Measures to diminish the parameter drift in the modeling of ship manoeuvring using system identification

System identification provides an effective way to predict the ship manoeuvrability. In this paper several measures are proposed to diminish the parameter drift in the parametric identification of ship manoeuvring models. The drift of linear hydrodynamic coefficients can be accounted for from the point of view of dynamic cancellation, while the drift of nonlinear hydrodynamic coefficients is explained from the point of view of regression analysis. To diminish the parameter drift, reconstruction of the samples and modification of the mathematical model of ship manoeuvring motion are carried out. Difference method and the method of additional excitation are proposed to reconstruct the samples. Using correlation analysis, the structure of a manoeuvring model is simplified. Combined with the measures proposed, support vector machines based identification is employed to determine the hydrodynamic coefficients in a modified Abkowitz model. Experimental data from the free-running model tests of a KVLCC2 ship are analyzed and the hydrodynamic coefficients are identified. Based on the regressive model, simulation of manoeuvres is conducted. Comparison between the simulation results and the experimental results demonstrates the validity of the proposed measures.     

System Identification Modeling of Ship Manoeuvring Motion in 4 Degrees of Freedom Based on Support Vector Machines

Based on support vector machines, three modeling methods, i.e., white-box modeling, grey-box modeling and black-box modeling of ship manoeuvring motion in 4 degrees of freedom are investigated. With the whole-ship mathematical model for ship manoeuvring motion, in which the hydrodynamic coefficients are obtained from roll planar motion mechanism test, some zigzag tests and turning circle manoeuvres are simulated. In the white-box modeling and grey-box modeling, the training data taken every 5 s from the simulated 20°/20° zigzag test are used, while in the black-box modeling, the training data taken every 5 s from the simulated 15°/15°, 20°/20° zigzag tests and 15°, 25° turning manoeuvres are used; and the trained support vector machines are used to predict the whole 20°/20° zigzag test. Comparisons between the simulated and predicted 20?/20° zigzag tests show good predictive ability of the proposed methods. Besides, all mathematical models obtained by the proposed modeling methods are used to predict the 10°/10° zigzag test and 35° turning circle manoeuvre, and the predicted results are compared with those of simulation tests to demonstrate the good generalization performance of the mathematical models. Finally, the proposed modeling methods are analyzed and compared with each other in aspects of application conditions, prediction accuracy and computation speed. The appropriate modeling method can be chosen according to the intended use of the mathematical models and the available data needed for system identification.     

System-based investigation on 4-DOF ship maneuvering with hydrodynamic derivatives determined by RANS simulation of captive model tests

For the non-negligible roll-coupling effect on ship maneuvering motion, a system-based method is used to investigate 4-DOF ship maneuvering motion in calm water for the ONR tumblehome model. A 4-DOF MMG model is employed to describe ship maneuvering motion including surge, sway, roll, and yaw. Simulations of circular motion test, static drift and heel tests are performed by solving the Reynolds-averaged Navier-Stokes (RANS) equations, after a convergence study quantifying the necessary grid spacing and time step to resolve the flow field adequately. The local flow field is analyzed for the selected cases, and the global hydrodynamic forces acting on the ship model are compared with the available experiment data. Hydrodynamic derivatives relating to sway velocity, yaw rate, and heel angle are computed from the computed force/moment data using least square method, showing good agreement with those obtained from EFD data overall. In order to investigate further the validity of these derivatives, turning circle and zigzag tests are simulated by using the 4-DOF MMG model with these derivatives. The trajectories and the time histories of the kinematic variables show satisfactory agreement with the data of free-running model tests, indicating that the system-based method coupled with CFD simulation has promising capability to predict the 4-DOF ship maneuvering motion for the unconventional vessel.     

Parameter identification of nonlinear roll motion equation for floating structures in irregular waves

In order to predict the roll motion of a floating structure in irregular waves accurately, it is crucial to estimate the unknown damping coefficients and restoring moment coefficients in the nonlinear roll motion equation. In this paper, a parameter identification method based on a combination of random decrement technique and support vector regression (SVR) is proposed to identify the coefficients in the roll motion equation of a floating structure by using the measured roll response in irregular waves. Case studies based on the simulation data and model test data respectively are designed to validate the applicability and validity of the identification method. Firstly, the roll motion of a vessel is simulated by using the known coefficients from literature, and the simulated data are used to identify the coefficients in the roll motion equation. The identified coefficients are compared with the known values to validate the applicability of the identification method. Then the roll motion is predicted by using the identified coefficients. The prediction results are compared with the simulated data, and good agreement is achieved. Secondly, the model test data of a FPSO are used to identify the coefficients in the roll motion equation. Then the random decrement signature of the roll motion is predicted by using the identified coefficients and compared with that obtained from the model test data, and satisfactory agreement is achieved. From this study, it is shown that the identification method can be effectively applied to identify the coefficients in the nonlinear roll motion equation in irregular waves.     

