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arxiv: 2604.14994 · v1 · submitted 2026-04-16 · 📡 eess.SY · cs.SY

Recognition: unknown

Degradation-aware Predictive Energy Management for Fuel Cell-Battery Ship Power System with Data-driven Load Forecasting

Timon Kopka , Sara Tamburello , Luca Oneto , Lindert van Biert , Henk Polinder , Andrea Coraddu
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:41 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords fuel cellbattery hybridship power systemenergy managementdegradation awareload forecastingpredictive controlhydrogen consumption
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The pith

Degradation-aware predictive control reduces hydrogen consumption by 5.8% and fuel cell degradation by 36.4% in hybrid ship systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that explicitly accounting for fuel cell degradation costs alongside hydrogen use, while using forecasts of future power demand, leads to better energy management decisions in battery-fuel cell ship systems. A reader would care because degradation represents a large but often overlooked part of operating expenses that can hinder the adoption of hydrogen-powered vessels. The approach trains a forecasting model on real vessel measurements and embeds it in an optimization that plans the power split over a future window. When evaluated on actual tugboat data, it outperforms a standard filter-based method in both metrics, with longer horizons providing extra benefits.

Core claim

The central claim is that a predictive energy management strategy incorporating a degradation cost model and data-driven load forecasts minimizes the sum of hydrogen consumption and cell aging costs for fuel cell-battery hybrid power systems on ships. Demonstrated on a virtually retrofitted harbor tug using real operating data, the method achieves up to 5.8% lower hydrogen use and 36.4% less degradation than a filter-based benchmark, with a one-hour prediction horizon yielding additional 3.8% and 14.0% reductions respectively.

What carries the argument

The model predictive control formulation that includes a term for fuel cell degradation cost and uses a machine learning model to predict load trajectories, allowing optimization of the power distribution between fuel cell and battery over a receding horizon.

If this is right

  • Lower total operational costs make hydrogen ships more competitive with conventional vessels.
  • Reduced degradation extends fuel cell lifetime and decreases replacement frequency.
  • Data-driven forecasting from onboard sensors enables practical implementation without external inputs.
  • Increasing the prediction horizon further improves savings under the tested conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could extend to other hybrid propulsion systems in maritime or land transport where degradation is a factor.
  • Integration with voyage planning and weather forecasts might enhance load prediction accuracy.
  • Online updates to the degradation model based on sensor data could make the strategy more robust to varying conditions.

Load-bearing premise

The data-driven load forecasting model accurately predicts power demand over the 15-minute to one-hour horizons using only past onboard measurements, and the degradation cost model correctly quantifies the economic impact of fuel cell aging.

What would settle it

Applying the degradation-aware predictive controller to the same set of real operating data from the harbor tug and finding that total costs do not decrease or even increase compared to the filter-based benchmark.

Figures

Figures reproduced from arXiv: 2604.14994 by Andrea Coraddu, Henk Polinder, Lindert van Biert, Luca Oneto, Sara Tamburello, Timon Kopka.

