Nonlinear Ship Research Articles

A nonlinear model predictive control method for ship path following in waves

ABSTRACT With the development of intelligent ships, the problem of ship path following has attracted much attention in recent years. Ship motion is inevitably affected by an external environment and thus the design of the ship control system in currents or waves, etc. has always been a challenging work. In the present work, a Nonlinear Model Predictive Control (NMPC) method is proposed for ship path following in waves. The NMPC controller can obtain the desired rudder angle of nonlinear ship system by solving an open-loop optimisation problem. The NMPC controller integrated with a Line-of-Sight (LOS) guidance is proposed and applied for a container ship which is controlled to follow two desired paths in both calm water and waves. The simulation results demonstrate the more effectiveness and greater anti-interference of the proposed NMPC method, compared with that the results by using a traditional Proportional-Derivative (PD) control method.

A class of nonlinear ship stability analysis: Stochastic dynamics with time-delayed control in crosswind and wave conditions

The impact of ocean waves and crosswinds on ships has long been a focal point of research for many scholars. This paper proposes a stochastic ship rolling model influenced by crosswinds, ocean waves, and time delays. The safe operating region for ship navigation is presented through the phase space of the system. A quantitative discussion of the system is conducted using the stochastic Melnikov function, and the stochastic P-D bifurcation of the system is discussed using topological data analysis techniques. The research indicates that incorporating time delay feedback can effectively enhance the system’s stability.

Autonomous navigation decision-making for ships in complex estuarine waters: Methodology and validation

This study focused on key scientific issues in the autonomous navigation for ships, including constraints on environmental and navigation rules, limitations on ship maneuverability, and collision avoidance mechanisms, to address the challenges of autonomous navigation decision-making for ships in complex estuarine waters and validate the feasibility and accuracy of the proposed methodology. A novel autonomous navigation decision-making method that can dynamically adapt to residual errors in a system and the random movements of target ships was proposed. The predictive model used to calculate decision plans and the simulation model used to execute and validate decision plans were separated. Environmental constituent elements were classified and modeled to digitize the environment. A navigation scenario was constructed based on the fusion of virtual and real information. The control and process prediction methods were proposed based on the nonlinear ship maneuvering characteristics. Navigation rules were summarized, analyzed, and integrated into the decision-making and execution process. The collision avoidance mechanism and calculation method for feasible course and speed range were studied. Simulation experiments were conducted using the North Channel of the Yangtze River Estuary as an example. The results demonstrated that the proposed method can accurately make autonomous navigation decisions, safely avoid collisions, and timely track routes in nearly realistic scenarios.

Prediction of Wave-Induced Nonlinear Ship Motions Based on an IRF-LSTM Hybrid Approach

Prediction of Wave-Induced Nonlinear Ship Motions Based on an IRF-LSTM Hybrid Approach

Analysis of chaos and capsizing of a class of nonlinear ship rolling systems under excitation of random waves.

The action of wind and waves has a significant effect on the ship's roll, which can be a source of chaos and even capsize. The influence of random wave excitation is considered in order to investigate complex dynamic behavior by analytical and numerical methods. Chaotic rolling motions are theoretically studied in detail by means of the relevant Melnikov method with or without noise excitation. Numerical simulations are used to verify and analyze the appropriate parameter excitation and noise conditions. The results show that by changing the parameters of the excitation amplitude or the noise intensity, chaos can be induced or suppressed.

Stochastic bifurcation and chaos study for nonlinear ship rolling motion with random excitation and delayed feedback controls

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The Itoˆ-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. We also analyze the properties and shape changes of the system’s probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P-bifurcation and D-bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series.

Prediction of ship future motions at different predictable time scales for shipboard helicopter landing in regular and irregular waves

ABSTRACT Differing from the traditional helicopter landing on land, due to ship motions induced by actual waves, the landing safety of shipboard helicopter on vessels in waves deserves to be studied. To provide a judgment basis for the timing of shipboard helicopter landing, a hydrodynamic analysis method based on the Long-Short-Term Memory (LSTM) neural network is proposed to achieve the real-time prediction of ship motions in this study. Firstly, the hydrodynamic formulations based on potential flow theory for nonlinear ship motions in waves are presented. The implementation details of the LSTM neural networks are described. Secondly, the numerical verification study is carried out in regular and irregular waves, respectively. Furthermore, a destroyer model is employed to illustrate the proposed framework, and the results corresponding to the different time scales in waves are presented. Finally, the work of this paper is summarized and the certain conclusions are drawn.

