129

1 INTRODUCTION

In this world of advanced shipbuilding technology,

large volumes of cargo are transported worldwide by

ships. Recently, in addition to cost reduction, efficient

operation is required to reduce the global

environmental burden. Consequently, there is a

growing interest in weather routing, which can

provide energy-saving voyage plans by considering

the ship's performance and condition and forecast

information on weather and sea conditions

encountered during the voyage. In weather routing,

an optimal route is determined before the voyage

using optimization methods such as dynamic

programming, considering the forecast information

and the ship's propulsive performance in actual sea

conditions [1,2]. Therefore, high-quality weather

routing requires accurate prediction of a ship's fuel

consumption and ship’s speed. However, these

predictions are not straightforward and have been the

subject of extensive research. For instance, a method

of modelling using statistical regression equations

based on multiple tests of a ship's performance under

specific environmental conditions is available [3,4].

This makes it possible to estimate the fuel

consumption and speed of the vessel by inputting the

control variables such as main engine revolution,

propeller blade angel used to operate the vessel, in

addition to the forecast information on the weather

and sea conditions of the voyage. The advantage of

this method is its high interpretability because the

modelling is based on physical knowledge. However,

this method has limitations because it simplifies the

weather, sea conditions, and other conditions of actual

voyages. Consequently, the obtained models do not

represent all aspects of ship performance, and there

are issues with the accuracy of predicting fuel

consumption and ship’s speed. Therefore, machine

learning has been adopted for these predictions in

recent years [5]. This method models a ship's

navigation performance implicitly by training actual

navigation data on a machine learning model such as

Prediction of Ship's Speed Through Ground Using

the

Previous Voyage's Drift Speed

D. Yamane & T. Kano

NPO Marine Technologist, Tokyo, Japan

ABSTRACT: In recent years, 'weather routing' has been attracting increasing attention as a means of reducing

costs and environmental impact. In order to achieve high-quality weather routing, it is important to accurately

predict the ship's speed through ground during a voyage from ship control variables and predicted data on

weather and sea conditions. Because sea condition forecasts are difficult to produce in-house, external data is

often used, but there is a problem that the accuracy of sea condition forecasts is not sufficient and it is

impossible to improve the accuracy of the forecasts because the d

ata is external. In this study, we propose a

machine learning method for predicting speed through ground by considering the actual values of the previous

voyage’s drift speed for ships that regularly operate on the same route, such as ferries. Experimental results

showed that this method improves the prediction performance of ship’s speed through ground.

http://www.transnav.eu

the

International Journal

on Marine Navigation

and Safety of Sea Transporta

tion

Volume 17

Number 1

March 2023

DOI: 10.12716/1001.17.01.

130

a neural network (NN) [6]. Although this method

lacks interpretability, unlike modelling in simplified

situations, it can evaluate ships more accurately

because it considers actual voyage data. Therefore,

this method may also be effective in the current

situation where the data collection infrastructure

during voyages is becoming easier with the

development of IT and other technologies. However,

caution is required when applying machine learning

models as they may not be effective depending on the

target of prediction and the number of data available

for training. Also, one of the explanatory variables

used as input to the model is the forecast information

on weather and sea conditions provided by

meteorological agencies, but it should be noted that

there are forecast errors. Thus, the authors pay

attention to the fact that captains use the state of the

previous day's current for navigation. Since currents

generally change slowly over time, the previous day's

currents are expected to contribute to predicting

ship’s speed on the current day's voyage. Although it

is not possible to directly measure the actual values of

the ocean currents, the drift speed v

d, which indicates

the magnitude of the ship's current caused mainly by

the ocean currents, can be calculated using the ship's

speed through ground v

g and speed through water vw,

as shown in equation (1).

= −

d gw

vvv

(1)

Based on the mentioned above, this study

proposes a method for estimating the fuel

consumption and the ship’s speed using LightGBM

[7], which can incorporate information on the drift

speed of the previous voyage. This method improves

the prediction accuracy of ship’s speed through

ground, which is significantly affected by sea

conditions. The proposal method was also found to be

effective in predicting fuel consumption and ship’s

speed through water.

Finally, this paper is organized as follows: Section

2 introduces the research on the prediction of fuel

consumption and ship’s speed and machine learning-

based forecasting, while Section 3 identifies the

dataset's characteristics and the task to be solved.