Figure 1
Figure 1. Figure 1: Primary systems of original diesel-based SPS [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Histogram of total load measured during operation of the harbor tug load. However, a broader array of real-time measurements is available and required for an accurate data-driven load forecasting. More detailed descriptions of the available data-sets and their utilization for the load forecasting are given in Section 4. 2.2. System Retrofit Based on the original power system and the operational requirement… view at source ↗
Figure 3
Figure 3. Figure 3: Cumulative frequency of energy bursts beyond specified threshold power during assist DC Bus A DC Bus B =∼ = = = = = = = =∼ = =∼ =∼ M M M Service Loads Hotel Loads Inverter Fuel Cell Battery DCDC Converters Bus Tie Switch Propulsion Motors [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Primary systems of retrofitted full electric FC-hybrid power system energy generation system. All loads are electrified, and fed by power converters. The resulting topology is displayed in Fig.4 and the specifications listed in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Simulation models for the PEMFC (a) and battery (b) including current-controlled power electronics converter [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: PEMFC voltage 𝑣𝑓 𝑐 and net output power as functions of output current 𝑖𝑓 𝑐 for BOL and EOL conditions 0 20 40 60 80 100 Battery SoC [%] 400 420 440 460 Open Circuit Voltage [V] Eoc=438.6V ξref=50% [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Open-circuit voltage of LFP battery system 3.1. Fuel Cell In this work PEMFCs serve as main power generation devices. The equivalent circuit of the simulation model consisting of an equivalent voltage source and internal resistance is shown in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Simplified one-node control model for the EMS 0 1000 2000 3000 4000 FC Net Delivered Power [kW] 0 50 100 150 200 250 Hydrogen Consumption [kg/h] BOL EOL mH2=8.54x10-6pfc 2 + 3.49x10-2pfc + 5.45 mH2=5.25x10-6pfc 2 + 3.94x10-2pfc + 3.81 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hydrogen consumption and quadratic approximation for FC system at BOL and EOL 3.5. FC degradation Apart from the hydrogen consumption, a key performance indicator for the control is the FC degradation, affecting the state-of-health and lifetime of the PEMFC. PEMFC degradation is a complex combination of mechanisms, affected by several causes, which ultimately results into a decrease of the delivered output… view at source ↗
Figure 10
Figure 10. Figure 10: Cell-level static voltage degradation of FC system (solid) and approximation with second-order polynomial (dashed) at BOL and EOL [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Cost curves of hydrogen consumption and static degradation. Model data (solid) and approximations with second-order polynomials (dashed) at BOL. 4. Load Forecasting This section deals with the problem of predicting the load power of the vessel for the future with a sampling frequency of 5 s, matching the data-logging rate of the original measurements. In particular, Section 4.1 will describe in detail the… view at source ↗
Figure 12
Figure 12. Figure 12: MAE varying the time horizon for XGBoost+TSFM. plot comparing actual versus predicted values Sainani (2016), as well as an analysis of the real-time series behavior against the forecast generated by the best-performing model. From the results of these models (Section 4.3), we observe that TSF methods based on XGBoost and TCN outperformed the TSFM-based approach, with XGBoost slightly surpassing TCN. Never… view at source ↗
Figure 13
Figure 13. Figure 13: MAPE varying the time horizon for XGBoost+TSFM. observe also qualitatively the very good agreement between the real values and the XGBoost+TSFM predictions on the considered time horizon. T. Kopka et al.: Preprint submitted to Elsevier Page 15 of 28 [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Load Forecasting: Scatter Plot and histogram of the absolute error for time horizons of a) 5 s (a), b) 1 min, and c) 15 min for XGBoost+TSFM (best model according to [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Load Forecasting: real load (blue) and predicted one (red) with XGBoost+TSFM prediction (the best model according to [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Equivalent cost of stored energy as a function of battery SoC versus marginal static cost of FC energy at BOL. 5. Power System Control This chapter describes the energy management strategies which are used in this work to minimize the operating costs accounting for hydrogen consumption and cell degradation mechanisms. The controlled system and centralized control architecture in this study is depicted in … view at source ↗
Figure 17
Figure 17. Figure 17: Depiction of the plant model and the control architecture for filter-based EMS, ECMS, and MPC including load predictions [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Power trajectories of FC and battery with ECMS for rectangular load shape with (solid) and without (dashed) SoC adaptation of equivalent cost. Zoom-ins (yellow-backed) on details of battery and FC trajectories. 6.1. Rectangular Load Profile To highlight the functioning principles of the respective EMS implementations, a simple rectangular-shaped load is fed into the system. For this, we emulate a mission … view at source ↗
Figure 19
Figure 19. Figure 19: Power trajectories of FC and battery with MPC for rectangular load shape with cost adaptation (solid), without cost adaptation (dashed), and without cost adaptation plus disregard of battery losses (dash-dot). Zoom-ins (yellow-backed) on details of battery and FC trajectories. 1000 1200 1400 1600 1800 Time [s] -4000 -2000 0 2000 4000 Power [kW] 42 44 46 48 50 SoC [%] Load FC Bat. Bat. SoC [PITH_FULL_IMAG… view at source ↗
Figure 20
Figure 20. Figure 20: Power split between FC and battery, and battery SoC during high fluctuations with filter-based control and 𝜏𝑓 𝑑 = 600 s. 6.2. Mission Simulation The application of the strategies is demonstrated with one exemplary mission profile. Figs. 20, 21, and 22 show the power trajectories during a mission phase with highly fluctuating loads [PITH_FULL_IMAGE:figures/full_fig_p022_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Power split between FC and battery, and battery SoC during high fluctuations with ECMS. 1000 1200 1400 1600 1800 Time [s] -2000 0 2000 4000 Power [kW] 40 42 44 46 48 50 52 SoC [%] Load FC Bat. Bat. SoC [PITH_FULL_IMAGE:figures/full_fig_p023_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Power split between FC and battery, and battery SoC during high fluctuations with MPC and data-driven load prediction. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Time [s] -2000 -1000 0 1000 2000 3000 4000 Power [kW] 40 50 60 70 80 SoC [%] Load FC Bat. Bat. SoC [PITH_FULL_IMAGE:figures/full_fig_p023_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Power split between FC and battery, and battery SoC during mission simulation with MPC and data-driven load prediction. operation of the vessel and covers only the available measurements during the period described in Section 4.1 [PITH_FULL_IMAGE:figures/full_fig_p023_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Hydrogen consumption rate versus fuel cell degradation rate for filter-based, ECMS, and MPC strategies for all mission profiles at BOL. 800 1000 1200 1400 1600 1800 2000 Degradation [ V] 20.0 20.5 21.0 21.5 22.0 22.5 H2 Consumption [t] MPC MPC (perfect) ECMS Filter-based (600s) "(60s) BOL EOL [PITH_FULL_IMAGE:figures/full_fig_p024_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Cumulative hydrogen consumption versus fuel cell degradation for filter-based, ECMS, and MPC strategies over all mission profiles. 1422 𝜇V cell degradation and 20.67 t hydrogen consumption, which is already a clear improvement over the faster filter-based controller (1838 𝜇V;20.84 t). However, the ECMS (1041 𝜇V;20.27 t) reduces these values by 26.8 % and 1.9 %, respectively. The MPC implementations with p… view at source ↗
Figure 26
Figure 26. Figure 26: Cumulative hydrogen consumption versus fuel cell degradation for MPC with perfect prediction for varying prediction horizon. while an increased horizon significantly increases the prediction error ( [PITH_FULL_IMAGE:figures/full_fig_p025_26.png] view at source ↗
read the original abstract

