Estimation and Optimization of Ship Fuel Consumption in Maritime: Review, Challenges and Future Directions

Dusica Marijan; Hamza Haruna Mohammed; Bakht Zaman

cs.LGFeb 25, 2026

Estimation and Optimization of Ship Fuel Consumption in Maritime: Review, Challenges and Future Directions

Authors: Dusica Marijan, Hamza Haruna Mohammed, Bakht Zaman

Organizations: Simula Research Laboratory, Kristian Augusts 23, Oslo, 0164, Norway

Abstract

To reduce carbon emissions and minimize shipping costs, improving the fuel efficiency of ships is crucial. Various measures are taken to reduce the total fuel consumption of ships, including optimizing vessel parameters and selecting routes with the lowest fuel consumption. Different estimation methods are proposed for predicting fuel consumption, while various optimization methods are proposed to minimize fuel oil consumption. This paper provides a comprehensive review of methods for estimating and optimizing fuel oil consumption in maritime transport. Our novel contributions include categorizing fuel oil consumption & estimation methods into physics-based, machine-learning, and hybrid models, exploring their strengths and limitations. Furthermore, we highlight the importance of data fusion techniques, which combine AIS, onboard sensors, and meteorological data to enhance accuracy. We make the first attempt to discuss the emerging role of Explainable AI in enhancing model transparency for decision-making. Uniquely, key challenges, including data quality, availability, and the need for real-time optimization, are identified, and future research directions are proposed to address these gaps, with a focus on hybrid models, real-time optimization, and the standardization of datasets.

Figures & tables

Papers	FOC Est.	FOC Opt.	FOC-XAI	Feature Discussion	Challenges	Data Fusion
Fan et al. (2022b)	✓	$\times$	$\times$	✓	$\times$	$\times$
Wang et al. (2022)	✓	$\times$	$\times$	$\times$	$\times$	$\times$
Barreiro et al. (2022)	$\times$	$\checkmark$	$\times$	$\times$	$\checkmark$	$\times$
Mylonopoulos et al. (2023)	✓	✓	$\times$	$\times$	$\times$	$\times$
Yan et al. (2021b)	✓	✓	$\times$	✓	✓	$\times$
Our work	✓	✓	✓	✓	✓	✓

Table 1: Comparison of relevant survey papers with our paper highlighting the novel contributions of our work ( FOC Est. : FOC Estimation, FOC Opt. : FOC Optimization, FOC-XAI : FOC Explainable AI)

Nomenclature	Meaning
AIS	Automatic Identification System
AES	All-electric ship
ANN	Artificial Neural Network
BBM	Black Box Model
COG	Course Over Ground
CMEMS	Copernicus Marine Environment Monitoring Service

Table 2: List of abbreviations used in the paper

Data Type	Example Sources	Key Features
Navigation Data	AIS, Noon Reports	speed, draft, trim
Engine Data	Onboard Sensors	rpm, power output, fuel flow
Meteorological Data	ECMWF, NOAA, CMEMS	wind, waves, sea currents
Regulatory Data	MRV, IMO DCS	reported emissions, compliance metrics

Table 3: Data sources, their corresponding features, and example sources relevant for FOC estimation.

Panel of Figure 1 — Figure 1: FOC Estimation Data Sources: Overview of the key data types used in estimating FOC, incorporating navigational, engine, environmental, and regulatory inputs.

Source	Engine	Navigation	Metocean	FOC and GHG Emissions
AIS		SOG, COG, draft
Noon Reports	average propeller rpm, average engine rpm	draft, trim, average SOG, COG	wind magnitude and direction, sea conditions and sea swell	Fuel oil consumption (FOC), daily consumption
Onboard Sensors	rpm, engine power, torque, engine temperature	SOG, COG	wind magnitude and direction, sea waves	FOC (if fuel sensors are installed)
Online Sources			sea water temperature, wind direction, wind magnitude, wave direction, wave height, sea current direction, sea current speed
MRV				FOC, CO 2 emissions

Table 4: Data sources and their corresponding features related to engine performance, navigation, metocean conditions, FOC, and GHG emissions.