Section 4 describes the proposal method, and Section

5 presents numerical experiments on the drift speed

and the proposal method. Finally, Section 6

summarizes the paper and discusses future prospects.

2 RELATED WORKS

When predicting a value in various fields, it is a

common practice to express the relationship between

explanatory variables (inputs) and objective variables

(outputs) using mathematical formulas. Similar

methods have also been applied in the shipping field.

For instance, in [8], the relationship between hourly

fuel consumption l/h and ship’s speed v

s per hour is

expressed using a component-separated physical

model, as shown in equation (2).

= ++

∑

1 2 3, ,

s wind i wave i

aW v a f a f

(2)

The first term on the right side represents the

resistance in calm seas, the second term represents the

resistance due to wind, and the third term represents

the resistance due to waves. Here, W is displacement,

wind is the resistance component due to wind, and fwave,i

is the resistance component due to waves. These

constants, a,a

1,a2, and a3,i, can be estimated using

regression analysis or other methods based on the

ship's operating variables such as main engine

revolution and forecast information on weather and

sea conditions. Also, if the fuel consumption per hour

in equation (2) is assumed to be proportional to the

cube of the main engine revolution, as shown in

equation (3), the ship’s speed through water can be

predicted.

lh N

(3)

On the other hand, in recent years, machine

learning models, particularly neural networks, have

increasingly been utilized to make predictions across

various fields [9,10]. One of the advantages of using

machine learning models is their high expressive

power. Unlike a modeling using mathematical

formulas, where the regression function is set based

on assumptions of the relationship between

explanatory variables and objective variables,

machine learning models automatically learn the

relationship from the data and thus can capture more

detailed and complex phenomena. Although the

modeling using mathematical formulas, as shown in

equations (2) and (3), is highly interpretable, its

expressive power is limited. Moreover, the function

used for regression must be manually selected,

making it prone to errors. In contrast, machine

learning models are more complex and difficult for

humans to interpret, but they have the potential to

achieve high accuracy due to their high expressive

power. Therefore, in the shipping field, machine

learning models are being used to predict fuel

consumption and ship’s speed. For instance, in [11], a

neural network is used to predict fuel consumption

based on seven explanatory variables, including

ship’s speed, main engine revolution, average draft,

trim, cargo volume, and wind and sea effects.

Similarly, [5] employs a neural network to predict

ship’s speed through ground using explanatory

variables such as main engine revolution, wing angle,

wind direction, wind strength, sea current direction,

sea current strength, and elapsed time since entering

the dock. These studies indicate that the most

common variables used as explanatory variables in

predicting fuel consumption and ship’s speed are

operating variables of the ship, variables representing

weather and sea conditions, and elapsed time since

docking. It should be noted that the elapsed time since

docking is used as an explanatory variable since a

ship's performance tends to decrease over time due to

the attachment of marine organisms after it enters the

dock and is cleaned. Prediction using Transformer or

LSTM, types of neural network models that can

consider time series characteristics, has also been

investigated [12]. With this model, data obtained

131

during the voyage can be used as explanatory

variables, enabling more accurate predictions.

However, while this model is effective in situations

where real-time ship’s speed prediction is required, it

is not suitable when the model is intended to be used

before sailing, as in this study. Also, there is a study

that machine learning models, such as XGBoost[13]

and LightGBM[7], to predict and compare fuel

consumption of ships[14]. Both models have the

advantage of achieving high accuracy and speed even

without a large amount of data. However, as shown

in [14], LightGBM is generally preferred over XGBoost

because it is faster and more accurate. Although

neural networks are commonly used in machine

learning studies due to their versatility and name

recognition, decision tree-based machine learning

models are more effective in certain cases. As

demonstrated in [15], decision tree models perform

better than neural network models when the data is

limited and in tabular form, as in this study.

Therefore, we use LightGBM, one of the decision tree

models, in this study.

3 DESCRIPTION OF DATA CHARACTERISTICS

AND CHALLENGES IN DEVELOPING THE

METHOD

The target ship used in this study is sailing Japanese

southern part of Pacific Ocean, and from January 3,

2022 to May 11, 2022, monitoring data such as

datetime, fuel consumption, ship’s speed

(water/ground), position (latitude, longitude), wind

direction and speed (relative), main engine revolution,

propeller blade angle, direction of course, and

direction of moving are automatically collected every

10 minutes. The data is then transmitted to and stored

on a server on land via ship-to-shore communications.

