Improving Ship Fuel Consumption and Carbon Intensity Prediction Accuracy Based on a Long Short-Term Memory Model with Self-Attention Mechanism

Abstract

The prediction of fuel consumption and Carbon Intensity Index (CII) of ships is crucial for optimizing decarbonization strategies in the maritime industry. This study proposes a ship fuel consumption prediction model based on the Long Short-Term Memory with Self-Attention Mechanism (SA-LSTM). The model is applied to a container ship of 2400 TEU to predict its hourly fuel consumption, hourly CII, and annual CII rating. Four different feature sets are selected from these data sources and are used as inputs for SA-LSTM and another ten models. The results demonstrate that the SA-LSTM model outperforms the other models in prediction accuracy. Specifically, the Mean Absolute Percentage Error (MAPE) for fuel consumption predictions using the SA-LSTM model is reduced by up to 20% compared to the XGBoost and by up to 12% compared to the LSTM model. Additionally, the SA-LSTM model achieves the highest accuracy in annual CII predictions.

1. Introduction

The shipping industry is a significant source of global greenhouse gases, contributing 2.89% of global carbon emissions [1]. The IMO adopted the 2023 IMO Strategy on Reduction of GHG Emissions from Ships, which sets explicit phased targets for reducing both the total amount and intensity of ship carbon emissions, aiming for near-zero emissions by around 2050. The IMO has introduced a series of short-term, medium-term, and long-term measures to promote emission reductions. A key short-term measure is reducing the carbon emission intensity of ships [2]. From 1 January 2023, ships with a gross tonnage exceeding 5000 engaged in international navigation must comply with the Operational Carbon Intensity Index (CII) rating, which increases by 2% annually until 2026 (BIMCO, 2022). Ships that fail to meet the required ratings will need to make necessary adjustments, which could impact their operations, leasing, and sales [3].

Accurately forecasting ship carbon intensity and its rating is essential for effectively managing and controlling ship CII ratings [4]. The key to predicting a ship’s carbon intensity lies in forecasting its fuel consumption. By converting fuel consumption into carbon emissions and considering the sailing distance and capacity of the ship, the carbon emission intensity can be calculated. Ship carbon intensity can be measured on various time scales, including hourly, daily, and annually, with annual carbon intensity being the critical data for determining the ship’s CII rating.

The fuel consumption of ships is not only closely related to the operating cost of the ship, but it also has a significant connection with the ship’s carbon emissions. Hence, the research on ship fuel consumption prediction has received wide attention [5,6,7,8]. With the increasing availability of data, more researchers are using machine learning techniques to predict ship fuel consumption. Wang et al. (2018) employed the Least Absolute Shrinkage and Selection Operator (LASSO) regression algorithm, which proved particularly effective. The results demonstrated that the LASSO regression model had a superior prediction performance when compared to neural networks and support vector regression [9]. Jeon et al. (2018) investigated the Artificial Neural Network (ANN) model and found that it a had higher prediction accuracy for main engine fuel consumption than polynomial regression and support vector machines [10]. Ren et al. (2022) examined the ridge regression model with four different datasets, including Automatic Identification System (AIS) data, Measurement, Reporting and Verification (MRV) data, and MRV-normalized data. They found that the model based on MRV reports achieved the optimal result [11]. Li et al. (2022) compared the results of various prediction models under different combinations of data source such as nautical logs, meteorological data, and AIS data [12,13,14]. Uyanık et al. (2020) also investigated several fuel consumption prediction models, for example, the kernel ridge regression, Bayesian ridge regression, and Adaboost. They found that the ridge regression model had greater accuracy [15].

