An Innovation Machine Learning Approach for Ship Fuel-Consumption Prediction Under Climate-Change Scenarios and IMO Standards

Abstract

This study introduces an innovative Emotional Artificial Neural Network (EANN) model to predict ship fuel consumption with high accuracy, addressing the challenges posed by complex environmental conditions and operational variability. This research examines the impact of climate change on maritime operations and fuel efficiency by analyzing climatic variables such as wave period, wind speed, and sea-level rise. The model’s performance is assessed using two ship types (bulk carrier and container ship with max 60,000 dead weight tonnage (DWT)) under various climate scenarios. A comparative analysis demonstrates that the EANN model significantly outperforms the conventional Feedforward Neural Network (FFNN) in predictive accuracy. For bulk carriers, the EANN achieved a Root Mean Squared Error (RMSE) of 5.71 tons/day during testing, compared to 9.91 tons/day for the FFNN model. Similarly, for container ships, the EANN model achieved an RMSE of 5.97 tons/day, significantly better than the FFNN model’s 10.18 tons/day. A sensitivity analysis identified vessel speed as the most critical factor, contributing 33% to the variance in fuel consumption, followed by engine power and current speed. Climate-change simulations showed that fuel consumption increases by an average of 22% for bulk carriers and 19% for container ships, highlighting the importance of operational optimizations. This study emphasizes the efficacy of the EANN model in predicting fuel consumption and optimizing ship performance. The proposed model provides a framework for improving energy efficiency and supporting compliance with International Maritime Organization Standards (IMO) environmental standards. Meanwhile, the Carbon Intensity Indicator (CII) evaluation results emphasize the urgent need for measures to reduce carbon emissions to meet the IMO’s 2030 standards.

1. Introduction

Improving the fuel efficiency of marine vessels not only optimizes operational performance but also substantially increases profitability in ship management, given that fuel expenses constitute one of the largest components of operating costs [1,2,3]. However, accurately predicting fuel consumption remains a challenging endeavor, as it is influenced by a multitude of external factors. These include the operational status of the main engine, the cargo weight, vessel draft, as well as dynamic sea and weather conditions [4,5].

The International Maritime Organization (IMO), as the principal authority responsible for developing international regulations for shipping, ensures that maritime operations minimize their environmental impact [6]. With the growing emphasis on reducing pollutant emissions within the shipping industry, the implementation of increasingly stringent IMO regulations, and the substantial cost of marine fuels, ship owners have been actively seeking strategies to optimize fuel consumption [7]. Reducing fuel consumption not only mitigates greenhouse gas emissions but also offers significant economic benefits through cost savings [8]. In response to the IMO environmental regulations, the Carbon Intensity Indicator (CII) has been introduced as a critical metric for evaluating ship performance [9,10].

Global warming, driven by greenhouse gas emissions and pollution, is among the most significant challenges facing the world today [11,12]. To meet the objectives set by the IMO, various strategies have been proposed. Among these, the adoption of alternative fuels (biofuels, hydrogen, and other synthetic fuels) and the optimization of vessel speed exhibit the greatest potential for practical implementation [13,14,15]. Considering the high costs associated with clean fuels in maritime transport, the industry must look beyond fuel alternatives and accelerate the adoption of digital solutions, such as artificial intelligence and machine learning (ML) [16]. These technologies have the potential to enhance operational efficiency, promote sustainability within the shipping sector, and significantly reduce overall operational costs.

ML is centered on empowering computers to derive meaningful models and patterns from data, thereby enhancing efficiency and accuracy across various processes [17,18]. ML offers advanced solutions to forecast, optimize operations, improve performance, and address complex challenges [19,20,21]. ML-based algorithms can be utilized to predict ship fuel consumption under varying operational and environmental conditions [22]. This capability enables ships to optimize fuel usage, thereby contributing to a reduction in greenhouse gas emissions from maritime transport [23]. ML can analyze data related to sea routes, weather conditions, and ship performance to optimize various operational parameters, including speed, trim, and equipment utilization [24,25,26]. This approach can significantly reduce fuel consumption while enhancing the overall efficiency of ships. Optimizing ship performance has a direct impact on cost reduction, efficiency enhancement, and minimizing environmental impacts, making advancements in this area particularly significant [27,28].

Ships are significant contributors to environmental pollution, emitting harmful substances such as sulfur oxides (SO_x), nitrogen oxides (NO_x), and carbon dioxide (CO₂). Accurate fuel-consumption predictions allows maritime industry stakeholders to develop and implement effective strategies aimed at reducing these emissions, thereby mitigating the environmental footprint of shipping operations [29].

