Ship fuel consumption analysis and prediction method integrating data-driven modeling and causal inference

Abstract

The invention provides a ship fuel consumption analysis and prediction method integrating data-driven modeling and causal inference, and belongs to the technical field of ship energy efficiency management. Collecting ship historical data to construct a training set; determining input characteristics influencing the oil consumption of the ship; training a plurality of machine learning models through input features based on the training set; determining an optimal machine learning model according to the model evaluation index; screening out key features from the input features according to the optimal machine learning model; calculating an average processing effect of each key feature; and constructing a mapping relation between the key features and the ship fuel consumption based on the average processing effect of each key feature. According to the method, data of a plurality of heterogeneous sources are integrated to construct a fusion data set, and feature selection is performed to solve the limitation of dependence on a single data source; and according to the prediction performance of the machine learning model, an optimal ship fuel consumption prediction model is determined, and the generalization ability of the model is enhanced. And determining a mapping relation between the key features and ship fuel consumption through ATE, and further performing fuel consumption prediction.

Description

Technical Field

[0001] This invention relates to the field of ship energy efficiency management technology, and in particular to a method for analyzing and predicting ship fuel consumption that integrates data-driven modeling and causal inference. Background Technology

[0002] Currently, the global shipping industry bears approximately 90% of the burden of global trade transportation, and is also a significant contributor to energy consumption and environmental pollution. Reducing ship fuel consumption through operational optimization has become a crucial issue for shipping companies.

[0003] Ship fuel consumption prediction, as a core technology of energy efficiency management, is of great significance for cost control and energy conservation and emission reduction. However, fuel consumption is comprehensively affected by multiple factors such as sailing speed, load status, marine environment, and meteorological conditions, and there are complex nonlinear coupling relationships between these factors, which significantly limits traditional modeling methods in quantifying their influence mechanisms. Furthermore, the field of energy efficiency analysis still faces the following challenges: First, high-performance prediction models are disconnected from formal causal inference methods, lacking a unified analytical framework that systematically links prediction with causal relationships, which restricts the development of overall solutions for this complex system; Second, correlation analysis cannot distinguish between true causal relationships and spurious associations, and conclusions drawn from such methods are easily confounded by unobserved variables, potentially leading to incorrect attribution of causal mechanisms and systematic misjudgment of intervention effects; Third, the quantification of individual causal effects can only provide a non-hierarchical understanding of the system, presenting a series of independent causal connections, but failing to fully elucidate the underlying interdependent structure of these connections. Summary of the Invention

[0004] In view of this, the present invention provides a method for analyzing and predicting ship fuel consumption that integrates data-driven modeling and causal inference. It integrates multi-source heterogeneous data fusion, machine learning prediction modeling, model interpretability analysis, causal relationship identification, and causal effect quantification to achieve comprehensive ship fuel consumption analysis and effectively predict ship fuel consumption.

[0005] Therefore, the present invention provides the following technical solution: A method for analyzing and predicting ship fuel consumption that integrates data-driven modeling and causal inference includes: Collect historical ship data to construct a training set; Identify the input characteristics that affect ship fuel consumption; Multiple machine learning models are trained based on the training set by input features; Determine the optimal machine learning model based on model evaluation metrics; Key features are selected from the input features based on the optimal machine learning model; Calculate the average treatment effect for each key feature; The mapping relationship between key features and ship fuel consumption is determined based on the average processing effect of each key feature.

[0006] Furthermore, it also includes: Ship fuel consumption is predicted by utilizing the mapping relationship between the key features and ship fuel consumption.

[0007] Furthermore, the determination of input characteristics affecting ship fuel consumption includes: Ship noon reports, AIS data, ERA5 data, and GOPAF data were collected as initial features; The initial features were sorted using a topological sorting feature selection method, and feature importance distribution curves were plotted. Based on the value at the inflection point of the feature importance distribution curve as the critical value, all initial features ranked before the critical value are selected as input features.

