## 6 Conclusions  
This study aimed at investigating the capabilities of SHAP for explaining machine learning models in the intelligent fault diagnosis of industrial bearings. Additionally, this results in identifying the most relevant features for diagnosis. The explanations of the diagnosis outcomes were provided for the SVM and kNN models. The authors investigated the case provided by the test rig for industrial bearings available at the Mechanical Engineering Laboratory of Politecnico di Torino. The conclusions are as follows:  
* The SVM and the kNN models are able to achieve diagnosis accuracies higher than 98.5% for medium-sized industrial bearings;
* The SHAP values are effective for interpreting machine learning models that are aimed at industrial condition monitoring;
* The SHAP analysis is employed to show that four features out of twenty-three are really important to achieve good diagnosis accuracies;  
\begin{table}
\begin{tabular}{c c} \hline
**Model** & **Selected Features** \\ \hline SVM & \(p_{2}\), \(p_{3}\), \(p_{4}\), \(p_{6}\), \(p_{10}\), \(p_{13}\), \(p_{16}\), \(p_{18}\), \(p_{19}\) \\ kNN & \(p_{3}\), \(p_{6}\), \(p_{10}\), \(p_{18}\), \(p_{19}\) \\ \hline \end{tabular}
\end{table}
Table 4: Most important features according to SHAP analysis.  
Figure 8: Test accuracy for 100 different test sets: (**a**) SVM model; (**b**) kNN model.  
* The skewness and the shape factor of the vibration signals have the greatest impact on the outcomes of machine learning diagnosis models.  
The generalisability of these results is subjected to certain limitations. For instance, the choice of the diagnosis model could influence the explainability. Then, future works will provide explanations for different ML models, and the results will be compared with those of this study. Especially, research will be focused on deep learning, which is the most used in IFD nowadays, because it allows the automatic learning of fault features from the collected data instead of the artificial feature extraction, attempting to provide end-to-end diagnosis models when handling increasingly grown data and connecting the raw monitoring data to their corresponding health states of machines, which will further release the contribution of human labour [30; 103]. Another field of investigation will be the effect of the feature selection through the SHAP analysis on the computation time. We noticed a little improvement in the computation time between the ML model trained with all the features and those trained only with the selected ones, but since the SHAP analysis is computationally very expensive, an overall time saving could not be achieved. However, as it is reported in the literature [75; 76], ML models involving deep learning techniques could take advantage of the feature selection through the SHAP method in terms of the computation time, and, therefore, it will be the subject of our future study. Additionally, the feature selection capabilities should be assessed on a general level, and we will mainly focus on feature selection capabilities besides explainability, by providing proper comparisons with the common techniques targeted in this task.  
Conceptualisation, E.B., L.C., C.D., and L.G.D.M.; methodology, L.C. and L.G.D.M.; software, L.C.; investigation, L.C. and L.G.D.M.; data curation, L.G.D.M.; writing--original draft preparation, L.C. and L.G.D.M.; writing--review and editing, E.B. and C.D.; project administration, E.B. and C.D.; supervision, E.B. and C.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Data availability Statement: Data are not available due to privacy reasons.  
The authors declare no conflict of interest.