Tinrui Zhou ,Qinyou Hu ,Zhihui Hu ,Rong Zhen

a Merchant Marine College,Shanghai Maritime University,1550 Haigang Avenue,Pudong New Area,Shanghai,China

b Navigation College,Jimei University,Xiamen 361021,Fujian,China

Keywords:Ship fuel consumption Artificial neural network Bayesian optimization Hyperparameter tuning Environmental factors

ABSTRACT An accurate prediction of ship fuel consumption is critical for speed,trim,and voyage optimisation etc.While previous studies have focused on predicting ship fuel consumption with respect to a variety of factors,research on the impact of environmental factors on fuel consumption has been lacking.In addition,although recent research efforts have widely focused on machine learning methods to predict fuel consumption,studies on hyperparameter values that are suitable for these prediction models are limited.To compensate for this deficiency in existing literature,an adaptive hyperparameter tuning method is proposed,and the effects of maritime environmental factors on fuel consumption are taken into account.Through experimentation,the proposed adaptive hyperparameter tuning method was validated via artificial neural network (ANN),support vector regression (SVR),random forest (RF),and least absolute shrinkage and selection operator (Lasso).The hyperparameter tuning proportionally increased the amplitudes of the coefficients of determination (R 2) of these algorithms.The increase of the amplitude demonstrated the following trend,in the order of the largest increase to the lowest increase: ANN,Lasso,SVM,and RF.The rates of increase were between 0.0773% and 2.1653%.Furthermore,after the environmental factors were considered,the prediction accuracies of the ANN and Lasso increased; however,the opposite was observed for the SVR and RF.As such,we confirmed that the use of Bayesian optimisation for hyperparameter tuning can effectively improve the fuel consumption prediction accuracy,and our proposed model can therefore serve as a significant reference for calculating fuel consumption.

1.Introduction

Ocean shipping accounts for 80% of global trade volumes [1].During a shipping voyage,large amounts of carbon dioxide (CO 2),particulate matter (PM),sulphur oxides (SOx),and nitrogen oxides(NOx) are produced [2],which cause serious damage to the environment and human health [3,4].According to the research report released by the International Maritime Organization (IMO) related to the fourth greenhouse gas (GHG) [5],the total GHG emissions of the shipping industry increased from 978 million tons in 2012 to 1.076 billion tons in 2018,and the ratio of gas emissions from the shipping industry increased from 2.76% to 2.89%.With the increase in GHG emissions and the ongoing deterioration of marine environments,the reduction of gas emissions from ships has emerged as an important topic in the shipping industry.

To achieve the goal of mitigating gas emissions from ships,the IMO set a CO2emissions reduction target of up to 50% by 2050,relative to the amount of emissions in 2008 [6].Meanwhile,a number of effective measures,such as the Energy Efficiency Design Index (EEDI) for newly designed ships [7]and the Energy Efficiency Operational Indicator (EEOI) for already sailing ships [8],have been instituted.A series of technical and operational measures,such as speed optimisation [9],trim optimisation [10,11],weather routing[12,13],and ship energy efficiency monitoring [14],have also been adopted.These measures,which require no additional cost and can also achieve savings in bunker fuel consumption,are therefore widely used in shipping companies.

An accurate prediction of ship fuel consumption is an important prerequisite for speed optimisation and trim optimisation.However,the fuel consumption of a ship is affected by many factors,including speed,displacement,operating conditions of the main engine,and hull and propeller performance.In previous research studies on fuel consumption prediction modelling,either one single factor or a few factors are considered.For example,when the speed of a ship in a voyage is optimised,it is usually assumed that fuel consumption and ship speed are in a cubic relationship; however,the influence of wind,waves,currents,and other navigational weather environments are not considered.Thus,the optimisation result may be questionable.

Many studies have used machine learning methods for ship fuel consumption prediction,including support vector regression(SVR),random forests (RF),and decision trees (DT).To the authors’knowledge,most machine learning algorithms involve several hyperparameters,such as the number of hidden layers and neurons,the activation function of each layer,and the learning rate in an artificial neural network; obviously,the values of these hyperparameters will affect the accuracy of fuel consumption prediction.However,because research studies on hyperparameter values that are appropriate for a given model have been fairly rare,it is necessary to propose an adaptive algorithm for tuning hyperparameters.

