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5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia SWATH Ship Design Formulae Based on Artifical Neural Nets Volker Bertram, ENSIETA, Brest/France, volker.bertram@ensieta.fr Ehsan Mesbahi, University of Newcastle, Newcastle/UK, ehsan.mesbahi@newcastle.ac.uk Abstract Simple design formulae for resistance and power prediction for SWATH ships are derived using Artificial Neural Nets. These formulae can be programmed easily in spreadsheets or optimization routines. The formulae were derived from a database compiled at ENSIETA and are supplemented by previous work. The experience with the presented applications shows that artificial neural nets allow often a better approximation of data than classic regression analysis, but this is largely due to the more adaptable functional relations. 1. Introduction Experienced model basins have a long tradition of simple and fast power prediction of ships in initial design based on very few parameters like main dimensions and speed. These traditional methods work well for conventional ships. For unconventional ship types like SWATHs (small-waterplane area twin hulls), Gore (1985), Lang and Slogett (1985), Bertram and Seif (2004), Figure 1, new simple estimates must be developed and updated as more experience is gathered. Figure1: SWATH Conventional regression has been extensively used in naval architecture in system identification to provide required factors and coefficients. Based on databases of existing designs, coefficients are then interpolated or even extrapolated to calculate coefficients for a new application. This procedure requires the engineer to specify not only which input parameters mainly influence the output parameter(s), but also to specify the type of functional relation between input and output parameters. Designers plotted data and by visual inspection sometimes chose simple relations, often based on polynomials. This approach is cumbersome and unsuitable for many nonlinear relations. Shortcomings are especially apparent for multi-dimensional input/output data sets. Here we apply a more versatile and userfriendly approach to system identification: Artificial Neural Networks (ANNs) may be used to find functional relationship for certain ship data, Mesbahi (2003). ANNs are increasingly used in naval architecture and marine engineering for system identification. Hess and Faller (2000) give an overview of ANN application in naval architecture, Bertram and Mesbahi (2000,2004), Mesbahi and Bertram (2000), Hess et al. (2004) further applications to ship design. We present here work for SWATH ships based on previous work, Bertram and MacGregor (1992), and updating a SWATH database of Papanikolaou (1996). 15 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia 2. Artificial Neural Nets ANNs have the capability of storing data during a learning process and then reproducing these data during a recall process. ANNs can generally represent the mapping of multi-dimensional input/output data sets as: f: X Y f is a non-linear function, X=(x1,x2,…,xn) is real input vector, Y=(y1,y2,…,ym) is real output vector, Figure 2. ANNs are best used for interpolation, extrapolations can be problematic. An ANN structure consists of several layers. Each layer consists of several nodes. In the example shown in Figure 2 we have input layer, output layer, and one hidden layer. The values of the previous layer are weighted, reach a node, summed up and are transformed by a function F, before passed on to the next layer. Typically, this function is a sigmoid function of the form: sig (x) = 1/(1+e-x) In this study, we have used fully-connected feed-forward ANNs with one hidden layer. Hidden layer and output layer use sigmoidal activation functions. The hidden layer may have different number of processing