=Paper=
{{Paper
|id=Vol-3606/73
|storemode=property
|title=Prediction of Wave Energy Spectrum Based on Ship Motions Using a Data-Driven Approach
|pdfUrl=https://ceur-ws.org/Vol-3606/paper73.pdf
|volume=Vol-3606
|authors=Alessandro La Ferlita,Yan Qi,Emanuel Di Nardo,Simon Mewes,Ould el Moctar,Angelo Ciaramella,Claudia Diamantini,Alex Mircoli,Domenico Potena,Simone Vagnoni,Claudia Cavallaro,Vincenzo Cutello,Mario Pavone,Patrik Cavina,Federico Manzella,Giovanni Pagliarini,Guido Sciavicco,Eduard I. Stan,Paola Barra,Zied Mnasri,Danilo Greco,Valerio Bellandi,Silvana Castano,Alfio Ferrara,Stefano Montanelli,Davide Riva,Stefano Siccardi,Alessia Antelmi,Massimo Torquati,Daniele Gregori,Francesco Polzella,Gianmarco Spinatelli,Marco Aldinucci
|dblpUrl=https://dblp.org/rec/conf/itadata/FerlitaQNMMC23
}}
==Prediction of Wave Energy Spectrum Based on Ship Motions Using a Data-Driven Approach==
https://ceur-ws.org/Vol-3606/paper73.pdf
Prediction of Wave Energy Spectrum Based on Ship Motions
Using a Data-Driven Approach
Alessandro La Ferlita 1, Yan Qi 1, Emanuel Di Nardo 2, Simon Mewes 1, Ould El Moctar 1
Angelo Ciaramella 2
1
University of Duisburg-Essen, 47057 Duisburg, Germany, Institute of Ship Technology, Ocean Engineering
and Transport Systems, Department of Mechanical and Process Engineering.
2
University of Naples Parthenope, 80133 Naples, Italy, Department of Science and Technology
Abstract
Wave energy spectra are used to create sea states and to obtain ship motion transfer functions for
different frequencies. These transfer functions are non-linear. Hence, the precise estimation is not
straightforward. In this study, the spectral parameters, significant wave height and peak period, are
obtained via a deep neural network (DNN) approach using the ship motions as input variables. The
main advantage of such a method lies in its possibility to predict the spectral parameters without the
use of ship specific properties.
Keywords 1
Sea state, DNN, Ship motions, Data-driven approach
1. Introduction
Accurate prediction of the sea spectrum is an important task for marine and engineering applications
since the natural environment can expose the vessels to potential risks.
During the lifetime of the ship, waves and winds induce loads and related stresses to the hull structure,
sometimes imperil the safety of the vessel.
Instantaneous loads, such as accelerating forces, slamming and sloshing loads, are those effects that the
waves and the resulting ship motions impose on the ship's hull structure.
Therefore, the dynamic loads acting on the ship contribute to different effects such as fatigue, structural
failure, corrosion, or crack propagation.
Thus, the precise estimation of significant wave height and of sea state parameters plays a relevant role
since vessels may encounter adverse conditions during their route and experiencing an added resistance
due to waves. This leads to an increase in the total resistance, and consequently, the ship fuel
consumption.
To predict ship fuel consumption as well as fatigue and lifetime, a precise forecast of the environmental
condition is imperative. Data of weather forecast and hindcast are expensive and often not complete.
Therefore, alternatives are needed to fill the data gaps as well as to improve weather data.
The sea spectrum may be determined considering the so-called “wave buoy” analogy [1] approach often
deducted in frequency-domain approach.
Thus, the ship is viewed as a buoy, therefore an inverse mathematical link between measured responses
and the encountered directional wave spectrum is defined, i.e. the measured ship responses are used as
input to estimate wave spectrum and associated sea state parameters. As a matter of course, the
determination of the transfer functions is a fundamental requirement. The most relevant numerical
methods based on potential theory to determine the transfer function may be classed [2] as follows:
ITADATA2023: The 2nd Italian Conference on Big Data and Data Science, September 11-13, 2023, Naples, Italy
alessandro.laferlita@uni-due.de (A. La Ferlita) yan.qi@uni-due.de (Y. Qi) emanuel.dinardo@uniparthenope.it (E. Di Nardo)
simon.mewes@uni-due.de (S. Mewes) angelo.ciaramella@uniparthenope.it (A. Ciaramella) ould.el-moctar@uni-due.de (O. El Moctar)
0009-0007-1680-1741 (A. La Ferlita) yan.qi@uni-due.de (Y. Qi) 0000-0002-6589-9323 (E. Di Nardo)
0000-0002-0419-3423 (S. Mewes) 0000-0001-5592-7995 (A. Ciaramella) 0000-0002-5096-4436 (O. El Moctar)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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Workshop ISSN 1613-0073
