Abstract

Despite the substantive literature on remaining useful life (RUL) prediction, less attention is paid to the influence of epistemic uncertainty and aleatory uncertainty in multiple failure behaviors in the accuracy of RUL. The research question in this study was: can uncertainties be quantified in predicting the RUL of systems with multiple failure modes? The first objective was to quantify the uncertainties in the prediction of RUL, considering known multiple failure modes. This objective used vibration data from accelerated degradation experiments of rolling element bearings. The second objective was to calculate the uncertainties in the prediction of RUL, considering the multiple failure modes as unknown. The experimental data used in this objective were from run-to-failure tests of Li-ion batteries. An analysis was performed on how the uncertainties affect the RUL prediction in systems with known multiple failure modes and systems where the multiple failure modes were unknown. A Bayesian neural network (BNN) was used to quantify epistemic and aleatory uncertainty while predicting RUL. The results of the qualitative uncertainties on RUL in systems with multiple failure modes were presented and discussed. Also, the study yielded an RUL uncertainty quantification model for multiple failure modes. The proposed framework's performance in the RUL prediction was demonstrated. Finally, the epistemic and aleatory uncertainties were quantified in the system's RUL. It was shown that systems that fail due to the same failure mode tend to have similar uncertainty values over time. The results in this paper may lead to the design of more reliable systems that exhibit multiple failure modes.

References

1.
Yang
,
H.
,
Chen
,
C.
,
Chen
,
Y.
,
Scheppach
,
M.
,
Yip
,
H. C.
, and
Dou
,
Q.
,
2023
, “
Uncertainty Estimation for Safety-Critical Scene Segmentation Via Fine-Grained Reward Maximization
,”
Adv. Neural Inf. Process. Syst.
,
36
, pp.
1
12
.
2.
Li
,
G.
,
Yang
,
L.
,
Lee
,
C.-G.
,
Wang
,
X.
, and
Rong
,
M.
,
2021
, “
A Bayesian Deep Learning RUL Framework Integrating Epistemic and Aleatoric Uncertainties
,”
IEEE Trans. Ind. Electron.
,
68
(
9
), pp.
8829
8841
.10.1109/TIE.2020.3009593
3.
Soize
,
C.
,
2017
,
Uncertainty Quantification: An Accelerated Course With Advanced Applications in Computational Engineering
,
Springer
,
Cham, Switzerland
.
4.
Wan
,
S.
,
Sinclair
,
R. C.
, and
Coveney
,
P. V.
,
2021
, “
Uncertainty Quantification in Classical Molecular Dynamics
,”
Philos. Trans. R. Soc. A
,
379
(
2197
), p.
20200082
.10.1098/rsta.2020.0082
5.
Jospin
,
L. V.
,
Laga
,
H.
,
Boussaid
,
F.
,
Buntine
,
W.
, and
Bennamoun
,
M.
,
2022
, “
Hands-On Bayesian Neural Networks - A Tutorial for Deep Learning Users
,”
IEEE Comput. Intell. Mag.
,
17
(
2
), pp.
29
48
.10.1109/MCI.2022.3155327
6.
Abdar
,
M.
,
Pourpanah
,
F.
,
Hussain
,
S.
,
Rezazadegan
,
D.
,
Liu
,
L.
,
Ghavamzadeh
,
M.
,
Fieguth
,
P.
, et al.,
2021
, “
A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges
,”
Inf. Fusion
,
76
, pp.
243
297
.10.1016/j.inffus.2021.05.008
7.
Hüllermeier
,
E.
, and
Waegeman
,
W.
,
2021
, “
Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods
,”
Mach. Learn.
,
110
(
3
), pp.
457
506
.10.1007/s10994-021-05946-3
8.
Chan
,
M. A.
,
Molina
,
M. J.
, and
Metzler
,
C. A.
,
2024
, “
Hyper-Diffusion: Estimating Epistemic and Aleatoric Uncertainty With a Single Model
,”
arXiv:2402.03478
.10.48550/arXiv.2402.03478
9.
Valdenegro-Toro
,
M.
, and
Mori
,
D. S.
,
2022
, “
A Deeper Look Into Aleatoric and Epistemic Uncertainty Disentanglement
,”
IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops
,
New Orleans, LA
, June 19–20, pp.
1508
1516
.10.1109/CVPRW56347.2022.00157
10.
Deng
,
Y.
,
2020
, “
Uncertainty Measure in Evidence Theory
,”
Sci. China Inf. Sci.
,
63
(
11
), p.
210201
.10.1007/s11432-020-3006-9
11.
