## 3 Signal Processing and Artificial Intelligence for DT Development
### Data Augmentation in DT Applications  
Recent deep learning networks have become increasingly deeper in terms of the number of layers, nodes, and, consequently, the number of learnable parameters. Training these networks involves updating these parameters to perform tasks such as classification or regression. However, one major challenge is the significant number of parameters requiring a large amount of data for effective updating [111]. While signals corresponding to healthy states are often available in abundance, faulty state signals are typically scarce, as the goal is to detect faults at their earliest stages [106]. This challenge has been identified as the \"minimum knowledge\" problem, characterized by data scarcity or imbalanced datasets. To address this, a new discipline called data augmentation has emerged [112]. Data generation for augmentation can be achieved in various ways:  
* Removing elements from signals or images or adding noise [75].
* Traditional operations such as rotation, cropping, and shifting [113].
* Using generative networks to create signals or images resembling each class [114].
* Employing a faithful DT of the monitored component to generate signals for under-represented classes.  
The first three approaches can improve classification accuracy but require a substantial amount of data to train the generative networks or create new images or signals. Conversely, the DT offers the ability to generate unseen data with high fidelity, modeling any potential state the system may encounter, such as gearbox faults. Data generation using the DT has been the focus of numerous recent studies aimed at addressing the problem of monitoring under data scarcity.  
The issue of data scarcity has been the focus of several recent studies, and solutions based on Decision Trees have been proposed. [PERSON] et al. [22] addressed the data scarcity problem by using a five-DOF dynamic bearing model to augment the dataset and enhancebearing fault diagnosis. Similarly, [PERSON] et al. [97] tackled the lack of data for bearing fault prognosis and remaining useful life (RUL) estimation by developing a dynamic model to simulate bearing degradation and generate signals using the DT. [PERSON] et al. [99] also filled data gaps using a similar approach but focused on bearing fault diagnosis. Instead of generating additional data, [PERSON] et al. [100] introduced two modules for feature extraction and tracking between simulated and real-world data, achieving robust performance even with limited datasets. [PERSON] et al. [87] simulated scenarios of imbalanced bearing fault data and resolved this imbalance by generating data using a DT. [PERSON] et al. [88] addressed imbalanced datasets by generating signals with an inverse physics-informed neural network. This network learned the fault signatures of bearings from a dynamic model. [PERSON] et al. [115] distinguished the vibrational behavior of faulty bearings by measuring the impulsive characteristics of the signal. They then evaluated the uncertainty of fault severity using kernel density estimation. [PERSON] et al. [116] conducted a dynamic simulation of a planetary gearbox with five different classes. A subdomain adaptive mechanism was implemented between the model signals and the experimental signals. This step enhances the model's fidelity to address the issue of data scarcity in planetary gearbox diagnosis.