## 1 Introduction
The authors note that most of these models are built on synthetic or small laboratory datasets. In particular, the algorithms do not consider variable loads, material degradation, or long-term operational effects and are usually not validated on actual production equipment. The study by [15] presents an approach to state diagnosis using convolutional neural networks. The model achieves high accuracy in detecting defects but is trained on data with a fixed configuration and does not consider multi-physical interactions (e.g., thermal fluctuations and mechanical loading). Similar to many others, this approach assumes that the system's state is static and invalid in a real machine. The work by [16] presents a multi-input convolutional neural network (CNN) framework that fuses multiple image-based transforms for mechanical fault classification with high accuracy. However, training requires large labeled datasets and significant hardware resources. The authors also do not discuss the interpretability of the learned features. Machine learning is becoming widely adopted in diagnostics. For instance, the study by [17] introduces an advanced large-language-model (LLM)-optimized wavelet packet transformation (WPT) framework for early fault prediction in synchronous condensers, integrating intelligent parameter optimization with multi-head attention (MHA) gated recurrent unit (GRU) for temporal pattern recognition (TPR). This approach achieved a diagnostic accuracy of 98.7% and demonstrated significant reductions in false alarm rates and processing time. However, the reliance on high-quality, labeled data and substantial computational resources presents challenges for real-time industrial deployment. The method does not directly address residual life prediction or uncertainty quantification. Another work that conducted machine learning [18] applies Bayesian hyperparameter optimization (BHO) to a multilayer perceptron (MLP) model for broken-bar fault diagnosis, resulting in improved classification accuracy. However, the optimization process is computationally expensive in large parameter spaces. In addition, the method's robustness under noisy measurement conditions remains untested. Finally, an in-depth review of rotor diagnostics from an AI methods standpoint was provided by [14]. Although the paper exhibits a multitude of algorithms, the authors highlight that most studies were conducted using vibration data obtained under simple and idealized conditions. AI models do not accommodate boundary effects, nonlinearities, adaptive time-varying characteristics, or other essential aspects, severely restricting their validity in any real engineering system. Another class of modern techniques is formed by uncertainty quantification (UQ) methods. They purposely propagate parameter scatter--probabilistic (Monte Carlo, polynomial chaos) or non-probabilistic (interval, fuzzy, evidence)--through the dynamic model and deliver confidence bands or guaranteed envelopes for health metrics like critical speeds and vibration amplitudes. This capability benefits applications such as setting adequate alarm limits, prioritizing leading parameters, optimizing sensor placement, and supporting risk-informed maintenance or design optimization. Yet, UQ techniques have inherent limitations: probabilistic formulations may suffer from the curse of dimensionality and need trustworthy probability distributions, whereas interval or fuzzy counterparts are generally conservative and may cause overly large safety margins; in addition, most approaches depend on surrogate models, whose quality significantly affects accuracy. In the study by [19], the authors present a state-of-the-art review of uncertainty analysis of rotating machinery, classifying probabilistic, interval, and hybrid approaches and relate them to crack, rub-impact, and misalignment issues.