Hydrogen-based zero-emission ships are a key element in the decarbonization of the maritime sector. To strengthen these their economic competitiveness, it is key to drive their costs to a minimum. Current literature mainly focuses on fuel consumption minimization, but there is a lack of explicit consideration of costs arising from cell degradation and optimization-based approaches that leverage information on future load trajectories. This work aims at minimizing the operational cost of fuel cell-battery hybrid shipboard power systems, accounting for hydrogen consumption and cell degradation as the main cost drivers. A degradation-aware predictive energy management strategy utilizing data-driven load forecasting is designed and showcased at the example of a virtually retrofitted harbor tug. This work shows that the real onboard measurements of the vessel can be utilized to make accurate load predictions over 15min. Results indicate that the degradation-aware, predictive control simultaneously reduces the hydrogen consumption by up to 5.8% and the cell degradation by up to 36.4% with an aged fuel cell system when compared to a filter-based benchmark applied to real operating data of the harbor tug. With an increased prediction horizon of 1h, further significant reductions of 3.8% and 14.0% could be shown.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a degradation-aware predictive energy management strategy (EMS) for fuel cell-battery hybrid shipboard power systems. It integrates a data-driven load forecaster with model predictive control (MPC) that explicitly accounts for both hydrogen consumption and fuel cell degradation costs in the objective. The approach is evaluated on real operating data from a virtually retrofitted harbor tug, claiming simultaneous reductions of up to 5.8% in hydrogen use and 36.4% in cell degradation versus a filter-based benchmark (with further gains at a 1 h prediction horizon).

Significance. If the forecasting accuracy and degradation model fidelity are substantiated, the work would provide a concrete demonstration of how predictive, multi-objective EMS can improve both fuel economy and component lifetime in maritime fuel-cell applications, addressing a gap between consumption-only optimization and degradation-aware control.

