Abstract

A solid oxide fuel cell (SOFC) is a multiphysics system that involves heat transfer, mass transport, and electrochemical reactions to produce electrical power. Reduction and re-oxidation (Redox) cycling is a destructive reaction that can occur during SOFC operation. Redox induces various degradation mechanisms, such as electrode delamination, nickel agglomeration, and microstructural changes, which should be mitigated. The interplay of these mechanisms makes a post-Redox SOFC a nonlinear, time-varying, nonstationary dynamic system. Physics-based modeling of these complexities often leads to computationally expensive equations that are not suitable for the control and diagnostics of SOFCs. Here, a data-driven approach based on dilated convolutions and a self-attention mechanism is introduced to effectively capture the dynamics underlying SOFCs affected by Redox. Controlled Redox cycles are designed to collect appropriate experimental data for developing deep learning models, which are lacking in the current literature. The performance of the proposed model is validated on diverse unseen data sets gathered from different fuel cells and benchmarked against state-of-the-art models, in terms of prediction accuracy and computation complexity. The results indicate 31% accuracy improvement and 27% computation speed enhancement compared to the benchmarks.

References

1.
Xu
,
Q.
,
Guo
,
Z.
,
Xia
,
L.
,
He
,
Q.
,
Li
,
Z.
,
Bello
,
I. T.
,
Zheng
,
K.
, and
Ni
,
M.
,
2022
, “
A Comprehensive Review of Solid Oxide Fuel Cells Operating on Various Promising Alternative Fuels
,”
Energy Convers. Manage.
,
253
, p.
115175
.10.1016/j.enconman.2021.115175
2.
Chi
,
Y.
,
Lin
,
J.
,
Li
,
P.
, and
Song
,
Y.
,
2024
, “
Investigating the Performance of a Solid Oxide Electrolyzer Multi-Stack Module With a Multiphysics Homogenized Model
,”
J. Power Sources
,
594
, p.
234019
.10.1016/j.jpowsour.2023.234019
3.
Boldrin
,
P.
, and
Brandon
,
N. P.
,
2019
, “
Progress and Outlook for Solid Oxide Fuel Cells for Transportation Applications
,”
Nat. Catal.
,
2
(
7
), pp.
571
577
.10.1038/s41929-019-0310-y
4.
Subotić
,
V.
, and
Hochenauer
,
C.
,
2022
, “
Analysis of Solid Oxide Fuel and Electrolysis Cells Operated in a Real-System Environment: State-of-the-Health Diagnostic, Failure Modes, Degradation Mitigation and Performance Regeneration
,”
Prog. Energy Combust. Sci.
,
93
, p.
101011
.10.1016/j.pecs.2022.101011
5.
Andrade
,
P.
,
Laadjal
,
K.
,
Alcaso
,
A. N.
, and
Cardoso
,
A. J. M.
,
2024
, “
A Comprehensive Review on Condition Monitoring and Fault Diagnosis in Fuel Cell Systems: Challenges and Issues
,”
Energies
,
17
(
3
), p.
657
.10.3390/en17030657
6.
Yang
,
C.
,
Guo
,
R.
,
Jing
,
X.
,
Li
,
P.
,
Yuan
,
J.
, and
Wu
,
Y.
,
2022
, “
Degradation Mechanism and Modeling Study on Reversible Solid Oxide Cell in Dual-Mode—A Review
,”
Int. J. Hydrogen Energy
,
47
(
89
), pp.
37895
37928
.10.1016/j.ijhydene.2022.08.240
7.
Wang
,
J.
,
Zhao
,
Y.
,
Yang
,
J.
,
Sang
,
J.
,
Wu
,
A.
,
Wang
,
J.
,
Guan
,
W.
,
Jiang
,
L.
, and
Singhal
,
S. C.
,
2023
, “
Understanding Thermal and Redox Cycling Behaviors of Flat-Tube Solid Oxide Fuel Cells
,”
Int. J. Hydrogen Energy
,
48
(
57
), pp.
21886
21897
.10.1016/j.ijhydene.2023.03.062
8.
Song
,
B.
,
Ruiz-Trejo
,
E.
,
Bertei
,
A.
, and
Brandon
,
N. P.
,
2018
, “
Quantification of the Degradation of Ni-YSZ Anodes Upon Redox Cycling
,”
J. Power Sources
,
374
, pp.
61
68
.10.1016/j.jpowsour.2017.11.024
9.
Altan
,
T.
,
Celik
,
S.