Proceedings
1. Strip method.
2. Unified theory.
3. High speed Theory
4. Green function method
5. Rankine source method
Usually, these approaches are linear and cannot capture further nonlinear aspects such as turbulence,
wave dispersion, or water compressibility. In fact, often such kind of codes assume linearized small
unit wave amplitudes hypothesis. In these approaches, the fluid is assumed to be inviscid,
incompressible and irrotational without surface tension, such that the spatial flow velocity vector can
be expressed as the gradient of a scalar 3D velocity [3].
Nevertheless, considering the improvement of computational power and parallel computing, the
Reynolds-Averaged Navier–Stokes (RANS) approach is more frequently applied to solve also unsteady
seakeeping problems [4].
However, the same task of obtaining the sea spectrum may also be realized using supervised machine
learning. The fundamental idea is to learn the mapping from measured ship motion responses to the
actual sea state from historical data. The cost in terms of computational time for the transfer function
obtained with CFD (Computation Fluid Dynamics) is typically higher if compared to machine learning
approaches. In addition, some problems regarding accuracy of free-surface due to the limited grid
quality can be encountered [4].
The main advantage of data-driven methods is that it is not required to define specific vessel properties,
such as radius inertia or hydrostatics of the vessels to discover the pattern between ship motions and
sea states [5].
Regarding this aspect the literature does not offer many examples of such kind of approaches. For
instance, Nielsen et al. [6] proposed a hybrid approach for wave spectrum estimation. Mittendorf et al.
[7] proposed a prediction of sea states based on ship motions using a data-driven approach, considering
the in-service data of a container vessel.
The application of machine learning and especially of DNN (Deep Neural Network) is used and spread
in several naval architecture disciplines, e.g., in structural field ( [8] [9]) or ship performances or engine
break power and ship fuel consumption predictions [10], [11], [12].
The applicability and high performance of such methods lead to a high interest of many researchers
when the nature of the problem is complex and when many nonlinear effects must be considered.
Therefore, the application in the subject topic can lead to many advantages. Hence, the main objective
of the study is to show the accuracy of a machine learning approach to predict the significant wave
height and peak period.
2. Methodology
A simplified model for approaching the problem, which consists mainly of demonstrating the accuracy
of a machine learning approach by using ship motions to predict significant wave height and peak
period, was established. This consists of the following steps: at first a database with the measured data
is generated, part of the data (90%) is used to train the DNN, and the remaining set of the data is used
to perform the validation. Afterwards, unknown samples to the algorithm were used to test the model.
Finally, the spectrums are determined and compared against the observed ones. The methodology is
graphically presented in Figure 1.
A database of public domain data has been used [13]. The movement of 46 moored vessels for a total
of 1609 hours in the duration from October 2015 to February 2020 were taken into consideration during
five field campaigns. These data are used to train and test the model to predict the significant wave
height and the peak period. The data is originally published by Alvarellos et al. [13]. The objective of
their study was to predict the ship’s movements in advance using an ANN (Artificial Neural Network).
Here, the input data were the weather conditions, the ship characteristics and berthing location. Thus,
more detailed input data than in the present study. This led to a high level of accuracy but requires more
knowledge about the ship itself.
Figure 1: Schematic representation of the approach
A database of public domain data has been used [13]. The movement of 46 moored vessels for a total
of 1609 hours in the duration from October 2015 to February 2020 were taken into consideration during
five field campaigns measurements. These data are used to train and test the model to predict the
significant wave height and the peak period.
The data is originally published by Alvarellos et al. [13]. The objective of their study was to predict the
ship’s movements in advance using an ANN (Artificial Neural Network). Thus, more detailed input
data than in the present study. This led to a high level of accuracy but requires more knowledge about
the ship itself. The input variables available for performing the training and validation tasks have been
grouped into weather related features, such as:
• Hs [m]: significant wave height
• Tp [s]: peak wave period,
• θm [deg]: mean wave direction
• Ws [km/h]: mean wind speed.
• Wd [deg]: mean wind direction.