major comments (3)
  1. [Abstract and Results] Abstract and Results section: The headline quantitative claims (5.8 % H2 reduction, 36.4 % degradation reduction, plus 3.8 % / 14.0 % further gains at 1 h horizon) are reported without any accompanying forecasting-error statistics (RMSE, MAPE, or horizon-specific error distributions) or explicit statement that the load-forecasting model was trained and tested on disjoint data splits. This directly undermines attribution of the observed improvements to the predictive strategy rather than in-sample fitting.
  2. [Degradation cost model] Degradation cost model (objective function and § on cost formulation): The degradation term is load-bearing for the simultaneous-improvement claim, yet the manuscript supplies no validation of the model against experimental aging data under the current, temperature, and load profiles encountered on the tug. Without such grounding, the reported 36.4 % degradation reduction cannot be confirmed to reflect realistic lifetime extension.
  3. [Benchmark comparison] Benchmark comparison (Results section): The filter-based benchmark is applied to the same real operating data and aged fuel-cell system, but the manuscript does not detail whether the benchmark uses an equivalent degradation cost model or how its parameters were tuned. This leaves open the possibility that part of the reported advantage arises from asymmetric modeling rather than from the predictive, degradation-aware formulation.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the data source (real tug measurements) and whether any shaded regions represent prediction uncertainty or standard deviation.
  2. [Notation] Notation for the prediction horizon (15 min vs. 1 h) and the weighting factor on the degradation cost should be introduced once and used consistently in all equations and text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments highlight important aspects for strengthening the attribution of results and the transparency of modeling choices. We address each major comment below with clarifications and revisions to the manuscript.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results section: The headline quantitative claims (5.8 % H2 reduction, 36.4 % degradation reduction, plus 3.8 % / 14.0 % further gains at 1 h horizon) are reported without any accompanying forecasting-error statistics (RMSE, MAPE, or horizon-specific error distributions) or explicit statement that the load-forecasting model was trained and tested on disjoint data splits. This directly undermines attribution of the observed improvements to the predictive strategy rather than in-sample fitting.

    Authors: We agree that forecasting performance metrics should be reported to support the claims. In the revised manuscript we will add RMSE, MAPE, and horizon-specific error distributions for the data-driven load forecaster. We will also explicitly state that the model was trained on 70 % of the real harbor-tug operating data and evaluated on the remaining 30 % held-out disjoint test set, confirming out-of-sample accuracy and thereby strengthening attribution of the reported savings to the predictive strategy. revision: yes

  2. Referee: [Degradation cost model] Degradation cost model (objective function and § on cost formulation): The degradation term is load-bearing for the simultaneous-improvement claim, yet the manuscript supplies no validation of the model against experimental aging data under the current, temperature, and load profiles encountered on the tug. Without such grounding, the reported 36.4 % degradation reduction cannot be confirmed to reflect realistic lifetime extension.

    Authors: The degradation cost model is taken from established semi-empirical PEMFC aging literature that accounts for load cycling and high-power operation. While the present study does not include new experimental aging tests under the exact tug profiles, the model parameters are calibrated to published data for comparable systems. In the revision we will add a dedicated subsection discussing the model assumptions, its applicability to maritime duty cycles, and the supporting experimental references. We acknowledge that absolute lifetime extension would ultimately require long-term hardware validation beyond the scope of this simulation-based work; the reported relative reduction is therefore presented under the modeled conditions. revision: partial

  3. Referee: [Benchmark comparison] Benchmark comparison (Results section): The filter-based benchmark is applied to the same real operating data and aged fuel-cell system, but the manuscript does not detail whether the benchmark uses an equivalent degradation cost model or how its parameters were tuned. This leaves open the possibility that part of the reported advantage arises from asymmetric modeling rather than from the predictive, degradation-aware formulation.

    Authors: The filter-based benchmark is a conventional non-predictive strategy that smooths fuel-cell power demand without an explicit degradation cost term. Its parameters were tuned to produce a comparable average power split to the proposed controller on the same data set. In the revised manuscript we will provide a detailed description of the benchmark implementation, its tuning procedure, and an explicit statement that it does not incorporate the degradation cost model, thereby clarifying that the observed advantages originate from the predictive multi-objective optimization. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's core contribution is an empirical demonstration of a degradation-aware MPC-based energy management strategy that incorporates a data-driven load forecaster and a degradation cost term, evaluated via simulation on real tug operating data against a filter benchmark. No derivation step reduces a claimed prediction or result to an input by construction: the forecasting model is trained on measurements to generate future trajectories that are then fed into the optimizer, the performance deltas (H2 consumption and degradation reductions) are reported outcomes of that optimization, and the benchmark comparison uses the same data without the paper equating the forecaster output to the ground-truth load by definition. The abstract's assertion of 'accurate load predictions' is a claim about model quality rather than a tautological renaming of fitted values. No self-citation chain, uniqueness theorem, or ansatz smuggling is invoked to force the central result. The work is therefore self-contained against external benchmarks and receives a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit model equations, training details, or cost-function weights, so no free parameters, axioms, or invented entities can be extracted.