[0008] Furthermore, the machine learning model includes: Linear regression, ridge regression, lasso regression, elastic network, support vector machine, random forest, gradient boosting, extreme random tree and XGBoost.

[0009] Furthermore, the optimal machine learning model is: Random forest.

[0010] Furthermore, the step of selecting key features from the input features based on the optimal machine learning model includes: Construct a sequence based on the average of the absolute values ​​of the SHAP values ​​of each input feature; The first n features of the sequence are used as key features.

[0011] Furthermore, the calculation of the average processing effect of each key feature includes: S1. Randomly divide the dataset into K equal-sized subsets; S2, for each subset Use except All subsets except those used to train the LASSO regression model, predicting key features respectively. and outcome variables And for subsets Calculate residuals and ; S3, Based on all residuals and original confounding variables Train the causal forest model to learn the conditional treatment effect function; S4. Estimate the average treatment effect based on the conditional treatment effect function.

[0012] Furthermore, the model evaluation metrics include: Correlation coefficient, root mean square error, and standard deviation.

[0013] Furthermore, the input features include: Daily sailing hours, main engine speed, draft, sea state, climate, surface roughness prediction, 10-meter wind speed, synthetic effective wave height, average wave period, average surge period, wave-induced drag coefficient, total wave speed, ship heading, daily average speed, overall average speed, daily sailing distance, relative surge direction angle, atmospheric temperature, total sailing distance, total time, and effective surge height.

[0014] Furthermore, the key features include: Daily sailing hours, main engine speed, daily sailing distance, and ship's course.

[0015] Advantages and positive effects of the present invention: This method constructs a fused dataset by integrating data from multiple heterogeneous sources and applies feature selection techniques to overcome the limitations of relying on a single data source, laying a solid foundation for subsequent causal inference. Based on this, the method evaluates the predictive performance of nine machine learning models, identifies the model that most accurately predicts ship fuel consumption, and enhances the model's generalization ability in complex and ever-changing marine environments.

[0016] The mapping relationship between key variables and fuel consumption established by this method can be used by ship owners and operators to predict fuel consumption, and further develop data-driven navigation strategies and energy management plans, thereby reducing operating costs and carbon intensity. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 The flowchart illustrates a method for analyzing and predicting ship fuel consumption that integrates data-driven modeling and causal inference, as shown in the example. Figure 2 This is a schematic diagram illustrating the feature ranking and regression performance of TopoRankFS in the embodiment; Figure 3 The example graph is a causal graph constructed using DirectLiNGAM. Figure 4 In this example, the Taylor plot is used to compare model performance; Figure 5 This is a graph showing the SHAP importance analysis results of the ship fuel consumption model in the example; Figure 6 The bootstrap distribution of the average treatment effect in the examples; Figure 7 This is a causal hierarchy topology diagram in the embodiment. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] This invention provides a method for analyzing and predicting ship fuel consumption that integrates data-driven modeling and causal inference, including: S1. Using ship noon reports as the core data source, supplemented by AIS data, ERA5 data and GOPAF data, high-precision fusion of multi-source heterogeneous data is achieved, and the topology ranking feature selection method (TopoRankFS) is used for feature selection.

[0022] S2. The initial causal graph is constructed using the DirectLiNGAM algorithm.

[0023] S3. Select key features using Shapley Additive Explanations (SHAP).

[0024] S4. The average treatment effect (ATE) of key features is estimated using the Causal Forest-based Double Machine Learning (DML-CF) method.

[0025] S5. Interpretive Structural Modeling (ISM) is used to perform hierarchical decomposition of the initial causal graph generated by DirectLiNGAM, further clarifying the structural dependencies and transmission mechanisms among variables in the ship fuel consumption system.

[0026] S6. Predict ship fuel consumption by using the mapping relationship between key features and ship fuel consumption.

[0027] Specifically: S1. Using ship noon reports as the core data source, supplemented by AIS data, ERA5 data and GOPAF data, high-precision fusion of multi-source heterogeneous data is achieved, and the topology ranking feature selection method (TopoRankFS) is used for feature selection.