In this study,an adaptive hyperparameter tuning method for ship fuel consumption prediction was developed,with the purpose of improving the prediction accuracy and robustness of fuel consumption models.In addition,we consider the influence of weather and sea conditions based on the noon report data of a 310,000-dwt oil tanker.Four machine learning algorithms were used to establish a fuel consumption prediction model.

Having introduced the background and motivation behind our present research,the rest of the study is organised as follows.Section 2 reviews existing ship fuel consumption prediction models available in the literature,such as the white box model,black box model,and grey box model,summarising the gaps in these models.Section 3 reveals the data and pre-processing method used in this study.Section 4 outlines various models for ship fuel consumption prediction and sets our adopted hyperparameter tuning method.Section 5 presents an analysis of the experimental results with and without hyperparameter tuning,and discusses the influence of weather and sea conditions on fuel consumption.Finally,Section 6 provides the conclusions and discusses the practical applications of the study.

2.Existing ship fuel consumption prediction models

Many studies focusing on ship fuel consumption prediction have thus far been conducted.In these studies,a variety of methods have been used to construct fuel consumption prediction models.Based on the existing literature,three methods for predicting ship fuel consumption can be identified: the white box models(WBM),black box model (BBM),and grey box model (GBM).In the following sections,we describe fuel consumption prediction modelling based on these three methods and summarise the gaps found in existing research.

2.1.Studies on fuel consumption based on the white box model

In several available studies,ship speed and fuel consumption are initially assumed to follow the functionfc=kvn+a[15].The relationship between ship speed and fuel consumption per unit time is then obtained based on data fitting,and the value ofnvaries mainly between 2 and 4.However,for large containers,the value ofnis assumed to be 4,5,or higher.In some studies,fuel consumption is determined based on the analysis of ship resistance in an actual voyage.The ship resistance originates mainly from two components: resistance of still water and added resistance [16];however,added resistance can be difficult to obtain because of the impact of wind and waves.

In one study,the use of the Holtrop’s method [17]required a series of empirical values.However,the research object and data used were different,and thus,it was difficult to guarantee a high prediction accuracy for the resulting model,based on the same empirical values.Another factor to consider is the speed loss of the vessel in actual voyaging,especially in harsh sea conditions.To solve this problem,Kwon et al.[18]established a method for determining the speed loss of a vessel for different wind scales and relative directions.However,the method is only suitable for some specific ship types.Furthermore,the estimation accuracy is not high,and thus,the method cannot be widely used.

Studies on fuel consumption based on the white box model require the configuration of a series of parameters,including ship parameters,operational working curves of the main engine,and propeller parameters.These parameters could change with the sailing time of the ship.The superposition of a series of parameters increases the error of prediction,leading to a limited application of the resulting model.

2.2.Studies on fuel consumption based on the black box and grey box models

In recent years,with the development of intelligent technology,information technology,wireless network technology,and data mining,vast amounts of data are being collected by sensors that are installed onboard ships [19–21].These data contain abundant information,including ship speed,ship over course,main engine speed,fore draft,aft draft,wind speed,wave height,and current speed.Machine learning algorithms,such as the artificial neural network (ANN) [22,23],the support vector machine (SVM) [24],the decision tree [25],and the Gaussian process (GP) regression[26],can be used to obtain mapping relations between multiple factors and fuel consumption.These methods are therefore widely used for fuel consumption prediction.For example,Parkes et al.[27]used the ANN to predict fuel consumption based on relevant voyaging data obtained from three sister ships and analysed the correlation between fuel consumption and influencing factors.Wang et al.[28]computed the ship resistance via an adopted theoretical formula method and used a wavelet neural network to predict ship and wind speeds.Uyan?k et al.[29]proposed the use of machine learning methods,including multiple linear (ML) regression,ridge regression,least absolute shrinkage and selection operator (Lasso),SVM,K-nearest neighbours (KNN),and DT,for predicting fuel consumption.Their experimental results indicated that ridge regression had the highest prediction accuracy amongst the 13 machine learning algorithms that were investigated.Yuan et al.[30]considered the impact of trim,speed,wind speed,and wave height on fuel consumption and proposed a Gaussian distribution method for modelling fuel consumption.