Researchers utilize ML-based techniques to interpret, parse, and analyze complex datasets. Panda [30] explored the application of ML algorithms to address various challenges in coastal and marine environments. Their work includes predicting wave heights, estimating wind forces acting on ships, detecting structural damage to offshore rigs, calculating ship drag, and other related applications. Ship speed is a critical determinant of fuel consumption and plays a significant role in minimizing environmental impacts. Gharib and Kovács [31] investigated the application of fuzzy logic techniques to improve engine operation and facilitate the early detection of faults in marine engines. Their research proposed a versatile framework for managing engine performance. The findings indicated that using fuzzy logic-based control systems could significantly support predictive maintenance, minimizing equipment downtime, reducing maintenance expenses, and boosting operational efficiency. Beşikçi et al. [32] conducted a study to predict ship fuel consumption under various conditions and developed a decision support system to enhance energy efficiency using artificial neural networks (ANNs). The findings demonstrated that the ANN outperformed the multiple regression algorithm in predictive accuracy. The proposed method provides valuable support for ship operators in making informed economic and environmental decisions. Liu et al. [33] employed a combination of temporal convolutional networks and gated recurrent units to effectively model time-dependent patterns in the dataset, resulting in highly accurate ship fuel-consumption predictions. Berthelsen and Berthelsen [34] developed a hybrid model combining data-driven techniques with marine engineering principles. The model utilized a dataset of 50,000 samples collected from 88 oil tankers. The results indicated that the power required at speeds below the design speed was significantly lower than predicted by the cubic function. The study emphasized optimizing fuel consumption by adjusting ship speed and reducing carbon monoxide emissions.

Moreira et al. [35] employed the Levenberg–Marquardt algorithm, based on ANN, to develop a predictive model for ship speed and fuel consumption. The proposed method utilized a neural network trained on simulated data, which provided realistic ship performance data under varying sea conditions. This tool simulated datasets collected from actual ship operations to predict ship speed under different operational scenarios. The study demonstrated that neural networks could achieve acceptable accuracy in predicting both ship speed and fuel consumption. After evaluating the predictive performance of two algorithms (Levenberg–Marquardt and standard backpropagation), it was shown that accurate predictions could be made using only input data related to sea conditions, without relying on engine-specific parameters such as engine speed or torque. The comparison of the two algorithms revealed that their performance was similar in handling changes within the dataset’s internal structure. The primary objective of this research was to propose an accurate predictive approach and integrate it into ship-monitoring systems. Jeon et al. [36] developed a precise regression approach for forecasting main-engine fuel consumption by the ANN model and big data analytics. Their results demonstrated that the accuracy of ANN model outperformed both polynomial regression and support vector machines. An adaptive learning framework was proposed by Gao et al. [37] to improve fuel-consumption prediction in changing marine environments. It updates models incrementally using real-time data, enhancing responsiveness. Tests on liquefied-petroleum-gas carrier data showed a notable accuracy boost over standard machine learning methods. Lee et al. [38] introduced a predictive method using smart ship data to estimate fuel use and CO₂ emissions with high accuracy. It outperforms existing LSTM model, achieving up to 91.2% accuracy in gas mode.

A ship’s hydrodynamic performance evolves over its operational lifespan due to factors such as the accumulation of marine sediments on the hull and the type of antifouling paint used. Accurately estimating the relationship between required power and fuel consumption during a voyage necessitates thoroughly evaluating the ship’s hydrodynamic performance, as it is critical in optimizing energy efficiency and operational costs. Accurately estimating the relationship between required power and fuel consumption during a voyage also requires assessing a ship’s hydrodynamic performance [39]. Gupta et al. [40] employed three ML models to monitor the technical performance of a ship, calibrated using operational data from two similar vessels. These models were used to identify trends in hydrodynamic performance changes over time and predict these changes following surface cleaning of the propeller blades and hull. The predicted changes were subsequently compared against friction coefficients, providing valuable insights into the impact of maintenance activities on performance optimization.

Despite the advancements in ML techniques for predicting ship fuel consumption, significant gaps remain in the existing research. Most prior studies rely on conventional models such as ANN or regression-based methods, which often struggle to accurately capture the nonlinear and dynamic relationships between environmental and operational parameters. Additionally, while climate change has been acknowledged as a critical factor affecting maritime operations, existing models seldom integrate realistic climate scenarios, such as variations in sea-level rise, into their predictive frameworks. Furthermore, many studies focus on a single ship type, limiting the generalizability of their findings across different vessel categories. These gaps underline the need for more advanced, adaptive, and comprehensive approaches to address the growing complexity of maritime operations in the face of evolving environmental and regulatory challenges.

To address these gaps, this study proposes an innovative Emotional Artificial Neural Network (EANN) model as a robust predictive tool for estimating ship fuel consumption. By utilizing the unique hormonal adaptation mechanisms of the EANN framework, this research dynamically captures nonlinear and complex interactions between climatic and operational variables. A key innovation of this study is the integration of climate-change scenarios into the predictive framework, allowing for the assessment of future environmental impacts on ship performance. Additionally, the analysis includes two distinct ship types (a bulk carrier and a container ship) representing diverse operational profiles and design characteristics. This dual focus enhances the applicability and relevance of the findings to a broader range of maritime operations.

2. Methodology

This section outlines the methodological framework adopted to predict ship fuel consumption by integrating climate-change scenarios and an EANN model. The primary objective is to analyze the impact of key climatic variables, such as wave period, wind speed, and sea-level rise, on ship performance and fuel efficiency. By implementation of EANN’s capabilities, which excel at capturing complicated and nonlinear interactions, the study presents a reliable prediction method for fuel consumption under different operating and environmental situations. Two types of ships are considered for this analysis: a container ship, representing high-speed commercial vessels typically operating on fixed routes, and a bulk carrier, representing slower vessels often navigating variable routes.

The methodology adopted in this study is illustrated through a structured flowchart (Figure 1), showing the sequential steps required to predict ship fuel consumption under varying climatic and operational conditions. The process begins with data collection, where environmental data are extracted from the existing literature. The operational data are gathered from Automatic Identification Systems (AISs) and ship-monitoring systems. Following this, the collected data undergoes preprocessing, including cleaning, normalization, and integration to ensure compatibility for model input.

