## 1 Introduction  
Pursuing optimal operational efficiency and safety in complex industrial systems, particularly turbofan engines, hinges on effective predictive maintenance (PdM). While sensor data offers immense potential for anticipating equipment failures, a critical barrier remains: the pervasive scarcity of labeled failure data. This fundamental limitation renderstraditional supervised learning approaches largely unfeasible for robust health monitoring and Remaining Useful Life (RUL) prediction in real-world industrial environments [1].  
To address this challenge, this article introduces a novel, entirely unsupervised framework designed for turbofan engines. This comprehensive solution unifies health state classification and RUL prediction, moving beyond fragmented analytical methods. The framework synergistically integrates three advanced machine learning components: autoencoders (AEs) for deep feature extraction, Gaussian Mixture Models (GMMs) for robust unsupervised health state classification (categorizing engines into \"Healthy\", \"Middle\", and \"Unhealthy\" states), and state-specific Long Short-Term Memory (LSTM) networks enhanced with Self-Attention Layers (SAL) for accurate RUL prediction.  
Rigorous empirical validation on both a large, real-life turbofan engine operational dataset (which crucially lacks explicit run-to-failure labels, mirroring industrial conditions) and the widely used simulated NASA Turbofan Engine Degradation Dataset (CMAPSS) demonstrates the framework's practical viability and robustness. This unsupervised approach not only effectively captures subtle, high-dimensional degradation patterns but also achieves superior RUL prediction performance compared to numerous state-of-the-art deep neural network models on benchmark datasets, showcasing its competitive advantage.  
Recent advances in machine learning for fatigue and life prediction have increasingly emphasized models that can handle data scarcity and uncertainty. For example, [PERSON] et al. [2] proposed a Gaussian Variational Bayes Network (GVBN) to predict the fatigue life of orthotropic steel bridge deck welds using small-sample experimental data. Their method excels at probabilistic inference under limited data availability and provides posterior distributions over the model parameters, making it highly suitable for structural components with sparse degradation histories. In contrast, our proposed AE-GMM-LSTM-SA framework is designed for multivariate time series data with rich temporal and sensor information, such as those recorded from turbofan engines, and focuses on unsupervised health state discovery and state-specific RUL forecasting. Unlike GVBNs, our method does not assume prior distributions or require Bayesian training; instead, it decomposes the learning process into three interpretable stages: dimensionality reduction via autoencoders, latent clustering with GMMs, and sequential modeling using LSTM with self-attention. Furthermore, our approach is designed to scale to large unlabeled industrial datasets and supports early RUL forecasting, a requirement critical for proactive maintenance in aviation. While GVBNs are well-suited for small, structured fatigue datasets, the proposed framework addresses a complementary class of problems involving high-dimensional, nonlinear degradation dynamics under weak supervision.  
The remainder of this article provides a detailed exploration of the presented framework, its methodology, empirical results, and a comprehensive discussion of its industrial applicability, limitations, and future directions.