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Abstract

This paper tests two data-driven approaches for predicting the state of health (SOH) of lithium-ion-batteries (LIBs) for the purpose of monitoring maritime battery systems. First, non-sequential approaches are investigated and various models are tested: ridge, lasso, support vector regression, and gradient boosted trees. Binning is proposed for feature engineering for these types of models to capture the temporal structure in the data. Such binning creates histograms for the accumulated time the LIB has been within various voltage, temperature, and current ranges. Further binning to combine these histograms into 2D or 3D histograms is explored in order to capture relationships between voltage, temperature, and current. Second, a sequential approach is explored where different deep learning architectures are tried out: long short-term memory, transformer, and temporal convolutional network. Finally, the various models and the two approaches are compared in terms of their SOH prediction ability. Results indicate that the binning with ridge regression models performed best. The same publicly available sensor data from laboratory cycling tests are used for both approaches.

References

1.
Albuquerque
,
F. D.
,
Maraqa
,
M. A.
,
Chowdhury
,
R.
,
Mauga
,
T.
, and
Alzard
,
M.
,
2020
, “
Greenhouse Gas Emissions Associated With Road Transport Projects: Current Status, Benchmarking, and Assessment Tools
,”
Transp. Res. Proc.
,
48
, pp.
2018
2030
.
2.
Bach
,
H.
, and
Hansen
,
T.
,
2023
, “
IMO Off Course for Decarbonisation OG Shipping? Three Challenges for Stricter Policy
,”
Mar. Pol.
,
147
, p.
105379
.
3.
Tomos
,
B. A. D.
,
Stamford
,
L.
,
Welfle
,
A.
, and
Larkin
,
A.
,
2024
, “
Decarbonising International Shipping – A Life Cycle Perspective on Alternative Fuel Options
,”
Energy Convers. Manage.
,
299
, p.
117848
.
4.
Placke
,
T.
,
Kloepsch
,
R.
,
Dühnen
,
S.
, and
Winter
,
M.
,
2017
, “
Lithium Ion, Lithium Metal, and Alternative Rechargeable Battery Technologies: The Odyssey for High Energy Density
,”
J. Solid State Electrochem.
,
21
(
7
), pp.
1939
1964
.
5.
DNV
,
2021
.
Rules for Classification: Ships. DNVGL-RU-SHIP.
6.
DNV
,
2021
.
Rules for Classification: Ships. Part 6: Additional Class Notations. Chapter 2 Propulsion, Power Generation and Auxiliary Systems. DNV-RU-SHIP Pt. 6 Ch. 2.
7.
Pop
,
V.
,
Bergveld
,
H. J.
,
Danilov
,
D.
,
Regiten
,
P. P. L.
, and
Notten
,
P. H. L.
,
2008
,
Battery Management Systems. Accurate State-of-Charge Indication for Battery-Powered Applications
,
Springer
,
Dordrecht, The Netherlands
.
8.
Vanem
,
E.
,
Bertinelli Salucci
,
C.
,
Bakdi
,
A.
, and
Alnes
,
Ø. Å.
,
2021
, “
Data-Driven State of Health Modelling – A Review of State of the Art and Reflections on Applications for Maritime Battery Systems
,”
J. Energy Storage
,
43
, p.
103158
.
9.
Bertinelli Salucci
,
C.
,
Bakdi
,
A.
,
Glad
,
I. K.
,
Vanem
,
E.
, and
De Bin
,
R.
,
2022
, “
Multivariable Fractional Polynomials for Lithium-Ion Batteries Degradation Models Under Dynamic Conditions
,”
J. Energy Storage
,
52
(
Part B
), p.
104903
.
10.
Bertinelli Salucci
,
C.
,
Bakdi
,
A.
,
Glad
,
I. K.
,
Vanem
,
E.
, and
De Bin
,
R.
,
2023
, “
A Novel Semi-Supervised Learning Approach for State of Health Monitoring of Maritime Lithium-Ion Batteries
,”
J. Power Sources
,
556
, p.
232429
.
11.
