Procjena dodatnog otpora broda na valovima od velike je važnosti s ekološkog i ekonomskog aspekta. Dodatni otpor uzrokuje pad brzine plovidbe te utječe na povećanje zahtijevane snage i potrošnje goriva broda, a samim time i emisije štetnih plinova. Međunarodna pomorska organizacija (engl. International Maritime Organization, IMO), uvodi sve strože propise za smanjenje i kontrolu emisije štetnih plinova u pomorskoj industriji. Tako novi brodovi moraju zadovoljiti tehničke mjere, a postojeći brodovi operativne mjere s ciljem povećanja energetske učinkovitosti brodova i smanjenja emisije CO2. Iz tog je razloga već u preliminarnoj fazi osnivanja broda vrlo važno procijeniti povećanje otpora uslijed plovidbe broda na valovima za stanja mora na kojima će brod tijekom službe ploviti. Dodatni otpor na valovima vremenski je osrednjena vrijednost sile drugog reda, koja nastaje uslijed interakcije nailaznih valova i valova generiranih odzivom broda. S obzirom na zanemarive učinke viskoznosti, dodatni otpor moguće je razmatrati kao neviskoznu pojavu što omogućuje primjenu metoda i rješavača temeljenih na teoriji potencijalnog strujanja idealnog fluida, ali i ekstrapolaciju rezultata s modela na brod bez utjecaja mjerila. Obzirom da pouzdano određivanje dodatnog otpora na valovima zahtijeva provođenje složenih hidrodinamičkih proračuna, u okviru doktorskog rada razvijen je numerički model, koji se temelji na rezultatima hidrodinamičkih proračuna i umjetnoj neuronskoj mreži. Jedna od prednosti umjetne neuronske mreže je mogućnost aproksimacije rješenja složenih nelinearnih i viševarijabilnih problema bez poznavanja fizikalnog modela. Kako bi osnovani numerički model osigurao rezultate zadovoljavajuće točnosti, proveden je proces učenja umjetne neuronske mreže na temelju rezultata hidrodinamičkih proračuna kontejnerskih brodova različitih formi i značajki te za različita stanja mora. Dodatni otpor broda na pravilnim valovima određen je metodom rubnih integralnih jednadžbi (engl. Boundary Integral Equation Method, BIEM), a primjenom spektralne analize energije nepravilnih morskih valova određene su srednje vrijednosti dodatnog otpora za različita stanja mora definirana sa značajnom valnom visinom i periodom vala. Također, proveden je postupak validacije i verifikacije dobivenih numeričkih rezultata. U radu je provedena analiza osjetljivosti dodatnog otpora na pravilnim i nepravilnim valovima na različite značajke broda, s ciljem definiranja varijabli ulaznog vektora umjetne neuronske mreže. Analizirane su različite strukture unaprijedne statičke umjetne neuronske mreže s povratnim prostiranjem pogreške i jednim skrivenim slojem, parametri te različiti algoritmi učenja mreže. Istražen je i utjecaj načina pripreme podataka za proces učenja mreže na dobivene rezultate te prednosti primjene analize glavnih komponenata kao i klasifikacije podataka za učenje. Osnovani numerički model od posebne je praktične koristi u preliminarnoj fazi projektiranja kontejnerskog broda, kako bi se u kratkom roku i s točnošću procijenio dodatni otpor broda na valovima ovisno o planiranoj ruti plovidbe za koju se brod projektira. Za postojeće kontejnerske brodove, osnovani numerički model moguće je koristiti za procjenu dodatnog otpora pri različitim brzinama plovidbe i za različita stanja mora te tako doprinijeti planiranju rute plovidbe, posebice za izraženija stanja mora, uz ograničenje valova direktno u pramac.
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Evaluation of the ship added resistance in waves has increased in importance, especially from an economic as well as from an environmental protection point of view. Ship added resistance in waves causes a reduction in ship speed and has an impact on the increase in the fuel consumption and CO2 emission. The International Maritime Organization, IMO subjected the emission of harmful gases to increasingly stringent regulations, via the introduction of mandatory technical measures for new ships and operational measures for existing ships, with the aim of increasing the energy efficiency of ships and reducing CO2 emissions. For that reason, it is very important to predict the increase in ship resistance due to waves and power required for the ship sailing at an actual sea state, already in the ship design phase and when planning the sailing route of existing ships.
