437

1 INTRODUCTION

A growing demand for optimization tools utilized in

decision support systems (DSS) in marine navigation

may be clearly seen in last decade. The persistently

relatively high level of bunker oil prices has

encouraged ship operators to search for weather

routing solutions that are capable to adjust a ship

voyage plan according to a weather forecast and a set

of predefined goals. The latter typically include time

of passage and fuel consumption mitigation. Thus,

modeling of speed and a demand for bunker oil

becomes issues worthy investigation.

Scientific efforts both undertaken to examine an

interesting and important complex phenomena and,

not less importantly, to address a practical problem of

a ship resistance, speed and power demand modeling,

are not new. A variety of approaches have been

implemented over time, including modeling of

physical phenomena governing the resistance [14, 27],

statistical analysis of relatively numerous group of

existing ships [9], some semi-empirical methods [21],

Computational Fluid Dynamics utilization [31] and

model testes carried out in numerous towing tanks

worldwide. Another promising research direction

here assumes utilization of Artificial Neural Networks

(ANN) to benefit from their capability to deal with

multi-input nonlinear systems [6, 20, 22]. Such

approach finds its place in marine applications for

more than a decade, still being in a phase of dynamic

development. ANNs have been already tested for

numerous characteristics modeling like for instance

cargo carrying capacity of ships [22], hydrodynamic

coefficients [22], a ship response to wave excitation

[20], a ship stability [6], her structural issues [6, 17],

maneuvering capabilities [10] and others. The

The Development of a Combined Method to Quickly

Assess Ship Speed and Fuel Consumption at Different

Powertrain Load and Sea Conditions

P. Krata

, A. Kniat

, R. Vettor

, H. Krata

& C. Guedes Soares

Gdynia Maritime University, Gdynia, Poland

Gdańsk University of Technology, Gdańsk, Poland

Centre for Marine Technology and Ocean Engineering (CENTEC), Universidade de Lisboa, Portugal

Waterborne Transport Innovation, Łapino, Poland

ABSTRACT: Decision support systems (DSS) recently have been increasingly in use during ships operation.

They require realistic input data regarding different aspects of navigation. To address the optimal weather

routing of a ship, which is one of the most promising field of DSS application, it is necessary to accurately

predict an actually attainable speed of a ship and corresponding fuel consumption at given loading conditions

and predicted weather conditions. In this paper, authors present a combined calculation method to predict

those values. First, a deterministic modeling is applied and then an artificial neural network (ANN) is

structured and trained to quickly mimic the calculations. The sensitivity of the ANN to adopted settings is

analyzed as well. The research results confirm a more than satisfactory quality of reproduction of speed and

fuel consumption data as the ANN response meet the calculation results with high accuracy. The ANN-based

approach, however, requires a significantly shorter time of execution. The directions of future research are

outlined.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 15

Number 2

June 2021

DOI: 10.12716/1001.15.02.23

438

resistance and propulsion problems remain within the

scope of trial application of ANNs as well [6].

Modelling accurately the ship behavior at sea,

accounting for all components of resistance, degraded

performance of the propulsion system in unsteady

environment, and their effect on ship speed and fuel

consumption is a complex task which may lead to

poor predictions. Therefore, the ANN-based approach

may be handy from the operational point of view.

There are some scientific works dealing with ANNs

aiming at towing tank resistance results reproduction

[7] or marine propeller geometry related phenomena

[19]. Some others are even closer to the pending

problem we focus in this research. In [26] authors

train an ANN on the basis of noon reports that record

a ship speed and fuel consumption. The ANN model

input variables were speed, displacement, wind force,

wind wave height, swell height, sea current factor and

trim, though such set of data allows only for a rough

estimation of speed and fuel consumption that ought

to be referred rather as an average value for a day

period. Very similar approach is presented in [13]

where some data are measured by sensors and

recorded to be supplemented by noon reports.

Authors of the study [1] also use quite sparse data

recorded by a ship machinery sensors and they finally

announce the need for further enhancement of the

scope of measurements. Realistic navigation data set

obtained from ship operations simulated by a

weather routing software are used in [18] to train an

ANN for the prediction of a ship speed and fuel

consumption.