elements (neurons), which depend on the number of patterns and complexity of the relationship to be approximated. The standard choice is one hidden layer. Conventional back-propagation is used for network training. Momentum terms are added to the learning algorithm to achieve a higher convergence rate, Rumelhart and McClelland (1986). xi and yi are input and output data respectively, which are normalised between 0 and 1: Normalised value = (Real value -Min. Value)/(Max. value - Min. value) Therefore, as far as ANN training is concerned, the units of the input and output data sets are irrelevant; they are only used when the out put data is to be de-normalised to its real value. The following equation shows the mathematical relationship between x and y the single-input/singleoutput (SISO) ANN used here: y = c0+c1sig [b0+b1sig(a10+a11x1+a12x2+…) +b2sig(a20+a21x1+a22x2+…) +…] After sufficient training, adjusted values for the coefficients a, b, and c are derived and the non-linear relationship is determined. +1 F +1 F x1 F x2 . . . . . xn F y1 F y2 . ym F F F F F W( n 1h ) F W( h 1m ) Figure 2: General structure of an Artificial Neural Network 16 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia 3. Simple power prediction We follow the ITTC standard notation here. The break power may be estimated in a most simple early estimate by considering only speed and displacement as input variables. Conventional regression analysis gave more than a decade ago, Bertram and MacGregor (1992): PB = 0.0026 0.598 V2.691 and PB = 0.077 (/LOA)0.928 V2.784 The speed V is to be taken in knots, the displacement in tons, length overall LOA in m, giving the power in kW. In analogy, we expressed PB= f(,V) PB = -1562.3 +33333.33sig [1.082914 +2.848013sig(-2.509744+6.448005sig(*)+4.113247sig(V*)) – 4.638891sig(12.526969-7.726960sig(*)-12.093710sig(V*))] with * = 0.000075+0.049024 and V* = 0.035928V-0.223054 The ANN structure representing this formula has 2 inputs (, V), 2 neurons in the hidden layer and one output. PB results are shown in Figure 3 for 45 SWATHS: Shaft power (KW) 35000 Shaft power (KW) ANN 30000 Pb (Bertram and McGregor,1992) 25000 20000 15000 10000 5000 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 Figure 3: Comparison between real and calculated shaft power using different equations or even simpler PB/ =f(Fn) and PB/ =f(V): PB/ = -0.88918 +3.1416sig [0.24729+1.0533sig(-1.7707+3.6916x1)-3.8069sig(2.3202-9.0464x1)] with x1 = 0.929796Fn-0.127229 PB/ = -0.88918+3.1416sig[0.83637–0.5291sig(6.5743-12.114x1)-2.70668sig(9.7109-30.404x1)] with x1 = 0.035928V-0.223054 17 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia While such a simple approach may still give reasonable estimates for a narrow class of geometries, we may alternatively use a classical decomposition of power and resistance, focusing essentially on an approximation of the residual resistance as in traditional ship model testing. This is described in the following section. 4. Power prediction per resistance decomposition We express then the installed engine power as: PB = (RTV)(SM+1)/(sD) = ((RF+RR+RAP+RAA)V)(SM+1)/(sD) SM is the service margin, typically taken at 10% to 15%. We take typical values for shafting efficiency s=97% and the propulsive efficiency D= 72%. The resistance components of the total resistance RT are frictional resistance RF, residual resistance RR, appendage resistance RAP, and air resistance RAA. RF is predicted following ITTC’57: RF = ½ (CF+CA)SV2 If the wetted surface S is not yet known, we may estimate, Numata (1981): S = 2/3 (7.4+0.31L/D) Where L/D is the slenderness of the submerged hull, L its length, D its diameter. Typically L/D < 14 for modern SWATHs. The correlation allowance CA is estimated to 0.0005 as in Numata (1981). CF follows ITTC’57: CF = 0.075/(log10 Rn – 2)2 The Reynolds