In this study, we performed spatiotemporal

corrections to the grid point value (GPV) data

provided by the Japan Meteorological Agency (JMA),

and calculated and appended the wind (wind

direction and wind speed), waves (wave height, wave

direction and wave period), and Sea and tidal currents

(current speed) corresponding to the time and ship

position of the collected data. The number of data

recorded during ship operations is approximately 80-

100 per day. Table 1 summarizes the information on

the data, and Table 2 shows an image of the data

obtained.

Note that if the same data is used for both training

and testing the model, the model already knows the

answers, resulting in a high prediction accuracy. In

the field of machine learning, this problem is known

as leakage, and measures need to be taken to prevent

it during model evaluation. On the other hand, in the

data analysed in this study, measurements taken

during the same voyage tend to be similar. Thus,

indirect leakage may occur even if the measurements

were taken at different times, and the data from the

same voyage needs to be handled with care.

Table 1. Information on data

________________________________________________

Period Number Measurement Forecast data

of data data used in used in

this study this study

________________________________________________

2022/1/3- 10329 datetime, wind

2022/5/11 (Data while latitude/ direction(deg),

the ship is longitude(deg), wind

moving fuel speed(m/s),

during the consumption(ℓ), wave

measurement ship’s speed height(m),

period) through water wave direction

(knot), (deg), wave

ship’s speed period (s),

through ground wave height

(knot), (m),

main engine wave

revolution(rpm), period(s),

propeller blade current speed

angle(deg), (m/s)

direction of

course(deg),

direction of

moving(deg),

inlet and outlet

________________________________________________

Table 2. Image of data

________________________________________________

datetime latitude longtitude … current

speed

________________________________________________

2022/1/3 0:00 33.4334 131.7932 … 0.22

2022/1/3 0:10 33.4003 131.7121 … 0.17

: : : : :

2022/5/11 23:50 32.7342 132.4278 … 0.21

________________________________________________

Although the data used in this paper is comparable

to data typically measured on a ship, there are three

issues that need to be addressed. The first issue is that

the ship’s speed through water includes errors. While

the ship’s speed through ground can be measured

almost accurately using GPS, the ship’s speed through

water is measured using a sensor installed on the

bottom of the ship. These errors include bias and

change over time and can affect the value of the

prevailing current, which is calculated using equation

(1). Therefore, it is necessary to develop a method that

is somewhat robust to errors.

The second issue involves devising a method to

incorporate information on the previous voyage's drift

speed. As previously mentioned, data is measured

every 10 minutes, and a certain amount of data from

the previous voyage has been accumulated. While it is

possible to use all of the data for forecasting, there is a

lot of unnecessary information, and the computation

time increases significantly. Thus, it is necessary to

appropriately extract the necessary information and

use it for forecasting.

The third issue pertains to the limited information

available from the previous day's data. While data

from the previous day can be obtained, only data

from on the actual navigated route can be collected

(refer to Figure 1). Therefore, it is necessary to

supplement the drift speed for coordinates other than

the route taken. However, the completion of

coordinates for which no data is available may

introduce noise. Thus, a method needs to be

developed to incorporate the drift speed information

as noise-free as possible.

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Figure 1. Relationship between the route and the data

4 PROPOSAL METHOD

In this section, the proposal method is explained in

detail. Section 4.1 provides an overview of the

proposal method, while Section 4.2 describes the

module designed to extract the necessary information

on the drift speed from the previous day's voyage

data. Section 4.3 explains LightGBM machine learning

method and the advantages of using it in the

proposed model.

4.1 Overview of the Proposal method

Figure 2 illustrates the overall diagram of the proposal

method: LightGBM receives inputs that include the

features extracted by the module that appropriately

extracts drift speeds from the previous voyage's data,

ship coordinates, ship operating variables, and

forecast data on weather and sea conditions. Based on

these feature values, the system estimates and outputs

the target variables, namely fuel consumption, ship’s

speed through water, and ship’s speed through

ground.