Taking into account the state-of-the-art, two main

observations could be made. First of all the utilization

of ANN is promising and more and more frequently

applied, worthy to be examined with no doubt.

Secondly, the problem of accurate and reliable ship

speed and fuel consumption prediction is still

challenging and not fully solved. Having the gap

identified, we studied the prospect of application the

ANN aiming at accurate and quick assessment of a

ship speed and fuel consumption with the view on

future application in weather routing DSS.

The rest of this paper is organized as follows.

Section 2 elaborates on the method adopted to

compute predictions of the ship speed and fuel

consumption in a variety of conditions and on the

ANN development. In Section 3 the obtained

deterministic data are utilized to train the ANN, then

the accuracy of predictions by the ANN is examined,

finally a verification is applied. Section 4 provides

discussion on the results, while Section 5 concludes.

2 METHODS

The method applied in this research comprises of two

components. Firstly, a deterministic approach is

utilized to obtain a set of predictions of the ship speed

and fuel consumption in a variety of conditions. That

part of the work stems from modeling of physical

phenomena related to the ship resistance and

propulsion characteristics. The second component of

the proposed method includes development of the

ANN, its training and evaluation of the outcome.

2.1 Resistance-thrust balance method

Ship performance at sea depends on the amount and

distribution of cargo onboard, the meteocean

conditions in which it operates, and the command of

the engine. The input variables are divided in three

categories:

− Loading conditions summarized by the

displacement (∆) and the trim (δT);

− Weather conditions including both waves

(significant wave height HS, peak period TP and

mean relative wave direction χm) and wind

(relative speed VWrel and mean wind direction θWrel);

− Navigation condition given as the revolutions of

the main engine (RPM).

The latter assumes the presence of a fixed pitch

propeller (FPP) and that the ship speed is controlled

by actuating on the RPM of the main engine [30]. Each

of the input variables assumes a range of suitable

values, where number and resolution is chosen in a

trade-off between improving the model accuracy and

limiting the computational effort. The attainable speed

and fuel consumption are computed for 1.5 million of

combinations.

The resistance that the ship must experience at a

given speed depends, besides on its form, on the

loading and weather conditions being faced. The total

resistance obtained as a sum of still water resistance

[10], added resistance in waves and wind resistance

[12, 28]. The numerical approaches proposed in the

literature for the estimation of wave added resistance

are often relatively accurate for restricted range of

wave directions and frequencies, while tendentially

unreliable in others. For this reason a combination of a

far-field method [23] for the radiation component in

head/bow seas and a semi-empirical approach [16] in

following/quartering seas and for the diffraction

component is adopted.

A preliminary information required is the specific

fuel consumption (SFC) of the engine at different

working conditions, namely different combinations of

power and revolutions. Manufacturers publicize

typically these kind of information only for a limited

number of settings, not sufficient to cover all the

operative conditions expectable at sea. The SFC is than

assessed numerically by an engine model developed

in [24] and the appropriate match with the propeller is

consequently obtained as described in [25].

For a given value of RPM, and known loading and

weather conditions, the following iterative procedure

is adopted:

1. assuming an initial value for the ship speed V_S, in

this case the design speed;

2. computing the total resistance;

3. computing the brake power and RPM required to

achieve this speed;

4. if the latter differs from the given value of RPM,

varying the V_S and returning to point 2. until

convergence;

5. verifying if the engine can operate at the required

settings;

6. obtaining the SFC from the engine model, dividing

it by the ship speed and multiplying by the power

to get the fuel consumption per nautical mile.

The presented deterministic approach, though

feasible, could be hardly found time-effective since

439

the required effort is 242 minutes to calculate 4.1

million different combinations on Dell server with

Intel Xeon 6130 2.1GHz processor and 64GB RAM

running Windows Server 2016 operating system. As

the number of governing variables is significant and

the range of their values is wide, the resultant number

of combinations makes the sole application of the

deterministic approach impractical in terms of

weather routing applications. Thus, the ANN is

expected to help.

2.2 Artificial Neural Network development

In complex systems, especially in presence on

numerous nonlinearities in their characteristics,

artificial intelligence techniques find their application.

Artificial neural networks (ANN) seem to notice a

rapid growth in application among other AI

approaches.