number is here defined as Rn = VLOA/ and =1.1910-6 m2/s. There is not much information on the appendage resistance of SWATH ships in the open literature. Nethercote and Schmitke (1982) estimate RAP to 10% RF, Bertram and MacGergeor (1992) to 28% RF. These global estimates are always plagued by considerable scatter and it is recommended to estimated the appendage resistance for all appendages separately using simple resistance coefficients, but actual appendage geometry, e.g. following Salvesen et al. (1985). The air resistance RAA is estimated using a force coefficient: RAA = ½ CAA AF V2 AF is the front area above water of the SWATH, which may be estimated initially to A F =0.04 LOA2, Devine (1987). Chapman (1972a) sets the air resistance coefficient CAA =0.5, Mulligan and Etkins (1985) to 0.7. Blendermann (2003) gives a more detailed approach based on wind tunnel test data. This leaves the residual resistance, encompassing wave resistance RW, viscous pressure resistance RFF and spray resistance RSP. The wave resistance can be computed quite accurately using more or less sophisticated computational methods, e.g. Bertram (1993). The viscous pressure resistance is typically 18 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia estimated separately for strut and lower displacement hull. Hoerner (1965) gives form factors for the strut, where ts/Ls is the thickness/length ratio of the strut: RVP,strut = RF,strut [1+(ts/Ls)+30(ts/Ls)4] The viscous pressure resistance of the lower hull is typically 10% to17% of its frictional resistance, Chapman (1972a), Nethercote and Schmitke (1982). Zou and Luo (2004) estimate following Hoerner (1965): RVP,hull = RF,hull [1+1.5 (Dh/Lh)1.5+7(Dh/Lh)3] Dh = 2(A0/)0.5 is the equivalent diameter of the lower hull, where A0 is its maximum section area, Lh its length. Spray resistance becomes significant only at higher Froude numbers. Papanikolaou (1988) gives: RSP = 0.12 ts V 2 2 with = 1.0 2.30 Fn,s 0.694 Fn,s-0.597 for 0.86 Fn,s < 2.3 0.0 Fn,s< 0.86 Fn,s is the Froude number based on strut length Ls. Savitsky and Breslin (1966) and Chapman (1972b) give formulae which yields generally higher values than the one of Papanikolaou (1988), possibly due to scaling effects, as these formulae are intended for surface-piercing struts of hydrofoil boats rather than big struts of SWATH ships. These formulae require already a certain knowledge of the main dimensions. Bertram and MacGregor (1992) give a global estimate for the residual resistance coefficient, where Fn is the Froude number based on the cubic root of the displacement 1/3: CR = 0.00436 Fn 0.0108-0.0113 Fn -0.007+0.0092 Fn 0.0127-0.0059 Fn 0.002 for 0.000 < Fn < 0.688 for 0.688 Fn < 0.865 for 0.865 Fn < 1.300 for 1.300 Fn < 1.808 for 1.808 Fn Using our new database, we derived now a simple estimate based on ANN for the residual resistance coefficient: CR = -0.001005 +0.047712sig [5.08580 +7.04224sig(3.05889-7.98939x1-29.84767x2) -7.34271sig(13.24880-21.75015x1-44.57205x2) -6.33253sig(-6.75647+12.86496x1+10.95574x2) -0.67298sig(-0.29977-15.27102x1+13.36564x2)] 1/3 x1 = 0.29347(L/ )-1.03073 x2 = 0.9298Fn-0.12723 The ANN structure representing this formula has 2 inputs (L/1/3, Fn), 4 neurons in the hidden layer and one output CR results for 45 SWATHS are shown in Figure 4. 19 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia Cr 0.05 0.045 Cr (ANN) 0.04 Cr (Bertram and McGregor,1992)) 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 Figure 4: Comparison between real and calculated CR using different equations 5. Conclusions The user-friendly ANN approach allows more general curve fitting than classical regression analysis based on simple polynomial expressions. However, the general problem remains that depending on how well the input parameters are chosen, more or less scatter appears and extrapolation of experience remains in principle risky. For the particular application chosen here, the ANN formulae appear to be an excellent first estimate aiding preliminary SWATH design. 