However, there are not too many studies that focuses on applying deep learning methods to ship fuel consumption prediction. In 2017, Google put forward the Transformer model based on the self-attention mechanism, which enhanced the accuracy of 11 Natural Language Processing (NLP) tasks [16]. Since then, the self-attention mechanism has been introduced in many fields and scenarios, achieving remarkable research results. For instance, Liu et al. (2022) proposed a prediction model based on Long Short-Term Memory (LSTM) and the spatial attention mechanism, which effectively enhanced the accuracy of power consumption prediction in the raw cement material grinding system [17]. Han et al. (2022) proposed a load classification Long Short-Term Memory with Self-Attention Mechanism (SA-LSTM) model in response to the problems of category imbalance and insufficient performance of the classification model in user load classification [18]. Cai et al. (2024) presented a method based on the self-attention long short-term memory network to investigate the problem of dam deformation prediction, and the results indicated that this approach achieved relatively good prediction effects on the actual dam deformation data [19]. Hu et al. (2024) employed a new model combining the long short-term memory network and the self-attention mechanism to address the accuracy problem of photovoltaic power generation output prediction, especially under the influence of weather conditions [20]. Rao et al. (2023) presented a new type of statistical model called non-linear function-on-function regression and found it is effective for analyzing complicated data through simulations and real-world examples [21].

However, relevant research in the shipping carbon emission reduction field is still rather rare [22,23,24,25,26,27]. Since the prediction of fuel consumption and carbon intensity possesses temporal characteristics [28], the LSTM model can capture the short-term dependency relationship in the sequence, but there may be certain limitations in handling long-term dependency relationships. The self-attention mechanism can effectively capture the long-distance dependency relationship between different positions in the sequence. Introducing the self-attention mechanism increases the model’s ability to model the overall information of the sequence, making it more suitable for processing ship operation data that contains long-term dependencies. Therefore, the SA-LSTM model with the introduction of the self-attention mechanism may have the potential to further improve the accuracy of ship fuel consumption prediction.

The main objectives of this study are to investigate the impact of the self-attention mechanism on the LSTM model and to evaluate the performance of the SA-LSTM model in predicting ship fuel consumption using multi-source heterogeneous data, including AIS data, fuel flow sensor data, meteorological data, and sea condition data.

This study is one of the few studies that investigates the application of the self-attention mechanism and LSTM model in predicting ship fuel consumption. It considerably improved the prediction accuracy as compared to most machine learning methods and traditional LSTM models.

The organization of the paper is as follows: Section 1 introduces the research background of this paper and a review of relevant literature. Section 2 introduces the main data and processing of this research. Section 3 introduces the main methodological approach in this research. Section 4 takes a container ship equipped with multiple sensing devices as an example to comparatively analyze the fuel consumption and carbon intensity prediction results of various methods. Finally, relevant discussions are conducted and the conclusions of this paper are summarized.

2. Data Acquisition and Processing

The principal data examined in this study include ship AIS data, sensor data, and meteorological and sea condition data. The meteorological and sea condition data are collected hourly with a spatio-temporal resolution of 0.25° × 0.25°. AIS and sensor data are processed to match this spatio-temporal resolution through aggregation and interpolation.

2.1. AIS Data Acquisition and Processing

AIS data consist of dynamic and static information. Due to various factors, such as weather, location, and equipment, the update frequency of AIS data varies, leading to significant data gaps in some areas. To address this, linear interpolation is employed to fill in missing data, interpolating longitude, latitude, and speed every five minutes. The ship’s sailing distance is calculated by altering the longitude and latitude of adjacent AIS points in the interpolated data. Given the hourly collection frequency of meteorological and sea condition data, the AIS data are aggregated hourly to maintain consistent time resolution.

2.2. Sensor Data Acquisition and Processing

Real-time data related to ships are acquired through various sensors. The real-time fuel consumption data of the ship’s main engine, auxiliary engine, and boiler are obtained using mass flowmeters. Sensor data also provide information on the ship’s main engine speed and trim. The original units for heavy and light oil data (kg/h) are converted to kg based on each data time interval. Missing values in the fuel consumption data are addressed using linear interpolation, interpolating fuel consumption, speed, and trim data with a one-hour interval.

2.3. Navigational Environment Data Acquisition and Processing

Navigational environment data (included meteorological and sea condition data) are sourced from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Copernicus Marine Service. These data are collected hourly and downloaded in grid format (0.25° × 0.25°).