Data Source	Example Providers	Typical Features	Resolution / Access	Advantages and Limitations
AIS	MarineTraffic, EMSA	SOG, COG, position, draft, ETA	Sec–min; public	Standardized and global coverage; lacks direct engine/fuel data; possible signal gaps and spoofing; timestamps may need resampling.
Noon Reports	Ship logbooks	Avg. speed, RPM, draft, trim, FOC	Daily; internal	Contains direct daily FOC; coarse granularity and subject to manual entry noise; limited for short-term/real-time analysis.
Onboard Sensors	ECU, shaft/fuel meters	RPM, torque, shaft power, fuel flow, temp/pressure	Seconds; proprietary	High fidelity and suitable for real-time modeling; access restricted by confidentiality; sensor drift and calibration needed.
Online Sources	ECMWF, NOAA, CMEMS	Wind, wave, current, SST, pressure	Hour–daily; open	Essential for weather routing and exogenous features; spatial/temporal mismatch with vessel tracks; interpolation and co-location required.
MRV	EMSA (EU MRV)	Annual FOC, CO 2 , vessel data	Annual; public (EU)	Regulatory-grade, standardized aggregates; low temporal resolution limits operational analytics; useful as benchmarking/validation.

Table 5: Summary and comparison of key data sources relevant to FOC estimation.

Figure 2: Taxonomy of FOC estimation models

Figure 3: Schematic representation of a resistance-based model for FOC estimation. The process begins with environmental and ship condition inputs (e.g., wind, waves, current, draft, and hull roughness) to compute the total resistance components (calm-water, wave, wind, fouling, and shallow-water resistance). These are then translated into effective engine power requirements through propulsion models. Finally, fuel oil consumption is estimated using SFOC and loading conditions.

Papers	Noon Reports	MetOcean	MRV	AIS	Sensors
Li et al. (2022) , Hajli et al. (2024) , Luo et al. (2023b)	✓	✓	$\times$	$\times$	$\times$
Zhou et al. (2023)	$\times$	✓	$\times$	$\times$	✓
Du et al. (2022b) ; Yan et al. (2024)	✓	✓	$\times$	✓	$\times$
Du et al. (2022c)	$\times$	✓		$\times$	✓
Ren et al. (2022) , Wang et al. (2023c)	$\times$	✓	✓	✓	$\times$
Farag and Ölçer (2020) ; Zhang et al. (2023b)	$\times$	✓	$\times$	✓	✓

Table 6: Papers on data fusion of different sources (AIS, noon reports, meteorological, MRV, and onboard sensors data) for FOC estimation.

Paper	Output	Features Included	Method Type	Results
Hajli et al. (2024)	Metric ton per nautical mile	rpm, sog, slip, wind factor, averaged wind factor, wave factor, averaged wave factor, current factor, averaged current factor	multiple linear regression	MAE: $5.49\times 10^{-3}$ , RMSE: $7.36\times 10^{-3}$ (metric tons per nautical mile)
Du et al. (2019)	Metric ton per day	Speed, displacement, wave height, wave direction, wind force, current speed, current direction, sea water temperature, trim	ANN	RMSE of less than 9.5 MT/day
Papandreou and Ziakopoulos (2022)	FOC (main engine) [tn]	Speed through water, Relative wind direction, Relative wind speed, Mean draft, Trim, Days since last drydock, Laden or Ballast (binary format)	XGBoost	prediction error with 5%
Yan et al. (2024)	Hourly average ME fuel consumption rate	average sailing speed, sailing condition (laden/ballast), wind direction, wind force, draft, air density over the oceans, forecast surface roughness, mean sea level pressure, mean direction of total wave, mean period of total wave, significant height of the total wave, temperature of water near sea surface	ANN	MAE of 7.5%
Uyanık et al. (2020)	FOC (ton/day)	M/E fuel oil inlet pressure (bar), temperature (°C), viscosity (cSt), Air coolers cooling water temperature (°C), Jacket cooling water inlet pressure (bar) and temperature (°C), Scavenging air receiver temperature (°C), Bearing temperatures (°C), Start air inlet pressure (bar), Fuel mass flow (kg/h), Shaft power (kW), rpm, torque (kNm), M/E lubrication oil temperature (°C) and pressure (bar), M/E fuel flow counter, M/E power, Exhaust temperature of the cylinders (°C), Turbocharger rpm and exhaust gas inlet temperature (°C).	Bayesian ridge regression, Kernel ridge regression, Multiple linear regression and Ridge regression	Bayesian Ridge (RMSE=0.0001 MAE=0.003 $\text{R}^{2}$ =99.999%), Multiple LR & Ridge (RMSE=0.0001 MAE=0.002 $\text{R}^{2}$ =99.999%), Kernel Ridge (RMSE=0.0001 MAE=0.003 $\text{R}^{2}$ =99.999%)
Fan et al. (2024)	ME FOC (kg/h)	Wind speed/direction, water depth, speed (over ground/water), engine fuel use/power, propeller speed/power, bearing temp, exhaust temp/pressure, intercooler air temp, cylinder liner water temp, fuel pressure/temp, and exhaust temp after vortex.	Random Forest and Extreme Gradient Boosting	RF ( $\text{R}^{2}$ =0.9747, MAE=1.72)

