### Motivations of This Research  
The intense working conditions of a gearbox can cause recognizable characteristics in vibration spectra when specific system components are monitored. However, this approach usually does not operate in real time, occasioning a delay in maintenance actions such that opportunities to make timely interventions and address developing faults may be missed. Thus, SHM has the advantage of maintaining a system under constant control with the assistance of an online monitoring. CM techniques can be used to check and repair a system synchronously instead of only checking it at fixed intervals. This can avoid downtimes, which can be due to failures, as well as guarantee the working life of a machine [43] and even its prolongation via structural modification approaches [44; 45]. Moreover, this efficient procedure benefits its operation in terms of low maintenance actions and economic efforts since it has the capability of inspecting the system continuously. To implement such a technique, an experimentally based configuration, which provides a realistic view of the process, can be inviable due to the huge costs involved, especially when it comes to the experimental replication of damage to a system. Hence, a model-based approach can be a solution; the data responses of models can be used preliminarily for SHM, and the data generated from analytical and numerical models can be employed for modeling and training. Indeed, for numerical simulation, less time and equipment are required to obtain a large number of experimental data from a complex structure, especially for systems for which it is a complicated matter to develop tests for carrying out experimental investigation [46]. Considering these conditions, in this study, an innovative hybrid FEM-analytical model for a test rig system was implemented to reduce the computational effort and increase the numerical performance compared to a traditional FEM approach. With this model, complex systems can be numerically simulated with good accuracy and without geometrical simplifications. Healthy and damaged (e.g., crack) conditions can be evaluated, considering that the approach can generate vibrational results in terms of spectra for both sorts of conditions. In addition, adding different positions and dimensions to the cracks on the tooth roots of gears, as well as adding multiple damages separately or simultaneously to them, can offer new ways to investigate the health states of systems. After performing the numerical simulations, the displacements from each simulated condition could be extracted and a damage identification could be made based on ML algorithms using a database of simulated signals in healthy and faulty conditions. Moreover, in the present paper, the detection of damage to the test rig system was performed using the ANN approach, adopting the following three procedures: (1) information extraction of signals, which can be shown in time and frequency domains; (2) characterization of extractions, that is, the transformation of the coarse data into applicable data which generate aspects that preserve numerical information in its original form; and (3) classification, which is used for feature categorization. Then, the method of classification parameters used to detect and predict damages and their severity conditions could be applied. In this way, a framework is established to diagnose the state of the system (classification technique) and multiple classes of gearbox faults (multi-class classification technique). Therefore, these outcomes are a set of visualized decision rules of the damage characterization framework that can be automated through machine learning algorithms, thus presenting a starting point for the implementation of effective prognostic algorithms for predictive maintenance. Predicting damage to a system and defining its severity are considered the goals for this work, which can be achieved by the support of the ANN approach. The structure of this research paper is as follows.