### Failure of Mechanical Systems  
Fracture mechanics is mainly the study of the complex stress field around the tip of a crack, which is generally used to investigate whether an existing crack will propagate in a system. Additionally, fatigue analysis is the study of fracture behavior under repeated cyclic loading. When the material of a structure gets worn out due to repetitive loads, fatigue occurs, which may result in failure [10]. Thus, gearboxes and their components, such as gears, shafts, bearings, rotors, couplings, and housings, can be subject to many types of failures, which can influence the systems and affect their behavior and working operations. Furthermore, even though several gearbox components are subject to failures, most of the damages occur in the gears. Considering the failure modes of mechanical systems, cracking, pitting, scuffing, wear, and spalling are generally considered the common ones [11]. In this regard, a number of referenced scholars have conducted research into the failure of mechanical systems. Among others, ref. [12] developed research for investigating the consequences of mild wear and rolling-sliding with respect to contact fatigue of gears. Ref. [13] used dynamic modeling to study a planetary gearbox analyzing the effect of clearance with respect to damage to its components. A numerical model was created in [14] to study a wind turbine gear and check the behavior of contact fatigue to analyze its responses. Ref. [15] investigated the effects of a crack on the gear mesh stiffness of a gear by adopting an analytical approach and then applied a dynamic model for understanding the behavior of a planetary gear.  
The detection (diagnosis) of failure can be understood as the identification of a specific condition (damage) of a machine based on the presence of symptoms. Diagnosis can isolate a symptom of a gearbox, whose characteristics such as the design, degradation process of certain faults, production technology and change in condition can provide important information for further decision making related to the detection of failure [16]. Then, the failure mode requires a good understanding of each possible case of damage, so that techniques for evaluating their indicators can be developed. For this, a great number of faults can be detected by physical examination of a system component. Such examinations can be performed using various techniques, such as X-ray, microscopic, magnetic rubber methods, etc. However, it is difficult to apply such techniques without removing the relevant component from the mechanical system and, in specific cases, without damaging the component. In addition, some inspections for verifying a system require human operators to visually inspect the structure. Thus, the number of components fabricated, the variety of damaged structures, and inspection time, for instance, make this procedure unfeasible [17]. In this case, for periodic monitoring, other effective fault-detection techniques should be used in place of intrusive damage detection. In addition, monitoring techniques are considered suitable ways to inspect the evolution and level of a damage in a structure [18]. The methods used for diagnosing gearbox problems are based on vibration analysis, the spectra for which can be collected from, e.g., the housing of the gearbox. Vibration analysis is usually carried out to detect the presence and location of damage as well as to discover its pattern and harshness level. During operation, housing vibrations can indicate gearbox faults by comparing signals with a baseline over a period of time [19]. Indeed, this diagnostic can reveal information related to the fault stage and provide evidence for its evolution; thus, the estimation of the machine's residual life can be properly analyzed for maintenance action.