Table 7: Summary of the data-driven papers for FOC estimation in maritime.

Papers	Engine Data	Weather/Ocean Data	Operational Data	ML Method	Tree-based
Hajli et al. (2024)	$\times$	✓	✓	$\checkmark$	$\times$
Du et al. (2019)	$\times$	✓	✓	✓	$\times$
Papandreou and Ziakopoulos (2022)	$\times$	✓	✓	✓	✓
Yan et al. (2024)	$\times$	✓	✓	✓	$\times$
Uyanık et al. (2020)	✓	$\times$	✓	✓	✓
Fan et al. (2024)	✓	✓	✓	✓	✓

Table 8: Summary of data-driven papers for FOC estimation with their data types and methods. ”Engine Data” refers to onboard sensor readings; ”Operational Data” includes voyage characteristics such as speed, trim, or draft; ”Weather/Ocean Data” refers to environmental inputs.

Paper	GBM Type	Physics-Based Role	ML Role	Key Advantage	Weaknesses
[1]	Serial (S-GBM)	Input for ML model	Corrects residual errors	Balances accuracy & interpretability	Performance depends on quality of the physics-based model; limited adaptability if underlying physics is inaccurate.
[2]	Constraint (C-GBM)	Encodes physical laws as constraints during ML training	Learns within physics-informed boundaries	Ensures physically valid outputs	Requires careful formulation of constraints; may restrict flexibility and increase training complexity.
[3]	Embedding (E-GBM)	Embeds physics components directly in ML architecture	Replaces computationally expensive physics solvers	Enables fast, real-time estimation	Implementation is complex; may lose interpretability and risk overfitting without sufficient physical guidance.

Table 9: Comparison of Grey-Box Modeling (GBM) approaches across physics integration, machine learning role, advantages, and weaknesses. [1] DeKeyser et al. (2022) , [2] Coraddu et al. (2017) , [3] Guo et al. (2022)

Paper	XAI Method	Interpretability	Accuracy	Key Trade-Off
[1]	SHAP	High	Moderate	Loss of some model flexibility
[2]	PI-NN & MIO	PI-NN: Moderate, MIO: High	PI-NN: High, MIO: Moderate	MIO is highly interpretable but less accurate
[3]	SHAP + XGBoost	High	High (R² = 0.95)	Computational overhead due to SHAP analysis
[4]	SHAP + XGBoost	High	Very High (R² = 0.99)	Model sensitivity to different load conditions

Table 10: Comparison of XAI Approaches in FOC Estimation. [1] Ma et al. (2023b) , [2] Wang et al. (2023a) , [3] Handayani et al. (2023) , [4] Handayani et al. (2025)

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Ship fuel consumption (SFC) prediction supports vessel operation optimisation, emissions estimation, and decision support systems (DSS) for sustainable maritime transportation. Numerous data-driven fuel models have been developed over the past two decades, but a critical and often overlooked limitation lies in their validation practices: most studies evaluate performance using random train--test splits, which, applied to high-frequency records, admit temporal leakage and yield optimistic results that do not reflect deployment conditions. This paper examines that gap using time-aware evaluation, specifically Time Series Cross-Validation (TSCV) and Blocked TSCV (BTSCV). Using the Canadian Coast Guard Ship (CCGS) Sir Wilfrid Laurier as a case study, six regression models and a physics baseline are tuned under three time-aware schemes and three feature configurations, then evaluated on a common chronological hold-out set drawn from approximately 3.88 million steady-state 1,Hz records.

Abstract

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