The next step involves conducting a sensitivity analysis to identify the most critical climatic variables impacting fuel consumption, thereby reducing model complexity and improving prediction accuracy. Subsequently, Feedforward Neural Network (FFNN) and EANN models are designed and trained using the processed data. Finally, the simulation results are analyzed under various climate scenarios to assess the impact of climate change on ship performance and to propose operational optimizations.

2.1. Data Collection and Preprocessing

This study focuses on the key climatic variables that significantly influence ship performance and fuel consumption under changing environmental conditions (

Table 1. Environmental data statistics.

Parameter	Statistical Characteristic	Value	References
Significant Wave Height (m)	Mean	0.9	[41]
	Standard Deviation	0.08
Mean Wave Period (s)	Mean	4.34	[41]
	Standard Deviation	0.98
Current Speed (cm/s)	Mean	4	[42]
	Standard Deviation	0.1
Wind Speed (m/s)	Mean	5.78	[43]
	Standard Deviation	1.12
Sea Level (m)	Mean	0.51	[44,45]
	Standard Deviation	0.05

). Wave period is a critical factor affecting hydrodynamic resistance and propulsion efficiency. Wind speed and direction play a crucial role in determining aerodynamic resistance, especially when interacting with the ship’s route and orientation. Ocean currents, characterized by their direction and magnitude, influence the propulsion system by altering the effective resistance against the vessel. Additionally, long-term changes in sea level can impact ship hydrodynamics, particularly in shallow waters or near coastal regions. These variables were carefully selected for their direct and measurable impact on ship performance, enabling the model to account for dynamic operational conditions and long-term climate-change scenarios.

Future climate scenarios up to 2050 are incorporated to evaluate the impact of scenarios. Spatially, the study focuses on the operational zones most relevant to the selected ships, including Red Sea.

Table 2. Ship-type characteristics and scenarios.

Characteristics	Bulk Carrier	Container Ship
Engine type	Two-stroke diesel	Four-stroke diesel
Fuel type	Marine Gas Oil	Marine Gas Oil
Engine power (kW)	30,000	35,000
Speed (knots)	14	22.5
DWT (ton)	56,907	49,844
Draft (m)	13	13
Length (m)	190	276
Width (m)	32	32
Load (%)	85 to 100	80 to 100
Voyage duration range (days)	4 to 10	7 to 13

represents the technical specifications and operational parameters for the bulk carrier and container ship vessels used in this study.

2.2. Machine Learning Models

2.2.1. FeedForward Neural Network

The FFNN, a subset of ANN models, has been extensively utilized for modeling various engineering systems. An FFNN typically comprises three types of layers: input, hidden, and output layers [46]. When trained using the Backpropagation (BP) algorithm, the explicit mathematical formulation for determining the network’s objective can be expressed as shown in Equation (1) [47].

$$\widehat{\mathrm{Y}}=\mathrm{f}\mathrm{j}\left[{\sum }_{h=1}^m w_{jh}\times {\mathrm{f}}_{\mathrm{h}}\left({\sum }_{h=1}^m w_{jh}{\mathrm{X}}_{\mathrm{i}}+\mathrm{w}\mathrm{h}\mathrm{b}\right)+{\mathrm{w}}_{\mathrm{j}\mathrm{b}}\right],$$

(1)

where i, h, j, b, and W represent the neurons of the input, hidden and output layers, the bias and weight applied (or bias) by the neuron, f_j, f_h represent the activation functions of the hidden layer and the output layer, respectively. x_i, n, and m represent the input value, input and hidden neuron numbers, respectively. y, j, and $\widehat{\mathrm{Y}}$ represent the observed and calculated values, respectively.

2.2.2. Emotional Artificial Neural Network

The EANN model represents an advanced generation of the traditional ANN framework. It introduces an artificial sensing unit capable of secreting hormones to dynamically regulate the functionality of nodes (neurons). These hormonal weights are adaptable and adjust according to the input and output values of the nodes [48].

As shown in Figure 1, each node within the EANN can continuously exchange information between the input and output components while generating dynamic hormonal responses. Initially, the coefficients are aligned based on the observed patterns between the inputs and outputs and are progressively refined during the model training process through iterative adjustments. These hormonal coefficients influence key node parameters such as the activation function, net function, and weights. In Figure 1, solid lines denote neural connections, while dotted lines represent hormonal communication pathways. The output of the EANN model, incorporating the three hormones H_a, H_b, and H_c, is mathematically described in Equation (2) [49].

$$Y_i=\stackrel{1}{\overbrace{({\lambda }_i+{\sum }_h {\sigma }_{i,h}{H}_h)}}\times f\stackrel{2}{\overbrace{\left({\sum }_j \left({\beta }_i+{\sum }_h {\xi }_{i,h}{H}_h\right)\right)}}\times \stackrel{3}{\overbrace{\left(\left({\theta }_{i,j}+{\mathsf{\Phi }}_{i,j,k}{H}_h\right)X_{i,j}\right)}}+\stackrel{4}{\overbrace{\left({\alpha }_i+{\sum }_h {\chi }_{i,h}{H}_h\right)}},$$

(2)

where h, i and j denote the input, hidden, and output layers, and f() denotes an activation function. Synthetic hormones are calculated as Equation (3).