[0028] 1. Collect multi-source data from ships, construct a multi-source heterogeneous dataset, and perform feature selection.

[0029] 1) The initial dataset came from four different sources: The ship midday report provides the core dataset; concurrent high-frequency AIS data, using high-precision geospatial coordinates and timestamps, supplements and validates navigation parameters, overcoming the limitations of the midday report in terms of temporal resolution and potential subjectivity. ERA5 and GOPAF data are introduced to comprehensively present the ship's operating environment. ERA5 data, provided by the European Centre for Medium-Range Weather Forecasts, offers high-resolution atmospheric and wave variable support; GOPAF data provides key ocean variables.

[0030] 2) Systematically identify and rank the predictive factors that influence ship fuel consumption from high-dimensional datasets.

[0031] The topological sorting feature selection method is used: Based on the three-weighted LeaderRank (3-WLR) algorithm, the support and confidence threshold settings for association rule mining were optimized to adapt to the distribution characteristics of ship fuel consumption data. Simultaneously, the weight configuration in the 3WLR algorithm was adjusted to enhance the ability to capture fuel consumption-specific influence patterns. The predictive factors that influence ship fuel consumption are systematically identified and ranked from high-dimensional datasets, laying a data foundation for subsequent predictive modeling and causal analysis.

[0032] S2. The initial causal graph is constructed using the DirectLiNGAM algorithm.

[0033] Based on the non-Gaussian distribution assumption and the principle of independent component analysis, this method determines the causal order by iteratively identifying the most exogenous variable in the system. Unlike methods that rely on simple correlation, it assesses the statistical independence between the regression residuals of candidate variables and other variables.

[0034] If a variable is independent of the residuals of all other variables, it is considered exogenous because it is unaffected by those variables. Once the most exogenous variable is identified, its influence is mathematically removed from the remaining dataset, and this process is repeated to find the next variable in the causal sequence. This process continues until the complete causal order is determined.

[0035] After establishing the directed acyclic structure, the strength of each causal relationship is quantified through a series of linear regressions, thereby obtaining a fully deterministic causal network that depicts the path of influence on ship fuel consumption.

[0036] S3. Train multiple machine learning models based on the training set and input features; determine the optimal machine learning model based on model evaluation metrics; select key features using SHAP, and construct a sequence based on the average absolute value of the SHAP values ​​of each input feature; the first n features of the sequence are used as key features.

[0037] S4. Use the DML-CF method to estimate the average treatment effect of key features.

[0038] 1) Utilize a dual machine learning framework to eliminate endogeneity bias caused by confounding variables through orthogonalization. For key features... Outcome variables and confounding variables The DML framework estimates ATE through the following steps: Assume the real data generation process is described by the following structure equations:

[0039]

[0040] in, A function representing the influence of confounding variables on key features; A function that represents the direct effect of confounding variables on the outcome variable; and It is a random error term with a mean of zero. For the target ATE parameter. In this model, if If this happens, the simple regression estimator will be biased. Indicates when key features Values ​​and confounding variables When the value is fixed or known, the random error term What is the average value?

[0041] DML will then address these issues through the following three key steps: Step 1: Predictive Model Construction. Establish key features respectively. Regarding confounding variables Prediction model and outcome variables Regarding confounding variables Prediction model :

[0042]

[0043] Step 2: Residual Calculation. Calculate the orthogonalized residuals of key features and outcome variables: (18) (19) This step achieves the crucial orthogonalization process, namely, eliminating confounding variables. right and The effects of these factors mean that the remaining variation originates from treatment effects and unrelated random errors.

[0044] Step 3: Estimating the average treatment effect. The treatment effect is estimated using orthogonalized residuals:

[0045] This residualization strategy effectively eliminates the influence of confounding variables and reduces the endogeneity bias of the estimation.