Wang et al.[31]considered that some features influencing energy efficiency are highly correlated; however,if all of these features are used as input variables,overfitting would easily occur.To solve this problem,they proposed a Lasso algorithm that shrunk irrelevant variables and predicted fuel consumption based on the noon report data of a container ship.Their experimental results showed that the Lasso had a higher prediction accuracy than the GP,ANN,and SVM.On a similar vein,Yan et al.[32]adopted the RF algorithm to predict fuel consumption based on the noon report data of a dry bulk ship.They applied the prediction result to speed optimisation and saved on fuel consumption by 2–7%.Because noon report data collection does not require the installation of additional sensors (unlike sensor data) and contains information regarding ship navigation,main engine fuel,and weather and sea conditions,several studies have used these data to predict fuel consumption.

Studies on fuel consumption based on the grey box model combine the advantages of the WBM and BBM [33].Coraddu et al.[34]transplanted prior knowledge of the WBM into the BBM and established a WBM,BBM,and GBM.Their results showed that the GBM had a higher prediction accuracy than the WBM and BBM.They applied their prediction results to trim optimisation,achieving fuel savings in the order of 0.4–3%.On the other hand,Yang et al.[35]considered speed losses due to the impact of wind and wave on a ship,especially in harsh sea weather conditions,and proposed a novel genetic algorithm for the GBM.Their results showed that the genetic-algorithm-based GBM had a higher prediction accuracy than the GBM.

The relationships amongst the many factors that affect ship fuel consumption tend to be very complicated,making it difficult to devise a function that expresses the relationships between these factors and fuel consumption.The black box model does not require empirical data input and has strong nonlinear fitting capabilities,thus explaining the relatively widespread use of the BBM for fuel consumption prediction.

2.3.Research gaps and contributions

Several studies have already applied machine learning algorithms to ship fuel consumption modelling.However,for many of these algorithms,hyperparameter values are expected to affect the prediction accuracy and robustness of the models,and there have only been a few studies on the suitability of the values of these hyperparameters for these models.Moreover,the influence of weather and sea conditions on ship fuel consumption has rarely been investigated.

In this study,based on the noon report data of an oil tanker,an adaptive hyperparameter tuning method is proposed for fuel consumption prediction modelling.The main contributions of this study are in two aspects:

1) The experimental results verified the superiority of the proposed adaptive hyperparameter tuning method and that the effects on prediction accuracy and robustness after adaptive hyperparameter tuning vary amongst the tested algorithms.After hyperparameter tuning,the ratios of the increase in prediction accuracy for the four tested algorithms ranged between 0.0773%and 2.1653%.In terms of robustness,ANN,SVM,and RF improved after hyperparameter tuning,whereas the opposite occurred for Lasso.

2) The experimental results confirmed that weather and sea conditions have an impact on ship fuel consumption and that the effects on prediction performance vary amongst the tested algorithms.After weather and sea conditions were considered in the calculations,the prediction accuracy and robustness of ANN and Lasso increased,whereas the opposite occurred for RF and SVR.

3.Fuel consumption data source and pre-processing

3.1.Source of ship fuel consumption data

In this study,the data source was the noon report of an oil tanker from the COSCO shipping company.Relevant information regarding the ship is presented in Table 1.For the sake of confidentiality and privacy,the name of the object vessel is not listed.The noon report data are filled in manually by the crew,usually once a day.The recorded information includes the main engine speed,speed through water,speed over ground,fore and aft draft,and sea and weather conditions.Table 2 outlines a sample from the data collection.The time span of data collection is from 21st January 2018 to 11th September 2019,covering a total of 635 data items.

Table 2 Sample characteristics from collected data *.

3.2.Data pre-processing

Interruptions in wireless networks,human error,bad network signals,and other similar factors lead to the production of noise in the process of collecting data.If raw data collected in such environments are directly used for model training,useful and valuable data mining will be difficult to achieve.Therefore,we must implement data pre-processing procedures,including the identification of data anomalies,as well as data cleaning and deletion.Based on relevant domain knowledge,we propose the method outlined below for filtering of the collected data.

