## 7 Conclusions
For the first case (the classification approach), Test 5 presented the best performance model, while for the second case (the first multi-class classification approach), Test 8 presented the best one. The results for Test 9, which was the third case (the second multi-class classification approach), were consistent with the results for the previous cases due to the good prediction performance of the algorithm, even when using a limited number of objects for each case of damage. Moreover, overfitting may arise, given the limited amount of data acquired by FEM simulations that were used to construct the database. However, even with the restriction of usable data for the ANN architecture, the results obtained were coherent with respect to the examined scenario. Furthermore, the \"nprtool\" was able to avoid overfitting by using the validation dataset, since the \"nprtool\" algorithm separated part of the objects for the validation phase, which is not always done, yet it is strongly recommended. Then, the percentage of all confusion matrixes, from each ANN model (Tests 5, 8, and 9), which identified the system characteristics, considering the training, validation, and test performance, indicated that these models predicted well the planned initial idea. Test 5 classifies well whether the system has damage or not (classification approach). Test 8 and Test 9 classify well whether the system has damage or not in addition to the severity of damage that can be predicted (multi-class classification approaches). Thus, these results show how well the classification model performs and what kinds of errors it makes. Even requiring a long time for the dynamic FEM simulations (still more viable than a traditional FEM), post-processing of the results, and performance of the ANN technique, this methodology was suitable and consistent for the test bench presented in this paper. Moreover, this methodology is valid for other types of test rig configurations, considering that the implementation of their digital models and creation of their databases should be carried out. The accuracy of the ANN models can yield even better responses if more objects are extracted from the FEM simulations and used to train the ANN. Indeed, this can be applied to the one-element damage example, the analysis of which was considered unfeasible for the current research paper because its ANN model was unable to recognize whether the data (extracted signals from the healthy and damaged systems) signified a damaged or an undamaged system. Thus, for future studies, to complement and advance the research in relation to damage severity, more damage simulations for positions related to all axial dimensions analyzed here could be performed. On the other hand, another possibility is the addition of multiple damage conditions, separately or simultaneously, to the crack on the tooth root of the spur gear. Then, by collecting more objects from these different cases of damage from FEM simulations, other ANN models could be developed to identify more locations and severities of damage in order to characterize and create a robust SHM system. Conceptualization: all; methodology: all; formal analysis, implementation, data curation, and validation: R.d.P.M. and A.L.M. ; resources: R.V., F.C. and C.G. ; writing--original draft preparation: R.d.P.M. ; writing--review and editing: all; supervision, R.V., F.C. and C.G. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. The authors declare no conflict of interest.