Added resistance in waves is a time-averaged second order force consisted of three parts. When sailing in waves, ship generates two systems of waves: waves due to sailing in calm water and waves caused by the ship response to incoming waves. The first and largest part of added resistance arises due to the interference of waves generated by the ship, i.e. radiation waves mainly due to heave and pitch motions, and incoming waves. It is often called the drift force, although the drift force in the longitudinal direction of a ship is equal to the added resistance in waves only in the case of zero speed. The ship relative motions become large when the length of the ship is approximately equal to the wavelength, which corresponds to peak value of added resistance. At very long waves, when relative motions are negligible, the wave force corresponds to Froude-Krylov force that would ideally act on the ship hull in the absence of a diffraction component. On the other hand, in short waves the diffraction of incoming waves on the ship hull increases the second part of added resistance, i.e. the diffraction force with emphasized nonlinear effects. The third component is related to the viscous damping of the heave and pitch motions of the ship and is negligible in relation to the hydrodynamic damping of the motions (radiation waves). Therefore, added resistance is considered as a non-viscous phenomenon, which allows the application of methods and solvers based on the potential flow theory, but also an extrapolation of the results from model scale to ship scale without the scale effects.
Analytical methods, methods based on the potential flow theory and the ones based on viscous flow theory are used for the evaluation of the ship added resistance in waves. Since the determination of the ship seakeeping characteristics and added resistance in waves requires
rather complex hydrodynamic calculations to ensure an acceptable accuracy of the results, within this research a model that allows simple but sufficiently accurate and reliable evaluation of the ship added resistance sailing at an actual sea state is developed. Such model can have a practical benefit both during the ship design phase or while planning a favourable sailing route of a ship in service. The basis of the developed model is the results of hydrodynamic calculations of added resistance in waves for various hull forms at different sea states and artificial neural network, which has the ability to learn from examples and to discover relationships between the input data and solutions to the nonlinear multivariable regression problems.
Hull forms of modern container ships with different types of bow and stern, section type and block coefficient (prismatic coefficient) are generated in order to create a sufficiently large database for the training process. The original hull forms with different main characteristics are modified in order to extend the range of prismatic coefficients and to obtain different longitudinal positions of the center of buoyancy. The influence of the ship mass characteristics, i.e. the vertical position of the center of gravity and the pitch radius of inertia, on the added resistance in regular regular waves is investigated, while the ship design speed is determined based on the regression analysis results. The results of the regression analysis also defined the variation range of the prismatic coefficient, in respect to the limitations of the method used for the hull form modification.
Hydrodynamic calculations are conducted using the Boundary Integral Equations Method, BIEM based on the potential flow theory. Generated hull forms are discretized by flat panels and hydrodynamic calculations of added resistance in regular waves are performed. The numerical results obtained using panel method are compared to the ones obtained using finite volume method, FVM based on the viscous flow theory for benchmark containership KCS. In the defined incoming wave frequency range, the sensitivity analysis is carried out in order to define the neural network input parameters. The most important parameters affecting the added resistance in waves are the ship geometry, response in waves and the characteristics of the incoming waves. Since the ship response to incoming waves is highly dependent on the hull geometry, and transfer functions are often unknown in the preliminary design phase, it is practical to define ship main characteristics as the input parameters of the neural network. The obtained numerical results are validated against the available experimental data and verified, i.e. the numerical uncertainty is assessed.
Top container ship sailing routes are analyzed and sea states with the highest probability of occurrence for waves coming from all directions and head waves for a given route are extracted based on the global wave atlas (Global Wave Statistics). For the numerically obtained results of added resistance in regular waves, spectral analysis is performed using two-parameter theoretical wave energy spectra: Bretschneider spectrum for unlimited and JONSWAP spectrum for limited fetch. In this way, the results of added resistance in irregular waves, i.e. at different sea states that ship may encounter during lifetime, are obtained.
Feedforward artificial neural network with error back propagation and one hidden layer of neurons is generated as the basis of the numerical model for the estimation of ship added resistance in waves. A possible significant advantage of neural networks is that they do not require a known physical model of the before mentioned complex hydrodynamic problem. Based on the analysis of different neural network architectures, i.e. by varying the number of neurons in the hidden layer, learning rate and momentum parameters, as well as by performing an analysis of the results obtained using different learning algorithms, an adequate artificial neural network is set. The training process is performed using the results of hydrodynamic calculations, which are adequately prepared and divided into data sets for learning, validation and testing. The evaluation of the accuracy and generalization property of the neural network is evaluated based on the normalized value of the root mean square error. A multivariable linear regression analysis is also performed as well as principal component analysis in order to represent the input variables of the neural network with linearly independent variables. The generalization properties of the neural network employed for the evaluation of added resistance in waves is also analyzed for different wave headings, which increases the complexity and nonlinearity of the given problem. The developed numerical model has 12 input variables, 65 neurons in one hidden layer and is based on Levenberg-Marquard learning algorithm with Bayesian regularization. The model incorporates three sub models based on the classification of data according to the wave zero crossing period.