## 1 Introduction
(2019) employed deep belief networks (DBN) to predict PR, cutterhead speed, torque, and thrust, introducing the field penetration index (FPI) to quantify TBM performance. [PERSON] et al. (2019) evaluated statistical and ensemble machine learning methods, including Bayesian ridge regression (BR), nearest neighbor regression, random forests, gradient tree boosting (GTB), and deep neural networks like convolutional neural networks (CNN) and long short-term memory (LSTM). GTB demonstrated the highest prediction accuracy, while BR achieved the shortest computation time. Studies revealed that ensemble methods excel in small datasets, whereas deep learning models show potential when ample data are available. [PERSON] et al. (2019) explored Gaussian process regression (GPR), SVR, decision trees (DT), and KNN for predicting TBM disc cutter life. [PERSON] et al. (2019) used evolutionary polynomial regression (EPR) and random forests (RF) to develop models for predicting PR and FPI. [PERSON] et al. (2019) proposed an interpretable machine learning model with data augmentation to predict abnormal disc cutter wear, considering mixed ground conditions. [PERSON] et al. (2019) developed a model for predicting cutter wear based on cutter travel distance and CHI intervals. Despite the advancements, machine learning's \"black box\" nature limits interpretability. In contrast, empirical models and traditional theoretical models primarily rely on existing empirical data and fundamental theoretical frameworks to explore the dynamic relationships among excavation parameters through data mining and multivariate regression analysis. For instance, [PERSON] et al. (2019) developed an excavation efficiency model based on linear cutting tests, unveiling physical relationships among certain parameters. However, these models exhibit limitations when dealing with small datasets and addressing nonlinear relationships, which hinders their ability to accurately describe and predict real-world problems. To address these challenges, recent studies have sought to integrate physical knowledge with machine learning, among which dimensional analysis has emerged as a widely used approach [24; 25]. In the field of TBM tunneling, dimensional analysis has mainly been applied for data preprocessing, while its direct application in model development remains relatively unexplored. Effectively integrating dimensional analysis with TBM excavation data is thus a key research challenge. TBM excavation involves numerous parameters, but for hard rock TBMs, cutterhead speed is one of the key operational parameters directly specified by operators. It determines the rotational speed of the cutterhead during rock excavation and significantly impacts tunneling costs, construction planning, and risk assessment [26]. Since TBM performance is highly sensitive to geological conditions and rock properties [27], matching the cutterhead speed to the geological conditions is critical. Mismatched speeds can cause severe wear on disc cutters during hard rock excavation, significantly increasing construction costs and reducing efficiency. For example, studies have shown that excessively high cutterhead speeds dramatically accelerate cutter wear, while appropriately increasing the penetration rate can effectively reduce wear rates [28; 29]. Therefore, investigating the factors influencing cutterhead speed based on TBM field data and developing reliable predictive models are crucial for optimizing TBM performance, reducing construction risks, and controlling costs. This study focuses on predicting TBM cutterhead rotation speed using dimensional analysis. By selecting appropriate operational and mechanical parameters, dimensionless variable relationships were constructed and combined with elastic net regression to develop a linear prediction model. Validation on an independent test set demonstrates that the proposed model achieves high prediction accuracy and strong generalizability.