Application artificial neural networks for predicting wave resistance of ro-ro ferry in initial designing stage

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1 Scientific Journals Maritime University of Szczecin Zeszyty Naukowe Akademia Morska w Szczecinie 2011, 26(98) pp , 26(98) s 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 Szczecin, ul. Wały Chrobrego 1 2, 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 projektowania promów ro-ro. Wartości wzorcowe dodatkowego oporu od fali obliczono przy użyciu programu SEAWAY. Aproksymacje opracowano za pomocą sztucznych sieci neuronowych. Wartości wzorcowe obliczono dla 448 wariantów kształtu promu, przyjmując umowne parametry falowania oraz parametry ruchu promu. Takie podejście pozwoliło zastąpić skomplikowany model numeryczny prostym modelem regresyjnym, bazującym na podstawowych parametrach geometrycznych kadłuba. Introduction Various optimization methods of ship design parameters or operational ones are often applied to problems associated with ship designing and operation. Economic profits are the main criteria for which target functions are usually formulated. Economic criteria are made up of number of requirements 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 conditions 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. 10 Scientific Journals 26(98)

2 Resistance [kn] Application artificial neural networks for predicting wave resistance of ro-ro ferry in initial designing stage Still water resistance R SW + Mean added resistance R AW Still water resistance R SW Resistance 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 neural networks. A detailed research algorithm [3] has been presented in figure 2. List of ro-ro ferry variants Time [s] Fig. 1. Added resistance in regular waves [1] Rys. 1. Dodatkowy opór od fali [1] Wave added resistance is in an essential way affected 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 certain global coefficients characterising hull shape, e.g. block coefficient. This modest amount of information does not permit using known methods of determining added wave resistance based on the classical linear or non-linear theory. The next problem 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 dimension after construction is economically unprofitable. Method The aim of research was solved by means of analysis of results obtained from numerical calculations of vessel s motions on the wave. The research methods was based on [3] and consisted of the following 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 conditions were replaced with statistical conditions; 3. Using a numerical accurate methods for calculating model values of wave added resistance; 4. Analysis of results and determining hull parameters essentially affecting added wave resistance; 5. Selection of functions approximating the set of discrete results of numerical model; 6. Verification and assessment of determined modelling methods. In the work [3] have been presented design guidelines concerning the predicting of added wave Calculating model values of added wave resistance R Analysis of results and determining hull parameters X 1, X 2, X n essentially affecting added wave resistance R Determining a function approximating the added wave resistance R Conventional operational scenario Fig. 2. Algorithm presenting research method, where: X 1, X 2 X n vessel s design parameters, R added wave resistance [3] Rys. 2. Algorytm przedstawiający metodę badań, gdzie: X 1, X 2 X n 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 variants, 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) = , , , m 3 ; 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- Zeszyty Naukowe 26(98) 11

3 Table 1. Ro-ro ferry shape variants, where: CB block coefficient, CM frame section coefficient, CB L longitudinal block coefficient, CB V vertical prismatic coefficient, CWL waterline block coefficient, XF distance of waterline 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 współczynnik pełnotliwości podwodzia, CM współczynnik pełnotliwości owręża, CB L wzdłużny współczynnik pełnotliwości podwodzia, CB V pionowy współczynnik pełnotliwości podwodzia, 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 [%] Tomasz Cepowski XB/Lpp [%] Beukelman method is the simplest and yields results most consistent with the experiment. It is based on comparing energy discharged from a rolling vessel in the form of back wash with the work performed by the added resistance force [6]. The Gerritsma-Beukelman method permits a fairly accurate determination of added resistance for vessels of any shape, although the accuracy of this method is smaller for vessels with low values of block coefficient [7]. Calculations were made by means of SEAWAY program. SEAWAY accuracy tests shown in [5, 8] point to fairly large calculation accuracy. 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 H s = 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 calculated for assumed ferry shapes and accepted waving parameters. R H 2 S 1 e L pp 1 Hull parameters essentially affecting added vessel resistance on the wave For determining a function approximating the added resistance on wave, the artificial neural networks 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 backpropagation method); testing a network; assessment of approximation accuracy obtainable within a network on the basis of the testing data. To validate and test the networks the set containing 50% amount of the variants deleted by sampling 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 characterized 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): Lpp 1, CM 31.27, CB, V A1 A2 B A (1) 12 Scientific Journals 26(98)