Effect of Sampling Rate in Sea Trial Tests on the Estimation of Hydrodynamic Parameters for a Nonlinear Ship Manoeuvring Model

This paper explores the impact of sampling rates during sea trials on the estimation of hydrodynamic parameters in a nonlinear manoeuvring model. Sea trials were carried out using an offshore patrol vessel and test data were collected. A nonlinear manoeuvring model is introduced to characterise the ship’s manoeuvring motion, and the truncated least squares support vector machine is employed to estimate nondimensional hydrodynamic coefficients and their corresponding uncertainties using the 25°–25° zigzag test. To assess the influence of the sampling rates, the training set is resampled offline with 14 sampling rates, ranging from 0.2 Hz to 5 Hz, encompassing a rate 10 times the highest frequency component of the signal of interest. The results show that the higher sampling rate can significantly diminish the parameter uncertainty. To obtain a robust estimation of linear and nonlinear hydrodynamic coefficients, the sampling rate should be higher than 10 times the highest frequency component of the signal of interest, and 3–5 Hz is recommended for the case in this paper. The validation is also carried out, which indicates that the proposed truncated least square support vector machine can provide a robust parameter estimation.

Neural Networks Based-Adaptive Control of Nonlinear Ship Manoeuvring System

Neural Networks Based-Adaptive Control of Nonlinear Ship Manoeuvring System

Non-stationary probabilistic analysis of non-linear ship roll motion due to modulated periodic and random excitations

This paper is about the study on the non-stationary probability density function (PDF) solution of the non-linear ship rolling system under modulated periodic and random excitations. The quadratic and cubic damping terms are introduced to describe the non-linear damping moment and the power terms in state variables are adopted to describe the righting moment in the ship rolling system, respectively. The relevant Fokker–Planck–Kolmogorov (FPK) equation of the ship rolling system is constructed and the non-stationary probabilistic solutions are obtained by the presented solution procedure. In the solution process, the time variable t is introduced to the traditional exponential-polynomial-closure (EPC) method to obtain the non-stationary PDF solutions of the ship rolling system. The obtained non-stationary PDF solutions of the non-linear ship rolling systems demonstrate that the presented solution procedure can give high solution accuracy even in the PDF tails when they are compared with Monte Carlo simulation (MCS). Moreover, owing to the strong system nonlinearity and the interaction of the periodic excitation and random excitation, the achieved non-stationary PDF solutions of the system responses can deviate significantly from the Gaussian PDF. It is also found that the PDFs of responses are not even symmetrical about the means of responses due to the interaction of the periodic excitation and the random excitation even if the system only contains odd nonlinear terms. In addition, the computational efficiency is increased by over five hundred times by the presented solution procedure compared to MCS.

RAO-based translation process for estimating extreme value distribution of nonlinear ship response in irregular waves

The authors propose a new method named the RAO-based Translation Process (RTP) method for simply estimating the extreme value distribution of the nonlinear ship response in irregular waves based on the nonlinear response in regular waves. The proposed method combines the existing idea of the Nonlinear Correction (NLC) method, which is based on wave height-dependent RAO, with the theory of the translation process, and thus has both simplicity and a clear theoretical background. Furthermore, it is positioned as an extension of the Equivalent Design Wave (EDW) method used in conventional ship structural design. The validity of the proposed method is confirmed through a numerical study on the extreme value distribution of hull-girder sectional forces considering body nonlinear effects. The proposed method can be used for various purposes, and in particular, it can reduce the computational demand for strength evaluation by Direct Load and Structure Analysis (DLSA), which is a computationally extensive analysis method. Therefore, the proposed method is expected to make a significant contribution to structural design.

