Multistep Probabilistic Forecasting Approach for Tunnel Boring Machine Cutterhead Torque and Thrust Based on VMD-BDNN

Accurate prediction of cutterhead torque and thrust is crucial for achieving efficient and safe propulsion of a tunnel boring machine (TBM). However, several uncertainties within the predictions of TBM parameters may diminish prediction accuracy and credibility. To address this issue, a multistep probabilistic forecasting approach that combines variational mode decomposition (VMD) and a Bayesian deep neural network (BDNN) is first proposed for cutterhead torque and thrust. In this approach, the nonlinear original series is decomposed initially into multiple subsequences and residual sequences to reduce complexity. Then, the multistep probabilistic prediction-based independent subsequence is implemented using three BDNN models, and the results, including multistep point and probabilistic predictions, are obtained by summing all the subsequences. The final results show that all three models, especially the VMD-bidirectional gated recurrent unit model, have excellent performance in terms of multistep prediction, with prediction accuracy exceeding 99.414% and 99.554% for cutterhead torque and thrust in the five-step prediction, respectively. In addition, a high-quality evaluation of uncertainty is obtained via multistep prediction, confirmed by a mean prediction interval width (MPIWep) above 0.8 and all PICPal up to 1. Compared with preexisting models, this approach not only achieves high accuracy in multistep prediction but also infers high-quality aleatoric and epistemic uncertainties in predicting cutterhead torque and thrust.