,
Toros
,
S.
,
Korkmaz
,
H. G.
, and
Timurkutluk
,
B.
,
2023
, “
Estimation of Microscale Redox Tolerance for Ni-Based Solid Oxide Fuel Cell Anodes Via Three-Dimensional Finite Element Modeling
,”
Int. J. Hydrogen Energy
,
48
(
3
), pp.
1060
1074
.10.1016/j.ijhydene.2022.10.019
10.
Nguyen
,
B. N.
,
Karri
,
N. K.
,
Mason
,
C. T.
,
Fitzpatrick
,
J. F.
, and
Koeppel
,
B. J.
,
2021
, “
Damage Modeling of Solid Oxide Fuel Cells Accounting for Redox Effects
,”
J. Electrochem. Soc.
,
168
(
11
), p.
114514
.10.1149/1945-7111/ac39de
11.
Abeysiriwardena
,
S.
, and
Das
,
T.
,
2016
, “
An Adaptive Observer for Recirculation-Based Solid Oxide Fuel Cells
,”
ASME J. Dyn. Syst., Meas., Control
,
138
(
8
), p.
081004
.10.1115/1.4033271
12.
Nguyen
,
B. N.
,
Karri
,
N. K.
,
Mason
,
C. T.
,
Fitzpatrick
,
J. F.
, and
Koeppel
,
B. J.
,
2022
, “
A Mechanistic Damage Model for Solid Oxide Fuel Cell Ceramic Materials-Part I: Constitutive Modeling
,”
Int. J. Hydrogen Energy
,
47
(
11
), pp.
7388
7402
.10.1016/j.ijhydene.2021.10.101
13.
Zhang
,
Z.
, and
Song
,
X.
,
2023
, “
Designing Hybrid Neural Network Using Physical Neurons-A Case Study of Drill Bit-Rock Interaction Modeling
,”
ASME J. Dyn. Syst., Meas., Control
,
145
(
9
), pp.
1
9
.10.1115/1.4062631
14.
Hu
,
Q.
,
Amini
,
M. R.
,
Wiese
,
A.
,
Seeds
,
J. B.
,
Kolmanovsky
,
I.
, and
Sun
,
J.
,
2022
, “
A Multirange Vehicle Speed Prediction With Application to Model Predictive Control-Based Integrated Power and Thermal Management of Connected Hybrid Electric Vehicles
,”
ASME J. Dyn. Syst., Meas., Control
,
144
(
1
), p.
011105
.10.1115/1.4052819
15.
Eagon
,
M. J.
,
Kindem
,
D. K.
,
Panneer Selvam
,
H.
, and
Northrop
,
W. F.
,
2022
, “
Neural Network-Based Electric Vehicle Range Prediction for Smart Charging Optimization
,”
ASME J. Dyn. Syst., Meas., Control
,
144
(
1
), p.
011110
.10.1115/1.4053306
16.
Li
,
M.
,
Wu
,
H.
,
Wang
,
Y.
,
Handroos
,
H.
, and
Carbone
,
G.
,
2017
, “
Modified Levenberg–Marquardt Algorithm for Backpropagation Neural Network Training in Dynamic Model Identification of Mechanical Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
139
(
3
), p.
031012
.10.1115/1.4035010
17.
Tofigh
,
M.
,
Salehi
,
Z.
,
Kharazmi
,
A.
,
Smith
,
D. J.
,
Hanifi
,
A. R.
,
Koch
,
C. R.
, and
Shahbakhti
,
M.
,
2024
, “
Transient Modeling of a Solid Oxide Fuel Cell Using an Efficient Deep Learning HY-CNN-NARX Paradigm
,”
J. Power Sources
,
606
, p.
234555
.10.1016/j.jpowsour.2024.234555
18.
Yan
,
L.
, and
Devasia
,
S.
,
2024
, “
What Observables Are Needed for Precision Data-Enabled Learning of Inverse Operators?
,”
ASME J. Dyn. Syst., Meas., Control
,
146
(
3
), p.
18
.10.1115/1.4064655
19.
Chiuso
,
A.
, and
Pillonetto
,
G.
,
2019
, “
System Identification: A Machine Learning Perspective
,”
Annu. Rev. Control, Rob., Auton. Syst.
,
2
(
1
), pp.
281
304
.10.1146/annurev-control-053018-023744
20.
Hu
,
X.
,
Yang
,
X.
,
Feng
,
F.
,
Liu
,
K.
, and
Lin
,
X.