Meteorological and sea condition data are matched with the longitude, latitude, and time in AIS. Wind speed and current rate components are combined to determine the actual wind speed, wind direction, current speed, and current direction. The relative direction of the case ship is calculated by combing course and direction data. Three parts of the data are fused based on time in Figure 1.

3. Methodological Approach

3.1. Carbon Intensity Prediction Methodology

This article begins by cleansing and preprocessing ship AIS data, sensor data, meteorological data, and sea condition data, followed by spatio-temporal fusion. Next, it extracts relevant features and examines their correlations. The data are then divided into a training set and a test set based on a 0.75:0.25 time series split. Using the devised SA-LSTM model, the study compares its performance with traditional machine learning models [29,30,31]. The hyperparameters of the different models are optimized using Bayesian search and cross-validation. Figure 2 illustrates the overall methodology for ship CII prediction.

3.2. Ship Fuel Consumption Prediction Model Based on SA-LSTM

Due to the successful application of the SA-LSTM model in previous studies across various fields, this paper considers applying it to predict ship fuel consumption. This model can concurrently consider information from each time step within a sequence and dynamically adjust based on the significance of elements in the sequence, effectively capturing patterns and trends in the time series data. The self-attention mechanism, originating from the Transformer model, weighs elements at different positions in a sequence to determine their importance. The structure of the SA-LSTM model used in this study is depicted in Figure 3.

In the SA-LSTM model, the self-attention mechanism is integrated into the LSTM model to enhance the model’s ability to focus on information at various positions in the sequence, thereby better capturing long-distance dependencies within the sequence. The introduction of the self-attention mechanism involves the following steps:

(1) Input Sequence Representation: The sequence signifying the ship’s operating parameters is presented as $X=x_1,x_2\dots ,x_t$, where t is the sequence length.

(2) Setting queries, keys, and values: For any given input, first set the weights $W^q$, $W^k$, $W^v$ of the query, key, and value, respectively, and transform the input linearly to obtain the corresponding results $Q$, $K$, and $V$, and the expression is:

$$\left\{\begin{array}{l}Q=W^{q}X\\ K=W^{k}X\\ V=W^{v}X\end{array}\right.$$

(1)

Embedding the input sequence, mapping each parameter, x_i, to a vector in a high-dimensional space, $E(X)=e_1,e_2,\dots e_t$. According to the high-dimensional mapping, it can assist the model in better comprehending the relationships among different parameters.

(3) Self-attention calculation: Evaluates the correlation, $S$, between the $Q$ and $K$, and then performs a softmax operation on each row of the attention score matrix, $S$, to obtain the attention weight matrix, $A$. The specific calculation formula is as follows:

$$\left\{\begin{array}{l}S(q,k)=v\ast \tanh (W_{q}Q+W_{k}K)\\ A=\mathrm{softmax}(S(q,k))\end{array}\right.$$

(2)

where $v$ is the learnable vector, $\tanh$ is the activation function, and $W_q$ and $W_k$ are the learnable parameters.

(4) Attention-weighted representation: Use the attention weights to perform a weighted sum of the embedded vectors to obtain the attention-weighted representation vector, $C$, at each position.

$$C=A(Q,K,V)=\mathrm{softmax}(S(q,k))V$$

(3)

where $C$ is the attention-weighted representation vector.

(5) Combination with the LSTM model: Input the obtained attention-weighted representation vector, $C$, into the LSTM model as its input sequence. SA-LSTM can capture the long-term dependency relationships in the sequence through the recursive operation of the time step, $t$, and the recursive formula is as follows:

$$\left\{\begin{array}{l}{i}_t=\sigma \left(W_{ii}·x_t+b_{ii}+W_{hi}·h_{t-1}+b_{hi}\right),\\ f_t=\sigma \left(W_{if}·x_t+b_{if}+W_{hf}\cdot h_{t-1}+b_{hf}\right),\\ g_t=\tanh (W_{ig}\cdot x_t+b_{ig}+W_{hg}\cdot h_{t-1}+b_{hg}),\\ o_t=\sigma (W_{io}\cdot x_t+b_{io}+W_{ho}\cdot h_{t-1}+b_{ho}),\\ c_t=f_t+c_{t-1}+i_t·g_{t,}\\ h_t=o_t·\tanh \left(c_t\right),\end{array}\right.$$

(4)

where the parameters in Equation (4) are described as follows in the

Table 1. Interpretation of the parameters in Equation (4).

