RESEARCH PAPER
Remaining useful life prediction via a bivariate Wiener process incorporating complex correlation structures
1
School of Transportation Engineering, Dalian Jiaotong University, Dalian 116028, China, China
A – Conceptualization; B – Methodology; C – Software; D – Validation; E – Formal analysis; F – Investigation; G – Resources; H – Data curation; I – Writing – original draft; J – Writing – review & editing; K – Visualization; L – Supervision; M – Project administration; N – Funding acquisition
Submission date: 2026-05-18
Final revision date: 2026-08-16
Acceptance date: 2026-09-17
Online publication date: 2026-10-17
Corresponding author
Yali Jiang
School of Transportation Engineering, Dalian Jiaotong University, Dalian 116028, China, China
School of Transportation Engineering, Dalian Jiaotong University, Dalian 116028, China, China
KEYWORDS
copula functionbivariate Wiener processmultiple health indicatorsmultivariate degradation modelingcomplex correlation
TOPICS
ABSTRACT
Remaining useful life (RUL) prediction is critical to enhance the reliability of the device. But such prediction is difficult owing to the multiple health indicators (MHI) in the degradation process. However, the complex correlation between MHI is generally ignored in current models, which leads to inaccurate issues in RUL prediction. Bivariate degradation serves as the basis for the multivariate degradation modeling in RUL prediction. Therefore, to solve the above issues, a novel RUL prediction method via a bivariate Wiener process incorporating complex correlation structures is proposed in this paper, which considers the intricate nonlinear correlation between MHI, and a RUL prediction model based on the bivariate Copula function (BCF) is constructed. After that, the Akaike Information Criterion is utilized to select the optimal BCF for analyzing the correlation structure of the two health indicators. Finally, considering the complex correlation in the degradation process, XJTU-SY datasets are used as an example for the effectiveness and predictability of the proposed method.
REFERENCES (30)
1.
Brombacher A. Reliability prediction and ‘deepwater horizon’: lessons learned. Quality and Reliability Engineering International 2010; 26(5): 397-397. https://doi.org/10.1002/qre.11....
2.
Camci F, Chinnam RB. Health-state estimation and prognostics in machining processes. IEEE Transactions on Automation Science and Engineering 2010; 7(3): 581-583. https://doi.org/10.1109/TASE.2....
3.
Zhou JH, Yang JH, Xiang S, Qin Y. Remaining useful life prediction methodologies with health indicator dependence for rotating machinery: A comprehensive review. IEEE Transactions on Instrumentation and Measurement 2025; 74: 1-19. https://doi.org/10.1109/TIM.20....
4.
Guan QL, Zuo ZY, Teng YQ, Zhang HX, Jia LM. Two-stage remaining useful life prediction based on the Wiener process with multi-feature fusion and stage division. Eksploatacja i NiezawodnoscMaintenance and Reliability 2024; 26(4): 189803. https://doi.org/10.17531/ein/1....
5.
Zhang SY, Zhai QQ, Li YQ. Degradation modeling and RUL prediction with Wiener process considering measurable and unobservable external impacts. Reliability Engineering & System Safety 2023; 231: 109021. https://doi.org/10.1016/j.ress....
6.
Chen Z, Wang ZR, Wu W, Xia TB, Pan E. Neural representation-based Wiener process with meta-learning for battery RUL prediction under time-varying degradation rate. IEEE Transactions on Instrumentation and Measurement 2025; 74: 1-13. https://doi.org/10.1109/TIM.20....
7.
Shi R, Lü Y, Zhang Y, Zhang YF, Meng JC, Chen RB, Hu RY. Remaining useful life estimation with coupling dual random effects based on nonlinear Wiener process. Eksploatacja i NiezawodnoscMaintenance and Reliability 2025; 27(4): 202908. https://doi.org/10.17531/ein/2....
8.
Li Q, Lin, JT, Niu PY. Remaining useful life prediction method for jointless track circuits based on multivariate feature fusion and nonlinear wiener process. Measurement Science and Technology 2025; 36(1): 016118. https://doi.org/10.1088/1361-6....
9.
Wang XL, Jiang B, Wu SM, Lu NY, Ding SX. Multivariate relevance vector regression based degradation modeling and remaining useful life prediction. IEEE Transactions on Industrial Electronics 2022; 69(9): 9514-9523. https://doi.org/10.1109/TIE.20....
10.
Yan BX, Wang H, Ma XB. Correlation-driven multivariate degradation modeling and RUL prediction based on Wiener process model. Quality and Reliability Engineering International 2023; 39(8): 3203-3229. https://doi.org/10.1002/qre.31....
