## 4 Discussion  
In this article the correlation between the drilling data of rigid inclusions and the values of dynamic penetrometers has been analysed. The goal was for drilling data to provide the same information as penetrometers.  
The results obtained show that the analytical formulas are too rigid for the range of terrains analysed. ML algorithms showed to be better adapted to the penetrometric profile of the ground.  
It was also decided to introduce depth as an input variable for the algorithms. By taking the depth into account, a significant improvement in the coefficients was achieved.  
It must be considered that by adding depth to the set of input variables, we are turning the data into a kind of time series, in the sense that the values can now be ordered sequentially. Time series present a very strong correlation with the variable that functions  
Figure 10: Values of the correlation coefficient for the different algorithms depending on the maximum distance to the penetrometer considered.  
as time, masking other possible relationships. It could cause the algorithms to be unable to predict changes in the nature of the terrain layers.  
However, the nature of the terrain is related to the depth at which it is found. We are indirectly giving information to the algorithms such as the increase in friction in the tool or the difficulty in displacing the ground depending on the depth. The introduction of the depth must be done with caution, considering that it could mask the presence of layers that do not follow the prevailing trend.  
On the other hand, the sequential nature of the drilling data allows the use of techniques such as DTW. This metric is easily understandable for the visual comparison of series in a plot.  
Regarding oversampling, it has not proven useful in this case.  
About the effect of distance when choosing the data set, it is observed that the maximum correlation coefficient was not reached at the minimum distance since the number of samples was small and the model is not behaving well in the training set. The highest correlations were reached considering a distance of about 2 m from which the correlation coefficients decreased. This validates the distance chosen to initially train the algorithms.  
Regarding the algorithms used, after the analysis carried out, the regression approach seems to have better results.  
The algorithms that have shown the best results for these datasets have been the tree ensemble methods (RF and XGB). This is expected, as these algorithms are top performers for tabular data. In general, XGB regressor has shown the best results.  
The models perform slightly better in the train set than in the test set, which is to be expected. However, in some cases, the performance in the train set is perfect, a signal of overfitting. This could be solved with some adjustment to the hyperparameters given by grid search that are adjusting too much to the train set.  
This paper is one of the few that deal with data from rigid inclusions. Compared with previous works this article presents a more robust methodology and addresses the issue of imbalanced data. The paper employs a shape-based metric--dynamic time warping (DTW)--to compare the predicted and actual penetrometric profiles, allowing for a more nuanced assessment of profile similarity than standard error metrics alone. The use of DTW for this kind of application is a newly proposed approach. In addition, the performance of the most important kind of algorithm has been analysed. The proposed methodology is a starting point for the characterisation of the bored soil based on the analysis of drilling data during the execution of rigid inclusions.