Parametric estimation of ship maneuvering motion with integral sample structure for identification

This documentation presents the parametric identification modeling of ship maneuvering motion with integral sample structure for identification (ISSI) and Euler sample structure for identification (ESSI) based on least square support vector machines (LS-SVM), where ISSI is used for the construction of in–out sample pairs. By using Mariner Class Vessel, the sample dataset are obtained from 15°/15° zigzag maneuvering simulation based on Abkowitz model. By analyzing the simulation data including rudder angle, surge velocity, sway velocity, yaw rate and so forth, the hydrodynamic derivatives in Abkowitz model are all identified. The validation of the proposed identification algorithm is verified by the high precisions of the identified hydrodynamic derivatives and maneuvering prediction results. The comparison is also conducted between the proposed ISSI and the conventional Euler sample structure for identification (ESSI), and the experimental results shows that ISSI is much more appropriate for parametric identification modeling of ship maneuvering motion.     

Numerical simulation of PMM tests for a ship in close proximity to sidewall and maneuvering stability analysis

As the maneuverability of a ship navigating close to a bank is influenced by the sidewall, the assessment of ship maneuvering stability is important. The hydrodynamic derivatives measured by the planar motion mechanism (PMM) test provide a way to predict the change of ship maneuverability. This paper presents a numerical simulation of PMM model tests with variant distances to a vertical bank by using unsteady RANS equations. A hybrid dynamic mesh technique is developed to realize the mesh configuration and remeshing of dynamic PMM tests when the ship is close to the bank. The proposed method is validated by comparing numerical results with results of PMM tests in a circulating water channel. The first-order hydrodynamic derivatives of the ship are analyzed from the time history of lateral force and yaw moment according to the multiple-run simulating procedure and the variations of hydrodynamic derivatives with the ship-sidewall distance are given. The straight line stability and directional stability are also discussed and stable or unstable zone of proportional-derivative (PD) controller parameters for directional stability is shown, which can be a reference for course keeping operation when sailing near a bank.     

Stochastic inverse modeling of nonlinear roll damping moment of a ship

This work presents an application of stochastic inverse method for the determination of nonlinear roll damping moment of a ship at zero forward speed. Nonlinear roll damping moment was estimated from the measured dynamic responses through stochastic inverse model. It is shown that this method enables nonlinear characteristic of the roll damping to be estimated without any assumption on its form of nonlinearity, including its confidence intervals given noisy data. The accuracy and practicability were assessed with laboratory tests related to both free-decay and forced rolling motions. The estimation results of the nonlinear damping moment show good agreement in all cases.     

Investigation of ship hydroelasticity

The importance of hydroelastic analysis of large and flexible container ships of today is pointed out. A methodology for investigation of this challenging phenomenon is drawn up and a mathematical model is worked out. It includes definition of ship geometry, mass distribution, structure stiffness, and combines ship hydrostatics, hydrodynamics, wave load, ship motion and vibrations. Based on the presented theory, a computer program is developed and applied for hydroelastic analysis of a flexible segmented barge for which model test results of motion and distortion in waves have been available. A correlation analysis of numerical simulation and measured response shows quite good agreement of the transfer functions for heave, pitch, roll, vertical and horizontal bending and torsion. The tool checked in such a way can be further used for reliable hydroelastic analysis of ship-like structures.     

Application of the extended Melnikov's method for single-degree-of-freedom vessel roll motion

Traditionally, when using Melnikov's method to analyze ship motions, the damping terms are treated as small. This is typically true for roll motion but not always true for other and/or multiple degrees of freedom. In order to apply Melnikov's method to other and/or multiple-degree-of-freedom motions, the small damping assumption must be addressed. In this paper, the extended Melnikov method is used to analyze ship motion without the constraint of small linear damping. Two roll motion models are analyzed here. One is a simple roll model with nonlinear damping and cubic restoring moment. The other is the model with biased restoring moment. Numerical simulations are investigated for both models. The effectiveness and accuracy of this method is demonstrated.     

