## 1 Introduction  
With the rapid development of the new generation of information technologies, such as cloud computing, the Internet of Things, and big data, countries around the world are committed to realizing the interconnection and intelligent operation of the physical world and the information world of the manufacturing industry, thereby realizing intelligent manufacturing [1]. Intelligent manufacturing is the integration of intelligent technology and manufacturing technology. Its core purpose is to improve manufacturing technology by using intelligent technology in the whole life cycle of products. How to realize the real-time interaction between virtual information and physical equipment information during product processing is one of the main obstacles faced by the application of intelligent manufacturing concepts in actual production and processing. With the deepening of research on digital twins, the expansion of the field and the combination of industries have gradually increased. When the concept of digital twins penetrates the processing and manufacturing industries, a new and feasible method for the intelligent production of factories will emerge. A digital twin is a virtual model that creates physical entities in a digital way. It simulates the behavior of physical entities in the real environment with the help of models and data and adds new capabilities to physical entities through virtual and real interactive feedback, data fusion analysis, decision iteration optimization, and other means [2]. In the process of the product life cycle, it plays a bridge and link role between the physical world and the information world by using models, data, and multidisciplinary technologies, and provides more real-time, efficient, and intelligent services [3; 4; 5]. The concept of the digital twin was first proposed by Professor [PERSON] in the product life cycle management course at the University of Michigan in 2003. At that time, it was defined as a three-dimensional model: a physical product, a virtual product, and the connection between the two [6]. In 2010, the National Aeronautics and Space Administration (NASA) introduced the concept of a digital twin for the first time in the space technology roadmap. Its purpose was to realize the comprehensive diagnosis and prediction function of the flight system by using digital twin technology, so as to ensure the continuous and safe operation of the whole system during its service life [7]. In 2011, NASA and the US Air Force Research Laboratory jointly proposed the digital twin paradigm for future aircraft and defined the digital twin as a simulation process that integrates multi-physical fields, multi-scale, and probability. Based on the aircraft's physical model, historical data, and sensor real-time data, a fully mapped virtual model was constructed to represent the full life cycle process of the physical system, thereby realizing the prediction of the aircraft's health status, remaining useful life, and mission completion progress [8]. Due to the promotion of GE, Siemens, and other companies, digital twin technology has begun to develop rapidly in the field of industrial processing and manufacturing. Gartner, the world's most authoritative IT research and consulting firm, has listed the digital twin as one of the top ten strategic technology development trends in 2016 and 2017 [9; 10]. Since then, the concept of the digital twin has attracted the attention of Chinese scholars, and some scholars and experts have begun to conduct in-depth research on the digital twin. As shown in Table 1, experts and scholars in various fields have given their own definitions and understandings of the concept of the digital twin. With the further deepening of the research, Chinese scholars began to apply digital twins to all walks of life and studied the concept of digital twins, the parameters of theoretical models, the elements of actual models, and the expansion of application scenarios in the corresponding fields.