## 2 Related Work  
During the last decade, researchers have been working on the development of DT due to its characteristics and functionalities shown; however, in the industrial area, there are many challenges still existing mainly in undefined methodologies and architectures. Below are several works carried out in the industry with DT at the implementation and simulation level. Among the industry 4.0 applications, there are many related works, where authors have conducted studies using different enabling technologies to create the virtual model of the process. For example, refs. [26; 27; 28] shows a path for creating completely functional DTs where continuous production systems are used to reproduce their physical features for registration, inspection, and digital communication. The objective is to have a structure without automation and obtain the data to perform a virtual analysis of various parameters such as predictive maintenance, dynamics, multiservice platform, configuration, and adaptation with high-efficiency automatic systems that are compatible with the planning system and the ERP (Enterprise Resource Planning) to obtain clients' requirements and gradually develop the automation, to achieve better planning and cost reduction. In addition, the scenarios of industry 4.0 DT applications will enable the creation of vertical and horizontal life cycle integration concepts. Different architectures with DTs have been proposed for the design and improvements of CPS. An open-source modular and flexible architecture is developed in [29] for process control, light protocols, and flexible tools for 3D modeling and visualization. The tools were chosen to model and represent machinery and production systems. The virtual environment converges with reality, producing reliable data to validate execution time and enable the implementation of actions on the real plant based on data obtained through simulation. A CPS is created in [30] for the design and control using three enabling technologies: fast mapping method of distributed controllers, extensible distributed communication framework, and multiscale modeling method. Experimental results show that the CPS may achieve a fast design and distributed control for customized and flexible design. A digital mapping model of a physical production plant is realized in [31]. The model has four layers: dimension modeling, object modeling, monitoring, and prediction using the Markov chain. Results showed that the DT is the key technology in the virtual physical merging of the CPS, and in turn, increases the capabilities of operators. A systematic method is proposed in [32] for customized production of furniture, which includes high-fidelity 3D modeling, modeling of mechanisms to simulate movement, and data synchronization in real-time. Results showed that product quality and efficiency may be improved and may achieve virtual monitoring of devices in real-time. An operational decision-making system is proposed in [33] for an industrial environment with a high variety of products and demand; for this purpose, the principles of Industry 4.0 were adapted with a DT constituted by simulation and artificial intelligence focused on the planning of operational resources and cyclic and continuous decision-making. Results showed a decrease in the number of operators and a reduction in the delivery time. A way to integrate a digital shadow (unidirectional communication) system with an MES system is proposed in [34] to create a DT that will be used for decision-making about the error state, and another to unchain low-quality dismantling processes, using the M2M communication protocol to create a communication channel between two levels and with an intelligent layer that houses rules and knowledge. The DT is simulated and integrated with the MES of the Industry 4.0 Laboratory, where the proposed frameworks have been tested and validated.