Degradation Modeling Based on Polynomial Uncertain Process: a Case Study on Raliway Gyroscope

Constructing an accurate performance degradation model is significant for analyzing equipment reliability and developing efficient maintenance strategies. In practical work scenarios, the available degradation data for equipment is often limited due to economic and technical constraints. This data contains a significant amount of epistemic uncertainty that cannot be adequately described by conventional probabilistic theories. To tackle this issue, this paper proposes a polynomial uncertain process within the framework of uncertainty theory to effectively characterize equipment's performance degradation. Compared to general linear or nonlinear uncertain processes, the polynomial uncertain process demonstrates the ability to accurately depict the degradation trajectories of equipment with different degradation characteristics at various stages. To estimate the unknown parameters of the polynomial uncertain process, this paper introduces a parameter estimation method based on the principles of least squares and minimum noise. Furthermore, the reliability of the equipment is analyzed and evaluated using the concepts of uncertainty theory and first hitting time. Finally, the effectiveness of the proposed method is illustrated in detail through an example involving a railway gyroscope.