$${\mathrm{H}}_{\mathrm{h}}={\sum }_{\mathrm{i}} {\mathrm{H}}_{\mathrm{i},\mathrm{h}}(\mathrm{h}=\mathrm{a},\mathrm{b},\mathrm{c}),$$

(3)

In Equation (2), the first part presents the statistical neural weight ${\lambda }_i$ and the hormonal weight $\sum _h {\sigma }_{i,h}{H}_h$ that are applied to the activation function (f()). The second and third parts are, respectively, related to the applied weights, the net function, and the input value $X_{i,j}$, resulting from neuron j of the previous layer. The fourth part is the pure performance bias, including the neural and hormonal weights ${\alpha }_i$, $\sum _h {\chi }_{i,h}{H}_h$, ${\mathsf{\Phi }}_{i,j,k}$, ${\xi }_{i,h}$, ${\sigma }_{i,h}$, and ${\chi }_{i,h}$. The parameters control the hormone level (H_h) in each hormone, which in turn gives the weight and the neuronal output (Y_i), as well as the hormonal feedback H_i,h, to the system (Equation (4)) [50].

$${\mathrm{H}}_{\mathrm{i},\mathrm{h}}={\mathrm{glandity} }_{\mathrm{i},\mathrm{h}}\times {\mathrm{Y}}_{\mathrm{i}},$$

(4)

The glandity factor in the EANN model must be calibrated during the training phase to ensure the secretion of appropriate hormone levels by the gland. Specific techniques can be employed to provide an initial estimate of the H_h hormone based on input samples, such as calculating the input mean or utilizing the characteristics of the training dataset. Subsequently, the hormone values are iteratively updated based on the network output (Y_i) to minimize the discrepancy between the estimated and observed noise levels, thereby achieving optimal hormonal regulation. In this study, the Emotional Backpropagation (EmBP) algorithm was utilized for network training, ensuring the efficient calibration of hormonal coefficients and glandity factors [51].

The Emotional Backpropagation (EmBP) algorithm enhances the traditional Backpropagation (BP) approach by integrating learning parameters, such as the learning factor (n) and the momentum rate (α), with sensitivity parameters, including the perturbation coefficient (μ) and the confidence coefficient (k). This combination aims to reduce both computational error and training time. The value of μ is influenced by the input patterns and the net output error during each iteration. Throughout the training process, μ gradually decreases while k increases, reaching the maximum level of the self-confidence hormone and the minimum level of the anxiety hormone at the end of training.

The EANN employs the same weight update mechanism as the BP algorithm. However, it conducts forward calculations exclusively during network convergence, with classification tasks performed in the output layer. In each iteration of the EmBP training process, the error at the output neuron (A) is propagated backward to adjust the normalized weights (w_jh) and biases (wj_b) in the hidden layer, as described by Equations (5) and (6) [52].

$${\mathrm{W}}_{\mathrm{j}\mathrm{h}}\left(\mathrm{new}\right)={\mathrm{w}}_{\mathrm{j}\mathrm{h}}\left(\mathrm{old}\right)+\mu .\mathsf{\Delta }.{\mathrm{Y}\mathrm{H}}_{\mathrm{h}}+\alpha .\left[{\delta }_{\mathrm{w}\mathrm{j}\mathrm{h}}\left(\mathrm{old}\right)\right],$$

(5)

$$\mathrm{W}\mathrm{j}\mathrm{b}\left(\mathrm{new}\right)=\mathrm{w}\mathrm{j}\mathrm{b}\left(\mathrm{old}\right)+\mu .\mathsf{\Delta }+\alpha .\left[\delta \mathrm{w}\mathrm{j}\mathrm{b}\right(\mathrm{old}\left)\right].$$

(6)

The hormonal system functions as a mechanism that modulates the rate of learning, either enhancing or diminishing it. The hormone level increases when a specific input pattern results in a notable prediction error or signals an environmental shift (such as a rise in sea level or an anomaly in wind speed). Significant weight alterations facilitate the network’s rapid adaptation, thereby enhancing its plasticity. Conversely, the hormone level decreases gradually and stabilizes the learning process when predictions are accurate and reliable. This adaptive behavior helps the EANN avoid overfitting to noise by remaining responsive to pertinent climatic and operational anomalies.

In the EANN unit method (Figure 1), the integer values a, b, c, and d correspond to the neural elements of the input weights, net function, activation function, and output unit, respectively, analogous to their roles in a classical FFNN. Additionally, e, f, g, and h represent the net output weight, the hormonal gland (H_h), and the input and output hormone units, respectively. Furthermore, i, j, and k denote the net hormone unit, the hormone activation function, the net function, and the input static weight. These components collectively form the structural and functional framework of the EANN model, integrating neural and hormonal elements to enhance computational performance and adaptability. The models were assessed on Windows 10 with an Intel Core i7 processor, 16 GB RAM, and an NVIDIA RTX 3090 GPU.

Figure 1. Framework of the fuel consumption using FANN and EANN unit.

Figure 1. Framework of the fuel consumption using FANN and EANN unit.

