# Fault Diagnosis of Intelligent Production Line Based on Digital Twin and Improved Random Forest
## 3 Digital-Twin-Assisted Fault Diagnosis Method Using Transfer Learning  
### Digital-Twin-Assisted Transfer Learning  
In 2003, Dr. [PERSON] [29] first proposed the digital twin concept in a product lifecycle management course at the University of Michigan. Digital twin serves as a bridge between the physical world and the virtual world. It has the characteristics of real-time synchronization, high fidelity, and faithful mapping. With the development of high-performance computing, system simulation, the industrial Internet of Things, big data, and machine learning technology, digital twin has become a research hotspot. DT refers to the construction of a one-to-one real-time mapping model corresponding to a physical entity in a virtual space. The concept of Cyber-Physical Systems (CPS) is the basis of DT. The difference between DT and CPS is that DT emphasizes real-time simulation of physical entities. Digital twin is a digital model that integrates multiple physical fields, including the real working conditions of physical entities, materials, and data obtained through real-time sensors. [PERSON] et al. [30] discussed the role of big data in supporting intelligent manufacturing and summarized the historical viewpoint of the data lifecycle in the manufacturing industry. [PERSON] et al. [31] selected 123 representative projects and 22 supplementary works to analyze DT from the perspective of product lifecycle management and business innovation and confirmed eight potential future uses of DT. [PERSON] et al. [32] presented the results of research on the development of digital twins of technical objects. [PERSON] et al. [33] used intelligent DT combined with machine learning for bearing-anomaly detection and crack-size identification. [PERSON] et al. [34] proposed a five-step approach to planning data-driven digital twins of manufacturing systems and their processes. Transfer learning [35; 36] refers to the use of knowledge obtained through learning in massive adjacent data domains to realize the transfer of knowledge so as to solve similar problems in new data domains faster and more effectively. During the operation of an actual production line, due to a lack of training data in case of failure, most of the data obtained are on the normal operation of the production line. This makes it difficult to obtain a relatively balanced dataset, and thus it is difficult to train a classifier with generalization. In transfer learning, the data domain from which the knowledge is learned is called the source domain (Dos), and the data domain used as the predictive output is called the target domain (Dot). For a task, \(T_{a}=\{Y,f(\cdot)\}\), where \(Y\) is the label space, \(Y=\{y_{1},\ldots,y_{m}\}\), \(f(\cdot)\) is the target prediction function, which cannot be directly observed, and needs to pass training data \(\{x_{i},y_{i}\}\) to learn, and \(f(\cdot)\) predicts the corresponding output label \(f(x_{i})\) according to the current data \(x_{i}\). \(f(x_{i})\) can be written as the conditional distribution function \(\mathrm{P}(y_{i}|x_{i})\), and the source domain can be written as:  
\[Do_{s}=\{(x_{s1},y_{s1}),\ldots,(x_{st},y_{sn})\}\ x_{si}\in\chi_{s} \tag{12}\]  
In machine learning, this represents the data domain where the training data are located, and \(y_{si}\in Y_{s}\) is the corresponding class label. Similarly, the target domain can be written as follows:  
\[Do_{t}=\{(x_{t1},y_{t1}),\ldots,(x_{tn},y_{tn})\}\ x_{t}\in\chi_{t} \tag{13}\]  
Equation (2) indicates the data domain where the test set is located, and \(y_{ti}\in Y_{s}\) is the corresponding label output. The task learned in the source domain is called the Source task (Tas), and the task applied in the target domain is called the Target task (Tat). When the target task has less high-quality training data, the learning technology is transferred from some previous tasks to the target task. In this case, transfer learning can save a lot of labeled data in the target domain [37].