The target ship is assumed to be in a state of ocean voyaging,and the normal sailing time recorded for each point is generally 24 h During days when the ship is loading or unloading cargo at port,the voyage time is shorter,and the threshold time is set at 12 h If the voyage time is lower than the threshold time,we delete that particular row of data.Data points that are not in the voyaging state are also deleted.When the ship is in a state of ocean voyaging,an excessively high or low engine speed decreases the level of operational efficiency.Therefore,the main engine speed is kept within a reasonable range during normal voyaging,as shown in Fig.1.The range of the main engine speed is between 30 r/min and 70 r/min,and the range of the speed over ground is between 4 kn and 16 kn Thus,we setLMES=30r/min,UMES=70r/min

LSOG=4kn,USOG=16kn.Due to the limited capacity of each ship,its draft is kept within a reasonable range.Thus,LAFD=7m,LFOD=7m,UAFD=21m,UFOD=21m.

Method for noon report data processing:

Input data: raw data Output data: clean data[1] Initialise, clear data set ← ?[2]Sort data record time[3]Delete duplicated data when record time is same[4] Delete data when voyage time is below threshold time; ID_1=find(data[voyage time] ＞threshold time)[5]Delete data when voyage state is not in voyaging; ID_2=find(data[voyage state]==voyaging)[6]Delete data when main engine speed is beyond interval range;ID_3=find(data[MES]∈[LMES,UMES ])[7]Delete data whe n S OG is beyond interval range; ID_4=find (data[SOG]∈[ LSOG ,USOG] )[8] Delete data when COG is beyond interval range; ID_5=find (data[COG]∈[0 ,360 ])[9] Delete data when aft draft is beyond interval range; ID_6=find(data[AFD] ∈[ LAFD ,UAFD] )[10]Delete data when fore draft is beyond interval range;ID_7=find(data[FOD]∈[LFOD ,UFOD ])[11] Find clean data set after data processing; I D_ 8=7 i=1 ∩ I D_ i

After pre-processing according to the aforementioned rules,the data size was decreased from the original size of 635 rows to 197 rows.The fuel consumption during a voyage is primarily related to the main engine and auxiliary engine.According to historical data,the daily fuel consumption of the auxiliary engine is approximately 5 tons,which barely changes during normal navigation.Because the fuel consumption of the auxiliary engine is relatively stable and does not need to be predicted,the fuel consumption of the main engine is assumed to be the index for measuring the fuel consumption of the ship.The corresponding time for fuel consumption is different for each row of data,and thus,for the sake of convenience,the fuel consumption value is converted based on a uniform 24-h fuel consumption,as shown in Eq.(1):

Fig.1.Changes after data pre-processing; data entries in red rectangles will be deleted: (a) Distribution of main engine speed; (b) Distribution of ship speed over ground.

whereFCmis the value of fuel consumption corresponding to them-th data entry,Tmis the voyage time corresponding to them-th data entry,TFCmis the value of fuel consumption corresponding to 24 h

3.3.Selection of influencing features for ship fuel consumption

As previously stated,since the fuel consumption of a ship is affected by many factors,a function that expresses the relationships between all these factors and fuel consumption is difficult to obtain.If an excessively large number of input variables are selected,overfitting can easily occur,and the consumption time of the program will increase exponentially because of dimensional disasters.As a result,we selected few important variables according to our research objectives and the master data.

A major influencing factor affecting fuel consumption is vessel speed [36,37].Du et al.[10]have characterized the relationship between fuel consumption of the vessel and its speed to be exponential,with an index between 2.7 and 3.3,and found that the ship speed directly or indirectly affects the level of energy efficiency.Many studies assumed speed as a determinant variable and subsequently used statistical methods to obtain the functional relationship between ship speed and fuel consumption.The main engine speed has a linear relationship with the vessel speed in still water.However,the coefficient of the index is expected to change because of the influence of sea and weather conditions on the ship in an actual voyage.These environmental conditions,which include wind,wave,and swell,cause the ship to appear to speed loss [38].If the vessel speed is directly assumed to be the input variable,the crew onboard will need to constantly adjust the main engine speed during an actual voyage.Consequently,we chose to select the main engine speed,instead of the vessel speed,as the input variable.