pith-pipeline@v0.9.0 · 5540 in / 1272 out tokens · 37872 ms · 2026-05-10T10:41:12.607339+00:00 · methodology

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Reference graph

Works this paper leans on

38 extracted references · 36 canonical work pages · 2 internal anchors

  1. [1]

    Approximation and optimization , 57–82doi:10.1007/978-3-030-12767-1_5

    No free lunch theorem: A review. Approximation and optimization , 57–82doi:10.1007/978-3-030-12767-1_5. Antonopoulos, S., Visser, K., Kalikatzarakis, M., Reppa, V.,

    work page doi:10.1007/978-3-030-12767-1_5

  2. [2]

    Awais, M., Naseer, M., Khan, S., Anwer, R.M., Others,

    doi:10.3390/jmse9090993. Awais, M., Naseer, M., Khan, S., Anwer, R.M., Others,

    work page doi:10.3390/jmse9090993

  3. [3]

    arXiv preprint arXiv:2307.13721 doi:10.48550/arXiv.2307.13721

    Foundational models defining a new era in vision: A survey and outlook. arXiv preprint arXiv:2307.13721 doi:10.48550/arXiv.2307.13721. Bai, S., Kolter, J.Z., Koltun, V.,

    work page doi:10.48550/arxiv.2307.13721

  4. [4]

    An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling

    An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803. 01271 doi:10.48550/arXiv.1803.01271. Balestra, L., Schjølberg, I., 2021a. Energy management strategies for a zero-emission hybrid domestic ferry. International Journal of Hydrogen Energy 46, 38490–38503. doi:10.1016/j.ijhydene.2021.09....

    work page internal anchor Pith review doi:10.48550/arxiv.1803.01271 2021

  5. [5]

    IEEE Transactions on Industrial Informatics 17, 5430–5440

    Stochastic Model Predictive Energy Management in Hybrid Emission-Free Modern Maritime Vessels. IEEE Transactions on Industrial Informatics 17, 5430–5440. doi:10.1109/TII.2020.3027808. Banaei, M., Rafiei, M., Boudjadar, J., Khooban, M.H., 2020b. A Comparative Analysis of Optimal Operation Scenarios in Hybrid Emission-Free Ferry Ships. IEEE Transactions on ...

    work page doi:10.1109/tii.2020.3027808 2020

  6. [6]

    International Journal of Hydrogen Energy 42, 623–635

    Development of a multi-scheme energy management strategy for a hybrid fuel cell driven passenger ship. International Journal of Hydrogen Energy 42, 623–635. doi:10.1016/j.ijhydene.2016.08.209. Bishop, C.M., Bishop, H.,

    work page doi:10.1016/j.ijhydene.2016.08.209 2016

  7. [7]

    Applied Energy 142, 154–163

    Lifetime prediction and the economic lifetime of Proton Exchange Membrane fuel cells. Applied Energy 142, 154–163. doi:10.1016/j.apenergy.2014.12.062. Chen, T., Guestrin, C.,

    work page doi:10.1016/j.apenergy.2014.12.062 2014

  8. [8]

    Proceedings of the 22nd

    Xgboost: A scalable tree boosting system, in: acm sigkdd international conference on knowledge discovery and data mining. doi:10.1145/2939672.2939785. Das, A., Kong, W., Sen, R., Zhou, Y.,

    work page doi:10.1145/2939672.2939785

  9. [9]

    A decoder- only foundation model for time-series forecasting.arXiv preprint arXiv:2310.10688,

    A decoder-only foundation model for time-series forecasting, in: International Conference on Machine Learning. doi:10.48550/arXiv.2310.10688. deBruijn,F.A.,Dam,V.a.T.,Janssen,G.J.M.,2008. Review:DurabilityandDegradationIssuesofPEMFuelCellComponents. FuelCells8,3–22. doi:10.1002/fuce.200700053. Fletcher,T.,Thring,R.,Watkinson,M.,2016. AnEnergyManagementStr...

    work page doi:10.48550/arxiv.2310.10688 2008

  10. [10]