6. References Bertram, V. MacGregor, J.R. (1992): “Leistungsprognose von SWATH-Schiffen in der frühen Entwurfsphase“, Schiff & Hafen 44/10, pp.188-191 Bertram, V. (1993): “SUS-B: A computational fluid dynamics method for SWATH ships”, Proc. of the 2nd International Conference on Fast Sea Transportation (FAST 1993), Yokohama Bertram, V., Mesbahi, E. (2000): “Adaptive Neural Network Applications in Ship Design“, Jahrbuch der Schiffbautechnischen Gesellschaft, Springer Bertram, V., Mesbahi, E. (2004): “Estimating resistance and power of fast monohulls employing artificial neural nets”, Proc. of the 4th International Conference on. High-Performance Marine Vehicles (HIPER 2004), Rome Bertram, V., Seif, M.S. (2004): “New developments for fast and unconventional marine vehicles”, Proc. of the 4th International Conference on. High-Performance Marine Vehicles (HIPER 2004), Rome, pp.28-43 Blendermann, W. (2003): “Consideration of Reynolds number and shear wind effects on a SWATH in wind tunnel tests”, Ship Technology Research/Schiffstechnik , 47, pp.3-10 20 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia Chapman, R.B. (1972a): “Hydrodynamic drag of semi-submerged ships”, Trans. ASME, J. Basic Eng. 94, pp.879-884 Chapman, R.B. (1972b): “Spray drag of surface piercing struts”, AIAA/SNAME Advanced Vehicles Conference, Annapolis Devine, M.D. (1986): “ASSET - A computer aided engineering tool for the early stage design of advanced marine vehicles”, AIAA-1986-2389, Proc. of the 8th Advanced Marine Systems Conf., San Diego Gore, J.L. (1985): “SWATH ships”, Naval Engineers Journal, 97/2, pp.83-112 Hess, D., Faller, W. (2000): “Simulation of ship maneuvers using recursive neural networks”, Proc. of the 23rd Symposium on Naval Hydrodynamics, Val de Reuil Hess, D., Faller, W., Ammeen, E. Fu, T. (2004): “Neural networks for naval applications, Proc. of the 3rd International Conference on Computer und IT Application Mar. Industries (COMPIT), Siguenza, pp.430-446 Hoerner, S.F. (1965): “Fluid dynamic drag, Hoerner Fluid Dynamics”, Ed.1993, ISBN 9993623938 Lang, T.G., Slogett, J.E. (1985): “SWATH developments and performance comparisons with other craft”, Proc. of the International Conference SWATH Ships and Advanced Multi-Hulled Vessels, RINA, pp.7-23 Mesbahi, E. (2003): “Artificial neural networks – Fundamentals, OPTIMISTIC – Optimization in Marine Design”, Mensch&Buch Verlag, pp.191-216 Mesbahi, E., Bertram, V. (2000): “Empirical design formulae using artificial neural networks, Proc. of the 1st International Conference on Computer und IT Application Mar. Industries (COMPIT), Potsdam, pp.292-301 Mulligan, R.D. Edkins, J.N. (1985): “Asset-Swath – A computer based model for SWATH ships”, Proc. of the International Conference SWATH Ships and Advanced Multi-Hulled Vessels, RINA, London Nethercote, W.C.E., Schmitke, R.T. (1982): “A Concept Exploration Model for SWATH ships”, Trans. RINA, Vol.124 Numata, E. (1981): “Predicting Hydrodynamic Behaviour of SWATH ships”, Marine Technology, 18 Papanikolaou, A.D. (1988): “Hydrodynamic aspects and conceptual design of a SWATHpassenger/car ferry”, J. Technica Italiana 52 Papanikolaou, A.D. (1996): “Developments and potential In open sea SWATH Concepts”, WEGEMT Workshop on Conceptual Designs of Fast Sea Transportation, Glasgow Rumelhart, D.E., McClelland, J.L. (1986): “Parallel distributed processing: explorations in the microstructure of cognition”, I&II, MIT Press, Cambridge Salvesen, N., von Kerczek, C.H., Scragg, C.A., Cressy, C.P., Meinhold, M.J. (1985): “Hydro-numeric design of SWATH-ships”, Trans. SNAME, pp.325-346 21 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia