Maritime University of Szczecin
Akademia Morska w Szczecinie
2011, 26(98) pp. 10–14 2011, 26(98) s. 10–14
Application artificial neural networks for predicting wave
resistance of ro-ro ferry in initial designing stage
Zastosowanie sztucznych sieci neuronowych
do prognozowania dodatkowego oporu od fali promu ro-ro
na wstępnym etapie projektowania
Tomasz Cepowski
Maritime University of Szczecin, Faculty of Navigation, Institut of Marine Navigation Akademia Morska w Szczecinie, Wydział Nawigacyjny, Instytut Nawigacji Morskiej 70-500 Szczecin, ul. Wały Chrobrego 1–2, e-mail: t.cepowski@am.szczecin.pl
Key words: ro-ro ferries, artificial neural networks, added wave resistance, approximation, hull shape
parameters
Abstract
The paper presents approximations of added wave resistance useful in the early stage of designing ro-ro ferries. Reference added wave resistance values were calculated by means of SEAWAY software based on accurate numerical methods. Approximating function was elaborated by using the artificial neural networks. The model values were calculated by means of 448 ferry shape variants assuming conventional waving parameters and ferry movement parameters. Such approach permitted the replacement of the complicated numerical model with a simple analytical model based on basic hull shape parameters.
Słowa kluczowe: prom ro-ro, sztuczne sieci neuronowe, dodatkowy opór od fali, aproksymacja, parametry
kształtu kadłuba
Abstrakt
W pracy przedstawiono aproksymacje dodatkowego oporu od fali przydatne na wstępnym etapie projekto-wania promów ro-ro. Wartości wzorcowe dodatkowego oporu od fali obliczono przy użyciu programu SEAWAY. Aproksymacje opracowano za pomocą sztucznych sieci neuronowych. Wartości wzorcowe obli-czono dla 448 wariantów kształtu promu, przyjmując umowne parametry falowania oraz parametry ruchu promu. Takie podejście pozwoliło zastąpić skomplikowany model numeryczny prostym modelem regresyj-nym, bazującym na podstawowych parametrach geometrycznych kadłuba.
Introduction
Various optimization methods of ship design pa-rameters or operational ones are often applied to problems associated with ship designing and opera-tion. Economic profits are the main criteria for which target functions are usually formulated. Eco-nomic criteria are made up of number of require-ments set by the shipowner, among which there are proper internal capacity and operational speed, which significantly affects the profitability of the vessel’s operation of a given shipping line. The ship’s reaching the assumed operational speed
depends inter alia on the parameters and work con-ditions of the propulsion system and the values of total hull resistance. The hull’s total resistance is made up, among other things, the wave’s added wave resistance, bound with the vessel’s sailing in stormy conditions, which can constitute even up to 30–50% of the vessel’s total resistance (Fig. 1) [1, 2]. Predicting the vessel’s added wave resistance is an essential challenge to ship designers due to the economic aspect of propulsion system’s parameter selection, fuel consumption and estimation of time of voyage.
Fig. 1. Added resistance in regular waves [1] Rys. 1. Dodatkowy opór od fali [1]
Wave added resistance is in an essential way af-fected by the hull’s shape and dimension, which is why it should be modelled already in the stage of initial design. An essential feature of the vessel’s initial designing is that the hull’s exact shape is presented by means of “main dimensions” and cer-tain global coefficients characterising hull shape, e.g. block coefficient. This modest amount of in-formation does not permit using known methods of determining added wave resistance based on the classical linear or non-linear theory. The next prob-lem is that the selection of improper values of main dimensions and block coefficients may cause large wave resistance, as the change of any ship’s dimen-sion after construction is economically unprofit-able.
Method
The aim of research was solved by means of analysis of results obtained from numerical calcula-tions of vessel’s mocalcula-tions on the wave. The research methods was based on [3] and consisted of the fol-lowing stages:
1. Preparing a list of ferries in a wide scope of shapes and sizes;
2. Assuming a conventional operational scenario in which, among other things, real waving condi-tions were replaced with statistical condicondi-tions; 3. Using a numerical accurate methods for
calcu-lating model values of wave added resistance; 4. Analysis of results and determining hull
parame-ters essentially affecting added wave resistance; 5. Selection of functions approximating the set of
discrete results of numerical model;
6. Verification and assessment of determined mod-elling methods.
In the work [3] have been presented design guidelines concerning the predicting of added wave
resistance useful in the early stage of designing ro-ro ferries. The guidelines were prepared on the basis of regression analysis of model values of added wave resistance. In this paper, approximating function was elaborated by using the artificial neu-ral networks.
A detailed research algorithm [3] has been pre-sented in figure 2.
