## 1 Introduction  
With the development of modern science and technology, the transformation from traditional manufacturing to intelligent manufacturing is an inevitable trend [1; 2; 3]. Correspondingly, in order to reduce the waste in the production process and improve quality while reducing costs, the production mode under the function subdivision needs to strictly monitor and control the manufacturing process. For this purpose, efficient monitoring requires physical devices to have mapping information that can be manipulated in cyber space: that is, it is necessary to complete virtual-real mapping from the physical entity to the digital object of information and achieve effective control. In the process of enterprise development, the realization of virtual-reality mapping and knowledge-based decision has become an urgent problem to be solved [4; 5; 6]. The virtual-reality mapping function needs to realize the mapping, feedback, interaction, linkage and other activities between physical entities (people, equipment, materials, technological process/methods, environment, etc.) in the whole manufacturing process [7; 8]. Under this requirement, cyber-physical systems (CPSs) stand out [9]. The functions of CPSs include four functional domains: business domain, fusion domain, support domain and security domain, as shown in Figure 1 (based on GB/T 40020-2021 \"Cyber physics systems--Reference architecture\"). Among them, the fusion domain, as the core of a CPS, realizes the fusion application of cyber space and physical space. In the fusion domain, the intelligent factory realizes the high interaction and integration between the production information and the manufacturing environment through the closed-loop function system of perception, analysis, decision-making and execution, including the virtual-real mapping between the physical entity and the information digital object. This virtual-real mapping function is an important guarantee for a CPS to effectively realize production monitoring, dynamic exception handling and decision optimization. At the same time, a CPS should also be able to process multi-source information resources such as data resources, algorithm resources and model resources and to assist in optimizing decisions at the commercial, organizational and operational levels. In response to the problem of virtual-real mapping, many scholars have conducted in-depth exploration. The concept of DT shopfloor (DTS) was put forward in [10], and its four key components were discussed. Further, not only were the operation mechanism and implementation method of DTS studied but also the key technologies and challenges. In [11], the authors paid special attention to sensor networks, manipulators and power systems and summarize several typical distributed algorithms based on Kalman real-time monitoring. A digital-twin-based cyber-physical production system (DT-CPPS) based on DT was established in [12], and the configuration mechanism, operation mechanism and real-time data-driven job control of DT-CPPS were discussed in detail. [PERSON]. [13] introduced in detail the DT framework of a robotic dual-arm cooperation system based on Petri net and transformed the loose DT metaphor into strict comprehensive practice in an industrial field, which made positive and effective exploration for the development of DT and CPS. The above scholars have given some solutions to virtual-real mapping, but there are also some problems such as too much theoretical research, less practical operation, narrow scopes of application and so on. In summary, the problems addressed in this study are as follows:  
1. The virtual-reality mapping between the cyber layer and physical layer in CPS (namely the DT function in the system operation);
2. The problem generalization of knowledge-based decision processes and the implementation of solutions.