Liang
,
Q.
,
Vanem
,
E.
,
Alnes
,
Ø.
,
Xue
,
Y.
,
Zhang
,
H.
,
Lam
,
J.
, and
Bruvik
,
K.
,
2023
, “
Data-Driven State of Health Monitoring for Maritime Battery Systems – A Case Study on Sensor Data From a Ship in Operation
,”
Ships Offshore Struct.
, pp.
1
13
.
12.
Vanem
,
E.
,
Bruch
,
M.
,
Liang
,
Q.
,
Thorbjørnsen
,
K.
,
Valøen
,
L. O.
, and
Alnes
,
Ø. Å.
,
2023
, “
Data-Driven Snapshot Methods Leveraging Data Fusion to Estimate State of Health for Maritime Battery Systems
,”
Energy Storage
,
5
(
8
), p.
e476
.
13.
Vanem
,
E.
,
Liang
,
Q.
,
Ferreira
,
C.
,
Agrell
,
C.
,
Karandikar
,
N.
,
Wang
,
S.
,
Bruch
,
M.
,
Bertinelli Salucci
,
C.
,
Grindheim
,
C.
,
Kejvalova
,
A.
,
Alnes
,
Ø.Å.
,
Thorbjørnsen
,
K.
,
Bakdi
,
A.
, and
Kandepu
,
R.
,
2023
, “
Data-Driven Approaches to Diagnostics and State of Health Monitoring of Maritime Battery Systems
,”
Proceedings of Annual Conference of the Prognostics and Health Management Society 2023 (PHM 2023)
,
Salt Lake City, UT
,
Oct. 28–Nov. 2
, Vol. 15, No. 1.
14.
Vanem
,
E.
,
Liang
,
Q.
,
Bruch
,
M.
,
Bøthun
,
G.
,
Bruvik
,
K.
,
Thorbjørnsen
,
K.
, and
Bakdi
,
A.
,
2024
, “
Statistical Models for Condition Monitoring and State of Health Estimation of Lithium-Ion Batteries for Ships
,”
J. Dyn. Monit. Diagn.
,
3
(
1
), pp.
11
20
.
15.
Grindheim
,
C. A.
,
2022
, “
Methods For Battery State of Health Estimation
,”
Master’s thesis
,
Department of Mathematics, University of Oslo
,
Oslo, Norway
.
16.
NASA
,
2022
.
AMES Prognostics Center of Excellence.
https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/.
17.
Bole
,
B.
,
Kulkarni
,
C. S.
, and
Daigle
,
M.
,
2014
,
Adaptation of an Electrochemistry-Based Li-ion Battery Model to Account for Deterioration Observed Under Randomized Use.
Technical Report, SGT, Inc.
,
Moffett Field, CA
.
18.
Venugopal
,
P.
, and
Vigneswaran
,
T.
,
2019
, “
State-of-Health Estimation of Li-Ion Batteries in Electric Vehicle Using IndRNN Under Variable Load Condition
,”
Energies
,
12
(
22
), p.
4338
.
19.
Moseley
,
P. T.
, and
Garche
,
J.
,
2014
,
Electrochemical Energy Storage for Renewable Sources and Grid Balancing
,
Elsevier Science & Technology
.
20.
Salehabadi
,
M.
,
Zandigohar
,
M.
,
Lotfi
,
N.
, and
Fajri
,
P.
,
2019
, “
Investigating the Sources of Uncertainty in Capacity Estimation of Li-Ion Batteries
,”
2019 IEEE Transportation Electrification Conference and Expo (ITEC)
, pp.
1
6
.
21.
Eddahech
,
A.
,
Briat
,
O.
, and
Vinassa
,
J.-M.
,
2013
, “
Lithium-Ion Battery Performance Improvement Based on Capacity Recovery Exploitation
,”
Electrochim. Acta
,
114
, pp.
750
757
.
22.
Epding
,
B.
,
Rumberg
,
B.
,
Jahnke
,
H.
,
Stradtmann
,
I.
, and
Kwade
,
A.