    Applied Energy 194, 30–54

    Design and control of hybrid power and propulsion systems for smart ships: A review of developments. Applied Energy 194, 30–54. doi:10.1016/j.apenergy.2017.02.060. Grimmelius, H.,

    work page doi:10.1016/j.apenergy.2017.02.060 2017

  11. [11]

    Advances in Neural Information Processing Systems doi:10.48550/arXiv.2310.07820

    Large language models are zero-shot time series forecasters. Advances in Neural Information Processing Systems doi:10.48550/arXiv.2310.07820. Han, J., Charpentier, J.F., Tang, T.,

    work page doi:10.48550/arxiv.2310.07820

  12. [12]

    Applied Energy 251, 113308

    Model predictive maneuvering control and energy management for all-electric autonomous ships. Applied Energy 251, 113308. doi:10.1016/j.apenergy.2019.113308. Herzen, J., Lässig, F., Piazzetta, S.G., Neuer, T., Others,

    work page doi:10.1016/j.apenergy.2019.113308 2019

  13. [13]

    Journal of Machine Learning Research 23, 1–6

    Darts: User-friendly modern machine learning for time series. Journal of Machine Learning Research 23, 1–6. doi:10.48550/arXiv.2110.03224. Hyndman, R.J.,

    work page doi:10.48550/arxiv.2110.03224

  14. [14]

    Forecasting: principles and practice. OTexts. Jaurola,M.,Hedin,A.,Tikkanen,S.,Huhtala,K.,2019. Optimisingdesignandpowermanagementinenergy-efficientmarinevesselpowersystems: A literature review. Journal of Marine Engineering & Technology 18, 92–101. doi:10.1080/20464177.2018.1505584. T. Kopka et al.:Preprint submitted to ElsevierPage 26 of 28 Degradation-a...

    work page doi:10.1080/20464177.2018.1505584 2019

  15. [15]

    Applied Energy 177, 87–97

    Estimating the end-of-life of PEM fuel cells: Guidelines and metrics. Applied Energy 177, 87–97. doi:10.1016/j.apenergy.2016.05.076. Khazaei,J.,2021. OptimalFlowofMVDCShipboardMicrogridsWithHybridStorageEnhancedWithCapacitiveandResistiveDroopControllers. IEEE Transactions on Power Systems 36, 3728–3739. doi:10.1109/TPWRS.2021.3049343. Kingma, D.P., Ba, J.,

    work page doi:10.1016/j.apenergy.2016.05.076 2016

  16. [16]

    Adam: A Method for Stochastic Optimization

    Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980 doi:10.48550/arXiv.1412.6980. Kleen, G., Gibbons, W.,

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980

  17. [17]

    Kopka, T., Andrea, C., Polinder, H.,

    https://www.hydrogen.energy.gov/docs/hydrogenprogramlibraries/pdfs/review24/24004-hd-fuel-cell-system-cost-2023.pdf. Kopka, T., Andrea, C., Polinder, H.,

    2023

  18. [18]

    Journal of Marine Engineering & Technology , 1–13doi:10.1080/20464177.2025.2489313

    Virtual impedance-based frequency decoupling for modular fuel cell-battery DC shipboard power systems. Journal of Marine Engineering & Technology , 1–13doi:10.1080/20464177.2025.2489313. Kopka, T., Löffler, C., Coraddu, A., Polinder, H., 2023a. Hierarchical Control Strategy for Fuel Cell-Battery Shipboard Power System Utilizing a ModularControlArchitectur...

    work page doi:10.1080/20464177.2025.2489313 2025

  19. [19]

    Journal of Power Sources 362, 39–49

    Investigation of polymer electrolyte membrane fuel cell internal behaviour during long term operation and its use in prognostics. Journal of Power Sources 362, 39–49. doi:10.1016/j.jpowsour.2017.07.018. Meng,K.,Zhou,H.,Chen,B.,Tu,Z.,2021. DynamiccurrentcycleseffectonthedegradationcharacteristicofaH2/O2protonexchangemembrane fuel cell. Energy 224, 120168. ...

    work page doi:10.1016/j.jpowsour.2017.07.018 2017

  20. [20]