,
2021
, “
A Particle Filter and Long Short-Term Memory Fusion Technique for Lithium-Ion Battery Remaining Useful Life Prediction
,”
ASME J. Dyn. Syst., Meas., Control
,
143
(
6
), p.
061001
.10.1115/1.4049234
21.
Tofigh
,
M.
,
Salehi
,
Z.
,
Smith
,
D.
,
Ali
,
K.
,
Amir
,
H. Y.
,
Koch
,
C. R.
, and
Shahbakhti
,
M.
,
2024
, “
Developing an Efficient Model for a SOFC System Using Self-Supervised Convolutional Autoencoder and Stateful LSTM Network
,”
American Control Conference (ACC)
, Toronto, ON, Canada, July 8–12, pp.
86
91
.
22.
Bai
,
S.
,
Kolter
,
J. Z.
, and
Koltun
,
V.
,
2018
, “
An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling
,” arXiv:1803.01271.
23.
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:1609.03499.
24.
Wu
,
P.
,
Sun
,
J.
,
Chang
,
X.
,
Zhang
,
W.
,
Arcucci
,
R.
,
Guo
,
Y.
, and
Pain
,
C. C.
,
2020
, “
Data-Driven Reduced Order Model With Temporal Convolutional Neural Network
,”
Comput. Methods Appl. Mech. Eng.
,
360
, p.
112766
.10.1016/j.cma.2019.112766
25.
Cheng
,
S.
,
Quilodrán-Casas
,
C.
,
Ouala
,
S.
,
Farchi
,
A.
,
Liu
,
C.
,
Tandeo
,
P.
,
Fablet
,
R.
, et al.,
2023
, “
Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems: A Review
,”
IEEE/CAA J. Automat. Sin.
,
10
(
6
), pp.
1361
1387
.10.1109/JAS.2023.123537
26.
Tofigh
,
M.
,
Kharazmi
,
A.
,
Smith
,
D. J.
,
Koch
,
C. R.
, and
Shahbakhti
,
M.
,
2024
, “
Temporal Dilated Convolution and Nonlinear Autoregressive Network for Predicting Solid Oxide Fuel Cell Performance
,”
Eng. Appl. Artif. Intell.
,
136
, p.
108994
.10.1016/j.engappai.2024.108994
27.
Vaswani
,
A.
,
Shazeer
,
N.
,
Parmar
,
N.
,
Uszkoreit
,
J.
,
Jones
,
L.
,
Gomez
,
A. N.
,
Kaiser
,
Ł.
, and
Polosukhin
,
I.
,
2017
, “
Attention is All You Need
,” arXiv:1706.03762.
28.
Huang
,
B.
,
Qi
,
Y.
, and
Murshed
,
M.
,
2011
, “
Solid Oxide Fuel Cell: Perspective of Dynamic Modeling and Control
,”
J. Process Control
,
21
(
10
), pp.
1426
1437
.10.1016/j.jprocont.2011.06.017
29.
Peng
,
J.
,
Huang
,
J.
,
Wu
,
X.-L.
,
Xu
,
Y.-W.
,
Chen
,
H.
, and
Li
,
X.
,
2021
, “
Solid Oxide Fuel Cell (SOFC) Performance Evaluation, Fault Diagnosis and Health Control: A Review
,”
J. Power Sources
,
505
, p.
230058
.10.1016/j.jpowsour.2021.230058
30.
Yang
,
S.
,
Wang
,
F.
,
Che
,
Q.
,
Li
,
J.
,
Lu
,
Y.
,
Shang
,
S.
, and
Zhang
,
H.
,
2022
, “
Quantitative Characterization of Nickel Migration in Solid Oxide Fuel Cells Under Redox Cycling
,”
J. Alloys Compd.
,
921
, p.
166085
.10.1016/j.jallcom.2022.166085
31.
Razmi
,
A. R.
,
Sharifi
,
S.
,
Vafaeenezhad
,
S.
,
Hanifi
,
A. R.
, and
Shahbakhti
,
M.
,
2024
, “
Modeling and Microstructural Study of Anode-Supported Solid Oxide Fuel Cells: Experimental and Thermodynamic Analyses
,”
Int. J. Hydrogen Energy
,
54
, pp.
613
634
.10.1016/j.ijhydene.2023.08.296
32.
Hanifi
,
A. R.
,
Laguna-Bercero
,
M. A.
,
Sandhu
,
N. K.
,
Etsell
,
T. H.
, and
Sarkar
,
P.