2.3. Correlation Analysis and Variance Inflation Factor

Correlation analysis was employed to assess the linear and rank-based relationships among the input parameters to ensure their independence and suitability for inclusion in the model [53]. The Pearson correlation coefficient (r) quantifies the linear relationship between two variables (Equation (7)) [54].

$$r={\displaystyle \frac{\sum \left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{\sum {\left(x_i-\bar{x}\right)}^2\sum {\left(y_i-\bar{y}\right)}^2}}},$$

(7)

where $x_i$ and $y_i$ are the observed values of two parameters, and $\bar{x}$ and $\bar{y}$ are their respective means. The Spearman rank correlation coefficient ($\rho$) evaluates monotonic relationships by comparing ranks instead of actual values, computed (Equation (8)) [55].

$$\rho =1-{\displaystyle \frac{6\sum d_i^2}{\left(n^2-1\right)}},$$

(8)

where $d_i$ is the difference between the ranks of two variables, and $n$ is the total number of observations. Coefficients close to zero $\left(\right|r|,|\rho |<0.7)$ indicate weak or negligible relationships, confirming the independence of parameters [56].

To quantify multicollinearity among input variables, the Variance Inflation Factor (VIF) was computed. The VIF for each parameter is defined as Equation (9) [57].

$${\mathrm{V}\mathrm{I}\mathrm{F}}_i={\displaystyle \frac{1}{1-R_i^2}},$$

(9)

where $R_i^2$ is the coefficient of determination obtained by regressing the $i$-th variable against all other variables. A VIF > 5 indicates a significant degree of multicollinearity. Parameters with high VIF values were carefully examined and, if necessary, excluded or adjusted to preserve the model’s robustness and interpretability.

2.4. Sensitivity Analysis

Sensitivity analysis is employed to quantify the impact of individual input variables on the output of the predictive model. In this study, the Sobol index method is utilized due to its ability to capture nonlinear interactions between input variables and their relative importance. The Sobol method decomposes the variance of the output into contributions attributed to individual input variables and their interactions [58].

Given a model $f\left(X\right)$ that predicts fuel consumption, where $X=\left(x_1,x_2,\dots ,x_n\right)$ represents the set of input variables, the total variance $V$ of the model output can be expressed as Equation (10).

$$V=\int \left(f\right(X)-\mathbb{E}[f\left(X\right)\left]{)}^{2}p\right(X)dX,$$

(10)

where $\mathbb{E}\left[f\right(X\left)\right]$ is the expected value of the model output and $p\left(X\right)$ is the joint probability density function of the inputs.

The first-order Sobol index $S_i$ measures the contribution of a single input variable $x_i$ to the total variance (Equation (11)) [59].

$$S_i={\displaystyle \frac{V_i}{V}},$$

(11)

where $V_i=\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathbb{E}\left[f\left(X\right)\mid x_i\right]\right)$ is the variance of the conditional expectation of $f\left(X\right)$ given $x_i$.

The total Sobol index $S_{T_i}$ accounts for both the individual contribution of $x_i$ and its interactions with other variables (Equation (12)) [60].

$$S_{T_i}=1-{\displaystyle \frac{V_{\sim i}}{V}},$$

(12)

where $V_{\sim i}$ represents the variance of the model output excluding $x_i$.

2.5. Carbon Intensity Indicator (CII)

The Carbon Intensity Indicator (CII) is introduced to measure and regulate the environmental performance of ships. It evaluates the operational carbon intensity of a vessel, defined as the amount of CO₂ emitted per unit of cargo transported over a nautical mile (Equation (13)) [10].

$$CII={\displaystyle \frac{M_{\mathrm{C}\mathrm{O}2}}{W\times D}},$$

(13)

where M_CO2 the total mass of CO₂ emissions during a specific operational period, W is the vessel’s deadweight tonnage, and D is the total distance traveled by the ship. To calculate M_CO2, the fuel consumption of the vessel is converted into CO₂ emissions using Equation (14) [10].

$$M_{\mathrm{C}\mathrm{O}2}=F_{\mathrm{fuel} }\times E{F}_{\mathrm{fuel}},$$

(14)

where $F_{\mathrm{fuel} }$ is the total fuel consumed, and $E{F}_{\mathrm{fuel}}$ is the emission factor specific to the type of fuel used, as provided by the IMO. The CII calculation integrates operational data such as speed, load, and environmental conditions, which significantly impact fuel consumption and emissions. Higher speeds typically increase fuel consumption, leading to a higher M_CO2 and a smaller CII value. Similarly, operating at partial load reduces fuel efficiency, affecting both W and the CII. Adverse weather conditions, such as strong winds and high waves, add resistance, further increasing fuel consumption.

3. Results

The input parameters selected for the FFNN and EANN models are wave period, wind speed, wind direction, currents speed, water depth, vessel speed, vessel cargo load, and vessel engine power. These parameters serve as critical inputs to the models, enabling accurate predictions under varying environmental and operational conditions. The output parameter of the models is the ship’s fuel consumption, which is predicted based on the relationship between the input variables and the ship’s performance.

3.1. Analysis of Parameter Independence

To ensure the avoidance of redundancy in model inputs, the independence of the parameters was assessed.

Table 3. The results of input variables independence analysis.

Input Variable	r (Max Pair)	$\mathit{\rho }$ (Max Pair)	(VIF)
Wave period	0.28	0.32	2.44
Wind speed	0.05	0.07	1.11
Wind direction	0.08	0.09	1.13
Currents speed	0.16	0.20	2.59
Water depth	0.22	0.25	1.05
Vessel speed	0.11	0.14	1.29
Vessel cargo load	0.10	0.12	1.15
Vessel engine power	0.09	0.11	2.10

presents the results of the correlation analysis and VIF for the input parameters.