[0046] Finally, to avoid estimation bias caused by overfitting, DML adopts a K-fold cross-fitting strategy (K=5 in this method): the dataset is divided into K non-overlapping subsets. For each subset, the prediction model is trained using the remaining K-1 subsets. Then, the residuals are calculated on the subset and the local treatment effect is estimated. Finally, the K local estimates are combined to obtain the final ATE estimate.

[0047] In this embodiment, LASSO regression is selected as the prediction model. and The implementation method automatically selects variables and captures potential nonlinear relationships between confounding variables and treatment / outcome variables. The objective function of LASSO regression is:

[0048] in, It is a regularization parameter determined through cross-validation, used to control the balance between model complexity and goodness of fit.

[0049] 2) The causal forest (CF) method was used to estimate the heterogeneous treatment effect.

[0050] The decision tree is constructed using a recursive binary search method, with each split designed to maximize the heterogeneity of treatment effects among subsamples.

[0051] Specifically, causal forests estimate the Conditional Average Treatment Effect (CATE) through the following steps: Step 1: Data Partitioning and Tree Generation. For each decision tree, training samples are drawn with replacement from the original dataset, and a subset of features is randomly selected. The tree generation process follows these rules: (a) For each node, find the optimal split point in the feature subspace that maximizes the heterogeneity of the processing effects of the split child nodes:

[0052] in, and These are features At the split point Estimated treatment effects for the left and right child nodes; and That is the corresponding number of samples.

[0053] (b) Repeat the splitting process until the preset stopping condition (such as minimum number of node samples or maximum tree depth) is reached.

[0054] Step 2: Estimation of the average treatment effect (ATE).

[0055] For any eigenvector The conditional average treatment effect is predicted by ensemble prediction of multiple decision trees. And calculate the local treatment effect value of the leaf node into which the sample falls. The calculation formula is as follows:

[0056]

[0057] in, It refers to the number of trees in the forest; It is the first Tree samples The predicted value of the treatment effect; It is the first The tree contains samples leaf nodes; It is a sample The propensity score estimate; It is the first The observed variable values ​​of each training sample; It is the first The processing allocation received by each training sample; It is the first The feature vectors of the training samples.

[0058] Step 3: Calculation of the average treatment effect. The population ATE is obtained by averaging the CATE estimates across all samples:

[0059] 3) A hybrid analytical framework integrating DML and CF methods is used to further improve the robustness of causal estimation of effects and effectively identify potential effect heterogeneity.

[0060] This DML-CF framework fully integrates the orthogonalization advantages of DML in bias control with the modeling capabilities of CF in characterizing individualized treatment effects, and achieves integrated modeling through the following steps: Step 1: Data partitioning.

[0061] The dataset is randomly divided into K equal-sized subsets (K=5 in this method).

[0062] Step 2: Orthogonalization process.

[0063] For each subset Use except All subsets except those used to train the LASSO regression model, predicting key features respectively. and outcome variables And for subsets Calculate residuals and .

[0064] Step 3: Constructing counterfactual facts.

[0065] Based on all residuals and original confounding variables Train the CF model and learn the CATE function:

[0066] Step 4: Averaging Treatment Effect Estimation and Uncertainty Assessment. The CATE estimates for all samples are averaged to obtain the final ATE estimate. Furthermore, to assess the uncertainty of the ATE estimate, this embodiment introduces the Bootstrap resampling method (n=1000) to construct a 95% confidence interval, and the statistical robustness of the estimate is visualized using a probability density distribution.

[0067] S5. The Interpretive Structural Model (ISM) is used to perform hierarchical decomposition on the initial causal graph generated by DirectLiNGAM, further clarifying the structural dependencies and transmission mechanisms among variables in the ship fuel consumption system.

[0068] The directed causal graph is transformed into an adjacency matrix representing the direct relationships between variables. Through Boolean matrix multiplication, this initial matrix is ​​evolved into a "reachability matrix." This crucial step not only systematically identifies direct connections in the network but also identifies all indirect transitive paths, thereby capturing the complete relational structure of the system.