• H0 [m]: sea level with respect to the zero of the port.
• Hsm [m]: significant wave height measured by the tide gauge.
And ship related features, such as:
• Surge [m]: linear longitudinal motion (bow-stern).
• Sway [m]: linear lateral motion (port-starboard).
• Heave [m]: linear vertical motion.
• Roll [deg]: tilting rotation of the vessel about its longitudinal axis (port/starboard)
• Pitch [deg]: up/down rotation of the vessel about its transverse axis
• Yaw [deg]: turning rotation of the vessel about its vertical axis.
• L [m]: ship length.
• B [m]: ship breadth.
• DWT [ton]: deadweight
Table 1
Sample’s number used to train the DNN (Deep Neural Network).
Ship Motion Roll Pitch Heave Surge Yaw Sway
Number of Samples 1349 1349 365 365 1249 1452
A total number of 6129 samples (considering the six degree of freedom of the vessels) has been used
for training the algorithm (see Table 1). The only two vessel topology available in the data set were
bulk carrier and general cargo ship.
The DNN method was chosen since it quickly provided outputs that are less prone to overfitting and
the computational durations are shorter [10], further the generalization ability of deep neural networks
helps to obtain very satisfying results. Only two hidden layers are present in the network since the
amount of data available is limited and the course of dimensionality aspect has to be taken into account.
[14]. TensorFlow [8], a deep learning computational toolkit, and Google Colab [15] were used to create
the DNN model, which was then trained on a nVidia Tesla K80 GPU (Graphic Processor Unit). In order
to do this, we used the ADAM optimizer [16] with an initial learning rate of 0.001 and an exponential
decay of 0.96 over a period of 10 epochs. As loss function the SmoothL1 is used to act as a L1 and L2
based on a threshold parameter, but preferring to act for the most as a L1 function.
Various idealized energy spectra exist to represent the sea state. The ITTC (International Towing Tank
Conference) recommends the use of the JONSWAP (Joint North Sea Wave Observation Project)
spectrum, which is based on the observations obtained in the North Sea westward from the Sylt Island
(Westerland, Germany). The observation lasted for a period of 10 weeks during the year 1968–1969
[17]. The sea spectrum reads:
"
* ,-)-! . (1)
𝐶# 5 𝜔% & "'%()&+ $/" -!" 01
𝑆! (𝜔" ) = 𝑒𝑥𝑝 *− . / 0 𝛾 ,
𝐶$ 4 𝜔
5𝐻2 $ (2)
𝐶# =
16𝜔%
0.925 (3)
𝐶$ = 1.15 + 0.1688𝛾 −
1.909 + 𝛾
Where the 𝜔% denotes the peak frequency, 𝜔 the wave frequency, Hs the significant wave height, and
𝛾 the peak enhancement factor. 𝜎 is defined as follows:
0.07, 𝜔 ≤ 𝜔% (4)
𝜎==
0.09, 𝜔 > 𝜔%
These values define the left and right sided widths of the spectral peak, respectively. The advantage of
the JONSWAP model, compared to other model (for instance Pierson-Moskovitz model), is that it can
consider effects of limited wind fetch length and water depth [18].
A theoretical estimate of the ship response spectrum can be obtained through a merge of the wave
spectrum and the transfer function of the given motion response [6]. The formula below provides a
mathematical representation of the problem:
5
DDDDDDDDDDDD (5)
𝑆3! (𝜔" ) = A 𝛷4 (𝜔" , 𝛽) 𝛷 6 (𝜔" , 𝛽)𝐸(𝜔" , 𝛽)𝑑𝛽
)5
Where:
• 𝑆3! (𝜔" ) is the response spectrum function of the frequency 𝜔" ;
5 DDDDDDDDDDDD
• ∫)5 𝛷4 (𝜔" , 𝛽) 𝛷 6 (𝜔" , 𝛽) is the transfer function or RAO (Response Amplitude Operator),
function of the frequency and of the spreading 𝛽, and
• 𝐸(𝜔" , 𝛽) is the sea spectrum
3. Results
Figure 2: Comparison between Hs (significant wave height) and Tp (peak period) observed
and predicted.
Figure 2 presents the comparison between predicted values of the significant wave heights and the peak
period obtained from the data driven model (marked in orange and the red color) and from the
measurements (marked in blue and green color).
The horizontal axis represents the number of samples. The vertical axis shows Hs and Tp, respectively
expressed in meters and seconds. Exemplarily, 120 samples measurement for the sway motion. are
considered as test cases (the so-called “wild data”).