Parameters	Interpretation
$i_t$	input gate
$f_t$	forget gate
$g_t$	cell state
$o_t$	output gate
$\sigma$	activation function
$W_{ii}$	the weight matrix from $x_t$ to the input gate $i_t$
$x_t$	the input at the current time step
$b_{ii}$	the bias of $x_t$ to the input gate $i_t$
$W_{hi}$	the weight matrix from $h_{t-1}$ to the input gate $i_t$
$h_{t-1}$	the hidden state at the previous time step
$b_{hi}$	the bias of $h_{t-1}$ to the input gate $i_t$
$W_{if}$	the weight matrix from $x_t$ to the forget gate $f_t$
$b_{if}$	the bias of $x_t$ to the forget gate $f_t$
$W_{hf}$	the weight matrix from $h_{t-1}$ to the forget gate $f_t$
$b_{hf}$	the bias of $h_{t-1}$ to the forget gate $f_t$
$\tanh$	activation function
$W_{ig}$	the weight matrix from input $x_t$ to the candidate memory cell
$b_{ig}$	the bias of the candidate memory cell
$W_{hg}$	the weight matrix from $h_{t-1}$ to the candidate memory cell
$b_{hg}$	the bias from $h_{t-1}$ to the candidate memory cell
$W_{io}$	the weight matrix from input $x_t$ to the output gate $o_t$
$b_{io}$	the bias of $x_t$ to the output gate $o_t$
$W_{ho}$	the weight matrix from $h_{t-1}$ to the output gate $o_t$
$b_{ho}$	the bias of from $h_{t-1}$ to the output gate $o_t$
$c_t$	the memory cell state at the current time step
$c_{t-1}$	the memory cell state at the previous time step
$h_t$	hidden state

.

Most previous literature has adopted traditional machine learning methods for relevant research, lacking the application of deep learning models, and the SA-LSTM model has shown excellent performance in studies related to temporal sequence prediction. Therefore, to determine the best fuel consumption prediction model, this study compares traditional machine learning models, LSTM, and SA-LSTM models using several regression evaluation indicators. The effectiveness of the predictive models is assessed using the following metrics: the Mean Absolute Error (MAE), the Mean Square Error (MSE), the Root Mean Square Error (RMSE), and the Mean Absolute Percentage Error (MAPE).

3.3. Carbon Intensity Rating Method

To evaluate the corresponding carbon intensity change yielded by the model, it is essential to further manipulate the fuel consumption data prognosticated by the aforementioned model and to convert it into the carbon intensity, $CI{I}_t$, up to a particular moment, and the specific computational means is as follows [32]:

$$CI{I}_t={\displaystyle \frac{\mathrm{CF}\times {\displaystyle \sum _{t=1}^t{FC}_t}}{\mathrm{C}\times {\displaystyle \sum _{t=1}^t{D}_t}}}$$

(5)

where $\mathrm{CF}$ represents the carbon conversion coefficient of fuel oil. Due to heavy oil being the main fuel consumed by ships and the limited availability of data, this paper only considers the fuel consumption of heavy oil, so the value is 3.114; ${\displaystyle \sum _{t=1}^t{FC}_t}$ represents the total fuel consumption up to moment $t$; $\mathrm{C}$ represents the deadweight tonnage of the target ship, and the value in this paper is 35337; and ${\displaystyle \sum _{t=1}^t{D}_t}$ represents the total sailing distance of the target ship up to moment $t$.

According to the formula above, the carbon intensity at each moment of the target ship can be acquired, thereby ascertaining the carbon intensity change in the ship within one year. Additionally, in accordance with the definition of carbon intensity, the mantissa obtained by computing through this approach is the annual carbon intensity value of the target ship.

