RULSurv: A probabilistic survival-based method for early censoring-aware prediction of remaining useful life in ball bearings

Censored data refers to situations where the full information about a particular event or process is only partially known. In survival analysis, censoring plays an important role, as ignoring such observations can bias the model parameters and overestimate the probability of when the event is likely to occur. There has been a renewed interest in using data-driven methods to predict the remaining useful life (RUL) of ball bearings for predictive maintenance. However, few studies have explicitly addressed the challenge of handling censored data. To address this issue, we introduce a novel and flexible method for early fault detection using Kullback-Leibler (KL) divergence and RUL estimation using survival analysis that naturally supports censored data. We demonstrate our approach in the XJTU-SY dataset using a 5-fold cross-validation across three different operating conditions. When predicting the time to failure for bearings under the highest load (C1, 12.0 kN and 2100 RPM) with 25\% random censoring, our approach achieves a mean absolute error (MAE) of 14.7 minutes (95\% CI 13.6-15.8) using a linear CoxPH model, and an MAE of 12.6 minutes (95\% CI 11.8-13.4) using a nonlinear Random Survival Forests model, compared to an MAE of 18.5 minutes (95\% 17.4-19.6) using a linear LASSO model that does not support censoring. Moreover, our approach achieves a mean cumulative relative accuracy (CRA) of 0.7586 over 5 bearings under the highest load, which improves over several state-of-the-art baselines. Our work highlights the importance of considering censored observations as part of the model design when building predictive models for early fault detection and RUL estimation.