[0069] The reachability matrix serves as the foundation for the iterative partitioning process. By analyzing the "reachable set" (all variables affected by a given variable) and the "antecedent set" (all variables affecting that variable), the algorithm stratifies all factors into different levels. This structured decomposition transforms the initially complex network into an ordered, multi-layered topology, clearly revealing the propagation path of influence from fundamental driving factors to the final system outcome.

[0070] Example Combination Figure 1 As shown, this method includes: S1. Collect multi-source data from ships and perform data preprocessing to obtain preprocessed multi-source heterogeneous data.

[0071] In this embodiment, the core data collected were the noon reports of an ocean-going bulk carrier from January 14, 2021 to July 30, 2024, comprising 479 complete ship operation records. These reports included key parameters such as fuel consumption rate, speed, draft, and loading status.

[0072] This embodiment integrates high-frequency AIS data from the same period (containing 162,036 valid trajectory points) and uses high-precision geospatial coordinates and timestamps to supplement and verify navigation parameters.

[0073] To comprehensively represent the ship's operating environment, high-quality external meteorological and oceanographic data were also incorporated. The European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis Version 5 (ERA5) dataset provides high-resolution atmospheric and wave variables. The Global Ocean Physical Analysis and Forecasting (GOPAF) dataset supplements this, providing key oceanographic variables. To ensure consistency, established methodologies in the field were followed, converting absolute wind and wave directions from the external datasets to directions relative to the ship's course. This multi-source data fusion process generates a rich, high-dimensional dataset capable of accurately capturing the complex interactions between ship operations and environmental conditions. Table 1 lists the feature sources and corresponding feature names of the multi-source data fusion.

[0074] Table 1

[0075] Figure 2 The process and results of systematically filtering the initial feature set using the TopoRankFs method are demonstrated. Feature importance ranking based on average TopoRankFS scores shows that variables such as daily sailing hours, main engine speed, and draft dominate fuel consumption prediction. Through a trade-off analysis of model performance and complexity, it was found that the model's coefficient of determination (R²) peaks when the number of features reaches 22. The feature importance distribution curve (logarithmic scale) shows a distinct elbow inflection point at the 22nd feature, indicating that the first 22 features contain the core information of the dataset, while the marginal contribution of subsequent features decreases sharply.

[0076] Therefore, in this embodiment, the first 22 features are selected as the optimal feature subset, which effectively reduces the model complexity while ensuring prediction accuracy.

[0077] S2. The initial causal graph is constructed using the DirectLiNGAM algorithm.

[0078] Figure 3 A multidimensional causal network structure was constructed for the application of the DirectLiNGAM algorithm. Structurally, the direction of the arrows in the figure indicates the potential causal flow, while the density of connections between nodes reflects the complexity of the interaction between variables.

[0079] Figure 3 This study visually reveals the causal transmission network between ship operation variables, showcasing not only the key factors directly affecting main engine fuel consumption but also elucidating the complex interactions among these variables. It is worth noting that... Figure 3The data reveals a causal relationship between the relative swell direction angle and the total sailing distance, indicating that route planning needs to consider the impact of sea state factors on navigation efficiency. This multi-level, multi-path causal network structure confirms the theory that ship fuel consumption is affected by the coupling of multiple factors. By identifying these key causal paths, this embodiment not only provides a theoretical framework for applying causal inference techniques to ship energy efficiency analysis but also lays a scientific foundation for formulating precise energy-saving and emission-reduction strategies and navigation optimization schemes.

[0080] S3. Use SHAP to select key features: 1. In this embodiment, nine mature machine learning models were selected for comparative analysis, namely: Linear regression, ridge regression, lasso regression, elastic network, support vector machine, random forest, gradient boosting, extreme random tree and XGBoost.

[0081] To ensure optimal performance for each model, a combination of five-fold cross-validation and Bayesian optimization was used to systematically tune the hyperparameters.