The results indicate that all parameters exhibit low pairwise correlations, with Pearson and Spearman coefficients remaining well below the threshold of 0.7. Similarly, the VIF values for all parameters are below 5, confirming that multicollinearity is not a concern. These findings confirm that the model inputs are independent, ensuring unbiased and efficient learning for the FFNN and EANN models.

3.2. The Results of Sensitivity Analysis

The results of the analysis are presented in

Table 4. The results of fuel-consumption sensitivity to input parameters.

Input Variable	${\mathit{S}}_{\mathit{i}}$	${\mathit{S}}_{{\mathit{T}}_{\mathit{i}}}$
Wave period	0.10	0.14
Wind speed	0.12	0.18
Wind direction	0.07	0.11
Currents speed	0.14	0.19
Water depth	0.08	0.10
Vessel speed	0.24	0.33
Vessel cargo load	0.17	0.09
Vessel engine power	0.23	0.27

. The first-order Sobol index highlights the direct influence of each parameter on fuel consumption, while the total Sobol index captures both direct and interactive effects.

The sensitivity analysis reveals that vessel speed is the most influential parameter, with the highest first-order (0.25) and total-order Sobol indices (0.33), indicating both a direct and interactive influence on fuel consumption. Vessel engine power also show considerable contributions, with total Sobol indices of 0.23 and 0.27, respectively.

A second-order Sobol sensitivity examination was carried out to further investigate how variable interactions affect ship fuel consumption. Input variable pairs’ second-order Sobol indices are displayed in the interaction matrix in

Table 5. Pairwise interaction effects on fuel consumption using second-order Sobol sensitivity indices.

	Wave Period	Wind Speed	Wind Direction	Currents Speed	Water Depth	Vessel Speed	Cargo Load	Engine Power
Wave Period	–	0.03	0.015	0.025	0.02	0.065	0.018	0.022
Wind Speed	0.03	–	0.014	0.05	0.035	0.06	0.02	0.024
Wind Direction	0.015	0.014	–	0.018	0.012	0.032	0.013	0.01
Currents Speed	0.025	0.05	0.018	–	0.026	0.048	0.017	0.021
Water Depth	0.02	0.035	0.012	0.026	–	0.052	0.019	0.023
Vessel Speed	0.065	0.06	0.032	0.048	0.052	–	0.045	0.074
Cargo Load	0.018	0.02	0.013	0.017	0.019	0.045	–	0.035
Engine Power	0.022	0.024	0.01	0.021	0.023	0.074	0.035	–

.

3.3. ML Model Results

This section presents a summary of the machine learning (ML) model results for estimating ship fuel consumption under varying climate-change scenarios. These scenarios were analyzed through simulations conducted using the NAPA 2020.1 software.

Table 6. Climate-change scenario for environmental input data.

Parameter	Range	Units
Wave period	5–10	s
Wind speed	0–20	m/s
Currents speed	0–5	cm/s
Sea-level rise	0.05–0.20	m

outlines the ranges of environmental input variables applied in the implementation of the climate-change scenarios.

Figure 2 illustrates the relationship between ship fuel consumption and vessel speed based on both observational data and simulation outcomes. Given the significant influence of vessel speed on fuel usage, Figure 3 presents a detailed fuel–speed profile. The results demonstrate that under projected climate change scenarios, fuel consumption increases considerably for both bulk carriers and container ships. In line with IMO standards, these findings underscore the necessity for operational optimization to mitigate fuel usage and reduce atmospheric emissions. Climate-change conditions result in a 22% increase in fuel consumption for bulk carriers and a 19% increase for container ships.

Bulk carriers exhibit a lower average fuel consumption compared to container ships. The bulk carrier’s fuel consumption generally ranges between 20 and 120 tons/day, while container ships operate within a broader range, extending from 40 to 160 tons/day. This disparity can be attributed to the differences in design, operational profiles, and the cargo handling requirements of the two ship types. Container ships, which are designed for higher speeds and more complex logistical operations, naturally consume more fuel than bulk carriers, which typically operate at lower speeds and transport bulk goods.

3.3.1. FFNN Model

The FFNN model demonstrates a moderate ability to predict the fuel consumption of bulk carriers, as shown in Figure 3a. While the predicted values generally follow the primary data trends, there are noticeable deviations in regions with higher variability.

The scatter plot in Figure 3b shows a significant spread of points around the diagonal line, indicating that the FFNN model fails to consistently predict accurate values. The R-squared value, approximately 0.90, suggests a reasonable fit; however, this metric alone does not capture the extent of errors in individual predictions. Figure 3c further highlights the limitations of the FFNN model, with absolute errors reaching up to 0.6. This error margin, especially for high-consumption values, raises concerns about the model’s reliability under varying operational conditions.

The performance of the FFNN model for container ships, as illustrated in Figure 4a, shows even greater limitations compared to bulk carriers. The predicted values deviate significantly from the primary data, particularly in the upper range of fuel consumption (above 120 tons/day).

In Figure 4b, the scatter plot reveals a broader dispersion of points around the diagonal line compared to bulk carriers, indicating less accurate predictions. The R-squared value of approximately 0.88, while still relatively high, does not fully account for the significant prediction errors. Figure 4c underscores the model’s shortcomings, with absolute errors frequently exceeding 0.4. The high error levels in both typical and extreme conditions demonstrate the FFNN model’s limited capacity to generalize across diverse scenarios, making it less reliable for practical applications.