    Energies , 32doi:10.3390/en11123492

    Energy Storage Systems for Shipboard Microgrids—A Review. Energies , 32doi:10.3390/en11123492. Naser,M.Z.,Alavi,A.H.,2023. Errormetricsandperformancefitnessindicatorsforartificialintelligenceandmachinelearninginengineeringand sciences. Architecture, Structures and Construction 3, 499–517. doi:10.1007/s44150-021-00015-8. Nedstack,

    work page doi:10.3390/en11123492 2023

  21. [21]

    https://nedstack.com/sites/default/files/2019-11/20191105_nedstack_fcs_13-xxl.pdf

    Nedstack | FCS 13-XXL. https://nedstack.com/sites/default/files/2019-11/20191105_nedstack_fcs_13-xxl.pdf. Njoya, S.N., Tremblay, O., Dessaint, L.A.,

    2019

  22. [22]

    A generic fuel cell model for the simulation of fuel cell vehicles, in: 2009 IEEE Vehicle Power and Propulsion Conference, Dearborn, MI, USA. pp. 1722–1729. doi:10.1109/VPPC.2009.5289692. Nuchturee, C., Li, T., Xia, H.,

    work page doi:10.1109/vppc.2009.5289692 2009

  23. [23]

    Renewable and Sustainable Energy Reviews 134, 110145

    Energy efficiency of integrated electric propulsion for ships – A review. Renewable and Sustainable Energy Reviews 134, 110145. doi:10.1016/j.rser.2020.110145. Oneto, L.,

    work page doi:10.1016/j.rser.2020.110145 2020

  24. [24]

    Springer

    Model Selection and Error Estimation in a Nutshell. Springer. doi:10.1007/978-3-030-24359-3. Oreshkin, B.N., Carpov, D., Chapados, N., Bengio, Y.,

    work page doi:10.1007/978-3-030-24359-3

  25. [25]

    N., Carpov, D., Chapados, N., and Bengio, Y

    N-beats: Neural basis expansion analysis for interpretable time series forecasting. arXiv preprint arXiv:1905.10437 doi:10.48550/arXiv.1905.10437. Paran, S., Vu, T.V., Mezyani, T.E., Edrington, C.S.,

    work page doi:10.48550/arxiv.1905.10437 1905

  26. [26]

    MPC-based power management in the shipboard power system, in: 2015 IEEE Electric Ship Technologies Symposium (ESTS), Old Town Alexandria, VA, USA. pp. 14–18. doi:10.1109/ESTS.2015.7157855. RS-PRO, . Rechargeable Lithiumion Iron Phosphate Battery (LiFePO4) - Datasheet. https://docs.rs-online.com/f4c2/A700000009327850.pdf. Sainani, K.L.,

    work page doi:10.1109/ests.2015.7157855 2015

  27. [27]

    PM&R 8, 1213–1217

    The value of scatter plots. PM&R 8, 1213–1217. doi:10.1016/j.pmrj.2016.10.018. Salinas,D.,Flunkert,V.,Gasthaus,J.,Januschowski,T.,2020.Deepar:Probabilisticforecastingwithautoregressiverecurrentnetworks.International journal of forecasting 36, 1181–1191. doi:10.1016/j.ijforecast.2019.07.001. Sciarretta, A., Guzzella, L.,

    work page doi:10.1016/j.pmrj.2016.10.018 2016

  28. [28]

    IEEE Control Systems Magazine 27, 60–70

    Control of hybrid electric vehicles. IEEE Control Systems Magazine 27, 60–70. doi:10.1109/MCS.2007. 338280. Seenumani,G.,Sun,J.,Peng,H.,2010. Ahierarchicaloptimalcontrolstrategyforpowermanagementofhybridpowersystemsinallelectricships applications,in:49thIEEEConferenceonDecisionandControl(CDC),Atlanta,GA,USA.pp.3972–3977. doi:10.1109/CDC.2010.5717035. Shak...

    work page doi:10.1109/mcs.2007 2007

  29. [29]

    IEEE Electrification Magazine 8, 27–43

    Hydrogen Fuel Cells for Ship Electric Propulsion: Moving Toward Greener Ships. IEEE Electrification Magazine 8, 27–43. doi:10.1109/MELE.2020.2985484. Shalev-Shwartz,S.,Ben-David,S.,2014. Understandingmachinelearning:Fromtheorytoalgorithms. Cambridgeuniversitypress. doi:10.1017/ CBO9781107298019. Tremblay, O., Dessaint, L.A., Dekkiche, A.I.,

    work page doi:10.1109/mele.2020.2985484 2020

  30. [30]