For the first 40 samples related to the Hs prediction, the DNN approach tends to slightly overestimate
the observed values. From sample 40 to 60 the accuracy improves. Starting from sample number 60,
the predictions derived from the DNN approach overestimate the measured values as observed in the
first 40 samples.
The comparison for the prediction of Tp presents some peaks. As seen at sample numbers 83, the data
driven model significantly underestimated the value compared to the corresponding measured value.
However, it is observable that the trend of the prediction qualitatively follows the observed one.
The two standard loss functions which are often used to indicate in machine learning the prediction
accuracy are the root mean squared error (RMSE) and mean absolute error (MAE) which yield
respectively: 0.66 and 0.54.
After the Tp and Hs computation, the spectrums were obtained. Exemplarily, six different scenarios (a
to f) to the unknown tested Hs and Tp cases are presented in Figure 3. The vertical axis represents the
789
wave spectra density in [ : ]𝑚$ , while the horizontal axis shows the wave frequency in [rad/s].
The spectra were calculated for the measured and for the predicted through the formula previously
shown in equation 1, assuming a fully developed sea.
A fixed peak enhancement factor of 3.3 has been chosen. The scenarios presented in Figure 3 reveal an
overall good agreement with the processed spectrum obtained using the observed data (Hs, Tp).
Figure 3: Observed and predicted spectra.
Figure 4: Difference distribution of Tp and Hs.
However, it must be said that scenario presented b, d and f show less agreement if compared to the
actual spectrum. This can be observed even from the Hs and Tp obtained (Table 2). The reason can be
related to the lack of data. The results obtained for the other scenarios (a, c, e) in term of Hs and Tp
values are given as well. For these cases, the prediction is better, and this is reflected in the spectrum.
A statistical representation of the deviation between the predicted and observed Tp and Hs values is
shown in figure 4.
With a limited sample size, the distribution can be approximated with the normal distribution. For the
gaussian Hs curve, a mean value of -0.2 and a standard deviation of 0.5 has been set. For the gaussian
Tp curve, a mean value of 1 and a standard deviation of 1 has been considered. In both cases, the spread
around the central tendency is almost symmetric.
Almost 10 % of the Tp test cases present a difference of 1 second, on the other side the 9.3% of the Hs
samples yield a difference of -0.1 m. For the Tp values only the 0.826% of samples has a deviation less
than -2.732s. For the same percentage value, the Hs test cases present a deviation of -2.173.
Approximately 9.917% of the Tp test cases predicted yield a difference of 0.445s with respect to the
observed ones. The 9.091% of the Hs wild data presents a difference of -0.634 m if compared to the
respective Hs values measured.
As for the great majority of machine learning algorithms, they cannot often quantify the
error/uncertainty associated with their predictions or granting data convergence as shown above.
In this study the error data has the statistical distribution as shown in figure 4, but the dataset is built
starting from specific ship features that can vary in different context, as it can happen with weather
features.
A mix of these two features in uncovered situations can lead to inaccurate results. This situation is one
of the possible problems that can happen with artificial neural networks due to a low robustness of the
model based on the model architecture itself and on type of data. This condition can be reduced when
a huge amount of data is available with coverage of multiple scenarios.
In the study case, the availability of approximately 6000 samples for training a simple DNN algorithm
had probably led to perform sufficient accuracy prediction.
Therefore, in such scenarios with reduced amount of data, the capacity for robust and sample-efficient
learning might be essential.
Table 2
Compared Hs and Tp
Scenario Hs observed Hs predicted Tp observed Tp predicted
[m] [m] [s] [s]
a 2.78 2.80 9.98 9.80
b 1.72 1.90 9.9 10.16
c 4.95 4.96 14.09 13.99
d 3.8 4.03 13.14 13.41
e 3.13 2.99 10.71 10.9
f 2.19 2.50 10.39 10.21
4. Conclusions and Future Work
A data driven model was presented for the determination of the wave energy spectrum. The training of
the model was performed with ship motion measurement data. This approach allows to circumvent the
need for transfer functions and ship characteristic information. The results presented show sufficient
agreement with the effective data measured despite the limited number of sample available for training
the neural network.
The increase of data samples to train and validate the network must be considered for further
development. Furthermore, parameters related to the spectrum, such as fetch length, might improve the
accuracy of the prediction.
5. References
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