3.3.2. EANN Model

The EANN model significantly outperforms the FFNN model in predicting fuel consumption for bulk carriers. As shown in Figure 5a, the predicted values exhibit an almost perfect alignment with the primary data across all data points. Unlike the FFNN model, the EANN model effectively captures the nonlinear relationships in the data, even in regions of high variability.

The scatter plot presented in Figure 5b demonstrates the predictive accuracy of the EANN model, with data points closely aligned along the diagonal, indicating a strong agreement between observed and predicted values. An R² value of approximately 0.95 confirms a high level of correlation, underscoring the model’s robustness in capturing the complex patterns in fuel consumption. This is further substantiated by Figure 5c, which shows that the majority of absolute prediction errors remain below 0.2 tons/day.

For container ships, the EANN model also achieves outstanding predictive performance. In Figure 6a, the predicted values align closely with the primary data, even in the upper consumption range where the FFNN model failed to provide accurate predictions.

The scatter plot in Figure 6b shows an even tighter clustering of points around the diagonal line compared to the FFNN model, with an R-squared value of approximately 0.93. This improvement is a testament to the EANN model’s ability to generalize effectively across diverse conditions. Figure 6c highlights a marked reduction in absolute errors, with most values falling below 0.2 tons/day. The EANN model’s low error margins across the entire data range make it a reliable tool for fuel-consumption estimation, particularly in scenarios with high variability.

3.3.3. Comparative Analysis

The FFNN model’s limitations are evident in its inability to accurately predict fuel consumption for both bulk carriers and container ships, particularly under high-consumption or highly variable conditions. This is reflected in the larger error margins and greater deviation from the primary data. In contrast, the EANN model demonstrates a clear superiority, achieving higher R-squared values and significantly lower absolute errors.

The performance evaluation of FFNN and EANN models for predicting fuel consumption in bulk carriers and container ships is presented in

Table 7. FFNN and EANN models’ performance evaluation and computational cost.

Model	Ship Type	Phase	MSE (tons/day)	RMSE (tons/day)	MAPE	Computational Cost (s)
FFNN	Bulk carrier	Train	71.42	9.07	13.47	1000
		Test	79.05	9.91	14.89	650
	Container ship	Train	73.18	9.15	11.97	1100
		Test	80.51	10.18	13.01	800
EANN	Bulk carrier	Train	26.55	5.15	7.68	1300
		Test	30.01	5.71	8.23	800
	Container ship	Train	27.55	5.19	6.69	1450
		Test	30.92	5.97	7.51	900

. The results indicate significant differences in the predictive capabilities of the two models. The FFNN model demonstrates limited accuracy, with high error metrics across both training and testing phases. For bulk carriers, the FFNN model yields a Mean Squared Error (MSE) of 71.42 tons/day in the training phase, which increases to 79.05 tons/day in the testing phase. Similarly, the Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) are 9.07 tons/day and 13.47%, respectively, during training and increase to 9.91 tons/day and 14.89% in testing. A similar trend is observed for container ships, where the FFNN model achieves an MSE of 73.18 tons/day in training and 80.51 tons/day in testing. The corresponding RMSE values are 9.15 tons/day and 10.18 tons/day, while the MAPE values are 11.97% and 13.01%.

In contrast, the EANN model significantly outperforms the FFNN model, showcasing superior predictive capabilities. For bulk carriers, the EANN model achieves an MSE of 26.55 tons/day in the training phase and 30.01 tons/day in the testing phase. The RMSE values are notably lower, at 5.15 tons/day during training and 5.71 tons/day during testing. The MAPE values are also reduced, with 7.68% in training and 8.23% in testing. Similar improvements are observed for container ships, where the EANN model achieves an MSE of 27.55 tons/day in training and 30.92 tons/day in testing. The RMSE and MAPE values for container ships are 5.19 tons/day and 6.69% during training, increasing slightly to 5.97 tons/day and 7.51% in testing.

The comparison of model performance across ship types reveals that the EANN model consistently outperforms the FFNN model in all metrics. For bulk carriers, the EANN model reduces the MSE by over 60% compared to the FFNN model in both training and testing phases. A similar improvement is observed for container ships, with the EANN model achieving significantly lower error rates.

The performance results of the proposed EANN model and also the FFNN model are consistent with the research results of Li et al. [61] so that the MSE index for the decision tree model, random forest, support vector machine, and ANN is 68, 20.35, 63.7, and 42.5 tons/day, respectively.

3.4. The Results of Carbon Emission

Figure 7 and Figure 8 provide a comprehensive evaluation of the CII for both bulk carriers and container ships, respectively, assessing their alignment with the IMO’s required CII standards for 2030 under current operational conditions and climate change scenarios.

Figure 7a presents the IMO guideline for the required CII in 2030, alongside the reference line showing the relationship between dead weight tonnage (DWT) and CII. Figure 7b compares the current state of bulk carriers’ CII with the 2030 required standard, as well as the potential impact of climate-change scenarios. The data points for the current state and climate-change scenarios show that the bulk carriers are predominantly above the 2030 required CII line, suggesting that their fuel consumption and carbon emissions will likely exceed the IMO’s target by 2030, under current and projected operational conditions. This discrepancy indicates the need for operational optimization and technological advancements to meet the IMO’s CII regulations.