Alves
,
D. S.
,
Daniel
,
G. B.
,
Castro
,
H. F. D.
,
Machado
,
T. H.
,
Cavalca
,
K. L.
,
Gecgel
,
O.
,
Dias
,
J. P.
, and
Ekwaro-Osire
,
S.
,
2020
, “
Uncertainty Quantification in Deep Convolutional Neural Network Diagnostics of Journal Bearings With Ovalization Fault
,”
Mech. Mach. Theory
,
149
, p.
103835
.10.1016/j.mechmachtheory.2020.103835
12.
Certa
,
A.
,
Hopps
,
F.
,
Inghilleri
,
R.
, and
La Fata
,
C. M.
,
2017
, “
A Dempster-Shafer Theory-Based Approach to the Failure Mode, Effects and Criticality Analysis (FMECA) Under Epistemic Uncertainty: Application to the Propulsion System of a Fishing Vessel
,”
Reliab. Eng. Syst. Saf.
,
159
, pp.
69
79
.10.1016/j.ress.2016.10.018
13.
Si
,
X. S.
,
Wang
,
W.
,
Hu
,
C. H.
, and
Zhou
,
D. H.
,
2011
, “
Remaining Useful Life estimation - A Review on the Statistical Data Driven Approaches
,”
Eur. J. Oper. Res.
,
213
(
1
), pp.
1
14
.10.1016/j.ejor.2010.11.018
14.
Alamri
,
T. O.
, and
Mo
,
J. P. T.
,
2023
, “
Optimisation of Preventive Maintenance Regime Based on Failure Mode System Modelling Considering Reliability
,”
Arab. J. Sci. Eng.
,
48
(
3
), pp.
3455
3477
.10.1007/s13369-022-07174-w
15.
Zhou
,
T.
,
Zhang
,
L.
,
Han
,
T.
,
Droguett
,
E. L.
,
Mosleh
,
A.
, and
Chan
,
F. T. S.
,
2023
, “
An Uncertainty-Informed Framework for Trustworthy Fault Diagnosis in Safety-Critical Applications
,”
Reliab. Eng. Syst. Saf.
,
229
, p.
108865
.10.1016/j.ress.2022.108865
16.
Carlson
,
C. S.
,
2012
,
Effective FMEAs
,
Wiley
,
New York
.
17.
Wu
,
Z.
,
Zeng
,
J.
,
Hu
,
Z.
, and
Todd
,
M. D.
,
2023
, “
Optimization of Unmanned Aerial Vehicle Inspection Strategy for Infrastructure Based on Model-Enabled Diagnostics and Prognostics
,”
Mech. Syst. Signal Process
,
204
, p.
110841
.10.1016/j.ymssp.2023.110841
18.
Wu
,
Z.
,
Fillmore
,
T. B.
,
Vega
,
M. A.
,
Hu
,
Z.
, and
Todd
,
M. D.
,
2022
, “
Diagnostics and Prognostics of Multi-Mode Failure Scenarios in Miter Gates Using Multiple Data Sources and a Dynamic Bayesian Network
,”
Struct. Multidiscip. Optim.
,
65
(
9
), p.
270
.
19.
The Institute of Electrical and Electronics Engineers
,
2017
, “
IEEE Standard for System, Software, and Hardware Verification and Validation
,” IEEESTD.2017.8055462, New York.
20.
European Standards
,
2018
, “
UNE EN 13306:2018 - Maintenance - Maintenance Terminology
,” Brussels, Belgium.
21.
Tolio
,
T.
,
Matta
,
A.
, and
Gershwin
,
S. B.
,
2002
, “
Analysis of Two-Machine Lines With Multiple Failure Modes
,”
IIE Trans.
,
34
(
1
), pp.
51
62
.10.1080/07408170208928849
22.
Zhu
,
L.
, and
Laptev
,
N.
,
2017
, “
Deep and Confident Prediction for Time Series at Uber
,”
IEEE International Conference on Data Mining Workshops (ICDMW)
,
New Orleans, LA
, Nov. 18–21, pp.
103
110
.10.1109/ICDMW.2017.19
23.
Lakshminarayanan
,
B.
,
Pritzel
,
A.
, and
Blundell
,
C.
,
2017
, “
Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles
,”
Conference on Neural Information Processing Systems
,
Long Beach, CA
, Dec. 4–9, pp.
6405
6416
.https://dl.acm.org/doi/pdf/10.5555/3295222.3295387
24.
Depeweg
,
S.
,
Hernandez-Lobato
,
J. M.
,
Doshi-Velez
,
F.
, and
Udluft
,
S.
,
2018
, “
Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-Sensitive Learning
,”
35th International Conference on Machine Learning
(
ICML
), July 10–15, Stockholm, Sweden, Vol.
3
, pp.
