Correlation‐driven multivariate degradation modeling and RUL prediction based on Wiener process model

Abstract

For degraded products with multiple performance characteristics (PCs), one way to model their degradation process is by using a multivariate independent Wiener process model with random drift. However, it fails to capture the latent correlation in degradation paths for multiple PCs caused by the common environmental condition. In this paper, we model the degradation processes of multiple PCs using multiple correlated Wiener processes. The commonly shared environmental condition function incorporates the degradation correlation and random effect. Thus, it directly catches the strong correlation of degradation rates and volatilities to all dimensions of multiple PCs. Our model is more economical in the number of parameters than the multivariate independent Wiener process. The correlation coefficients and RUL distribution approximation are provided in closed forms. We extend the proposed model to a two‐stage degradation process to correlate multiple PCs in each stage. An adaptive drift is adopted in the Wiener process model for the real‐time degradation states updating with the help of the Bayesian and the expectation‐maximization (EM) algorithm. The proposed model's effectiveness is illustrated by numerical studies and a real‐world application to the wheel treads on high‐speed trains.

Bayesian Fusion of Degradation and Failure Time Data for Reliability Assessment of Industrial Equipment Considering Individual Differences

“…Ma et al [29] introduced a multiphase Wiener-process-based degradation model that considers the impact of imperfect maintenance activities, utilizing a beta distribution for residual degradation and maximum likelihood estimation with Newton iteration for hyper-parameter estimation. Yan et al [30] developed a multivariate correlated Wiener process model for the RUL prediction of products with multiple performance characteristics.…”

Remaining Useful Life Estimation of Hollow Worn Railway Vehicle Wheels via On-Board Random Vibration-Based Wheel Tread Depth Estimation

“…Despite the significant progress of vibration-based RULE, related applications for automated RULE in railway vehicle wheels using on-board measurements remain scarce [ 11 , 12 , 13 , 14 ], while the considered wheels possess severe faults in their treads, such as cracks and spalling. The methods of these studies fall under the category of the prediction-based RULE with the majority relying on statistical models, which incorporate a Wiener process model integrated with a linear, power-law, or exponential deterministic function according to the considered defect [ 11 , 12 , 13 ], whereas only the study in [ 14 ] utilizes an AI/ML model via the Neural Basis Expansion Analysis for Time Series (N-BEATS). The vibration signals RMS is employed as the selected feature for RULE in [ 11 , 12 , 13 ], where statistical models are also employed and the obtained results indicate adequate agreement between the RMS evolution and the selected deterministic function representing wheel degradation.…”

“…The methods of these studies fall under the category of the prediction-based RULE with the majority relying on statistical models, which incorporate a Wiener process model integrated with a linear, power-law, or exponential deterministic function according to the considered defect [ 11 , 12 , 13 ], whereas only the study in [ 14 ] utilizes an AI/ML model via the Neural Basis Expansion Analysis for Time Series (N-BEATS). The vibration signals RMS is employed as the selected feature for RULE in [ 11 , 12 , 13 ], where statistical models are also employed and the obtained results indicate adequate agreement between the RMS evolution and the selected deterministic function representing wheel degradation. However, these studies explore quite severe wheel defects, as previously mentioned, implying RULE at the latest level of wheels’ lifetimes, while the RMS user selected threshold corresponding to the end-of-life is subjectively selected and may not always coincide with the actual failure event of the railway wheels, thus jeopardizing the vehicle’s safety.…”

A dual‐channel transferable RUL prediction method integrated with Bayesian deep learning and domain adaptation for rolling bearings

“…Prognostics and health management (PHM) significantly contributes to modern industry, ensuring the operational safety and long‐term reliability of mechanical equipment 6–10 . Particularly, as a crucial part of PHM, the remaining useful life (RUL) prediction holds a prominent position in decreasing maintenance expenses and preventing catastrophic accidents, and thus has received increasing attention 11–14 . Bearings, as a significant component of rotating machinery, are susceptible to degeneration and failure due to the harsh working conditions.…”

“…[6][7][8][9][10] Particularly, as a crucial part of PHM, the remaining useful life (RUL) prediction holds a prominent position in decreasing maintenance expenses and preventing catastrophic accidents, and thus has received increasing attention. [11][12][13][14] Bearings, as a significant component of rotating machinery, are susceptible to degeneration and failure due to the harsh working conditions. Therefore, the adoption of effective PHM, especially RUL prediction of rolling bearings, is of particular importance.…”