[0082] To systematically evaluate the performance of each candidate model, this embodiment uses Taylor diagrams for multi-dimensional visualization and comparison, such as... Figure 4 .

[0083] Taylor charts present three key metrics simultaneously in a single chart: correlation coefficient, root mean square error, and standard deviation.

[0084] Figure 4 The results clearly show that the Random Forest model (highlighted with a red diamond) achieves best performance on all key evaluation metrics. Its data points are closest to the reference point representing the perfect model, indicating that it simultaneously satisfies all three optimization criteria: (1) The predicted values ​​have the highest correlation with the observed values; (2) The standard deviation is closest to the observed data; (3) The centering root mean square error is the smallest. In contrast, other models either have lower correlation or show greater variability compared to the observed data. The combination of these advantages makes the random forest model significantly superior to all other candidate models, and also justifies its selection for subsequent analysis.

[0085] A random forest was trained on the dataset and determined to be the optimal prediction model.

[0086] The SHAP method is applied to this model to obtain a global ranking of feature importance. For example... Figure 5As shown, the SHAP global feature importance analysis results clearly present the ranking of the contributions of each variable to the prediction of ship fuel consumption and the relative magnitude of their influence.

[0087] S4. Based on the constructed causal network structure, DML-CF is introduced to quantitatively estimate the ATE of key features.

[0088] This embodiment selected daily sailing hours, main engine speed, daily sailing distance, and ship heading as core key features for causal effect analysis. Confounding variables were based on... Figure 2 The causal structure is determined by strictly following the DirectLiNGAM results for each key feature, selecting its direct parent node in the causal graph as a potential confounding factor to satisfy the backdoor criterion in causal inference and ensure that the estimated treatment effect has causal explanatory power.

[0089] In this embodiment, the estimated ATE value for daily flight hours is 1.3403 (95% confidence interval: [0.8564, 1.6986]). Figure 6 As shown in (a).

[0090] This result implies that, after controlling for other covariates, fuel consumption is expected to increase by an average of approximately 1.34 units for every additional hour of sailing time, and this estimate demonstrates significant distributional centralization and statistical robustness. This finding is highly consistent with empirical studies on the direct impact of sailing time on fuel efficiency, further supporting the methodological rationale for identifying daily sailing hours as the primary predictive feature.

[0091] at the same time, Figure 6 In (b), the estimated ATE value for the main engine speed is 0.5606 (95% confidence interval: [0.0716, 0.9355]). It is noteworthy that the uncertainty of this estimate (manifested as the relative width of the confidence interval) is significantly greater than other key features. This heterogeneity may stem from the complex nonlinear response mechanism between engine speed and fuel consumption, as well as the dynamic changes in the energy efficiency curve under different load conditions. Despite the estimation fluctuations, the overall effect remains significantly positive, which aligns with the fundamental thermodynamic principle in ship propulsion system dynamics that "increased engine load leads to increased fuel consumption rate."

[0092] In addition, the daily ATE (ate) of the sailing distance is as follows Figure 6As shown in (c), the estimated value is 0.0343 (95% confidence interval: [0.0231, 0.0514]). Although the unit effect size is relatively small, its statistical significance and estimation robustness remain clear. This relatively weak marginal effect may reveal an important phenomenon: when other variables (especially flight time) are effectively controlled, the contribution of flight distance itself to the incremental fuel consumption is significantly reduced. This finding echoes the theoretical model that "distance and fuel consumption are quasi-linear under constant speed conditions".

[0093] Additionally, the estimated ATE value for the ship's course is 0.0025 (95% confidence interval: [-0.0032, 0.0050]), such as Figure 6 As shown in (d), this exhibits a small but highly focused positive effect. This positive correlation suggests a potential systematic impact of ship navigation direction on fuel consumption, but the magnitude of the effect is relatively limited. Notably, the confidence interval for this variable spans across zero, indicating that it does not meet the traditional significance criteria at the statistical inference level, which is consistent with the marginal effect hypothesis of the influence of navigation parameters on fuel consumption.