,
2019
, “
Investigation of Significant Capacity Recovery Effects Due to Long Rest Periods During High Current Cyclic Aging Tests in Automotive Lithium Ion Cells and Their Influence on Lifetime
,”
J. Energy Storage
,
22
, pp.
249
256
.
23.
Vetter
,
J.
,
Novák
,
P.
,
Wagner
,
M.
,
Veit
,
C.
,
Möller
,
K.-C.
,
Besenhard
,
J.
,
Winter
,
M.
,
Wohlfart-Mehrens
,
M.
,
Vogler
,
C.
, and
Hammouche
,
A.
,
2005
, “
Ageing Mechanisms in Lithium-Ion Batteries
,”
J. Power Sources
,
147
(
1–2
), pp.
269
281
.
24.
Birkl
,
C. R.
,
Roberts
,
M. R.
,
McTurk
,
E.
,
Bruce
,
P. G.
, and
Howey
,
D. A.
,
2017
, “
Degradation Diagnostics for Lithium Ion Cells
,”
J. Power Sources
,
341
, pp.
373
386
.
25.
Zhang
,
D.
,
Cadet
,
C.
,
Yousfi-Steiner
,
N.
,
Druart
,
F.
, and
Bérenguer
,
C.
,
2017
, “
PHM-Oriented Degradation Indicators for Batteries and Fuel Cells
,”
Fuel Cells
,
17
(
2
), pp.
268
276
.
26.
Ji
,
Y.
,
Zhang
,
Y.
, and
Wang
,
C.-Y.
,
2013
, “
Li-Ion Cell Operation at Low Temperatures
,”
J. Electrochem. Soc.
,
160
(
4
), p.
A636
.
27.
Pesaran
,
A.
,
Santhanagopalan
,
S.
, and
Kim
,
G.
,
2013
,
Addressing the Impact of Temperature Extremes on Large Format Li-Ion Batteries for Vehicle Applications.
Technical Report,
National Renewable Energy Laboratory (NREL)
,
Golden, CO.
28.
Xu
,
B.
,
Oudalov
,
A.
,
Ulbig
,
A.
,
Andersson
,
G.
, and
Kirschen
,
D. S.
,
2016
, “
Modeling of Lithium-Ion Battery Degradation for Cell Life Assessment
,”
IEEE Trans. Smart Grid
,
9
(
2
), pp.
1131
1140
.
29.
Gao
,
Y.
,
Jiang
,
J.
,
Zhang
,
C.
,
Zhang
,
W.
,
Ma
,
Z.
, and
Jiang
,
Y.
,
2017
, “
Lithium-Ion Battery Aging Mechanisms and Life Model Under Different Charging Stresses
,”
J. Power Sources
,
356
, pp.
103
114
.
30.
LeCun
,
Y.
,
Bengio
,
Y.
, and
Hinton
,
G.
,
2015
, “
Deep Learning
,”
Nature
,
521
(
7553
), pp.
436
444
.
31.
Hastie
,
T.
,
Tibshirani
,
R.
,
Friedman
,
J. H.
, and
Friedman
,
J. H.
,
2009
,
The Elements of Statistical Learning: Data Mining, Inference, and Prediction
, Vol.
2
,
Springer
,
New York
.
32.
Hoerl
,
A. E.
, and
Kennard
,
R. W.
,
1970
, “
Ridge Regression: Biased Estimation for Nonorthogonal Problems
,”
Technometrics
,
12
(
1
), pp.
55
67
.
33.
Tibshirani
,
R.
,
1996
, “
Regression Shrinkage and Selection Via the Lasso
,”
J. R. Stat. Soc.: Ser. B (Methodol.)
,
58
(
1
), pp.
267
288
.
34.
Friedman
,
J. H.
, and
Meulman
,
J. J.
,
2003
, “
Multiple Additive Regression Trees With Application in Epidemiology
,”
Stat. Med.
,
22
(
9
), pp.
1365
1381
.
35.
Gunn
,
S. R.
,
1998
, “
Support Vector Machines for Classification and Regression
,”
ISIS Technical Report
,
14
(
1
), pp.
