Abstract: To improve the prediction accuracy of TBM excavation speed and address phase mismatch and insufficient long-term memory stability in strongly periodic sequences, this study proposes a Periodic Auto-correlation Routed xLSTM (PAXLSTM) model. The model introduces a learnable primary period via Time2Vec to explicitly encode phase information, and employs an autocorrelation delay selector (AC-Selector) to identify key phase-consistent lags, enabling phase-aligned historical context construction. In addition, phase-gated sLSTM and routing-written mLSTM modules are integrated into the xLSTM architecture to enhance stable modeling of long-term dependencies across cycles. Validation using TBM tunnelling data from a water conveyance tunnel in Xinjiang shows that PAXLSTM achieves an R² of 0.9171 on the test set, with RMSE of 1.2801 and MAE of 0.8574, outperforming DNN, LSTM, and Transformer models. Ablation results further confirm the critical role of sLSTM and mLSTM in long-term dependency modeling. The proposed model provides support for intelligent prediction and parameter decision-making in TBM tunnelling.