## 2 Materials and Methods  
### Data Augmentation  
#### 2.1.1 Data Augmentation Methods  
In machine diagnostics, imbalanced datasets are common, as failures occur less frequently than normal operations. Collecting failure data is challenging, costly, and time consuming, while failures themselves can be unpredictable and diverse. Historical data are often incomplete or lack detailed failure records, particularly in older monitoring systems. As a result, datasets are dominated by normal operations, making it difficult for machine learning algorithms to effectively process the minority class representing failures. This imbalance can lead to biased models that favor the majority class, resulting in poor fault detection performance. Balanced datasets are crucial in deep learning because they enable models to learn and generalize effectively for all classes, avoiding artificially high accuracy caused by predicting only the majority class. Balanced data better reflect actual model performance, minimizing overfitting risks and increasing the model's robustness to distribution variability. To address the issue of imbalance, techniques such as data augmentation, class weighting, and synthetic oversampling are used. These approaches enable fairer and more reliable training of deep learning models, improving their applicability in real-world scenarios. In this study, database augmentation was approached in a hybrid manner. Additional samples for fault-free cases were generated using the TimeGAN network, while for faulty cases, a superposition was applied, combining a fault-free signal with the system response to damage-induced excitation. The authors employed two distinct augmentation strategies to effectively increase and balance the strain gauge measurement dataset. For generating synthetic data representing an undamaged state, the TimeGAN (Time-Series Generative Adversarial Network) model was utilized. TimeGAN is an advanced generative model, a variant of GANs specifically adapted for time series. It combines GAN and autoencoder features, using hybrid training (both supervised and unsupervised) to effectively learn and replicate complex temporal dependencies and properties of the original data. This is crucial for precisely modeling \"normal\" system behavior, which serves as a reference point for anomaly detection. For rare fault data, a superposition method of one-dimensional observation sequences was applied. This procedure involves inserting segments of signals characterized by defects (simulated system responses to local damages) into randomly selected locations within a healthy signal. The amplitude of the damage signal is scaled to match actual defect conditions. This pragmatic and effective approach to augmenting rare, critical events ensures the physical plausibility of the generated defects. This method, based on explicit domain knowledge, directly addresses the problem of extreme data scarcity for faults, avoiding challenges such as \"mode collapse\" often encountered in generative models trained on very limited examples. Compared to other 1D data augmentation methods, the approach in the article stands out significantly. Simpler transformation-based methods, such as jittering, scaling, permutation, slicing, or time warping, while computationally inexpensive, often fail to preserve complex temporal dependencies or generate truly novel, realistic patterns, which is crucial for sensor data. TimeGAN and superposition offer significantly higher fidelity and domain relevance. Although other generative models exist, such as Variational Autoencoders (VAEs), other GAN variants (e.g., Conditional GANs, Wasserstein GANs, SeriesGAN), and emerging Diffusion Models, their application to extremely rare and critical fault data still faces challenges related to learning from very few examples, such as training instability or \"mode collapse.\"The innovativeness of the methods applied in the article lies in the strategic distinction and application of two fundamentally different augmentation methods for distinct data classes.