## 1 Introduction
This requires prior knowledge of geometric properties, material characteristics, and understanding and modeling of motion: this includes analyzing the movement of individual components, their interactions, and the forces involved [15]. It also involves developing mathematical representations of these dynamics to accurately simulate real-world behavior. By solving the multiphase system using mathematical methods, the machine signatures in various states can be obtained. This approach is studied using two main methods: numerical simulation and physical modeling. Numerical simulation is based on a series of steps, starting with computer-aided design (CAD) of the various components of the mechanism being studied. Next, these components are assembled using connections and contact constraints. This step can be performed using dedicated software such as SolidWorks or AutoCAD. The following step involves defining the type of analysis required: dynamic, static, thermal, etc. For machine monitoring in general, dynamic analysis is typically used, except for specific studies. Afterward, meshing and mesh analysis are carried out to ensure the convergence of the simulation. This allows the simulation to be run, ultimately concluding with the visualization and analysis of the results. The simulation steps can be executed using dedicated software such as ANSYS or Abaqus [7]. The physical modeling method is based on fundamental laws or pre-established models. The framework flow involves defining boundary conditions and initial conditions and solving the system using mathematical tools to address differential equations, including partial differential equations and ordinary differential equations. This approach offers a deeper understanding of the physical phenomena by breaking them down into fundamental principles [22]. The model-based approach is essential for diagnosing machine behavior, predicting failures, and optimizing performance, providing valuable insights for industrial applications. It allows for a detailed understanding of the phenomena underlying faults, contributing to greater reliability in the design and manufacturing of components and machinery. Additionally, it facilitates the estimation of component fatigue cycles and the prediction of part replacements, thereby strengthening predictive maintenance strategies [21]. However, its implementation comes with certain challenges. It requires multidisciplinary knowledge, which can pose a skill-related barrier. Moreover, associated simulations require significant computational time, especially when accounting for all operating parameters and potential phenomena. Another major limitation lies in the unavailability of some essential physical parameters required for accurate simulations, which can reduce the effectiveness of the approach [23]. To overcome the limitations of both data-driven and model-based approaches, a new concept was introduced by Professor [PERSON] in the early 21 st century, known as the digital twin (DT) [24]. This approach is designed to meet the requirements of Industry 4.0 while also serving as a key enabler for Industry 5.0, which aims to reintegrate humans into industrial processes [25]. This emerging technology is governed by a set of standards essential for its correct deployment. [PERSON] et al. [26] addressed this aspect by identifying seven key categories of standards: (1) Reference architecture standards for constructing the digital model from a physical system, primarily Reference Architectural Model for Industry (RAMI) 4.0 and the Industrial Internet Reference Architecture (IIRA) [27]. (2) Telecommunication and data exchange standards, such as IEEE P2413 [28] and ISO 23247-1 [29], ensure interoperability between components [26]. (3) Visualization and simulation standards, crucial for bridging the physical system and its virtual counterpart and for validating the twin through simulation. Examples include ISO/PAS 17506:2012 [30], used in computer-aided design (CAD) [31].