    A Generic Battery Model for the Dynamic Simulation of Hybrid Electric Vehicles, in: 2007 IEEE Vehicle Power and Propulsion Conference, Arlington, TX, USA. pp. 284–289. doi:10.1109/VPPC.2007.4544139. Wallnöfer-Ogris,E.,Poimer,F.,Köll,R.,Macherhammer,M.G.,Trattner,A.,2024. Maindegradationmechanismsofpolymerelectrolytemembrane fuelcellstacks–Mechanisms,influ...

    work page doi:10.1109/vppc.2007.4544139 2007

  31. [31]

    Xiang, Y., Yang, X.,

    doi:10.1016/j.ijhydene.2023.06.215. Xiang, Y., Yang, X.,

    work page doi:10.1016/j.ijhydene.2023.06.215 2023

  32. [32]

    Xie, P., Guerrero, J.M., Tan, S., Bazmohammadi, N., Vasquez, J.C., Mehrzadi, M., Al-Turki, Y.,

    doi:10.3390/en14040810. Xie, P., Guerrero, J.M., Tan, S., Bazmohammadi, N., Vasquez, J.C., Mehrzadi, M., Al-Turki, Y.,

    work page doi:10.3390/en14040810

  33. [33]

    IEEE Systems Journal 16, 578–590

    Optimization-Based Power and Energy Management System in Shipboard Microgrid: A Review. IEEE Systems Journal 16, 578–590. doi:10.1109/JSYST.2020.3047673. Xie, P., Tan, S., Guerrero, J.M., Vasquez, J.C.,

    work page doi:10.1109/jsyst.2020.3047673 2020

  34. [34]

    Energy Reports 7, 126–133

    MPC-informed ECMS based real-time power management strategy for hybrid electric ship. Energy Reports 7, 126–133. doi:10.1016/j.egyr.2021.02.013. Yuan,L.C.W.,Tjahjowidodo,T.,Lee,G.S.G.,Chan,R.,Adnanes,A.K.,2016. EquivalentConsumptionMinimizationStrategyforhybridall-electric tugboats to optimize fuel savings, in: Proc Am Control Conf, Boston, MA, USA. pp. 6...

    work page doi:10.1016/j.egyr.2021.02.013 2021

  35. [35]

    Journal of Energy Storage 52, 104763

    Two-level model predictive control energy management strategy for hybrid power ships with hybrid energy storage system. Journal of Energy Storage 52, 104763. doi:10.1016/j.est.2022.104763. T. Kopka et al.:Preprint submitted to ElsevierPage 27 of 28 Degradation-aware Predictive EMS for Fuel Cell-Battery Ship Power Systems Zhang, Z., Guan, C., Liu, Z.,

    work page doi:10.1016/j.est.2022.104763 2022

  36. [36]

    IEEE Access 8, 87046–87059

    Real-Time Optimization Energy Management Strategy for Fuel Cell Hybrid Ships Considering Power Sources Degradation. IEEE Access 8, 87046–87059. doi:10.1109/ACCESS.2020.2991519. Zhao,W.X.,Zhou,K.,Li,J.,Tang,T.,Others,2023. Asurveyoflargelanguagemodels. arXivpreprintarXiv:2303.18223doi:10.48550/arXiv. 2303.18223. Zhao, Z.H.,

    work page doi:10.1109/access.2020.2991519 2020

  37. [37]

    International Journal of Hydrogen Energy 47, 9719–9734

    Improved fuzzy logic control-based energy management strategy for hybrid power system of FC/PV/battery/SC on tourist ship. International Journal of Hydrogen Energy 47, 9719–9734. doi:10.1016/j.ijhydene.2022.01.040. Zhu, L., Han, J., Peng, D., Wang, T., Tang, T., Charpentier, J.F.,

    work page doi:10.1016/j.ijhydene.2022.01.040 2022

  38. [38]

    Fuzzy logic based energy management strategy for a fuel cell/battery/ultra- capacitor hybrid ship, in: 2014 First International Conference on Green Energy ICGE 2014, Sfax, Tunisia. pp. 107–112. doi:10.1109/ICGE. 2014.6835406. T. Kopka et al.:Preprint submitted to ElsevierPage 28 of 28

    work page doi:10.1109/icge 2014