# Investigating the Applications of Machine Learning Techniques to Predict the Rock Brittleness Index
## 5 Discussion and Conclusions  
This present study investigated the application of multiple ML techniques for predicting the rock \(BI\) using a dataset from a water transfer tunnel in Malaysia. The main aim of this study was to identify the best model (s) in terms of accuracy for both train and test stages. To compare the models, five performance indices, a ranking system, and a gain chart were used. Therefore, five ML models, including the RF, CHAID, ANN, KNN, and SMM were developed. While the results of performance indices showed that the RF outperformed other models for the training dataset, ANN achieved the best ranking for testing dataset. However, the KNN achieved the highest cumulative ranking. A possible explanation for this is that the KNN showed a stable behavior for train and test stages, while the RF and ANN resulted in too many different rankings for train and test stages. Concerning the importance of predictors in this study, all three models, RF, KNN, and ANN identified \(R_{n}\) as the most important factor for predicting the \(BI\). The KNN and ANN considered \(D\) as an important predictor, while the RF did not. This can be explained by the fact that the data of \(D\) diverged from the average value. It also showed that the RF is intolerable to the dispersion of data points in a data series around the mean.  
The RF method outperformed the single-tree based methods like CHAID for both the training and testing stages. The power of RF stems from its abilities to bag a huge number of single tree models and produce an ensemble tree. For categorical data, the RF produces a number of rules which can show the relationships between the predictors and the target variable. However, in this study, the target variable was continuous and the RF could not create a set of rules. While the ANN showed an acceptable performance to predict the \(BI\), this method is viewed as black-box. Thus, while it can predict the \(BI\), studying its structure does not provide an understanding on the structure of the function being measured. The future studies on the \(BI\) should cautiously use the KNN. While this method is an intuitive approach and immune to outliers on the predictors [25; 63], this may be vulnerable to irrelevant features and correlated inputs [64]. In addition, the ability of KNN to deal with data of mixed-types is still doubtful [25; 64].  
The last analysis section of this study was related to validation of the selected predictive models i.e., ANN, KNN and RF. To this end, 15 datasets with the same input parameters were considered and then, the ANN, KNN and RF models were run again using these 15 datasets. The results of validation stage showed that RF with \(R^{2}\) of 0.971 is more capable to predict rock \(BI\) compared to KNN model with \(R^{2}\) of 0.807 and ANN model with \(R^{2}\) of 0.860. This indicates that all models can be used for similar conditions in the future. More specifically, this research suggests to use RF and KNN models (or each of them) by the other researcher or designers in order to predict rock \(BI\) in design stage of geotechnical projects.  
Figure 15: Predicted \(BI\) values by RF, ANN and KNN together with their measured \(BI\) for all 15 data samples.  
**Author Contributions:** Formal analysis, Writing-original draft, D.S., and D.J.A.; Conceptualization, R.T.; Supervision, B.T.P.; Writing--review & editing, M.L. and R.T.; Resources, V.V.H.; Validation, B.A. All authors have read and agreed to the published version of the manuscript.  
**Acknowledgments:** This research paper is made possible through the support of the Universiti Teknologi Malaysia (UTM) and the authors wish to appreciate their help and support.  
**Conflicts of Interest:** The authors declare no conflict of interest.