Design similar scale model of a 10,000 TEU container ship through combined ultimate longitudinal bending and torsion analysis

This paper firstly figures out a similar scale model regarding ultimate strength experiment of a typical ultra large container ship (ULCS) through combined ultimate longitudinal bending and torsion analysis, in which the similarity theory is proposed to design the scale model for reflecting the progressive collapse behaviors of true ships in ultimate strength model test. The present study presents the similarity between scale model and true ship in cross-section considering the height of neutral axis, the section modulus, the inertia moment about neutral axis and the polar inertia moment should fit the geometrical similarity theory, and in strength considering buckling strength and shear ultimate strength of plates and stiffened panels should fit the strength similarity theory. Numerical investigations are conducted on the ultimate strength of a 10,000 TEU container ship and the similar scale model under pure hogging bending, pure torsion and combined bending and torsion, respectively. The nonlinear finite element method (NFEM) is adopted considering the effects of initial deformations and both material and geometric nonlinearities. Finally, the numerical results are compared with each other and discussed showing a good agreement in both elastic and inelastic range during the progressive collapse behaviors, which means the similar scale model can represent the true ship regarding ultimate strength test. And the similarity theory is verified quite stable after the uncertainty analysis.     

Application of advanced system identification technique to extract roll damping from model tests in order to accurately predict roll motions

In this paper our previously developed advanced system identification technique [1] has been applied to extract the frequency dependent roll damping from a series of model tests run in irregular (random) waves. It is shown that this methodology accurately models the roll damping which can then be used to produce accurate predictions of the ships roll motion. These roll motion predictions are not only more accurate than the potential flow predictions but more accurate than potential flow models corrected using either empirical prediction methods [2] and even those corrected using roll damping obtained from free decay sallying experiments. This methodology has the potential to significantly improve roll motion prediction during full scale at sea trails of vessels in order to dramatically improve safety of critical operations such as helicopter landing or ship to ship cargo transfer.     

Numerical analysis on ship maneuvering coupled with ship motion in waves

This paper considers a numerical analysis of ship maneuvering performance in the presence of incident waves and resultant ship motion responses. To this end, a time-domain ship motion program is developed to solve the wave–body interaction problem with the ship slip speed and rotation, and it is coupled with a modular-type 4-DOF maneuvering problem. In this coupled problem, the second-order mean drift force, which can play an important role in the ship maneuvering trajectory, is estimated by using a direct pressure integration method. The developed method is validated by observing the second-order mean drift force, and planar trajectories in maneuvering tests with and without the presence of incident waves. The comparisons are made for two ship models, Series 60 with block coefficient 0.7 and the S-175 containership, with existing experimental data. The maneuvering tests observed in this study include a zig-zag test in calm water, and turning tests in calm water and in regular waves. The present results show a fair agreement of overall tendency in maneuvering trajectories.     

An investigation into parametric roll resonance in regular waves using a partly non-linear numerical model

A partly non-linear time-domain numerical model is used for the prediction of parametric roll resonance in regular waves. The ship is assumed to be a system with four degrees of freedom, namely, sway, heave, roll and pitch. The non-linear incident wave and hydrostatic restoring forces/moments are evaluated considering the instantaneous wetted surface whereas the hydrodynamic forces and moments, including diffraction, are expressed in terms of convolution integrals based on the mean wetted surface. The model also accounts for non-potential roll damping expressed in an equivalent linearised form. Finally, the coupled equations of motion are solved in the time-domain referenced to a body fixed axis system.This method is applied to a range of hull forms, a post-Panamax C11 class containership, a transom stern Trawler and the ITTC-A1 containership, all travelling in regular waves. Obtained results are validated by comparison with numerical/experimental data available in the literature. A thorough investigation into the influence of the inclusion of sway motion is conducted. In addition, for the ITTC-A1 containership, an investigation is carried out into the influence of tuning the numerical model by modifying the numerical roll added inertia to match that obtained from roll decay curves.     

A 3D fully coupled analysis of nonlinear sloshing and ship motion

This study investigates the coupling effects of six degrees of freedom in ship motion with fluid oscillation inside a three-dimensional rectangular container using a novel time domain simulation scheme. During the time marching, the tank-sloshing algorithm is coupled with the vessel-motion algorithm so that the influence of tank sloshing on vessel motions and vice versa can be assessed. Several factors influencing the dynamic behavior of tank–liquid system due to moving ship are also investigated. These factors include container parameters, environmental settings such as the significant wave height, current velocity as well as the direction of wind, wave and flow current acting on the ship. The nonlinear sloshing is studied using a finite element model whereas nonlinear ship motion is simulated using a hybrid marine control system. Computed roll response is compared with the existing results, showing fair agreement. Although the two hull forms and the sea states are not identical, the numerical result shows the same trend of the roll motion when the anti-rolling tanks are considered. Thus, the numerical approach presented in this paper is expected to be very useful and realistic in evaluating the coupling effects of nonlinear sloshing and 6-DOF ship motion.     

