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

arXiv: https://arxiv.org/abs/2405.01614 · HTML: https://mlsanity.com/paper/2405.01614/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 74 references that are in the map.
- First posted on arXiv 2 May 2024.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [Effective Ways to Build and Evaluate Individual Survival Distributions](https://mlsanity.com/paper/1811.11347/) (2018)
- [Multivariate Variational Mode Decomposition](https://mlsanity.com/paper/1907.04509/) (2019)
- [Predicting Survival Time of Ball Bearings in the Presence of Censoring](https://mlsanity.com/paper/2309.07188/) (2023)

## Built on by (most cited first, 1 of 1)

- [Survival Analysis with Machine Learning for Predicting Li-ion Battery Remaining Useful Life](https://mlsanity.com/paper/2503.13558/) (2025)

## Abstract (arXiv)

Predicting the remaining useful life (RUL) of ball bearings is an active area of research, where novel machine learning techniques are continuously being applied to predict degradation trends and anticipate failures before they occur. However, few studies have explicitly addressed the challenge of handling censored data, where information about a specific event (eg mechanical failure) is incomplete or only partially observed. 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 strategy 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% CI = 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 data as part of the model design when building predictive models for early fault detection and RUL estimation.