[0094] By systematically comparing the ATE estimates of four key features, this embodiment reveals the differential causal mechanism of ship fuel consumption. The time dimension feature (daily sailing hours) exhibits the most significant causal effect strength (ATE=1.3403), followed by the power system state parameters (main engine speed, ATE=0.5606). While the spatial dimension variable (daily sailing distance, ATE=0.0343) and the ship's heading parameter (ship's heading, ATE=0.0025) are statistically valid, their unit effect sizes are relatively limited.

[0095] S5. Based on the preliminary exploration of the causal mechanism of ship fuel consumption using the DirectLiNGAM algorithm and DML-CF, the Interpretive Structural Model (ISM) is introduced to further analyze the hierarchical structure and transmission path of causal relationships.

[0096] Figure 7To classify the factors influencing ship fuel consumption into four levels (L1-L4) using the ISM method, and to identify nodes at each level with different colors, a complete hierarchical causal topology diagram was constructed. Blue nodes (L1 level) represent root drivers, which are at the upstream of the causal chain, exerting initial influence on downstream variables without being constrained by other factors. Orange nodes (L2 level) represent intermediate transmission factors, which are influenced by upstream drivers and also transmit downwards. Red nodes (L3 level) represent proximal factors close to the response variable. Green nodes (L4 level) represent the final response variable. Drivers at higher levels (L1) typically exhibit stronger causal dominance, while lower-level factors show higher causal dependence. This is fully validated in the ship fuel consumption system: daily sailing hours, as a core driver at L1 level, correspond to its significant ATE estimate (1.3403) in S4 of Example 1, further confirming the crucial role of the time dimension in ship fuel consumption prediction. It is worth noting that the ISM hierarchical structure analysis provides systematic cross-validation and theoretical supplementation for the quantification of feature importance and causal inference results. From the perspective of multi-methodological integration, the daily flight hours variable shows significant consistency.

[0097] Similarly, engine speed, as another key L1 layer variable, not only ranks high in the SHAP contribution ranking, but also shows a considerable average treatment effect estimate (0.5606). It is identified as a basic level driving factor in the ISM framework, further confirming the underlying structural impact of propulsion system operating parameters on navigation energy efficiency.

[0098] Among multiple candidate causal paths, this embodiment selects the path "Daily sailing hours (L1) → Total average speed (L2) → Daily sailing distance (L3) → Main engine fuel consumption (L4)" as a representative case to explore its hierarchical transmission effect and comprehensive impact on ship fuel consumption. This path fully reflects the hierarchical transmission mechanism between time, operating status, and sailing distance, serving as a crucial bridge connecting basic ship operating indicators and fuel consumption response. Through this hierarchical transmission mechanism from time and speed to distance, main engine fuel consumption is not only directly affected by daily sailing hours but also significantly amplified through the indirect effects of the two mediating variables, total average speed and daily sailing distance. This path verifies the dual effect mechanism of sailing time on fuel consumption: it has both a direct effect and an indirect impact through the mediating effects of operating status and sailing distance. Therefore, from the perspective of shipping practice, the identification of this causal path provides a theoretical basis for hierarchical intervention in fuel efficiency management. First, sailing time, as the driving variable at the source of the path, can be optimized through reasonable scheduling of ship operations and port stays. Secondly, airspeed, as a key mediating variable, can be dynamically adjusted through an intelligent airspeed planning system. Finally, optimizing the flight distance requires combining route planning with meteorological navigation technology to achieve a systematic reduction in fuel consumption.