List of ro-ro ferry variants
Calculating model values of added wave resistance R
Analysis of results and determining hull parameters
X1, X2, …Xn essentially
affecting added wave resistance R
Conventional operational scenario
Determining a function approximating the added
wave resistance R
Fig. 2. Algorithm presenting research method, where: X1, X2
… Xn – vessel’s design parameters, R – added wave resistance
[3]
Rys. 2. Algorytm przedstawiający metodę badań, gdzie: X1, X2
… Xn – parametry projektowe statku, R – dodatkowy opór od
fali [3]
Modelling added wave resistance
List of ro-ro ferry hull shape variants and model values of added wave resistance were based on [3]. For preparing a list of ro-ro ferry hull shape vari-ants, guidelines were used contained in report [4]. A list of 448 variants was made in the research, prepared on the basis of the following ranges of the ferry’s design parameters:
• LBd (L – waterline length, B – waterline breadth, d – vessel draft) = 19 000, 28 000, 37 000, 46 000 m3;
• L/B = 5.8, 6.6, 7.4, 8.2; • B/d = 3, 3.5, 4, 4.5
and a set of 7 ro-ro ferry shape variants (Tab. 1). For calculating model values of wave resistance the Gerritsma-Beukelman method was applied [1, 5]. This method is among methods restricted to first of all determining the resistance increment on the opposite wave. Among other methods of determining added wave resistance, the Gerritsma-
Time [s] Re sista nc e [k N]
Still water resistance RSW
Resistance Still water resistance RSW
+
Table 1. Ro-ro ferry shape variants, where: CB – block coeffi-cient, CM – frame section coefficoeffi-cient, CBL – longitudinal block
coefficient, CBV – vertical prismatic coefficient, CWL –
water-line block coefficient, XF – distance of waterwater-line’s geometric centre from after perpendicular, XB – distance of buoyancy centre from after perpendicular, Lpp – vessel’s length between perpendiculars [3]
Tabela 1. Warianty kształtu promu ro-ro, gdzie: CB – współ-czynnik pełnotliwości podwodzia, CM – współwspół-czynnik pełno-tliwości owręża, CBL – wzdłużny współczynnik pełnotliwości
podwodzia, CBV – pionowy współczynnik pełnotliwości
pod-wodzia, CWL – współczynnik pełnotliwości wodnicy, XF – odległość środka geometrycznego wodnicy od pionu rufowego, XB – odległość środka wyporu od pionu rufowego, Lpp – długość statku pomiędzy pionami [3]
CB [–] CM [–] CB[–] L CB[–] V CWL [–] XF/Lpp [%] XB/Lpp [%] 0.609 0.954 0.639 0.759 0.803 46.00 47.61 0.614 0.963 0.638 0.743 0.826 45.34 48.00 0.618 0.955 0.647 0.762 0.811 45.64 47.24 0.585 0.971 0.642 0.734 0.797 43.59 47.16 0.629 0.958 0.657 0.743 0.847 45.04 46.62 0.614 0.984 0.645 0.786 0.781 45.44 48.11 0.642 0.977 0.657 0.777 0.826 44.44 48.79
-Beukelman method is the simplest and yields results most consistent with the experiment. It is based on comparing energy discharged from a roll-ing vessel in the form of back wash with the work performed by the added resistance force [6]. The Gerritsma-Beukelman method permits a fairly ac-curate determination of added resistance for vessels of any shape, although the accuracy of this method is smaller for vessels with low values of block coef-ficient [7]. Calculations were made by means of SEAWAY program. SEAWAY accuracy tests shown in [5, 8] point to fairly large calculation ac-curacy. Calculations of added wave resistance were made on “statistical wave” assuming a conventional operational scenario:
the ferry is proceeding at progressive speed
v = 10 m/s on head wave;
waving spectrum conforms with JONSWAP; wave’s significant height Hs = 1–6 m at interval
every 1 m;
the wave reaches characteristic period T, for which there is maximum value of added wave resistance.
An effect of this part of research was a set of 2568 model values of added wave resistance calcu-lated for assumed ferry shapes and accepted waving parameters.
Hull parameters essentially affecting added vessel resistance on the wave
For determining a function approximating the added resistance on wave, the artificial neural net-works were applied. In this research the following types of them were tested:
Multilayer Perceptron (MLP) of a sigmoidal activation function,
Generalized Regression Neural Network (GRNN) – a regression network,
Radial Basic Function Network (RBF).
The phase of searching for the most appropriate network contained the following steps:
description of the best network structure by means of genetic algorithms;
learning a network (usually by using the back-propagation method);
testing a network;
assessment of approximation accuracy obtain-able within a network on the basis of the testing data.
To validate and test the networks the set con-taining 50% amount of the variants deleted by sam-pling from the learning data set. The MLP network of the structure: 4 (inputs) x 4 (hidden neurons) x 1 (output), appeared the most accurate being charac-terized by (Fig. 3):
the smallest learning RMS error = 0.44 kN; the smallest testing RMS error = 0.52 kN.