Savitsky, D., Breslin, J.P. (1966): “Experimental study of spray drag of some vertical surface-piercing struts”, Davidson Laboratory Report 1192, Hoboken Zou, Z.J., Luo, Q.S. (2004): “A practical resistance prediction system for SWATH ships”, Proc. of the 9th International Symposium on Practical Design of Ships and Other Floating Structures (PRADS 2004),Lübeck-Travemünde 22 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia Appendix: Database SWATH Ship Pursuit Ali Marine Ace Marine Wave Sun Marina Diana Bay Queen Suave Lino Betsy Halycon Alison Chubasco Houston Pilot Cutter NN F.G.Creed Exlorer RDC 400 Charwin SSP Kaimalino Kotozaki Ohtori Seagull 1 Cloud X Seagull 2 Navatek 1 Patria Simicat SMURV Thrileon Aegean Queen Built by Swath Ocean MacGregor Bros Mitsui Mitsui Mitsui Mitsui Mitsui Pool Boat Yard Swath Ocean RMI Metal Boat Inc James Betts Swath Ocean Swath Ocean Swath Ocean A&R Type St Augustine USCG Mitsui Mitsui Mitsui Nichols Bros Mitsui Thompson FBM Marine Alpha Marine NTUA NTUA NTUA workboat Prototype Research Research Pax Pax Pax Pax Pax Ferry Research Patrol Ferry Prototype Prototype Pleasure Pleasure Pleasure Pleasure Fishing Workboat Research Pilotboat Hull Alu Steel Alu FRP FRP Alu Alu Alu Alu Alu Alu Alu Alu Alu Alu Steel Steel+alu Steel+alu Steel Alu Alu Alu Steel+alu Alu Steel Steel+alu Steel Steel+alu [t] 13 21 22 25 25 30 35 40 53 62 67 76 79 80 80 130 180 193 220 236 240 338 340 350 365 400 446 610 900 1060 23 Loa [m] 10.90 11.27 12.30 15.10 15.05 20.80 18.00 21.34 19.30 18.30 26.50 21.94 20.40 21.90 20.40 36.40 24.40 26.27 27.00 27.00 35.90 37.52 39.30 43.00 36.50 41.00 39.00 48.00 51.50 Lpp [m] 9.14 11.00 11.95 11.93 15.90 15.90 16.76 17.70 18.89 18.40 16.80 25.65 22.90 22.23 25.00 24.08 31.50 32.40 33.70 34.14 31.70 35.00 33.00 43.00 50.00 B [m] 5.00 5.00 6.50 6.20 6.20 6.80 6.80 9.14 9.10 9.20 11.00 9.45 11.30 9.40 9.75 14.26 13.00 12.20 13.70 12.50 12.50 17.10 18.07 15.60 16.20 13.00 12.50 18.00 20.20 25.00 T [m] 1.00 1.60 1.60 1.60 1.60 1.60 1.60 1.46 2.10 2.29 2.10 3.05 2.44 2.10 2.40 2.70 2.74 4.60 3.20 3.41 3.15 3.44 3.50 3.65 2.70 3.80 4.50 4.50 5.00 PB [kW] 242 104 298 405 442 545 700 626 634 760 672 1104 1501 1119 1590 1576 4080 714 3239 2797 2797 5962 5748 7890 1914 4026 5888 6992 11040 14720 V [kn] 22.0 7.6 18.0 18.0 20.5 19.0 21.6 20.0 17.0 21.0 14.8 20.0 23.0 20.0 24.0 18.0 26.1 10.0 25.1 20.5 20.0 25.0 27.0 27.5 15.0 30.0 22.0 22.0 30.0 30.0 Year 1988 1976 1985 1987 1990 1989 1981 1985 1987 1990 2004 1984 1973 1980 1981 1979 1995 1989 1989 1990 1992 1995 1989 5th International Conference on High Performance Marine Vehicles, 8-10 November, 2006, Australia SMUCC NTUA container Steel Ship Twin Drill Duplus Regency Goutcat Haroula Able (T-Agos 20) Effective (T-Agos 21) Loyal (T-Agos 22) Victorious (T-Agos 19) Kaiyo Planet Harima (AOS 5202) Hibiki (AOS 5202) Impeccable (T-Agos 23) Radisson Diamond Built by Boele Boele Type Workboat workboat Alpha Marine McDermott McDermott McDermott McDermott Mitsui TNSW Mitsui Mitsui Tampa Finnyards Ferry Navy Navy Navy Navy Research navy Tow ship Surveillance Surveillance Pax Hull steel Steel Steel Steel Steel Steel Steel Steel Steel Steel Steel Steel Steel Steel 1060 51.50 [t] 1200 1450 1532 2180 3360 3360 3360 3360 3500 3500 3750 3750 5460 12000 24 Loa [m] 40.00 47.00 69.40 77.87 70.70 70.70 70.70 71.32 60.00 67.00 67.00 85.80 130.10 50.00 25.00 5.00 10893 26.0 1994 Lpp [m] 17.10 40.00 B [m] 5.20 17.10 24.40 22.00 28.70 28.70 28.70 28.70 28.00 25.00 29.90 29.90 29.90 32.00 T [m] PB [kW] 1269 1251 30000 8979 1194 1194 1194 1194 3444 4160 2239 2208 3730 11253 V [kn] 9.0 8.0 32.7 21.0 9.6 9.6 9.6 10.4 14.1 15.0 11.0 11.0 12.0 12.5 Year 1968 1969 65.00 57.91 53.00 61.00 61.87 116.00 5.49 5.10 5.00 7.50 7.50 7.50 7.56 6.30 6.80 7.50 7.62 7.90 8.00 1996 1992 1993 1993 1991 1984 2005 1991 1991 1992