As discussed in Section 3, there were three main

issues in this research: (1) extracting necessary

information from a large amount of previous voyage

data, (2) accounting for errors in ship’s speed through

water, and (3) appropriately supplementing the drift

speed at coordinates not covered by the previous

voyage. The proposal method addresses the first issue

by using a module to extract information on drift

speed from the previous voyage's data, and addresses

the second and third issues by using LightGBM.

Figure 2. Overall diagram of the proposal method

4.2 Module to properly extract drift speeds from the data

of the previous voyage

As mentioned earlier, it is necessary to extract only

the necessary information from the data from

previous voyages since there is a lot of unnecessary

information. Given that the drift speed typically

depends on the coordinates, we believe that the drift

speeds around the coordinates to be predicted are

useful for the forecast, and conversely, there is no

need to consider the drift speeds at coordinates

further away from the coordinates to be predicted.

Therefore, we extract data as follows. First, we

perform meshing (N × M) on the square region

containing the coordinates of the possible paths

during the voyage. Next, if the data corresponding to

each cell of the meshed coordinates is available in the

previous voyage data, we calculate the drift speed

using equation (1) and embed the information in the

cell. Then, the system extracts drift speeds contained

in the h cells on the left, right, top, and bottom of the

cell whose coordinates correspond to the coordinates

to be predicted. Cells with no information are also

extracted as None, indicating that they have no

information. The above flow is summarized in

Algorithm 1, and Figure 3 illustrates the algorithm

when N=6, M=12, and h=1. When inputting features to

LightGBM, they are named with the cell to be

predicted as the center (0, 0), and the positive

directions are right and down. An example of this is

shown in Figure 4.

Figure 3. Image of the algorithm when N=6, M=12, and h=1

Figure 4. Image of feature naming

________________________________________________

Algorithm 1 Extraction of drift speed from data of previous

voyage

________________________________________________

Require: Coordinate of target c, Data of previous voyage D

1: map ≔ Initialize an N × M array with None

2: for d in D do

3: i,j ≔ Calculate i,j corresponding to the squares of

map from the upper table of coordinates

contained in d

4: map[i,j] ≔ the value of the drift speed using

equation (1) from the ship's speed through

ground and water included in v

5: end for

6: drifts ≔ Initialize an (2h+1) × (2h+1) array with None

7: s,t ≔ Calculate s,t corresponding to the squares in

map from c

8: for i in -(2h+1)...(2h+1) do

9: for j in -(2h+1)...(2h+1) do

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10: drifts[i,j] ≔ map[s+i,t+j]

11: end for

12: end for

13: drifts ≔ Flatten drifts to one dimension

14: return drifts

________________________________________________

4.3 LightGBM

LightGBM is a machine learning method that employs

an ensemble of multiple decision trees and is widely

recognized for its speed and accuracy. To provide an

overview of LightGBM, we briefly describe the

decision tree on which LightGBM is based (for a

detailed description of LightGBM, refer to [7]). The

trained decision tree is a tree structure, in which non-

terminal nodes have rules expressed in terms of

specific features and threshold values, and terminal

nodes have predicted values of the objective variable.

When data is inputted into the model, a rule-based

decision is made to determine if a particular

explanatory variable in the data exceeds the threshold

value set at the node or not. The process is repeated

until the terminal node is reached, and the objective

variable value of the terminal node is output as a

predicted value. During training, the feature values

and threshold values of each node are determined to

ensure accurate predictions for the training data.

Figure 5 illustrates an example of a decision tree and

data for predicting ship’s speed through ground. This

figure is used to explain the forecasting process. At

the root node, the branching rule is whether the main

engine revolution is greater than or less than 620. The

example data has a main engine revolution of 630, so

it branches to the right child node. At the branched

child node, the rule for branching is whether the wave

height is greater than or less than 0.5, and since the

wave height is 0.199 in the data, the node branches to

the left child node. Since the branched child node is

the terminal node, the predicted ship’s speed through

ground is output as 28.31, which is set as the

predicted objective variable value. Although a

detailed explanation is omitted here, LightGBM

generates multiple decision trees and outputs the

predicted value of each tree. The model outputs a

final prediction that takes the predictions of each tree

into account.

Figure 5. Image of forecasting method using decision trees

In this study, LightGBM was utilized to predict the

objective variable, as shown in Figure 2. Drift speeds

from previous voyages and other variables, such as

ship coordinates, ship operating variables, and

forecast data on weather and sea conditions, were

included as explanatory variables for the model.