Figure 8a illustrates the IMO guidelines for container ships. In contrast, Figure 8b shows that the CII values for container ships, under both current and climate-change scenarios, consistently exceed the required CII threshold for 2030. These results showed the significant challenges faced by container ships in reducing their carbon intensity, which are compounded by both inherent operational characteristics and the influence of dynamic environmental factors.

The comparison of current and projected CII values for both bulk carriers and container ships reveals a concerning trend, with the impact of climate change, the required CII standards for 2030 set by the IMO are unlikely to be met.

Various techniques have been introduced to comply with the rigorous IMO standards and diminish carbon emissions. These encompass speed optimization and dynamic speed profiles. Reducing speed, particularly for long-term voyages, can significantly decrease fuel consumption without major disruptions to the schedule [62]. Meanwhile, vessels can dynamically adjust their speeds based on real environmental conditions, including weather forecasts, sea states, and the ship’s fuel-consumption rate [63]. Another method of reducing ship fuel consumption and consequently reducing pollutant emissions is exhaust gas cleaning systems (scrubbers). Retrofitting scrubbers can help reduce sulfur emissions and comply with the IMO’s sulfur cap regulations [64]. In addition, incorporating hybrid propulsion systems or transitioning to alternative fuels such as liquefied natural gas (LNG), methanol, or biofuels can reduce overall carbon emissions. Using battery–electric propulsion or the implementation of fuel cells into ship systems helps to lower dependence on conventional fuels [65,66]. However, alternative fuels usually have high costs. According to the marginal abatement cost approach a carbon price of USD 300–800 per ton of CO₂ emission is required to close the cost difference with conventional fuel-powered vessels, allowing for the use of alternative fuels economically [67].

4. Conclusions

This study presents an advanced approach to predicting ship fuel consumption using the EANN model. The integration of key climatic variables such as wave period, wind speed, and sea-level rise with operational data provides a comprehensive framework for assessing the impacts of climate change on maritime performance.

The results demonstrate the clear advantages of the EANN model over the FFNN model. For bulk carriers, the EANN model reduced the testing MSE from 79.05 tons/day to 30.01 tons/day, while for container ships, the reduction was from 80.51 tons/day to 30.92 tons/day. These improvements were also evident in RMSE and MAPE metrics, where the EANN model consistently outperformed the FFNN model, achieving reductions of over 40% in error rates. These findings highlight the EANN model’s ability to capture nonlinear relationships and dynamic interactions between input variables, which are critical for accurate fuel-consumption predictions.

Sensitivity analysis further revealed that vessel speed, with a total Sobol index of 0.33, is the most significant factor influencing fuel consumption. This insight emphasizes the importance of optimizing speed management to improve fuel efficiency. Other parameters, such as engine power and wave period, also demonstrated considerable contributions, underscoring the need for holistic optimization strategies.

Simulations incorporating climate-change scenarios highlighted the potential challenges posed by environmental changes. Bulk carriers and container ships experienced average fuel consumption increases of 22% and 19%, respectively, under simulated conditions. These findings emphasize the need for proactive measures, including route optimization, speed adjustment, and the adoption of energy-efficient technologies, to mitigate the impact of climate change on shipping operations. The results demonstrated that the necessity of adopting measures to reduce carbon emissions. These measures could include optimizing ship speed, improving fuel efficiency, and incorporating alternative fuels to align with the IMO’s 2030 standards. The results underline the critical need for further research and practical solutions to enhance the environmental performance of maritime vessels and achieve the stringent emission targets set for the industry in the coming years.

This research provides a novel predictive framework that combines the strengths of machine learning and environmental modeling. The EANN model offers a powerful tool for the maritime industry to optimize operations, reduce fuel consumption, and achieve compliance with IMO environmental standards. While this study demonstrates the effectiveness of the EANN model in predicting ship fuel consumption, certain limitations should be mentioned. The accuracy of the model relies on the quality and comprehensiveness of the input data. Limited access to real-time operational data, particularly for smaller or less-monitored ships, may affect model performance in broader applications. Although the study incorporates climate-change scenarios by varying key environmental parameters, these scenarios do not fully account for regional variations or the combined effects of extreme weather events, such as tropical storms or cyclones. The study focuses on two ship types. The findings may not directly apply to other vessel types, such as tankers or passenger ships, which have unique operational profiles. Meanwhile, this study utilizes AIS data to predict ship fuel consumption, but there are some limitations and challenges related to the ethical and logistical aspects of using these data. One of the limitations is privacy concerns, especially with regard to the identification of ships and their locations through publicly available AIS data. To address these concerns, the study used anonymous data and publicly available information.

For future studies, researchers could incorporating real-time data from ship sensors, weather-forecasting systems, and AIS could enhance the accuracy and adaptability of fuel-consumption predictions. Extending the analysis to include other ship types, such as oil tankers, LNG carriers, and passenger vessels, would provide broader insights into the model’s applicability. Future studies could integrate economic factors, such as fuel pricing, and emissions-related constraints into the predictive framework, providing a comprehensive tool for decision making. In addition the studies could explore the integration of hull-fouling parameters into predictive models of ship fuel consumption. Incorporating indicators of fouling severity into machine learning models may improve prediction accuracy, particularly in long-term operational assessments.