Fig. 3. Structure of the artificial neural network approximating the added resistance on wave
Rys. 3. Struktura sztucznej sieci neuronowej aproksymującej dodatkowy opór od fali
The searched function approximating the added resistance on wave R elaborated by means of the above mentioned neural network was represented analytically with the use of the equation (1):
057 . 0 28 . 1 1 1 3 41 . 2 42 . 0 , 42 . 19 , 27 . 31 79 . 32 , 1 008 . 0 2 2 1 A e H R A A B L CB CM L S pp V pp (1)
where:
R – significant value of added wave
resis-tance [kN];
B – waterline breadth [m]; Lpp – length [m];
CM – midship section coefficient [–];
CBV – vertical block coefficient [–];
HS – wave significant height [m];
A1 – matrix of weighting factors:
–0.188 –0.964 0.539 1.240 6.874 1.547 –4.798 0.825 –0.978 –1.519 3.450 –1.693 0.123 1.059 –0.074 –0.542 A2 – vector of threshold values:
[–1.418 –2.209 0.859 1.449];
A3 – vector of weighting factor values:
[4.611 –3.065 2.016 1.967].
Figures 4–6 compare the model values calcu-lated by means of accurate numerical methods with values approximated by equation (1). Equation (1) is characterised by trends in conformance with [6, 7, 9].
Fig. 4. Significant values of added resistance on bow wave Ra calculated by means of accurate numerical methods and equa-tion (1), HS = 1 m, waving spectrum JONSWAP, vessel speed
v = 10 m/s
Rys. 4. Wartości znaczące dodatkowego oporu od fali dziobo-wej Ra obliczone za pomocą dokładnych metod numerycznych oraz za pomocą równania (1), HS = 1 m, spectrum falowania
JONSWAP, prędkość statku v = 10 m/s
Fig. 5. Influence of design parameters for additional wave resistance, Lpp = 124.33 m, CM = var, CB(V) = var, Lpp/B =
5.8, HS = 12 m
Rys. 5. Wpływ parametrów projektowych na maksymalny dodatkowy opór od fali, Lpp = 124,33 m, CM = var, CB(V) =
var, Lpp/B = 5,8, HS = 12 m
Fig. 6. Influence of design parameters for additional wave resistance, Lpp = var, CM = 0.98, CB(V) = 0.78, Lpp/B = var,
HS = 12 m
Rys. 6. Wpływ parametrów projektowych na maksymalny dodatkowy opór od fali, Lpp = var, CM = 0,98, CB(V) = 0,78,
Lpp/B = var, HS = 12 m 0 5 10 15 20 25 30 35 10 15 20 25 30 Ra [k N] R [kN] Lpp/B [–] 5.8 8.2 Lpp [m] 124 256 13.7865 36.2013 CB(V) [–] 0.73 0.79 CM [–] 0.95 0.98 2.39727 42.1484
Conclusions
The added resistance on wave approximating function was elaborated with the use of artificial neural networks and presented in the analytical form. The function is highly accurate as compared with the testing data calculated by means of the exact methods.
The approach proposed permits the replacement of complicated numerical model with a simple lin-ear model characterised by high accuracy in the scope of assumed restrictions.
The model values, on the basis of which approx-imation (1) were prepared, were calculated with the assumptions made as described in the article. Therefore, approximations (1) have limitations resulting from the assumptions made and they con-cern:
limitations of Gerritsma-Beukelman method; assumed waving spectrum JONSWAP;
parameters and uprush directions of statistical wave: bow wave of significant height Hs = 1–
6 m and characteristic period causing the emer-gence of maximum values R;
vessel speed v = 10 m/s;
hull parameters and block coefficients conform-ing to assumptions, in particular B = 19–33 m,
CM = 0.954–0.985, CBV = 0,73–0,79, Lpp = 124–
256 m.
References
1. ARRIBAS F. PE´REZ: Some methods to obtain the added resistance of a ship advancing in waves. Ocean Engineer-ing 34 (2007) 946–955.
2. PAYNE S.,DALLINGA R.P.,GAILLARDE G.: Queen Mary 2
seakeeping assessment: the owner’s requirements, the de-sign verification and operational experience.
3. CEPOWSKI T.: Design guidelines for predicting wave resis-tance of ro-ro feries at the initial designing stage. Zeszyty Naukowe Akademii Morskiej w Szczecinie, 22(94), 2010, 5–9.
4. Future trends in the design of ro-ro and ro-pax vessels operating in the southern Baltic. BALTIC GATEWAY Report, Sea Highways Ltd, 2005.
5. GERRITSMA J.,BEUKELMAN W.: Analysis of the Resistance
Increase in Waves of a Fast Cargo-ship. International Ship-building Progress, 18(217), 1972.
6. DUDZIAK J.: Teoria okrętu. FPPOiGM, Gdańsk 2008.
7. NABERGOJ R.,JASNA PRPI-ORŠI: A comparison of different
methods for added resistance prediction. 22nd IWWWFB,
Plitvice, Croatia 2007.
8. Journée J.M.J. Verification and Validation of Ship Motions Program SEAWAY. Report1213a, Delft University of Technology, The Netherlands, 2001.
9. SCHNEEKLUTH H.,BERTRAM V.: Ship Design for Efficiency and Economy. Butterworth-Heinemann, 1998.
Recenzent: dr hab. inż. Marek Dzida, prof. PG Politechnika Gdańska
