleration, and drilling engineering parameters (such as weight on bit and torque), a multidimensional feature space is constructed. A Transformer-based model for lateral vibration classification prediction is then designed, utilizing the position encoding technology of Transformers to analyze the temporal dependencies within vibration signals. This ultimately enables the classification and prediction of lateral drill string vibrations during drilling operations. Experimental results demonstrate that, using measured data from a horizontal well in Aksu Prefecture, Xinjiang, the proposed model achieved an F1 score of 90.5% in the lateral vibration level classification prediction task on the validation set. This represents an improvement of 3% to 18.3% over benchmark models such as LSTM and XGBoost. Ablation analysis experiments further confirm that the position encoding module significantly enhances model performance, resulting in a 4.5% improvement in the F1 score. This work provides a high-precision and robust generalization solution for drill string vibration warnings during drilling operations.