[0099] In summary, this method integrates DirectLiNGAM and DML-CF to achieve a deep causal deconstruction of the mechanisms influencing ship fuel consumption, and uses ISM to thoroughly analyze the multi-level transmission mechanism of factors affecting ship fuel consumption. The former precisely quantifies the average effect of multiple key characteristics, while ISM divides influencing factors into multiple top-down levels, revealing the hierarchical transmission effect from fundamental driving variables to mediating variables, ultimately affecting main engine fuel consumption. This analytical framework not only verifies the dual mechanism of daily sailing hours in fuel consumption—having both a direct effect and an indirect effect through mediating paths—but also highlights the crucial regulatory role of operational status and sailing distance in energy accumulation. Therefore, this method provides a solid quantitative basis and theoretical support for ship energy efficiency optimization and fuel management strategies, and its methodological innovation and rigor open up new practical paths for subsequent research in related fields.

[0100] This invention establishes a comprehensive theoretical framework that extends from correlation analysis to the exploration of causal mechanisms by integrating machine learning into a robust causal inference framework. This framework provides a multi-dimensional and multi-layered scientific basis for the prediction and optimization of ship fuel consumption (SFC). By elucidating the underlying causal structure of the system, it transcends the limitations of purely predictive "black box" models, providing a practical approach to support the green and low-carbon transformation of the shipping industry.

[0101] The research framework proposed in this invention not only realizes the model transformation from "accurate but unexplainable" to "accurate and explainable", but also provides a full-chain theoretical support for ship energy efficiency management, from prediction and optimization to causal intervention. It has important theoretical and practical significance for promoting refined decision-making and sustainable development in the shipping industry.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of ship fuel consumption analysis and prediction that fuses data-driven modeling with causal inference, characterized by, The method comprises the following steps: Collecting ship historical data to construct a training set; Determining input features that affect ship fuel consumption; Training multiple machine learning models based on the training set through input features; Determining the optimal machine learning model according to the model evaluation index; Screening key features from input features according to the optimal machine learning model; Calculating the average treatment effect of each key feature; Determining the mapping relationship between key features and ship fuel consumption based on the average treatment effect of each key feature.

2. The method of claim 1, wherein, The method further comprises: Using the mapping relationship between key features and ship fuel consumption to predict ship fuel consumption.

3. The method of claim 1, wherein, The method of determining input features that affect ship fuel consumption comprises: Collecting ship noon report, AIS data, ERA5 data and GOPAF data as initial features; Using a topological sorting feature selection method to sort the initial features and draw a feature importance distribution curve; Selecting all initial features before the critical value as input features based on the value at the inflection point of the feature importance distribution curve as the critical value.

4. The method of claim 1, wherein, The machine learning model comprises: Linear regression, ridge regression, lasso regression, elastic net, support vector machine, random forest, gradient boosting, extreme random tree and XGBoost.

5. The method of claim 1, wherein, The optimal machine learning model is: Random forest.

6. The method of claim 1, wherein, The method of screening key features from input features according to the optimal machine learning model comprises: Constructing a sequence according to the average value of the absolute value of the SHAP value of each input feature; The first n features of the sequence are key features.

7. The method of claim 1, wherein, The method of calculating the average treatment effect of each key feature comprises: S1, randomly divide the data set into K equal size subsets; S2, for each subset using all subsets except the LASSO regression model is trained, respectively predicting key features and outcome variables and computing residuals for the subsets and ; S3, based on all residuals and the original confounders , training the causal forest model to learn the conditional treatment effect function; S4, estimate the average treatment effect based on the conditional treatment effect function.

8. The method of claim 1, wherein, The model evaluation index comprises: Correlation coefficient, center root mean square error and standard deviation.

9. The method of claim 1, wherein, The input features comprise: Daily sailing hours, main engine speed, draft, sea conditions, climate, surface roughness prediction, 10-meter wind speed, synthetic effective wave height, average wave period, average surge period, wave-induced resistance coefficient, total wave speed, ship heading, daily average speed, overall average speed, daily sailing distance, relative surge direction angle, atmospheric temperature, total sailing distance, total time and effective surge height.

10. The method of claim 1, wherein, The key features comprise: Daily sailing hours, main engine speed, daily sailing distance and ship heading.

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