TECHNICAL | MECHANISED TUNNELLING


Right, figure 7: Relative variable importance charts


generated via ‘R’ based on rock type categorisation


to prune the tree, considering the following


parameters – 0.01, 0.001 and 0.0001, according to the literature review. To compare the error for each cp value, tenfold cross-validation is performed to compute the associated error, and the one with lowest root mean square (RMSE) or no significant difference is selected. In brief, determining suitable combinations of design


parameters was of paramount importance. This allowed for operative, robust tree-based regression models with high generalisation capacity to be generated. Further information on the algorithm and its mathematical logic is in Breiman et al. (1984). Similar data employed in regression models are used


for presenting a tree-based model for estimation of the TBM FPI, in terms of rock type categorisation in training and validation stages. Figure 4 illustrates a preferable trees developed for TBM performance estimation for a rock type categorisation. Figure 5 displays the optimum tree size. Figure 6


shows the relationship between measured and predicted values obtained from the CART model for each rock type in training and testing stages. The relative variable importance for developed tree-


based models for each rock type, generated by CART, is shown in Figure. 7. This helps to standardise the importance of the values for ease of interpretation, and is definedas the percent improvement with respect to the most important predictor. An important variable is one to be used as a primary or surrogate splitter in a tree. The variable with the highest improvement score is set as the most important variable, and the other variables are ranked accordingly. The selected input parameters for model development


adequately reflect the effect of both intact and rock mass properties on TBM FPI. In general, it can be concluded that,


24 | July 2024


joint frequency has more significant role to play on TBM performance in contrast to intact rock properties, such as UCS. This is in agreement with previous investigations (Hassanpour et al. 2011; Bruland 1998). Also, the following formula can be used to calculate


ROP (m/h) from the FPI predicted by developed models (Equations & Graphs):


6 ROP (m/h) = 0.06 x Fn x RPM FPI ,


COMPARISON OF THE DEVELOPED MODELS Performance of the proposed models was evaluated according to statistical criteria, including RMSE, mean squared error (MSE), and R2


, as follows: 7 8 9 RMSE = R2 =1 −


MSE = 1 N


N y − y 2, i=1


where y, y’ and y are the measured, predicted and mean of the variable y, respectively; and N is the total number of datasets. It is worth noting that the excellent model is considered where R2


~ = 1, and RMSE as well as MSE


equal to zero. The results of applying these models are summarised in Table 7 and show that CART models offer higher accuracy in predicting FPI. As discussed before, the use of statistical analysis


alone cannot offer satisfactory results and application of ML methods can improve the result of regression


1 N


N i=1 y − y 2


N i=1 y − y 2


N i=1 y − ̃y


2


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