Time-domain numerical and segmented ship model experimental analyses of hydroelastic responses of a large container ship in oblique regular waves

Real sea conditions are characterized by multidirectional sea waves. However, the prediction of hull load responses in oblique waves is a difficult problem due to numeral divergence. This paper focuses on the investigation of numerical and experimental methods of load responses of ultra-large vessels in oblique regular waves. A three dimensional nonlinear hydroelastic method is proposed. In order to numerically solve the divergence problem of time-domain motion equations in oblique waves, a proportional, integral and derivative (PID) autopilot model is applied. A tank model measurement methodology is used to conduct experiments for hydroelastic responses of a large container ship in oblique regular waves. To implement the tests, a segmented ship model and oblique wave testing system are designed and assembled. Then a series of tests corresponding to various wave headings are carried out to investigate the vibrational characteristics of the model. Finally, time-domain numerical simulations of the ship are carried out. The numerical analysis results by the presented method show good agreement with experimental results.     

Optimized support vector regression algorithm-based modeling of ship dynamics

This study contributes to solving the problem of how to derive a simplistic model feasible for describing dynamics of different types of ships for maneuvering simulation employed to study maritime traffic and furthermore to provide ship models for simulation-based engineering test-beds. The problem is first addressed with the modification and simplification of a complicated and nonlinearly coupling vectorial representation in 6 degrees of freedom (DOF) to a 3 DOF model in a simple form for simultaneously capturing surge motions and steering motions based on several pieces of reasonable assumptions. The created simple dynamic model is aiming to be useful for different types of ships only with minor modifications on the experiment setup. Another issue concerning the proposed problem is the estimation of parameters in the model through a suitable technique, which is investigated by using the system identification in combination with full-scale ship trail tests, e.g., standard zigzag maneuvers. To improve the global optimization ability of support vector regression algorithm (SVR) based identification method, the artificial bee colony algorithm (ABC) presenting superior optimization performance with the advantage of few control parameters is used to optimize and assign the particular settings for structural parameters of SVR. Afterward, the simulation study on identifying a simplified dynamic model for a large container ship verifies the effectiveness of the optimized identification method at the same time inspires special considerations on further simplification of the initially simplified dynamic model. Finally, the further simplified dynamic model is validated through not only the simulation study on a container ship but also the experimental study on an unmanned surface vessel so-called I-Nav-II vessel. Either simulation study results or experimental study results demonstrate a valid model in a simple form for describing the dynamics of different types’ ships and also validate the performance of the proposed parameter estimation method.     

Recovering the functional form of the nonlinear roll damping of ships from a free-roll decay experiment: An inverse formulism

The purpose of this paper is to identify the functional form of the nonlinear roll damping for a particular ship based on an experiment. The problem of damping identification is formulated as an integral equation of the first kind. However, the solution of the problem lacks stability properties, due to the ill-posedness of the first-kind integral equation. To resolve this problem, a stabilization technique (known as a regularization method) is applied to the present problem of the identification of nonlinear damping. The identified results for nonlinear roll dampings are compared with those from a conventional roll identification method. The findings of the present study are validated by the direct comparison of experimental data on free-roll decay motion with the numerically simulated results.     

Solution of the nonlinear roll model by a generalized asymptotic method

Mathematical modeling of the nonlinear roll motion of ships is one subject widely dealt with in nonlinear ship dynamics. This paper investigates setting up a form of nonlinear roll motion model and developing its periodic solution by the generalized Krylov–Bogoliubov asymptotic method in the time domain. In this model, nonlinearities are introduced through damping and restoring terms. The restoring term is approximated as a third-order odd polynomial whereas the quadratic term is favored to represent the nonlinear damping. The ship is assumed to be under the influence of a sinusoidal exciting force. Although the method is expressible to contain any order of the perturbing term, a single degree is chosen to avoid cumbersome mathematical complexity. In order to improve the solution a first-order correction term is also included. Moreover, a numerical example is carried out for a small vessel in order to validate the solution scheme.     

Experimental investigation of the lift component of roll damping

The lift force and turning moment acting on a model towed obliquely to the direction of motion have been measured. Two models were used; one of them was tested fitted with and without a rudder. These measurements were used to determine the magnitude of the lift coefficient and the point of application of the transverse force acting on the model. The data were then used to determine the lift component of the roll damping moment. It has been found that the equivalent linear damping coefficient due to lift is a nonlinear function of the forward speed of the ship.