4 Ra [kn] Application artificial neural networks for predicting wave resistance of ro-ro ferry in initial designing stage where: R significant value of added wave resistance [kn]; B waterline breadth [m]; L pp length [m]; C M midship section coefficient ; C BV vertical block coefficient ; H S wave significant height [m]; A 1 matrix of weighting factors: A 2 vector of threshold values: [ ]; A 3 vector of weighting factor values: [ ]. Figures 4 6 compare the model values calculated by means of accurate numerical methods with values approximated by equation (1). Equation (1) is characterised by trends in conformance with [6, 7, 9] CM CB(V) 0.79 Fig. 5. Influence of design parameters for additional wave resistance, L pp = m, CM = var, CB(V) = var, L pp /B = 5.8, H S = 12 m Rys. 5. Wpływ parametrów projektowych na maksymalny dodatkowy opór od fali, L pp = 124,33 m, CM = var, CB(V) = var, L pp /B = 5,8, H S = 12 m R [kn] Fig. 4. Significant values of added resistance on bow wave Ra calculated by means of accurate numerical methods and equation (1), H S = 1 m, waving spectrum JONSWAP, vessel speed v = 10 m/s Rys. 4. Wartości znaczące dodatkowego oporu od fali dziobowej Ra obliczone za pomocą dokładnych metod numerycznych oraz za pomocą równania (1), H S = 1 m, spectrum falowania JONSWAP, prędkość statku v = 10 m/s L pp [m] L pp/b Fig. 6. Influence of design parameters for additional wave resistance, L pp = var, CM = 0.98, CB(V) = 0.78, L pp /B = var, H S = 12 m Rys. 6. Wpływ parametrów projektowych na maksymalny dodatkowy opór od fali, L pp = var, CM = 0,98, CB(V) = 0,78, L pp /B = var, H S = 12 m Zeszyty Naukowe 26(98) 13

5 Tomasz Cepowski 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 linear model characterised by high accuracy in the scope of assumed restrictions. The model values, on the basis of which approximation (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 concern: limitations of Gerritsma-Beukelman method; assumed waving spectrum JONSWAP; parameters and uprush directions of statistical wave: bow wave of significant height H s = 1 6 m and characteristic period causing the emergence of maximum values R; vessel speed v = 10 m/s; hull parameters and block coefficients conforming to assumptions, in particular B = m, C M = , C BV = 0,73 0,79, L pp = m. References 1. ARRIBAS F. PE REZ: Some methods to obtain the added resistance of a ship advancing in waves. Ocean Engineering 34 (2007) PAYNE S., DALLINGA R.P., GAILLARDE G.: Queen Mary 2 seakeeping assessment: the owner s requirements, the design verification and operational experience. 3. CEPOWSKI T.: Design guidelines for predicting wave resistance of ro-ro feries at the initial designing stage. Zeszyty Naukowe Akademii Morskiej w Szczecinie, 22(94), 2010, Future trends in the design of ro-ro and ro-pax vessels operating in the southern Baltic. BALTIC GATEWAY Report, Sea Highways Ltd, GERRITSMA J., BEUKELMAN W.: Analysis of the Resistance Increase in Waves of a Fast Cargo-ship. International Shipbuilding Progress, 18(217), DUDZIAK J.: Teoria okrętu. FPPOiGM, Gdańsk NABERGOJ R., JASNA PRPI-ORŠI: A comparison of different methods for added resistance prediction. 22 nd IWWWFB, Plitvice, Croatia Journée J.M.J. Verification and Validation of Ship Motions Program SEAWAY. Report1213a, Delft University of Technology, The Netherlands, SCHNEEKLUTH H., BERTRAM V.: Ship Design for Efficiency and Economy. Butterworth-Heinemann, Recenzent: dr hab. inż. Marek Dzida, prof. PG Politechnika Gdańska 14 Scientific Journals 26(98)