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<p>With the rapid expansion of underground works and transportation networks, online prediction of TBM performance, particularly penetration rate, has become critical for construction monitoring and safety. Addressing the nonstationary, multi-scale coupled nature of TBM penetration-rate signals, this paper proposes a hybrid prediction framework that integrates an improved ensemble empirical mode decomposition (CEEMDAN), multi-model frequencywise prediction, and formula-based constraints, and employs a lightweight hybrid gradient-boosting regression tree (HGBRT) as the final fusion module. Specifically, rock-grade-guided differentiated noise is injected during CEEMDAN’s ensemble-noise process to improve mode separation; the resulting 12 IMFs are split into high- and low-frequency channels and predicted by KAN–Informer (Kolmogorov–Arnold Network-based Informer) and IGWO–XGBoost (Improved Grey Wolf Optimization–optimized Extreme Gradient Boosting), respectively; concurrently, a CNN–BiGRU–Attention (Convolutional Neural Network–Bidirectional Gated Recurrent Unit with Attention mechanism) model predicts advance speed (AS) and cutterhead rotational speed (N), which are converted into a formula-based estimate; finally, the two paths’ outputs are used as new features and fed into HGBRT for fused correction. The proposed method is validated on field TBM data from a water-diversion tunnel in Xinjiang (2080 representative excavation-cycle samples). On the test set, the hybrid framework achieves <i>R</i><sup>2</sup> = 0.9746, MAPE = 2.78%, and RMSE = 0.1172, substantially outperforming data-decomposition-only and formula-only solutions. Component-level experiments further show that the improved CEEMDAN increases component predictability; KAN–Informer outperforms the original Informer on high-frequency components; and IGWO helps locate more robust hyperparameters for XGBoost. In summary, the proposed approach offers a favorable balance of accuracy, robustness and engineering applicability, and can support TBM online monitoring, parameter optimization and risk warning.</p>

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A Hybrid Modal-Decomposition and Formula-Constrained Framework for TBM Penetration-Rate Prediction

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Tao Shao,
  • Yiguo Xue,
  • Daohong Qiu,
  • Kang Fu

摘要

With the rapid expansion of underground works and transportation networks, online prediction of TBM performance, particularly penetration rate, has become critical for construction monitoring and safety. Addressing the nonstationary, multi-scale coupled nature of TBM penetration-rate signals, this paper proposes a hybrid prediction framework that integrates an improved ensemble empirical mode decomposition (CEEMDAN), multi-model frequencywise prediction, and formula-based constraints, and employs a lightweight hybrid gradient-boosting regression tree (HGBRT) as the final fusion module. Specifically, rock-grade-guided differentiated noise is injected during CEEMDAN’s ensemble-noise process to improve mode separation; the resulting 12 IMFs are split into high- and low-frequency channels and predicted by KAN–Informer (Kolmogorov–Arnold Network-based Informer) and IGWO–XGBoost (Improved Grey Wolf Optimization–optimized Extreme Gradient Boosting), respectively; concurrently, a CNN–BiGRU–Attention (Convolutional Neural Network–Bidirectional Gated Recurrent Unit with Attention mechanism) model predicts advance speed (AS) and cutterhead rotational speed (N), which are converted into a formula-based estimate; finally, the two paths’ outputs are used as new features and fed into HGBRT for fused correction. The proposed method is validated on field TBM data from a water-diversion tunnel in Xinjiang (2080 representative excavation-cycle samples). On the test set, the hybrid framework achieves R2 = 0.9746, MAPE = 2.78%, and RMSE = 0.1172, substantially outperforming data-decomposition-only and formula-only solutions. Component-level experiments further show that the improved CEEMDAN increases component predictability; KAN–Informer outperforms the original Informer on high-frequency components; and IGWO helps locate more robust hyperparameters for XGBoost. In summary, the proposed approach offers a favorable balance of accuracy, robustness and engineering applicability, and can support TBM online monitoring, parameter optimization and risk warning.