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Deep Bayesian survival analysis of rail useful lifetime

Deep Bayesian survival analysis of rail useful lifetime
Deep Bayesian survival analysis of rail useful lifetime

Reliable estimation of rail useful lifetime can provide valuable information for predictive maintenance in railway systems. However, in most cases, lifetime data is incomplete because not all pieces of rail experience failure by the end of the study horizon, a problem known as censoring. Ignoring or otherwise mistreating the censored cases might lead to false conclusions. Survival approach is particularly designed to handle censored data for analysing the expected duration of time until one event occurs, which is rail failure in this paper. This paper proposes a deep Bayesian survival approach named BNN-Surv to properly handle censored data for rail useful lifetime modelling. The proposed BNN-Surv model applies the deep neural network in the survival approach to capture the non-linear relationship between covariates and rail useful lifetime. To consider and quantify uncertainty in the model, Monte Carlo dropout, regarded as the approximate Bayesian inference, is incorporated into the deep neural network to provide the confidence interval of the estimated lifetime. The proposed approach is implemented on a four-year dataset including track geometry monitoring data, track characteristics data, various types of defect data, and maintenance and replacement (M&R) data collected from a section of railway tracks in Australia. Through extensive evaluation, including Concordance index (C-index) and root mean square error (RMSE) for evaluating model performance, as well as a proposed CW-index for evaluating uncertainty estimations, the effectiveness of the proposed approach is confirmed. The results show that, compared with other commonly used models, the proposed approach can achieve the best concordance index (C-index) of 0.80, and the estimated rail useful lifetimes are closer to real lifetimes. In addition, the proposed approach can provide the confidence interval of the estimated lifetime, with a correct coverage of 81% of the actual lifetime when the confidence interval is 1.38, which is more useful than point estimates in decision-making and maintenance planning of railroad systems.

Bayesian inference, Deep neural networks, Rail useful lifetime, Survival analysis
0141-0296
Zeng, Cheng
bb12ebfb-4c58-46c6-93fe-dc4b101cf5e9
Huang, Jinsong
da153fad-3446-47fc-8b4a-5799e42fb59e
Wang, Hongrui
739a7ca1-da63-4a7d-9457-681784e45c3c
Xie, Jiawei
8f5bdf89-fcac-4336-a371-9f138872a28b
Zhang, Yuting
821b7687-fe98-4525-b641-2ea503797319
Zeng, Cheng
bb12ebfb-4c58-46c6-93fe-dc4b101cf5e9
Huang, Jinsong
da153fad-3446-47fc-8b4a-5799e42fb59e
Wang, Hongrui
739a7ca1-da63-4a7d-9457-681784e45c3c
Xie, Jiawei
8f5bdf89-fcac-4336-a371-9f138872a28b
Zhang, Yuting
821b7687-fe98-4525-b641-2ea503797319

Zeng, Cheng, Huang, Jinsong, Wang, Hongrui, Xie, Jiawei and Zhang, Yuting (2023) Deep Bayesian survival analysis of rail useful lifetime. Engineering Structures, 295, [116822]. (doi:10.1016/j.engstruct.2023.116822).

Record type: Article

Abstract

Reliable estimation of rail useful lifetime can provide valuable information for predictive maintenance in railway systems. However, in most cases, lifetime data is incomplete because not all pieces of rail experience failure by the end of the study horizon, a problem known as censoring. Ignoring or otherwise mistreating the censored cases might lead to false conclusions. Survival approach is particularly designed to handle censored data for analysing the expected duration of time until one event occurs, which is rail failure in this paper. This paper proposes a deep Bayesian survival approach named BNN-Surv to properly handle censored data for rail useful lifetime modelling. The proposed BNN-Surv model applies the deep neural network in the survival approach to capture the non-linear relationship between covariates and rail useful lifetime. To consider and quantify uncertainty in the model, Monte Carlo dropout, regarded as the approximate Bayesian inference, is incorporated into the deep neural network to provide the confidence interval of the estimated lifetime. The proposed approach is implemented on a four-year dataset including track geometry monitoring data, track characteristics data, various types of defect data, and maintenance and replacement (M&R) data collected from a section of railway tracks in Australia. Through extensive evaluation, including Concordance index (C-index) and root mean square error (RMSE) for evaluating model performance, as well as a proposed CW-index for evaluating uncertainty estimations, the effectiveness of the proposed approach is confirmed. The results show that, compared with other commonly used models, the proposed approach can achieve the best concordance index (C-index) of 0.80, and the estimated rail useful lifetimes are closer to real lifetimes. In addition, the proposed approach can provide the confidence interval of the estimated lifetime, with a correct coverage of 81% of the actual lifetime when the confidence interval is 1.38, which is more useful than point estimates in decision-making and maintenance planning of railroad systems.

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More information

Published date: 15 November 2023
Additional Information: Publisher Copyright: © 2023 The Author(s)
Keywords: Bayesian inference, Deep neural networks, Rail useful lifetime, Survival analysis

Identifiers

Local EPrints ID: 505896
URI: http://eprints.soton.ac.uk/id/eprint/505896
ISSN: 0141-0296
PURE UUID: bd2476d6-2266-4cd8-a80a-6b0c7a5ff353
ORCID for Yuting Zhang: ORCID iD orcid.org/0000-0002-5683-7286

Catalogue record

Date deposited: 22 Oct 2025 16:56
Last modified: 23 Oct 2025 02:26

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Contributors

Author: Cheng Zeng
Author: Jinsong Huang
Author: Hongrui Wang
Author: Jiawei Xie
Author: Yuting Zhang ORCID iD

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