## 3 System Flexibility Digital Representation
### Flexibility Definition and Analysis  
(1) Flexibility Definition  
Flexibility is a complex and multidimensional concept, which has different definitions and meanings in different application scenarios. In product innovation research, [PERSON] (2018) emphasizes labour flexibility and mix flexibility. Labour flexibility exposes the workforce to a broad range of manufacturing tasks, and mix flexibility helps to quickly produce or develop different new product ideas to influence product innovation performance. [PERSON] (2018) defines flexibility as the balance management ability between energy storage and various heat sources (including renewable energy) in the heating demand in the study of the flexibility for the thermal system network. In the robot manufacturing system for SME, [PERSON] (2018) pays more attention to flexibility in customization and design. Flexibility in customization allows SMEs to customize the required manufacturing system by themselves. Flexibility in design (2018), helps to develop new manufacturing systems easily by making appropriate changes from the existing ones. [PERSON] (2018) considers the correct configuration or reconfiguration ability of the production system is the key technology in the flexibility transmission line design to meet the demand for new product characteristics change. Due to its multidimensional characteristics, researchers, especially the ones in the manufacturing area, identified many different but related classes of flexibility. The flexibility studied in this paper is mainly considering the ability of the production system to meet the demand for new products' production. The needs of a production system for an enterprise cover many aspects, such as efficiency, cost, performance, etc. If the production system can obtain high production efficiency and production performance at low costs, it indicates that the design scheme has higher flexibility. However, there is no positive correlation between the cost, efficiency and performance of the system. If the production system wants to achieve high efficiency, they must give up the desire for low cost, and high production performance in most cases loses part of the production efficiency. It can be seen that the relationship between the various needs of the production system for the enterprise is more complicated. Therefore, we only consider part of the requirements that the enterprise needs when evaluating the flexibility for the production system in the design phase, which include the ability to meet the multiple varieties, small batches and quick switch of products' production demands, etc. This ability, on the one hand, is expressed as the ability of the production system to meet the needs of the company's products, processes, and machines, which can be obtained through the analysis of the structural attributes for PSDS, which is called the PSDS static characteristic performance, on the other hand, it is expressed as the ability of the production system to meet the changes in demand that may occur in the enterprise can be obtained by simulation and prediction for the PSDS, which is called the dynamic characteristic performance of PSDS. System flexibility characteristics analysis  
In a review article, [PERSON] summarized dozens of flexibility types and made corresponding definitions for different flexibility types. The summarized flexibility types for the manufacturing industry include machine flexibility, operation flexibility, path flexibility, volume flexibility, product flexibility and so on. In the existing studies, scholars often evaluate system flexibility performance by measuring a certain dimension flexibility to help system development. [PERSON] [27] takes machine flexibility as an evaluation index for production system flexibility, and considers machine operation efficiency, function conversion probability, function conversion efficiency and number of operable states as characteristic parameters to evaluate system flexibility.