11.
Wu B, Zeng JC, Shi H, Zhang XH, Qin YK. Remaining useful life prediction for multiple degradation indicators systems considering random correlation. Computers & Industrial Engineering 2023; 186: 109736. https://doi.org/10.1016/j.cie.....
12.
Jin G, Matthews D. Measurement plan optimization for degradation test design based on the bivariate Wiener process. Quality and Reliability Engineering International 2014; 30(8): 1215-1231. https://doi.org/10.1002/qre.15....
13.
Liu TY, Pan ZQ, Sun Q, Feng J, Tang YZ. Residual useful life estimation for products with two performance characteristics based on a bivariate Wiener process. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability 2017; 231(1): 69-80. https://doi.org/10.1177/174800....
14.
Wu B, Zeng JC, Shi H, Zhang XH, Shi GN, Qin YK. Multi-sensor information fusion-based prediction of remaining useful life of nonlinear Wiener process. Measurement Science and Technology 2022; 33(10): 105106. https://doi.org/10.1088/1361-6....
15.
Sun FQ, Fu FY, Liao HT, Xu D. Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula. Reliability Engineering & System Safety 2020; 204: 107168. https://doi.org/1016/j.ress.20....
16.
Zheng BK, Chen C, Zhang W, Fu R, Hu YF, Wang CQ, Zhai GF. Reliability estimation of complex systems based on a Wiener process with random effects and D-vine copulas. Microelectronics Reliability 2022; 138: 114640. https://doi.org/10.1016/j.micr....
17.
Wang YP, Pham H. Modeling the dependent competing risks with multivariate degradation processes and random shock using time-varying copulas. IEEE Transactions on Reliability 2011; 61(1): 13-22. https://doi.org/10.1109/TR.201....
18.
Wang XL, Balakrishnan N, Guo B. Residual life estimation based on nonlinear-multivariate Wiener process. Journal of Statistical Computation and Simulation 2015; 85(9): 1742-1764. https://doi.org/10.1080/009496....
19.
Wang XL, Guo B, Cheng ZJ. Residual life estimation based on bivariate Wiener degradation process with time-scale transformations. Journal of Statistical Computation and Simulation, 2014, 84(3): 545-563. https://doi.org/10.1080/009496....
20.
Wang XL, Guo B, Cheng ZJ, Jiang P. Residual life estimation based on bivariate Wiener degradation process with measurement errors. Journal of Central South University 2013; 20(7): 1844-1851. https://doi.org/10.1007/s11771....
21.
Song C, Bian Z, Ding SN. Reliability life estimation considered fault correlation of aerial bearing. Materials Science and Engineering 2021; 1043 (4): 042011. https://doi.org/10.1088/1757-8....
22.
Wu B, Shi H, Zeng JC, Zhang XH, Wang ZJ, Wang ZL. Remaining useful life prediction of degraded systems based on multiple performance indicators constructed by multiple features. IEEE Sensors Journal 2025; 25(11): 19613-19631. https://doi.org/10.1109/JSEN.2....
24.
Sklar M. Fonctions de répartition à n dimensions et leurs marges. Annales de l'ISUP 1959; 8(3): 229-231. https://hal.science/hal-040944....
25.
Liew RQ, Wu Y. Pairs trading: A Copula approach. Journal of Derivatives & Hedge Funds 2013; 19(1): 12-30. https://doi.org/10.1057/jdhf.2....
26.
Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control 1974; 19(6): 716-723, https://doi.org/10.1109/TAC.19....
27.
Si XS, Wang WB, Hu CH, Zhou DH. A Wiener-process-based degradation model with a recursive filter algorithm for remaining useful life estimation. Mechanical Systems and Signal Processing 2013; 35(1-2): 219-237. https://doi.org/10.1016/j.ymss....
28.
Raanes PN. On the ensemble Rauch-Tung-Striebel smoother and its equivalence to the ensemble Kalman smoother. Quarterly Journal of the Royal Meteorological Society 2016; 142(696): 1259-1264. https://doi.org/10.1002/qj.272.
29.
Zhang JX, Hu CH, He X, Si XS, Liu Y, Zhou DH. A novel lifetime estimation method for two-phase degrading systems. IEEE Transactions on Reliability 2018; 68(2): 689-709. https://doi.org/10.1109/TR.201....
30.
Wang B, Lei YG, Li NP, Li NB. A hybrid prognostics approach for estimating remaining useful life of rolling element bearings. IEEE Transactions on Reliability 2020; 69(1): 401-412. https://doi.org/10.1109/TR.201....
| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
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