Abstract
The accurate estimation of Remaining Useful Life (RUL) is critical for ensuring the structural integrity and durability of engineering systems, particularly when subjected to complex, multi-modal degradation processes. This paper proposes a comprehensive probabilistic framework designed to predict RUL by integrating multiple degradation indicators and accounting for stochastic correlations. Traditional models often focus on single degradation paths, which fail to capture the synergistic effects of concurrent mechanisms such as fatigue, wear, and corrosion. Our approach leverages a hybrid methodology combining Nonlinear Wiener Processes with adaptive deep learning architectures to model non-stationary degradation signals. By incorporating stochastic correlation between indicators (Wu et al., 2023) and utilizing multi-scale similarity ensemble techniques (Xia et al., 2022), the framework quantifies uncertainty more effectively than conventional deterministic models. Validation is performed using datasets from aeronautical structures and bearing systems, demonstrating that the proposed framework significantly reduces prediction error in systems with multiple failure patterns (Xiong et al., 2023). Results indicate that the integration of non-crossing quantile long short-term memory (LSTM) networks (Ly et al., 2023) provides a robust estimation of the RUL probability density function, even under varying operational conditions. The findings suggest that considering the interaction between degradation mechanisms is essential for reliable predictive maintenance and structural health management in high-stakes industries such as aerospace and energy.