As discussed in Section 2, machine learning

methods have recently been applied to the shipping

field. However, many of the machine learning

methods employed are neural networks. Among

them, LightGBM was chosen for this research for

three reasons.

Firstly, LightGBM is more effective in learning for

the present data. Neural networks are better suited for

tasks with unstructured data, such as images and

sound, rather than structured data like table data used

as input in this study. Additionally, a large amount of

data is typically required for training neural

networks, as explained in Section 3. However, the

present data comprises only 10,000 cases, which is not

large enough to train a neural network effectively. On

the other hand, LightGBM can learn sufficiently with

this amount of data.

Secondly, LightGBM is robust to a certain degree

of error. This model is independent of the numerical

scale of explanatory variables due to its rule-based

module for determining outputs, as explained earlier.

Therefore, it is unaffected by implicit errors in drift

speeds computed in equation (1). For instance, even if

the data contains an error of ε, a rule with a threshold

shifted by ε is automatically learned when a rule is

created for a certain node.

Thirdly, there is no need for supplementation of

the drift speeds. As explained in Section 4.2, the drift

speeds around the coordinates to be predicted are

input to LightGBM. These features include None,

which indicates that there is no data. In general

machine learning methods, including neural

networks, when None is given as input, the user must

appropriately supplement the numerical values,

which can easily lead to a decrease in prediction

accuracy. However, LightGBM can treat None as

input as it is, and it learns by taking the None

information into account. This eliminates the need for

the user to be involved in the completion of numerical

values and has the advantage of achieving higher

prediction accuracy compared to other methods.

5 NUMERICAL EXPERIMENTS

This section aims to validate the accuracy of the drift

speed calculated by equation (1) and the proposal

method. Section 5.1 details the learning and

evaluation procedures utilized in numerical

experiments. In Section 5.2, experiments were

conducted to verify the accuracy of the drift speed,

and in Section 5.3, experiments were conducted to

validate the proposal method.

5.1 Model training and evaluation method

To conduct the training and testing, a walk-forward

method is utilized. Specifically, training is initially

performed using data collected from January 3, 2022,

to April 15, 2022, while the ship is in motion.

Subsequently, data from April 16, 2022, is used as the

134

test set to predict the fuel consumption and ship’s

speed of the ship during its operation. The training

and test sets are then shifted by one day, as depicted

in Figure 6. The accuracy of the predictions for all

data in the test period is evaluated using this method.

Note that the number of the data between January 3

and April 15 is 8602.

Figure 6. Walk-forward method

The accuracy of the error of the prediction for data

i, Accuracy

i is calculated as in equation (4). Note that

the average value of the objective variable for all data

while the ship is moving is

, the true value of the

objective variable in the data is y

, and the value of the

objective variable predicted by entering the

explanatory variables for data i in the model is y

−

Accuracy

(2)

Since this index is the accuracy of the error, the

unit is %, and the closer to 0, the better the value. We

also compute Accuracy

i for all data used in the test and

evaluate its mean value and standard deviation.

Note that the machine learning model has several

hyperparameters that must be set by the analyst

during training. These hyperparameters significantly

affect the performance of the model, and

hyperparameter tuning is a crucial step in model

learning. There are three main methods for

hyperparameter tuning: random search, grid search,

and Bayesian optimization. In this study, we use

Bayesian optimization, which efficiently searches for

the optimal parameters using Gaussian process

regression, and allows for efficient hyperparameter

tuning in a limited amount of time. Specifically, we

use the best parameters among 30 iterations for the

training of our model.

5.2 Experiment 1: Validity of the drift speed

In this study, we examined the effectiveness of this

method for predicting drifting speed based on the

captain's use of the previous day's sea conditions for

voyage planning. However, it is uncertain whether

the value is accurate enough for forecasting as it is not

directly measured. Therefore, in this section, we

conduct an experiment to verify the validity of the

predictions by comparing the prediction accuracy of

LightGBM with and without using the drift speed as

an explanatory variable, assuming that the prediction

of the ship’s speed through ground, which is most

affected by the sea conditions, will be performed.