1920
1934
.https://proceedings.mlr.press/v80/depeweg18a/depeweg18a.pdf
25.
Depeweg
,
S.
,
Runkler
,
T. A.
,
Laura Leal-Taixé
,
A.
, and
Miguel Hernández-Lobato
,
J.
,
2019
, “
Modeling Epistemic and Aleatoric Uncertainty With Bayesian Neural Networks and Latent Variables
,”
dissertation
, Technical University of Munich, Munich, Germany, p.
128
.https://mediatum.ub.tum.de/1482483
26.
Ekwaro-Osire
,
S.
,
Gandur
,
N. L.
, and
Lopez-Salazar
,
C. A.
,
2023
, “
Incipient Fault Point Detection Based on Multiscale Diversity Entropy
,”
ASME J. Nondestruct. Eval. Diagn. Progn. Eng. Syst.
,
6
(
3
), pp.
1
24
.10.1115/1.4062622
27.
Yang
,
B.
,
Liu
,
R.
, and
Zio
,
E.
,
2019
, “
Remaining Useful Life Prediction Based on a Double-Convolutional Neural Network Architecture
,”
IEEE Trans. Ind. Electron.
,
66
(
12
), pp.
9521
9530
.10.1109/TIE.2019.2924605
28.
Wang
,
B.
,
Lei
,
Y.
,
Li
,
N.
, and
Li
,
N.
,
2020
, “
A Hybrid Prognostics Approach for Estimating Remaining Useful Life of Rolling Element Bearings
,”
IEEE Trans. Reliab.
,
69
(
1
), pp.
401
412
.10.1109/TR.2018.2882682
29.
Wang
,
B.
, “
XJTU-SY Bearing Datasets
,” GitHub, GitHub Repository.
30.
Liu
,
Z.
, and
Zhang
,
L.
,
2020
, “
A Review of Failure Modes, Condition Monitoring and Fault Diagnosis Methods for Large-Scale Wind Turbine Bearings
,”
Measurement
,
149
, p.
107002
.10.1016/j.measurement.2019.107002
31.
Saha
,
B.
, and
Goebel
,
K.
,
2007
, “
Battery Data Set
,”
NASA Ames Research Center
,
Moffett Field, CA
.
32.
Saxena
,
A.
,
Goebel
,
K.
,
Larrosa
,
C. C.
, and
Chang
,
F.-K.
, “
CFRP Composites Data Set, NASA Ames Prognostics Data Repository
,” NASA Ames Research Center,
Moffett Field, CA
, accessed Jan. 2019, http://ti.arc.nasa.gov/project/prognostic-data-repository
33.
Hendricks
,
C.
,
Williard
,
N.
,
Mathew
,
S.
, and
Pecht
,
M.
,
2015
, “
A Failure Modes, Mechanisms, and Effects Analysis (FMMEA) of Lithium-Ion Batteries
,”
J. Power Sources
,
297
, pp.
113
120
.10.1016/j.jpowsour.2015.07.100
34.
Meyer
,
V. R.
,
2007
, “
Measurement Uncertainty
,”
J. Chromatogr. A
,
1158
(
1–2
), pp.
15
24
.10.1016/j.chroma.2007.02.082
35.
Sobol
,
I. M.
,
1993
, “
Sensitivity Estimates for Nonlinear Mathematical Models
,”
Math. Model. Comput. Exp.
,
1
, pp.
407
414
.
36.
Herman
,
J.
, and
Usher
,
W.
,
2017
, “
SALib: Sensitivity Analysis Library in Python (Numpy). Contains Sobol, SALib: An Open-Source Python Library for Sensitivity Analysis
,”
J. Open Source Software
,
2
(
9
), p.
97
.10.21105/joss.00097
37.
Wu
,
J.
,
He
,
D.
,
Li
,
J.
,
Miao
,
J.
,
Li
,
X.
,
Li
,
H.
, and
Shan
,
S.
,
2024
, “
Temporal Multi-Resolution Hypergraph Attention Network for Remaining Useful Life Prediction of Rolling Bearings
,”
Reliab. Eng. Syst. Saf.
,
247
, p.
110143
.10.1016/j.ress.2024.110143
38.
Nectoux
,
P.
,
Gouriveau
,
R.
,
Medjaher
,
K.
,
Ramasso
,
E.
,
Chebel-Morello
,
B.
,
Zerhouni
,
N.
, and
Varnier
,
C.
,
2012
, “
PRONOSTIA: An Experimental Platform for Bearings Accelerated Degradation Tests
,”
IEEE International Conference on Prognostics and Health Management, PHM'12
, Denver, Colorado, Jun. 2012, pp.
1
8
.
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