The CII reference baseline of a specific ship type and the rating boundary are combined to determine the carbon intensity rating of the ship. The formula of baseline is as follows [33,34,35]:

$$CI{I}_{\mathrm{Req}}=\left(1-{\displaystyle \frac{Z}{100}}\right)\times a{C}^{-c}$$

(6)

where $C$ is the deadweight tonnage (DWT) of the ship; $a$ and $c$ are parameters of different ship types; and $Z$ is the reduction coefficient of CII in different years. The formula of the boundary value, $B_i$, is as follows:

$$B_i=\exp \left(d_i\right)\cdot CI{I}_{\mathrm{Req}}$$

(7)

4. Results and Discussions

This study takes a container ship of 2400 TEU as an example to illustrate the proposed model. The ship was built in 2019 with a DWT of 35,337 and equipped with one main engine for propulsion and two auxiliary engines for electricity. A dataset of 3723 rows with 22 features associated with the fuel consumption of this ship during the year of 2022 was collected.

4.1. Feature Selection Analysis

To investigate the impact of different feature sets on model performance, this paper constructs five datasets with various feature selection methods including Filter, Wrapper, and Embedded.

(1)

Variance Selection

Features with low variance usually have little effect on final prediction results. In this study, features with variance below a threshold of three were removed, which includes draft, trim, wind wave period, combined wave height, wind wave height, wave height, and flow velocity.

(2)

Correlation Coefficient Selection

The setting of correlation coefficient threshold is generally based on experience and specific data, aiming to remove features with relatively weak correlations while preserving the features as much as possible. In this study, features with correlation coefficient greater than 0.1 were selected. Based on this criterion, six features—wind wave period, wind wave height, wind speed, turning rate, draft, and flow direction—were removed. Figure 4 shows correlation coefficient between features and fuel consumption.

(3)

Recursive feature elimination

Recursive feature elimination (RFE) is a feature selection method including a gradient boosting regression model and cross-validation. Four key features including rot, wind direction, merpm, and main engine power are identified by RFE. The specific result of recursive feature elimination is shown in Figure 5.

It is discernible from the figure that the cross-validation score corresponding to the feature amount of four is the highest. Through outputting the features that are in correspondence with this point, it is ascertained that the steering rate, wind direction, main engine speed, and main engine power have the most significant impact on fuel consumption.

(4)

Feature selection based on LASSO

The LASSO model (L1 = 0.001) and identified and discarded features with zero importance. Results are shown in Figure 6.

Combining filtering, wrapper, and embedding methods, this paper constructed four feature subsets for prediction analysis. The specific outcomes are summarized in

Table 2. Feature subsets under the results of different feature selecting methods.

Data Sources	Feature	Origin Data/(Set1)	Variance/(Set2)	Correlation Coefficient/(Set3)	RFECV/(Set4)	LASSO/(Set5)
AIS	speed	√	√	√		√
	rot	√	√		√	√
	draught	√				√
	distance	√	√	√		√
Meteorological and Sea State Data	wind speed	√	√			√
	mpts	√	√	√
	mpww	√				√
	mwp	√	√	√
	shww	√		√		√
	swh	√		√		√
	wwh	√
	swell direction	√	√	√		√
	dww	√	√	√		√
	wd	√	√	√		√
	sst	√	√	√		√
	current spped	√		√		√
	wind direction	√	√	√	√	√
	current direction	√	√			√
sensors data	merpm	√	√	√	√	√
	trim	√	√	√		√
	power	√	√	√	√	√
	FC	√	√	√	√	√

√: indicate selected features

.

Hyperparameters are crucial elements affecting model accuracy. To enhance model accuracy, this study analyzes hyperparameter optimization. Typical approaches include grid search, random search, manual adjustment, and Bayesian search. This study selects Bayesian search due to its global optimization capability based on Bayesian theory, proving more effective than grid or random searches. The optimization results are shown in Figure 7.

The results demonstrate that hyperparameter adjustment significantly improves model performance across diverse data sets. Enhancements in MAE, MSE, RMSE, and MAPE attest to the efficacy of the hyperparameter adjustment process in elevating the prediction accuracy of SA-LSTM.