At the same time,cargo loading has a greater impact on ship fuel consumption [39].With regard to the cargo loading state,under ballast and laden conditions for example,a vessel at a certain speed would consume more bunker fuel under a laden condition.Considering the effect of draft on fuel consumption,we selected fore and aft draft as the input variables.

In addition to the main engine speed,the fore draft,and the aft draft,the impact of environmental factors on ship fuel consumption,such as wind speed,wave height,and current speed,cannot be ignored [40,41].The wind resistance acting on the upper surface of the vessel hull and the resistance exerted by the wind from different directions are also different.To overcome this added resistance,the vessel will need to consume more bunker fuel.Because wind speed and wave height exhibit a strong correlation,we selected the wind speed and the relative wind direction as input variables.Wind speed is expressed based on a wind scale,to which the conversion scale defined by Townsin et al.[42],as outlined in Table 3,can be applied.The relative wind direction can be obtained according to Eq.(2),whereθRis the relative wind direction,θwis the absolute wind direction,andθsis the head course of the ship.

Table 3 Conversion between Beaufort wind scale and wind speed [42].

Table 4 Hyperparameter settings for each algorithm.

Table 5 Mean and variance of evaluation metrics for each algorithm*.

As per our above-mentioned analysis,the main engine speed,fore draft,aft draft,wind speed,and relative wind direction were selected as the main factors that influence ship fuel consumption,whereas the daily fuel consumption of the main engine was selected as the output of our proposed model.

3.4.Data standardisation

Because of the different dimensions and distribution ranges amongst the data features,directly using those data for training could lead to excessive time for attaining convergence.In this case,it would be unlikely for the training to yield appropriate results.Therefore,those data will need to be standardised before being used for model training.Commonly used standardisation methods include the max-min standardisation method and Z-score standardisation method.We adopted the latter Z-score standardisation method for the conversion of data,in accordance with the steps outlined below.

The average value for thej-th feature(j=1,2,...p)and the standard deviationS2jare calculated according to Eqs.(3) and (4),as follows:

whereNis the number of data samples,andpis the number of input features:

The standardised value of each data point is then calculated based on the transformation according to Eq.(5),as follows:

Eqs.(3)–(5) can therefore be used to transform the data points of each column,ensuring that each dimension of the data follows a normal distribution.

4.Methodology

4.1.Modelling method

As mentioned earlier,several machine learning algorithms have already been applied to the prediction of ship fuel consumption.Based on their respective principles used for data fitting,these algorithms can be divided into four types,namely: statisticallearning-based models (e.g.Lasso,Ridge) [29,31],instance-based models (e.g.SVR,KNN) [24,25],tree-based models (e.g.RF,DT)[25,32],and neural-network-based models (e.g.ANN,Long Short Term Memory network) [43–45].In this study,to compare the prediction accuracies of these different types of models,the ANN,SVR,RF,and Lasso algorithms were selected for fuel consumption prediction.

The establishment of the proposed ship fuel consumption prediction model is shown in Fig.2,including the partitioning of the dataset,the hyperparameter tuning,and the evaluation metrics used for the testing data.The dataset is divided into training data and testing data according to a ratio of 0.8:0.2,respectively.To ensure that the entire dataset is used for training,the training data can be divided intokfolds,where (k–1) folds of data are used for training,whereas the remaining fold is used for evaluation.The average ofkexperiment results is then considered as the value for the evaluation metrics model.The optimal hyperparameters are determined based on the coefficient of determination(R2).At present,there is no unified standard for the value ofk,but relevant studies [25]have shown thatk=10 is applicable to most datasets,and thus we adopted a 10-fold cross validation.