Specifically, we compared the accuracy of two

models: LightGBM that predicts the ship’s speed

through ground by entering the main engine

revolution, propeller blade angle, latitude, longitude,

direction of course, direction of proceeding, wind

direction, wind speed, wave height, wave direction,

wave period, ocean current, port arrival and

departure, and time since the last dock

entry(calculated from the date and time of the

modeling data) as explanatory variables, and a

LightGBM model that inputs drift speeds calculated

using equation (1) as additional explanatory variables,

the variables described above. If the prediction error

accuracy of the latter model is sufficiently smaller

than that of the former model, then the drift speed is

shown to be an effective feature. Note that ship’s

speed through water and ground are not used as

inputs, so no leakage occurs. The drift speeds are

calculated using the ship’s speed through water and

ground measured at the same time as the data to be

predicted, so they cannot be used in actual operation.

Therefore, this experiment was conducted to evaluate

the degree to which the characteristic drift speeds

reflect the state of the oceanographic phenomena.

The results of the experiment are shown in Table 2.

The results indicate that the use of drift speeds

improves the error accuracy by more than 1% on

average, and the standard deviation is also improved

by more than 0.5%. This suggests that the drift speed

is a good feature that captures the sea condition.

Table 2. Results of Experiment 1.

________________________________________________

Method Mean of Standard

Accuracy

i deviation of

Accuracy

________________________________________________

LightGBM without drift speeds 2.311 1.782

LightGBM with drift speeds 1.234 1.200

________________________________________________

5.3 Experiment 2: Effectiveness of the proposal method

This section presents experimental results conducted

to confirm the effectiveness of the proposal method.

Four methods, namely neural networks, LightGBM,

LightGBM with the drift speeds from the previous

voyage (proposal method), and a component-

separated physical model (for reference), are used to

predict fuel consumption, ship’s speed through water

and ground. Their evaluated values are compared.

The component-separated physical model is a model

that predicts using mathematical equations with

parameters estimated based on physical findings.

However, as introduced in [8], this experiment uses a

model with parameters identified by NPO Marine

Technologist using collected data from July 2, 2021, to

October 6, 2021, when the ship was put into service.

Therefore, this model is different from the machine

learning model evaluated using data up to the

previous day, and cannot be compared simply.

However, this comparison is made for reference

purposes in this experiment. Note that the model

outputs predicted values for the objective variable by

inputting the main engine revolution, propeller blade

angle, latitude, longitude, direction of course,

direction of proceeding, wind direction, wind speed,

wave height, wave direction, wave period, and ocean

current. In addition to the explanatory variables used

in the component-separated physical model, the

135

neural network and LightGBM make predictions by

inputting the elapsed time since the last docking and

the port arrival/departure as explanatory variables.

Note that the neural network is implemented using

scikit-learn's MLPRegressor. The hidden layer of the

neural network uses relu as the activation function

and Adam is used as the optimization algorithm for

the neural network. In addition to these variables, the

proposal method also inputs as explanatory variables

the drift speed extracted from the data of the previous

voyage using the module described in Section 4.2. In

the experiments described in this section, test data for

which no previous voyage’s data existed were

excluded from the evaluation. Moreover, while

machine learning models can be updated easily, the

component-separated physical model of [8] is difficult

to update frequently due to practical works. For this

reason, the parameter of the model already settled

and used in actual weather routing operations was

used in this experiment.

Table 3 presents the mean and standard deviation

of the errors in predicting fuel consumption

, ship’s

speed through water

, and ship’s speed through

ground

for each method. The frequency

distribution of the errors in the predictions is shown

in Figures 7-9. Note that the neural network

predictions are excluded from each figure due to their

large errors.

Table 3. Results of Experiment 2

________________________________________________

Method Fuel Ship’s speed Ship’s speed

consumption through water through ground

________________________________________________

Neural 7.492＋6.273 57.36±42.17 32.66±25.60

Network

LightGBM 0.666±0.594 1.316±1.354 2.225±1.761

LightGBM 0.651±0.617 1.300±1.408 2.033±1.666

with drift

speeds

(proposal

method)

component- 1.102±1.002 1.778±1.550 3.426±2.860

separated

physical

model

(for reference)

________________________________________________

Figure 7. Frequency distribution of errors related to

forecasting fuel consumption

Figure 8. Frequency distribution of errors related to the

prediction of ship’s speed through water

Figure 9. Frequency distribution of errors related to the

prediction of ship’s speed through ground

Following three findings were introduced from the

experimental results. Firstly, the neural network had

the worst performance for all prediction targets and

was unable to make any predictions. There are two

possible reasons for this outcome. The first is the

small amount of data available. The second is the

limited information relative to the number of data. We

did not prepared enough to work with in this

experiment for the neural network. In addition, as

explained in Section 2, the feature values of data from

same-day voyages tend to be similar, resulting in

insufficient learning due to a small amount of

substantially different data.