There are many different kinds of ANNs. Usually

feedforward, convolutional and recurrent ANNs are

distinguished [2, 4]. The simplest of them is a

feedforward ANN. Convolutional ANNs are applied

in more demanding scenarios like image and speech

recognition [3]. In recurrent ANNs the presence of

loops causes that the input may not determine the

output, as it will also depend on the initial state of the

ANN. Thus, recurrent ANNs can be used as

associative memories [2]. In the case of approximating

a multidimensional function the feed forward ANN is

sufficient [11, 15]. The size of feedforward ANN to

accurately mimic a function is also determined [11].

Choosing the right ANN kind and structure is a key

issue to obtain satisfactory results.

Another important issue is to choose the right

implementation of an ANN. Of course it is possible to

make your own implementation of an ANN, however

using a ready one gives an advantage to apply

standards and easily exchange data. There are

commercial packages including ANNs like e.g.

Matlab. On the other hand there are more and more

reliable open source solutions. One of them is

TensorFlow and Keras [5], which were chosen by the

authors for this project. TensorFlow with Keras is

versatile and scalable environment supported with

Python language. In this environment many different

kinds and structures of ANN may be defined, trained

and utilized. The scalability means that small cases

might be solved on a desktop PC and when they grow

the same environment is accessible on servers or in

the cloud. Thus, migration to more effective platforms

and applying multiprocessing is relatively easy and

does not require thorough reorganization of the entire

project.

The deterministic calculation procedure described

in chapter 2.1 is a multivariable function. The input

variable are the journey environmental conditions,

ship loading conditions and the engine RPM. The

results are the ship speed and fuel consumption. As

proved in [15] and [8] a feedforward ANN is enough

to approximate a function. To replace our function

with an ANN it was necessary to generate a vast set of

results using deterministic calculation procedure for

the entire spectrum of input parameters. This set was

then used to train the ANN. The Keras software was

utilized to develop the ANN for that purpose. This

feedforward network was named the base ANN and it

was intended as the reference network in further

undertaken verification process. The base ANN layers

settings are presented in Table 1.

Table 1. Number of neurons in each layer of the base ANN

_______________________________________________

Layer (disregarding layers used Number

for data input and result output) of neurons

_______________________________________________

1 32

2 64

3 64

_______________________________________________

The activation function applied in the base ANN

was ‘relu’ type (a rectified linear unit ) which is one of

the commonly used in ANN application. The mean

absolute error was selected as an evaluation function

remaining an essential element of the ANN training.

All examined ANNs, including the base one, were

trained within 50 epochs.

The verification process refers to the uncertainty

resulting from adoption of the ANN settings. The

validation process aims at assessing of uncertainty

with the use of experimental data. In this study only

verification was performed as the validation is

unfeasible at the present stage of the project execution.

Collecting of experimental data is planned at the next

stage of the project. Therefore, the sensitivity of

prediction accuracy to the following settings was

verified:

− the evaluation function utilized during training

process;

− the type of activation function;

− number of neurons in each of three layers of the

ANN.

The mean error and the standard deviation of

prediction were utilized to compare performance of

the ANN being modified with regard to each of the

listed settings. The results of such verification are

presented in section 3.

3 RESULTS AND VERIFICATION

The method described in section 2 was applied to a

container vessel. The main particulars of the vessel

and the ranges of considered operational variables are

summarized in Table 2.

Table 2. Particulars of the considered ship

_______________________________________________

Length between perpendiculars 175 m

Breadth 25.4 m

Nominal service speed 25 kn

Draft [8; 9] m

Trim (negative trim by the stern) [-0.75; 0.25] m

_______________________________________________

The vessel was assumed to sail in a variety of

conditions ranging from calm sea up to stormy

weather. The environmental data applied in this study

are shown in Table 3. The applied main engine

settings with regard to the engine speed covered a

feasible range of revolutions per minute (RPM). We

assumed the RPM[61; 144] min

-1

440

Table 3. Environmental conditions applied in the research

_______________________________________________

Significant wave height Hs [0; 10] m

Wave peak period Tp [0; 18.5] s

Relative wave angle [0; 180] deg

Wind speed [0; 25] m/s

Relative wind direction [0; 180] deg

_______________________________________________

The deterministic modeling of the ship speed and

related fuel consumption provides a set of data that

are pretty difficult for graphical presentation due to

the number of input variables. Namely, for each

considered loading condition of the vessel, there are

six values of governing variables that influence the

resultant speed and fuel consumption. Therefore

three-dimensional visualization may be shown only

for some parameters fixed, like presented in Fig. 1.