5
16
.
36.
Chollet
,
F.
,
2021
,
Deep Learning With Python
, 2nd ed.,
Manning Publications
.
37.
Chollet
,
F.
,
Kalinowski
,
T.
, and
Allaire
,
J.
,
2022
,
Deep Learning With R
, 2nd ed.,
Manning Publications
.
38.
Abadi
,
M.
,
Agarwal
,
A.
,
Barham
,
P.
,
Brevdo
,
E.
,
Chen
,
Z.
,
Citro
,
C.
,
Corrado
,
G. S.
, et al.,
2016
, Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems.
39.
Pal
,
S. K.
, and
Mitra
,
S.
,
1992
, “
Multilayer Perceptron, Fuzzy Sets, Classifiaction
,”
IEEE Trans. Neural Netw.
,
3
(
5
), pp.
683
697
.
40.
Bengio
,
Y.
,
Simard
,
P.
, and
Frasconi
,
P.
,
1994
, “
Learning Long-Term Dependencies With Gradient Descent is Difficult
,”
IEEE Trans. Neural Netw.
,
5
(
2
), pp.
157
166
.
41.
Hochreiter
,
S.
, and
Schmidhuber
,
J.
,
1997
, “
Long Short-Term Memory
,”
Neural Comput.
,
9
(
8
), pp.
1735
1780
.
42.
Vaswani
,
A.
,
Shazeer
,
N.
,
Parmar
,
N.
,
Uszkoreit
,
J.
,
Jones
,
L.
,
Gomez
,
A. N.
,
Kaiser
,
Ł.
, and
Polosukhin
,
I.
,
2017
, “Attention Is All You Need,”
Advances in Neural Information Processing Systems
,
San Francisco, CA
,
Aug. 13–17
, Vol.
30
,
NeurIPS
, pp.
5998
6008
. https://researchr.org/publication/kdd-2016
43.
Luong
,
M.-T.
,
Pham
,
H.
, and
Manning
,
C. D.
,
2015
, “
Effective Approaches to Attention-Based Neural Machine Translation
,”
arXiv preprint
.
44.
Oord
,
A. V. d.
,
Dieleman
,
S.
,
Zen
,
H.
,
Simonyan
,
K.
,
Vinyals
,
O.
,
Graves
,
A.
,
Kalchbrenner
,
N.
,
Senior
,
A.
, and
Kavukcuoglu
,
K.
,
2016
, “
Wavenet: A Generative Model for Raw Audio
,”
arXiv preprint
.
45.
Bai
,
S.
,
Kolter
,
J. Z.
, and
Koltun
,
V.
,
2018
,
An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling.
46.
Russo
,
A.
,
Fiore
,
A.
, and
Aprea
,
M.
,
2019
, “
Predicting Battery Health Capacity Through Machine Learning Techniques: SVR, Random Forest and Fully-Connected Network
”.
47.
Friedman
,
J.
,
Hastie
,
T.
, and
Tibshirani
,
R.
,
2010
, “
Regularization Paths for Generalized Linear Models Via Coordinate Descent
,”
J. Stat. Softw.
,
33
(
1
), pp.
1
22
.
48.
Chen
,
T.
, and
Guestrin
,
C.
,
2016
, “
XGBoost: A Scalable Tree Boosting System
,” Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16,
ACM
, pp.
785
794
.
49.
Meyer
,
D.
,
Dimitriadou
,
E.
,
Hornik
,
K.
,
Weingessel
,
A.
,
Leisch
,
F.
,
Chang
,
C.-C.
,
Lin
,
C.-C.
, and
Meyer
,
M. D.
,
2019
, Package ‘1071’. https://cran.r-project.org/package=e1071.
50.
Chang
,
C.-C.
, and
Lin
,
C.-J.
,
2011
, “
LIBSVM: A Library for Support Vector Machines
,”
ACM Trans. Intell. Syst. Technol. (TIST)
,
2
(
3
), pp.
1
27
.
51.
Hecht-Nielsen
,
R.