Secondly, the prediction accuracy of all methods

except neural networks is generally acceptable. Table

3 demonstrates that even in the worst case, the error

accuracy of the component-separated physical model

for predicting ship’s speed through ground is

approximately 3.4%, suggesting that all methods have

an accuracy that is generally acceptable in practical

terms.

Thirdly, the proposal method's predictions are the

most accurate for all prediction targets, and it

performed well even when the neural network could

not learn. This result indicates that the proposal

method can handle complex events in actual voyages

with not so much data and demonstrates its

superiority. However, as previously mentioned, it is

not possible to make a fair comparison with the

component-separated physical model since it has been

some time since its set parameters of the model.

Figure 10 shows the results obtained when the

component-separated physical model was applied to

136

data at the beginning of its creation to predict the

ship’s speed through water (referred to as the

component-separated physical model (original)),

added to the results in Figure 8. It can be seen that the

prediction for the ship’s speed at the beginning of the

model has a smaller error. This suggests that the

parameter of the component-separated model tends to

change over time due to hull fouling and other

factors, and that the estimated ship’s speed tend to be

larger than the actual measured values. Therefore, it is

essential to update the parameters as required to

make accurate estimates. Note that the proposal

method is completely black-boxed, and it is not

possible to explain the reasons for the outputs

generated from a given input. However, the proposal

method, which can be updated easily, is believed to

offer practical advantages.

Figure 10. Graph of component-separated physical model

(Original) added to the results in Figure 8

6 CONCLUSION

In this study, we aimed to enhance the prediction

accuracy of fuel consumption, ship’s speed through

water, and ground in order to achieve highly accurate

weather routing. In previous studies, many features

used to predict them were commonly measured and

readily available, such as ship operating control

variables and predicted values of weather and sea

conditions, while few other features were used.

Additionally, neural networks have often been

employed in machine learning models. In this study,

we focused on the fact that captains and crews use the

sea conditions from the previous voyage and

proposed a method that combines LightGBM with a

module for integrating the drift speed from the

previous voyage as feature. In experiments, after

confirming that the drift speed calculated using

equation (1) is an effective feature for predicting the

ship's speed over ground, we compared the

prediction accuracy of the neural network, LightGBM,

the proposal method, and the component-separated

physical model introduced in [8] as a reference for

comparison. The results showed that the proposal

method was more accurate than the other methods,

especially in predicting the ship’s speed through

ground. In addition, considering changes in hull

performance over time, it is desirable to update the

model frequently, but he proposal method has the

advantage that the model can be easily updated, and

is found to be useful in practice. However, the

proposal method lacks the ability to explain the

prediction results, and in practice, it is considered

effective when used in combination with a

component-separating physical model.

Although the proposal was made with pre-voyage

use in mind, as shown in experiment 1, if the drift

speed is an effective characteristic that represents the

state of the sea conditions, data measured during the

voyage several tens of minutes or hours in advance

can be used for forecasting as in [12]. Thus, it is

possible to optimize the route sequentially based on

the data measured during the voyage by extending

this study. Additionally, as described in Section 2, a

ship's operational performance temporarily improves

when it enters a dock due to cleaning, after which its

performance gradually declines due to the attachment

of marine organisms. Therefore, the time elapsed after

a ship enters the dock plays a critical role in

predicting the ship’s speed through ground. Hence,

creating a machine learning model using data that

includes the entire period from the day the dock ends

to the day the ship enters the next dock would be

desirable. However, the data used in this study were

not so much, and the period of data used for training

was only about four months, making such training

impossible. Thus, the accuracy of the proposal

method could be further improved by using several

years' worth of data for training.

Based on the above, future work will include

sequential route optimization and the creation of

more accurate models with more data for practical

use.

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