Latent Variable Modeling of Vibration Signals and Remaining Useful Life Prediction Based on Variational Autoencoders

Accurate prediction of the remaining useful life (RUL) of rolling bearings is a critical issue in reliability evaluation and predictive maintenance of rotating machinery. However, existing data-driven approaches still suffer from two major limitations. First, most deep learning-based methods rely on deterministic regression frameworks, which are incapable of explicitly characterizing predictive uncertainty. Second, although probabilistic models such as standard variational autoencoders (VAEs) have been introduced, the absence of physical constraints often leads to latent representations that inadequately capture frequency-domain degradation characteristics of vibration signals, thereby compromising the physical interpretability of uncertainty estimates.To address these challenges, this study proposes a probabilistic RUL prediction method based on a conditional variational autoencoder combined with a Transformer regressor (CVAE-TR). In this method, RUL prediction is formulated as a conditional generative inference problem, enabling point estimation and uncertainty quantification to be obtained simultaneously in a unified probabilistic manner.To enhance the physical consistency of latent representations with degradation evolution, a signal-processing-inspired multi-resolution spectral reconstruction mechanism is introduced. By imposing frequency-domain constraints, the proposed mechanism guides latent variables to encode the progressive spectral variations of vibration signals during degradation.Unlike existing probabilistic approaches that rely on unconstrained latent representations, the proposed method explicitly anchors latent degradation states to multi-resolution spectral evolution patterns of vibration signals.In addition, a risk-sensitive dynamic weighting strategy is incorporated to mitigate the impact of imbalanced sample distributions across the entire life cycle.Extensive experiments are conducted on the XJTU-SY bearing full-life dataset under a mixed-condition training scheme.The results demonstrate that the proposed CVAE-TR achieves superior or comparable predictive performance to state-of-the-art methods in terms of root mean square error (RMSE) and coefficient of determination($R^2$).Moreover, the predicted uncertainty intervals adaptively evolve with degradation stages: remaining compact during stable operation and expanding consistently with increasing degradation uncertainty during accelerated failure stages.These results indicate that the proposed method exhibits strong comprehensive performance between prediction accuracy and physical consistency for bearing RUL prediction.