For some machine learning algorithms,a series of hyperparameters needs to be set prior to the training procedure,because these hyperparameter values greatly affect the prediction accuracy and robustness of the model.Thus,we must determine suitable hyperparameter values that are able to improve the prediction accuracy of our proposed model.Known hyperparameter tuning methods include grid search [46],random search [47],and Bayesian optimisation [48].Grid search traverses all possible hyperparameter values.However,when several parameters are required,and large amounts of data are used for training,the computational time of the grid search method increases exponentially.On the other hand,in the case of random search,the hyperparameter values are randomly sampled with a given probability at each iteration.However,the random search method is mainly applicable to cases where the hyperparameter values are continuous.In the case of Bayesian optimisation,sample hyperparameter values based on prior knowledge are searched for,and thus some hyperparameter values are skipped in the next iteration,which can save computational time in comparison with random and grid search methods.For those reasons,we adopted the Bayesian optimisation method for our proposed tuning of hyperparameters.

4.2.Evaluation metrics

The main purpose of our study is to analyse the prediction accuracy of our proposed model,and thus it is necessary to measure the prediction performance of the model.To this end,the coeffi-cient of determination (R2),mean absolute error (MAE),and mean squared error (MSE) were used as evaluation metrics,and were calculated using Eqs.(6)–(8) as follows:

wheremis the number of testing data points,yiis the actual value of the testing data point,is the predicted value of the testing data point,andis the average value of the testing data.

5.Analysis of prediction accuracy

5.1.Fuel consumption prediction accuracy before and after hyperparameter tuning

The experiments were all performed using a Windows 10,64-bit operating system,with an Intel Core i5 processor,8GB of RAM,a Python version 3.8,and in a Spyder integrated development environment.

Fig.2.Architecture of ship fuel consumption prediction model.

With regard to the ANN algorithm,whereas no standard method exists for determining the number of hidden layers,this number largely depends on data volume and selected features.According to previous research [14],an ANN will have high prediction accuracy if one hidden layer exists,and thus we set the number of hidden layers to one.The final ANN structure adopted was 5–1–1.

For some of the algorithms,many hyperparameters need to be set up,which could result in a very long computational time,should all hyperparameters be traversed.Thus,in our analysis,only some important hyperparameters were selected to be set up.Based on the regression principle of each algorithm,and the existing literature [29,31,32],the relatively important hyperparameters for each algorithm were set up as shown in Table 4.

To validate whether the Bayesian search method improves the fuel consumption prediction accuracy of each model,we conducted experiments including and excluding hyperparameter tuning.For the experiments excluding hyperparameter tuning,the hyperparameters were set to the default values extracted from the scikitlearn library.Instability of the model due to different partitioning of the dataset was considered,and thus the dataset needed to be divided several times.The division between training data and testing data was controlled via configuration of the random state value in the library,which was rounded off [1,20].An average value taken from 20 different experiments was considered as the performance metric of the model.The prediction accuracies of each algorithm before and after hyperparameter tuning are shown in Table 5.

For the ANN,the value of R2increased after hyperparameter tuning,whereas the standard deviation decreased,which indicate that the use of the Bayesian optimisation method can effectively improve the prediction accuracy of the ANN.For the SVR,although the variance of R2increased,the variance remained small at 0.0301,whereas the mean values and variances of the MSE and MAE decreased.Therefore,we concluded that the prediction accuracy of the SVR increases once hyperparameter tuning is applied.For the RF,the deviation values of R2,the MSE,and the MAE decreased after hyperparameter tuning,whereas the values of the MAE and R2increased,and the value of the MSE decreased,which indicate that the prediction accuracy and robustness of the RF increases once hyperparameter tuning is applied.For the Lasso,the value of R2increased after hyperparameter tuning,whereas the values of the MSE and MAE decreased; however,the deviation values of R2,the MSE,and the MAE increased in this case.These results indicate that although the prediction accuracy of the Lasso increased,its robustness decreased after hyperparameter tuning.

Fig.3.Value of R 2 for each model.

Based on the analysis above,we can determine that the value of R2for each algorithm increases,and that the values of both the MSE and MAE decrease,which indicate that the prediction accuracy of each algorithm increases after hyperparameter tuning.As a result of the increase in the amplitude of R2,hyperparameter tuning is shown to improve the prediction accuracy for the different algorithms considered,proportionally as follows: ANN,Lasso,SVM,and RF.The rates of improvement are found to range between 0.0773% and 2.1653%.Furthermore,the robustness of the ANN,the SVM,and the RF is shown to increase after hyperparameter tuning,whereas the opposite occurs for the Lasso.