Figure 1. Modeled speed and fuel consumption for the wave

direction 180 deg, Tp=10.37 s, draft=9 m and trim=0 m

The full set of the deterministic modeling output

data was gathered in multidimensional matrices that

were subsequently used by the ANN as the training

data set, with respect to random fraction excluded

from input to be later utilized for the purpose of

evaluation, as described in section 2. The obtained

results of the ANN prediction were compared to that

share of data left. The visual presentation of the

prediction accuracy may be presented in a common

way as a projection and a histogram that are shown in

Fig. 2 for speed and in Fig. 3. for fuel consumption.

The closer results pattern follows the diagonal straight

line the more accurate prediction is.

Figure 2. Visualization of the base ANN prediction accuracy

for the ship speed.

Figure 3. Visualization of the base ANN prediction accuracy

for the ship fuel consumption.

441

The obtained results characterized by the mean

error of prediction and its standard deviation are

listed in Table 4.

Table 4. Accuracy of prediction performed by the base ANN

_______________________________________________

Predicted characteristics Speed Fuel consumption

_______________________________________________

Mean error 0.006 kts -0.022 kg/nm

Standard deviation 0.034 kts 0.548 kg/nm

_______________________________________________

As the base ANN achieved a high level of accuracy

the crucial question shall be raised what is the

sensitivity of the predictions to different possible

settings of the ANN. This problem is address within

the verification procedure as described in section 2.

First, the evaluation function was modified. The

mean squared error method was set instead of the

mean absolute error that was utilized in the base

ANN. The result of this modification is shown in Fig.

Figure 4. Influence of the evaluation function selection

(MAE - mean absolute error; MSE - mean squared error)

The second setting modified in order to reveal the

sensitivity of predictions was the type of the

activation function. The setting was changed from the

rectified linear unit (‘relu’) to the sigmoidal activation.

The effects of the applied modification are shown in

Fig. 5.

Figure 5. Influence of the activation function selection

The last, though the most thoroughly examined

setting applied to the ANN refers to the number of

neurons in each layer. The base ANN consisted of

three layers, disregarding layers used for data input

and result output. The number of neurons was set to

32, 64, 64 for the layers 1, 2 and 3 respectively (as

indicated in Table 1). The number of neurons seemed

to be massive so for the sake of verification we

decreased it dividing those figures by 2, 4 and 8.

Eventually, we structured the ANNs with:

− 32 / 64 / 64 neurons;

− 16 / 32 / 32 neurons;

− 8 / 16 / 16 neurons;

− and 4 / 8 / 8 neurons;

where the notation refers to 1st layer / 2nd layer / 3rd

layer of the tested ANN. Thus we trained four

networks with the use of exactly the same input data

set observing potential deterioration of the prediction

accuracy that might have been noticed for a dropping

number of neurons.

The ANN with the largest number of neurons is

the base ANN performing at the accuracy level

presented earlier in Fig. 2 and Fig. 3. The network

with the littlest number of neurons, counting only up

to 1/8th of the base ANN, predicted speed and fuel

consumption with the accuracy visualized in Fig. 6

and in fig. 7.

442

Figure 6. Visualization of the ANN prediction accuracy for

the ship speed for the smallest examined number of

neurons, e.g. 4 in 1st layer, 8 in 2nd layer and 3rd layer

Figure 7. Visualization of the ANN prediction accuracy for

the ship fuel consumption for the smallest examined

number of neurons, e.g. 4 in 1st layer, 8 in 2nd layer and 3rd

layer

The performance of all four examined ANNs with

regard to their accuracy indicators is shown in Fig. 8.

The observed trend of the rising standard deviation of

both predictions (i.e. speed and fuel) with the

decreasing number of neurons is dot-line plotted.