,
2016
, “
Tailoring the Microstructure of a Solid Oxide Fuel Cell Anode Support by Calcination and Milling of YSZ
,”
Sci. Rep.
,
6
(
1
), p.
27359
.10.1038/srep27359
33.
Wood
,
T.
, and
Ivey
,
D. G.
,
2017
, “
The Impact of Redox Cycling on Solid Oxide Fuel Cell Lifetime
,”
Solid Oxide Fuel Cell Lifetime and Reliability
,
Elsevier
, Academic Press, London, UK, pp.
51
77
.10.1016/B978-0-08-101102-7.00004-0
34.
Matsumoto
,
K.
,
Tachikawa
,
Y.
,
Lyth
,
S. M.
,
Matsuda
,
J.
, and
Sasaki
,
K.
,
2022
, “
Performance and Durability of Ni–Co Alloy Cermet Anodes for Solid Oxide Fuel Cells
,”
Int. J. Hydrogen Energy
,
47
(
68
), pp.
29441
29455
.10.1016/j.ijhydene.2022.06.268
35.
Burdin
,
B.
,
Sheikh
,
A.
,
Krapchanska
,
M.
,
Montinaro
,
D.
,
Piccardo
,
P.
,
Spotorno
,
R.
, and
Vladikova
,
D.
,
2021
, “
Redox-Cycling–A Tool for Artificial Electrochemical Aging of Solid Oxide Cells
,”
ECS Trans.
,
103
(
1
), pp.
1137
1149
.10.1149/10301.1137ecst
36.
Dikwal
,
C.
,
Bujalski
,
W.
, and
Kendall
,
K.
,
2008
, “
Characterization of the Electrochemical Performance of Micro-Tubular SOFC in Partial Reduction and Oxidation Conditions
,”
J. Power Sources
,
181
(
2
), pp.
267
273
.10.1016/j.jpowsour.2007.11.052
37.
Yang
,
J.
,
Zou
,
Z.
,
Zhang
,
H.
,
Chang
,
X.
,
Liu
,
W.
,
Xu
,
J.
,
Jiao
,
Z.
,
Wang
,
J.
, and
Guan
,
W.
,
2021
, “
Study on the Long-Term Discharge and Redox Stability of Symmetric Flat-Tube Solid Oxide Fuel Cells
,”
Int. J. Hydrogen Energy
,
46
(
15
), pp.
9741
9748
.10.1016/j.ijhydene.2020.12.227
38.
U. S. Department of Energy
,
2019
, “
Report on the Status of the Solid Oxide Fuel Cell Program
,” U. S. Department of Energy, Washington, DC, accessed Aug. 2019, https://www.energy.gov/
39.
Faes
,
A.
,
Hessler-Wyser
,
A.
,
Zryd
,
A.
, and
Van Herle
,
J.
,
2012
, “
A Review of RedOx Cycling of Solid Oxide Fuel Cells Anode
,”
Membranes
,
2
(
3
), pp.
585
664
.10.3390/membranes2030585
40.
He
,
K.
,
Zhang
,
X.
,
Ren
,
S.
, and
Sun
,
J.
,
2016
, “
Deep Residual Learning for Image Recognition
,”
IEEE Conference on Computer Vision and Pattern Recognition
(
CVPR
), Las Vegas, NV, June 27–30, pp.
770
778
.10.1109/CVPR.2016.90
41.
Salimans
,
T.
, and
Kingma
,
D. P.
,
2016
, “
Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks
,”
Proceedings of the 30th International Conference on Neural Information Processing Systems
, Barcelona, Spain, Dec. 5–10, pp. 901–909.https://dl.acm.org/doi/10.5555/3157096.3157197
42.
Lara-Benítez
,
P.
,
Carranza-García
,
M.
, and
Riquelme
,
J. C.
,
2021
, “
An Experimental Review on Deep Learning Architectures for Time Series Forecasting
,”
Int. J. Neural Syst.
,
31
(
3
), p.
2130001
.10.1142/S0129065721300011
43.
Lim
,
B.
, and
Zohren
,
S.
,
2021
, “
Time-Series Forecasting With Deep Learning: A Survey
,”
Philos. Trans. R. Soc. A
,
379
(
2194
), p.
20200209
.10.1098/rsta.2020.0209
44.
Ioffe
,
S.
, and
Szegedy
,
C.
,
2015
, “
Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
,”
International Conference on Machine Learning,
Lille, France, July 6–11, pp.
448
456
.https://dl.acm.org/doi/10.5555/3045118.3045167
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