5.2.Comparison of prediction accuracy with and without considering environmental factors

To validate whether the environmental factors affect the fuel consumption prediction accuracy,we have conducted an experiment,taking into account the possibility to include or exclude such factors.The dataset was divided into two cases: (i) the S1 case,considering the influence of wind direction and wind speed,with input variables including main engine speed,wind speed,relativewind direction,fore draft,and aft draft; (ii) the S2 case,excluding the influence of wind direction and speed,with input variables including main engine speed,fore draft,and aft draft.For both cases,the output was set as the daily fuel consumption of the main engine.The prediction accuracy of testing data relative to each model is shown in Table 6.

Table 6 Prediction accuracy of each model with and without considering environmental factors.

As shown in Table 6,when wind speed and relative wind direction were considered,the prediction accuracies of the ANN and Lasso increased,whereas those of the SVR and RF decreased,and the ANN was found to have the highest prediction accuracy amongst the four models.However,excluding wind speed and relative wind direction as influencing factors,the SVR was found to have the highest prediction accuracy amongst the four models.

The R2values for the experimental testing data are shown in Fig.3,illustrating the influence of environmental factors on the prediction accuracy of each model.For all four models,the deviation of the R2value was found to be less than 0.05,which indicates that all fuel consumption prediction models have strong robustness.Also,we observe that the prediction accuracy is sensitive to wind speed and relative wind direction.For the ANN model,the value of the R2increased in most experiments considering the environmental factors,whereas the opposite occurred for the SVR and RF.For the Lasso,the values of the R2in all experiments considering wind speed and relative wind direction were higher in comparison to experiments excluding wind speed and relative wind direction as influencing factors.

6.Conclusion

In this study,based on the noon report data of an oil tanker,an adaptive hyperparameter tuning method is proposed for fuel consumption prediction modelling.The Bayesian hyperparameter tuning method was used to determine reasonable values for the hyperparameters of different algorithms used for fuel consumption prediction.Considering the influence of weather and sea conditions,ship fuel consumption prediction models were established.The following conclusions are reached:

1) After the use of hyperparameter tuning,the R2value for each algorithm increased,whereas the MSE and MAE decreased,which indicate that the use of Bayesian optimisation can effectively improve fuel consumption prediction accuracy.

2) Both weather and sea conditions impact ship fuel consumption,and the effects on prediction performance vary amongst the tested algorithms.Considering weather and sea conditions in the calculations,the prediction accuracy and robustness of the ANN and Lasso algorithms increased,whereas the opposite occurred for the RF and SVR algorithms.

3) The experimental results confirm the validity of our proposed adaptive hyperparameter tuning method,and show that the effects on prediction accuracy and robustness also vary amongst the tested algorithms.Considering hyperparameter tuning in our analysis,the ratios for the increase in prediction accuracy of the four tested algorithms ranged between 0.0773% and 2.1653%.In terms of robustness,the ANN,SVM,and RF algorithms improved after hyperparameter tuning,whereas the opposite occurred for the Lasso algorithm.

The fuel consumption prediction model proposed in this study can be effectively extended to the real-time monitoring of ship energy efficiency and the detection of abnormal fuel consumption.An accurate calculation of ship fuel consumption is an important part of weather route optimisation,trim optimisation,and speed optimisation.In practice,the management staff of ship companies are very concerned about bunker fuel costs and gas emissions of ships.Since our chosen reference is an oil tanker,it remains to be verified whether our proposed model is applicable to other types of vessels.In addition,given that the collected data originated from noon reports,the sampling frequency and accuracy of sampled data are low,limiting the amount of useful information that can be extracted.In future investigations,we will need to collect highsampling-frequency and high-accuracy data,considering additional factors that may impact ship fuel consumption.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to acknowledge the support of COSCO,Shanghai Maritime University.This research was funded by National Natural Science Foundation of China (Grant no.52001134)and Major Project of Shanghai Science and Technology Commission(Grant no.18DZ1206300).