## 4 Conclusions  
A model-based approach to condition monitoring of gearbox transmissions was presented in this study, leveraging on a hybrid analytical-numerical model for the generation of signal examples to be used for algorithm training. The approach was applied to a  
\begin{table}
\begin{tabular}{c c} \hline \hline
**\# Observations** & **Equivalent Pitted Area** \\ \hline
55 & 0.2 \\ \hline
55 & 0.35 \\ \hline
55 & 0.48 \\ \hline
55 & 0.63 \\ \hline
55 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Training-set composition for damage quantification.  
Figure 23: Quantification ANN performances: (**a**) training, (**b**) validation, (**c**) test with the correct damage location as input, and (**d**) test with the estimated damage location as input.  
back-to-back test rig, and experimental data in normal conditions were used to validate the baseline model and to extract realistic noise components to be superposed on numerically simulated signals. After a feature-extraction module used principal component analysis to project data in a more compact space dimension, these were passed as input to a hierarchical structure of artificial neural networks. A classification ANN was used for detection of pitting damage positioned on the teeth flank, intuitively manifesting better performances when signals in the presence of larger damages were processed. After damage was detected, two regression ANNs were used to correlate the variations of the signal FFT with the radial position of the damage and its severity. Specifically, it was found that an improved performance of the damage assessment algorithm was obtained while the information about damage position, estimated by the localization ANN, was passed to the network through an additional input node.  
The algorithm performances were assessed at each level of the damage-identification hierarchy, and demonstrated to be extremely satisfactory, given the limited amount of simulations used to construct the training database, even in the presence of a realistic noise corrupting the ideal simulated data. Augmented accuracy and precision of the algorithm output was expected by increasing the density of the damage entity and position grids. However, considering the aim of this paper was to show the consistency of the approach, the adopted number of simulations was considered sufficient at this stage. Although the methodology described herein remains valid for any test configuration, it must be specified that the results obtained throughout this project were consistent and valid only for this bench test, since the digital model was coherent only with it, while a new database must be created for each examined scenario.  
A final note must be made regarding the future developments of the project. It could be expanded by adding different damages to the simulation database; for example, including fatigue damage at the root of different teeth, or analyzing the effect of multiple simultaneous damages. However, while the combinations are endless, a perfectly tuned condition-monitoring system could be built only by investing a great amount of computational effort.  
[PERSON] followed the development of the rig, performed the experimental tests and the FEM analyses, and wrote the paper; [PERSON] and [PERSON] post-processed the results via ANN and wrote the paper. All authors have read and agreed to the published version of the manuscript.  
This work is based on the project RTD 2018--SMOG, Structural health monitoring of mechanical gearboxes, funded by the Free University of Bozen-Bolzano (PI: [PERSON]) and supported by Politecnico di Milano. This work also was supported by the Open Access Publishing Fund of the Free University of Bozen-Bolzano.  
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.  
The authors declare that they have no competing interests.