## 7 Conclusions  
Since the SHM has the capability of maintaining a system through online monitoring, which provides an efficient procedure for continuous inspection of a system, experimental configuration can be an option to implement SHM. However, due to the costs involved, it can be impracticable. Thus, the solution proposed in this work was the implementation of a model-based approach, the data for which can be used for the SHM. These data were generated from numerical models, simulated through a hybrid FEM-analytical approach, and used for the implementation of the ANNs (SHM technique). For the test rig, a reference geared system, the hybrid FEM-analytical approach proved to be an efficient method for performing simulations of healthy and damaged systems, as a result of the low computational effort as compared to other methods and the accurate reproduction of the real geometric model. This is due to the analytical solution developed with a few equations. Furthermore, it was found that a satisfactory performance of the method related to each active contact, in the operation of the mechanical test bench system, was obtained even with the solution with a relatively coarse grid. Since the contacts are solved through analytical equations (based on Hertzian theory), the numerical FE model was developed to evaluate the responses in the contacts related to the forces present in the system, considering the macro-deflections in the components of the mechanism. Indeed, the contact pressures between the analyzed mechanisms are estimated. Furthermore, this approach does not require a mesh refinement to properly simulate contact and provide convergence to the simulation in the same way as a traditional FEM. Hence, this proves even more that the hybrid FEM-analytical approach is more viable, because the simulation of a real system, composed of several mechanical and rotating components, can be completely developed. Since the novelty of this work is associated with the model-based numerical approaches that are simulated in healthy and damaged conditions, the lack of need for geometrical simplifications makes the computational effort, for the approach, relatively low. In addition, the investigation of damages in terms of the health state of a system, as a new aspect, was employed in this work by adding different positions and dimensions to the cracks on the tooth root of the spur gear. The signal resolution of the overall data acquired was consistent, given all pre-process and post-process configurations from the numerical simulation techniques. The spectra, after adjustment of the sampling data and frequency range, showed the characteristics and differences between the healthy and damaged systems, beyond the clearness of the signals acquired. These predicted the visualization of the GMFs of the system (850 and 1700 Hz), the five harmonics (1700 \(\times\) 5 Hz), the sidebands and the peaks of 50 Hz, especially for the damaged systems. Moreover, separating the gearbox-related signal (a pure sinusoidal wave) from other components can be quite complicated. However, this was done to minimize noise that can interfere with the responses related to the gearbox signal. Therefore, this can be investigated to reduce the alteration of the signal from one affected component to the signal from other analyzed ones. The responses of the ANN models were adequate due to the resulting accuracy achieved after post-processing each object from the FEM simulations. Even considering the limited number of objects for these ANN architectures, the resulting accuracy observed in the plots, especially in the All Confusion Matrix for each ANN model, was demonstrated to be extremely satisfactory. This was possible to achieve by using several different points for data extraction from each simulation in order to have more objects than simulations. Indeed, analyzing histogram plots and their features for ANN models is highly recommended for FD in gearboxes.