4.2. The Result of Fuel Consumption Prediction

After three Bayesian searches and cross-validation to optimize hyperparameters, this study evaluated model performance on different data sets. The results are presented in

Table 3. The prediction results of models on different data sets.

Model	Data Sets	MAE	MSE	RMSE	MAPE
XGBoost	Set1	0.4173	0.2801	0.5292	0.3148
	Set2	0.4038	0.2924	0.5408	0.3004
	Set3	0.4167	0.2938	0.5420	0.3156
	Set4	0.4126	0.2828	0.5318	0.3083
	Set5	0.4172	0.2823	0.5313	0.3184
RF	Set1	0.4165	0.2843	0.5332	0.3161
	Set2	0.4131	0.2893	0.5328	0.3098
	Set3	0.4140	0.2866	0.5353	0.3132
	Set4	0.4130	0.2859	0.5347	0.3095
	Set5	0.4146	0.2846	0.5335	0.3156
LGB	Set1	0.4120	0.2831	0.5321	0.3111
	Set2	0.4082	0.2829	0.5319	0.3073
	Set3	0.4120	0.2877	0.5364	0.3119
	Set4	0.4127	0.2864	0.5351	0.3066
	Set5	0.4123	0.2782	0.5275	0.3109
ET	Set1	0.4227	0.2865	0.5353	0.3226
	Set2	0.4199	0.2861	0.5349	0.3152
	Set3	0.4195	0.2898	0.5383	0.3173
	Set4	0.4203	0.2911	0.5395	0.3172
	Set5	0.4223	0.2857	0.5345	0.3205
LASSO	Set1	0.4299	0.2859	0.5347	0.3172
	Set2	0.4301	0.2859	0.5347	0.3177
	Set3	0.4309	0.2860	0.5348	0.3197
	Set4	0.4341	0.2910	0.5394	0.3261
	Set5	0.4314	0.2862	0.5350	0.3207
SVR	Set1	0.5120	0.4932	0.7023	0.5000
	Set2	0.5110	0.5005	0.7075	0.4878
	Set3	0.5142	0.4892	0.6994	0.5091
	Set4	0.4717	0.3999	0.6324	0.3955
	Set5	0.5111	0.5021	0.7086	0.4858
ANN	Set1	0.4356	0.3285	0.5731	0.3434
	Set2	0.4245	0.2960	0.5440	0.3127
	Set3	0.4356	0.3285	0.5731	0.3434
	Set4	0.4238	0.3208	0.5664	0.3278
	Set5	0.4278	0.2915	0.5399	0.3305
ARIMA	Set1	0.5958	0.6142	0.7837	51.4353
	Set2	0.5908	0.6057	0.7783	51.4297
	Set3	0.5908	0.6057	0.7783	51.4297
	Set4	0.5824	0.6032	0.7767	51.4199
	Set5	0.5725	0.6012	0.7754	51.4138
Exponential Smoothing	Set1	0.5443	0.5121	0.7156	50.3562
	Set2	0.5343	0.5001	0.7072	50.3357
	Set3	0.5343	0.5001	0.7072	50.3357
	Set4	0.5312	0.4988	0.7063	50.3328
	Set5	0.5238	0.4957	0.7041	50.3255
LSTM	Set1	0.3726	0.3304	0.5748	0.2596
	Set2	0.3885	0.2749	0.5243	0.2891
	Set3	0.3793	0.3024	0.5499	0.2701
	Set4	0.3766	0.2880	0.5367	0.2646
	Set5	0.3720	0.2738	0.5233	0.2633
SA-LSTM	Set1	0.3270	0.2570	0.5070	0.2471
	Set2	0.3347	0.2492	0.4992	0.2541
	Set3	0.3474	0.2857	0.5345	0.2609
	Set4	0.3474	0.2857	0.5345	0.2609
	Set5	0.3067	0.2405	0.4904	0.2428

.

