## 4 Digital Twin Modelling Methodology
### Model Training  
A TBM is a complex system that undergoes operations such as much transport, ventilation, and ground support, providing rotational stability under different geological conditions and mass rock properties. This research covers the mechanical characteristics of the machine and  
Figure 10: Flowchart of information flow of proposed models.  
Figure 9: The basic architecture of an artificial neural network (ANN).  
geological conditions incorporated in the SVR model to enhance predictive accuracy. This paper implemented three algorithms (i.e., SVM, ANN, and SVM-ANN) to explore better methods for predicting TBM PR. Then, these three intelligent models were constructed using the training set. In the above optimization process, different hyperparameter configurations and different model prediction performances were obtained. The SVR represents the complex function depending on the number of support vectors irrespective of the input space's dimensionality. However, the selection of control parameters is crucial in SVR compared to other AI algorithms.  
Selecting optimal design parameters is a key step for the better performance of the SVR model. Generally, three parameters (the loss function parameter, the regularization term, and the Gaussian kernel parameter) should be selected appropriately for training an SVR model. The regularized constant (C) plays the role of minimizing the error term. The optimizer selects a smaller margin hyperplane to better predict results for a large value of C. The free parameter used in the model is C, and the \"RBF\" is the Gaussian kernel function used in this study. The parameter y denotes the variance in the Gaussian kernel, controlling the sensitivity of the kernel function. The MLP regressor iteratively trains the partial derivatives of the loss function at each time step to update the model parameters. A regularization term added to the loss function shrinks model parameters to prevent overfitting. The activation function, ReLU, and the solver, L-BFGS, used \"for weight optimization\" belong to the family of quasi-Newton methods used in this study. A total of nine (9) input layers, two (2) hidden layers, and one output layer are used in the architecture of this study. The number of neurons in the first and second layers is 150 and 100, respectively.  
Parameter C is responsible for the smooth decision boundary and accurate classification of the training data points. For that purpose, the controlling parameter C (penalty parameter of the error term) for the SVR model varied from 0.1 to 100 to analyze the effect of change in prediction performance and the results were collected. Similarly, the controlling parameter alpha (\(\alpha\)) of the ANN model varied from 0.1 to 100 to understand the variation in the prediction of results. Similarly, the \(\alpha\) is a regularization parameter responsible for better fitting the prediction results by controlling the size of the weights. The comparative results of SVR and ANN at different C and \(\alpha\) are presented in Figure 11. R\({}^{2}\) and RMSE values of these algorithms were compared at C and alpha values from 0.1 to 100. It is shown that both models show the best results at C = 10 and \(\alpha\) = 10. Therefore, these values are taken as an optimum value to conclude the results of the predictive models.  
Figure 11: Optimization of SVR and ANN models at different C and \(\alpha\) values: (**a1,b1**) comparative results of predictive models for PR; (**a2,b2**) comparative results of predictive models for AR.