,
1992
, “Theory of the Backpropagation Neural Network,”
Neural Networks for Perception
,
Academic Press
,
San Diego, CA
, pp.
65
93
.
52.
Werbos
,
P.
,
1990
, “
Backpropagation Through Time: What I Does and How to Do It
,”
Proc. IEEE
,
78
(
10
), pp.
1550
1560
.
53.
Kingma
,
D. P.
, and
Ba
,
J.
,
2014
, “
ADAM: A Method for Stochastic Optimization
,”
arXiv preprint
.
54.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
,
2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
, pp.
770
778
.
55.
Agarap
,
A. F.
,
2018
, “
Deep Learning Using Rectified Linear Units (ReLU)
,”
arXiv preprint
.
56.
Remy
,
P.
,
2020
,
Temporal Convolutional Networks for Keras
. https://github.com/philipperemy/keras-tcn.
57.
Tanim
,
T. R.
,
Dufek
,
E. J.
, and
Sazhin
,
S. V.
,
2021
, “
Challenges and Needs for System-Level Electrochemical Lithium-Ion Battery Management and Diagnostics
,”
MRS Bull.
,
46
, pp.
420
428
.
58.
Zheng
,
Y.
,
Ouyang
,
M.
,
Lu
,
L.
, and
Li
,
J.
,
2015
, “
Understanding Aging Mechanisms in Lithium-Ion Battery Packs: From Cell Capacity Loss to Pack Capacity Evolution
,”
J. Power Sources
,
278
, pp.
287
295
.
59.
Ouyang
,
M.
,
Gao
,
S.
,
Lu
,
L.
,
Feng
,
X.
,
Ren
,
D.
,
Li
,
J.
,
Zheng
,
Y.
, and
Shen
,
P.
,
2016
, “
Determination of the Battery Pack Capacity Considering the Estimation Error Using a Capacity-Quantity Diagram
,”
Appl. Energy
,
177
, pp.
384
392
.
60.
Cordoba-Arenas
,
A.
,
Onori
,
S.
, and
Rizzoni
,
G.
,
2015
, “
A Control-Oriented Lithium-Ion Battery Pack Model for Plug-In Hybrid Electric Vehicle Cycle-Life Studies and System Design With Consideration of Health Management
,”
J. Power Sources
,
279
, pp.
791
808
.
61.
Dubarry
,
M.
,
Pastor-Fernández
,
C.
,
Baure
,
G.
,
Yu
,
T. F.
,
Widanage
,
W. D.
, and
Marco
,
J.
,
2019
, “
Battery Energy Storage Modeling: Investigation of Intrinsic Cell-to-Cell Variations
,”
J. Energy Storage
,
23
, pp.
19
28
.
62.
Yang
,
C.
,
Wang
,
X.
,
Fang
,
Q.
,
Dai
,
H.
,
Cao
,
Y.
, and
Wei
,
X.
,
2020
, “
An Online SOC and Capacity Estimation Method for Aged Lithium-Ion Battery Pack Considering Cell Inconsistency
,”
J. Energy Storage
,
29
, p.
101250
.
63.
Dubarry
,
M.
,
Baure
,
G.
,
Pastor-Fernández
,
C.
,
Yu
,
T. F.
,
Widanage
,
W. D.
, and
Marco
,
J.
,
2019
, “
Battery Energy Storage System Modeling: A Combined Comprehensive Approach
,”
J. Energy Storage
,
21
, pp.
172
185
.
64.
Aas
,
K.
,
Jullum
,
M.
, and
Løland
,
A.
,
2021
, “
Explaining Individual Predictions When Features Are Dependent: More Accurate Approximations to Shapley Values
,”
Artif. Intell.
,
298
, p.
103502
.
65.
Ma
,
Q.
,
Zheng
,
Y.
,
Yang
,
W.
,
Zhang
,
Y.
, and
Zhang
,
H.
,
2021
, “
Remaining Useful Life Prediction of Lithium Battery Based on Capacity Regeneration Point Detection
,”
Energy
,
234
, p.
121233
.
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