As presented in Table 3, the SA-LSTM model shows the best prediction performance on the feature subset selected through the embedding method, whereas SVR has the highest prediction error. Compared to the pre-embedding state, the four evaluation indicators for the SA-LSTM model on the five data sets decreased noticeably, with MAPE decreasing by up to 12%. The specific results are depicted in Figure 8.

It can be found that adding the self-attention mechanism significantly impacts the SA-LSTM across each data set, reducing MAE by up to 17.5%, MSE by up to 22%, RMSE by up to 13%, and MAPE by up to 12%.

4.3. The Assessment of Carbon Intensity

In Figure 9, the CII of the target ship fluctuates significantly in January, stabilizing within 7 to 8 subsequently. This fluctuation is due to limited initial voyages and relatively large CO₂ emissions. As cumulative voyage values increase, CII stabilizes when calculated with deadweight tonnage.

By attaining the optimal state of each model through comparative analysis, we predict the fuel consumption within one year and transform the predictions into carbon intensity. The CII distribution for each model’s predictions is shown in Figure 10.

Figure 10 shows that the CII distribution from the SA-LSTM closely aligns with the actual distribution of the target ship, while LSTM and ANN models show larger discrepancies. To visually compare the fit of each model’s carbon intensity predictions to the actual values, a scatter plot is shown in Figure 11.

Figure 11 reveals that LASSO and SVR models have high dispersion and more outliers, deviating significantly from actual values. The ANN and LSTM models show reduced dispersion but still have numerous outliers. Ensemble models (XGBoost, RF, LGB, and ET) exhibit similar, more concentrated scatter distributions. The scatter points of SA-LSTM are concentrated near the fitting curve, indicating minimal dispersion and prediction deviation.

4.4. The Analysis of Carbon Intensity Rating Result

Given that the case ship is a container ship, the rating boundary is calculated with a = 1984 and c = 0.489; Zhang et al. (2023) showed the detailed calculation process [36]. A comparison of the results of all these models are shown in

Table 4. The annual carbon intensity results of the evaluation by models.

Model	Annual CII	Error	Accuracy	Rating Grade
XGBoost	7.7776	0.0338	99.58%	A
RF	7.7987	0.0128	99.84%	A
LGB	7.8211	0.0096	99.88%	A
ET	7.8219	0.0104	99.87%	A
LASSO	7.8013	0.0102	99.87%	A
SVR	7.7927	0.0188	99.76%	A
ANN	7.3837	0.4277	94.52%	A
ARIMA	1.3773	6.4342	17.63%	A
Exponential Smoothing	1.4739	6.3376	18.86%	A
LSTM	7.3723	0.4391	94.38%	A
SA-LSTM	7.8130	0.0016	99.98%	A
True	7.8115	0	100%	A

. It indicates that the proposed SA-LSTM model has the best performance in predicting the annual CII value of this ship.

5. Conclusions

This paper proposed an SA-LSTM model and compared it with ten other models to predict ship fuel consumption and the annual CII value. The self-attention mechanism is introduced to assign weights to the inputs, transforming them into a new matrix, which is fed into the LSTM for model training and prediction. The accuracy of the SA-LSTM model is validated through comparisons with the standard LSTM and traditional models.

The proposed SA-LSTM could be used to dynamically predict the CII rating of ships, and the ship operators could use this information to dynamically adjust their ship operational and management practices to enhance the CII ratings of their ships. (1) However, ships need to install the required sensors and their management systems to collect data in advance, which may be expensive and time-consuming. In practice, both data of history and real-time data should be prepared in order to take advantage of this algorithm.

One limitation of this study is that the proposed SA-LSTM model is simply tested by one case ship, due to the difficulty in collecting real-time fuel consumption data from ships, which may affect the generalization of the results. Additionally, the meteorological and sea condition data were obtained from ECMWF and Copernicus rather than from the ship’s sensors, potentially causing a discrepancy in environmental characteristics that could influence model accuracy.

Future research may focus on improving the generalization of the proposed model by training on data from more ships with different types and sizes. It is also necessary to integrate more real-time operational and environmental datasets and the latest techniques to further improve the performance of the proposed model.