Figure 8. Influence of the number of neurons in each layer

(notation: 1st layer / 2nd layer / 3rd layer)

4 DISCUSSION

The obtained results revealed the capability of the

ANN to reproduce deterministic input data with an

exceptional accuracy. The mean errors were negligible

for both the ship speed and the fuel consumption. The

standard deviation of the prediction outcome

remained more than satisfactory, ranging up to 0.034

knots of speed and up to 0.55 kg/nm of fuel for the

base ANN. From the practical point of view the input

characteristics were perfectly captured.

Both examined types of the evaluation function

applied during training performed similarly well. The

mean absolute error (MAE) function produced

slightly lower value of the fuel consumption mean

error while the mean squared error function (MSE) a

bit overcame MAE in terms of the mean error of speed

prediction. The standard deviations of the predictions

were similar.

The application of the sigmoidal activation

function produced a noticeably lower values of the

443

standard deviation both of the speed prediction and

the fuel consumption prediction than the ‘relu’

activation function. The resultant mean error of the

predictions did not vary significantly and in both

cases remained close to zero. Thus, we may find the

sigmoidal activation performing better out of two

examined types.

The most significant impact on the obtained

prediction results brought up the modification of the

number of neurons. Initially the reduction by factor

two did not cause any vital changes in the ANN

performance. However, the reduction of the neurons

number by the factor four caused the rapid rise in the

standard deviations of predictions. They grew about

four times in terms of both the speed and the fuel

consumption predictions. The further reduction of the

number of neurons resulted in peaking the standard

deviations of predictions.

However, it ought to be emphasized that the input

data characteristics are very regular, thus predictable.

The astonishing accuracy was obtained for the input

data set coming from the deterministic model, not

from real operation measurements, so data were

smoothly patterned without any random errors. The

validation against real data has not been performed

yet at the present stage of the ROUTING (ERA-NET

Cofund MarTERA-1) project [29].

5 CONCLUSIONS AND FUTURE WORKS

The research being a part of ROUTING project

focused of the capability of the Artificial Neural

Network to reproduce the ship speed characteristics

and the fuel consumption in a variety of conditions,

with the view on application as a prediction tool in a

weather routing software. The obtained accuracy of

predictions was very high and from the practical

future utilization point of view it may be assessed as

more than satisfactory.

The conducted verification revealed that both

examined evaluation function, i.e. mean absolute error

(MAE) and mean squared error (MSE) perform very

similar without a clear domination of any of them.

The choice of the activation function influences the

obtained predictions results to a greater extent. The

sigmoidal activation function noticeably overcomes

the ‘relu’ function performance. However, the greatest

impact on the predictions accuracy related to the

number of neurons used in the ANN. The too

excessive reduction of that number reduced the

accuracy. Therefore, according to the preliminary

results of the study, the most productive settings of

the ANN are as follows:

− the mean absolute error evaluation function;

− the sigmoidal activation function;

− the numbers of neurons set to 16 in 1st layer, 32 in

2nd layer and 32 in 3rd layer of the ANN.

The first attempt described here confirmed a

potential of the ANN based approach, so the

preliminary results justify further research efforts on

the ANN utilization for the ship speed and fuel

consumption prediction. Moreover, ANNs seem to be

very promising due to their capability to learn on data

acquired from sensors installed onboard a real ship

under actual operation. Combining data from

deterministic calculations with data collected during

ship voyages and using them to train the ANN may

lead to a complex solution that can evolve with time

covering a wide range of operational conditions. Once

designing the automatic training process, the ANN is

expected to become even more accurate when the set

of acquired data grows after completed voyages.

However, the actual performance of the ANN has

not been yet tested with the use of real data

containing intrinsic uncertainties and even sometimes

errors due to a variety of reasons. Thus, the future

works are required to research on additional settings

of the ANN that remain untouched in this study, like

for instance the number of epochs and their mutual

interaction with the number of neurons, and the

performance of the ANN trained on real data

acquired in the course of measurements under the

ship operation. The results obtained so far encourage

the continuation of the research.

ACKNOWLEDGEMENT

This research was supported by The National Centre for

Research and Development in Poland under grant on

ROUTING research project (MARTERA-

1/ROUTING/3/2018) in ERA-NET COFUND MarTERA-1

programme (2018-2021).

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