A GPU-Accelerated Method for 3D Nonlinear Kelvin Ship Wake Patterns Simulation

The study of ship waves is important for ship detection, coastal erosion and wave drag. This paper proposed a highly paralleled numerical computation method for efficiently simulating three-dimensional nonlinear kelvin waves. First, a numerical model for nonlinear ship waves is established based on potential flow theory, the Jacobian-free Newton–Krylov (JFNK) method and the boundary integral method. To reduce the amount of data stored in the JFNK method and improve the computational efficiency, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU)-based parallel computing framework is designed, and we used the Compute Unified Device Architecture (CUDA) language to develop a GPU solution. Finally, numerical simulations of 3D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved, and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

Real-time control of ship's roll motion with gyrostabilisers

The safety of ship manoeuvring operations is greatly affected by large roll motions under severe wave conditions. While existing studies have focused on optimizing hydrodynamic performance devices, these approaches may not be effective under realistic sea conditions where wave frequency and direction are irregular. Thus, predicting ship motion tendencies and implementing a reasonable control approach is crucial for improving ship safety. This study proposes a novel and practical control strategy that can effectively suppress roll motion of ships under realistic random wave conditions. The approach utilizes a real-time controller based on model predictive control (MPC) that is actuated by a dual gyrostabilizer. The ship's roll motion response in beam waves is calculated using one degree-of-freedom hydrodynamic modeling, and the wave memory effect is taken into consideration by employing system identification. A synthetic mathematical model of MPC and the dual gyrostabilizer method is introduced in state-space representation to compensate for wave excitation moment in real-time. The proposed method's efficacy is validated by comparing with a roll stabilization scenario of a particular ship in the literature, and control performance of a standard ship under regular and irregular wave conditions is separately discussed. Results indicate that the proposed method can significantly reduce roll motion amplitude and is feasible for nonlinear ship motion control problems. This study sheds light on the multi-degree-of-freedom motion control of ships under beam wave conditions.

Numerical investigation on nonlinear ship waves by LCM and WSAM

This paper investigates the nonlinear ship waves by implementing the longitudinal cut method (LCM) and wake survey analysis method (WSAM) in the computational fluid dynamics (CFD) simulation. LCM is first implemented and validated for a Series 60, Cb = 0.6 ship model to guarantee accurate prediction of the wave pattern resistance (Rwp). To illustrate the reliability, WSAM is performed for a wall-sided model, incorporating the local adaptive mesh refinement (LAMR) and surface tension models to capture nonlinear bow waves. Far and near-field wave patterns and momentum loss resistance (RML) are compared with the experiment.With the well-predicted nonlinear bow waves, the velocity discontinuity property across the nonlinear wavefront and the vortex motion beneath the nonlinear waves are clearly observed by velocity vector and Q-criteria iso-surface visualization. By LCM and WSAM analysis, the discrepancy between wave resistance (Rw) and Rwp is attributed to the nonlinearity in ship waves, and expression to evaluate this part of resistance (Rnw) is discussed and summarized. Finally, the influence of velocity and draft on Rnw and bow wave angle (β) is systematically analyzed and discussed. This study hopes to provide insights to evaluate the nonlinearity in ship waves and further understand its underlying mechanism.

Robust optimal control of a nonlinear surface vessel model with parametric uncertainties

This paper presents a fast alternative optimization method for developing a reliable optimal controller that can handle system model parameter uncertainties. The source of uncertainty in this study is identified as hydrodynamic coefficients, which are prone to errors due to the challenges involved in obtaining accurate values. The proposed optimization method utilizes a complex nonlinear ship model provided by Maneuver Modelling Group (MMG) as the reference for the ship motion model. The optimization process is divided into two stages: a blind search followed by bisection optimization, to obtain a robust optimal controller. To demonstrate the effectiveness of the proposed approach, system response analysis and practical tests were performed on Step, M-Turn, and Doublet maneuvers. The results show that the controller parameters obtained from the proposed optimization method are capable of achieving high success rates in controlling a system with uncertain parameters.

Observer-based [formula omitted] fuzzy fault-tolerant switching control for ship course tracking with steering machine fault detection

To enhance the robustness of ship autopilot (SA) system with nonlinear dynamics, unmeasured states, and unknown steering machine fault, an observer-based H∞ fuzzy fault-tolerant switching control for ship course tracking is proposed. Firstly, a global Takagi–Sugeno (T-S) fuzzy nonlinear ship autopilot (NSA) is developed with full consideration of ship steering characteristics. And the actual navigation data collected from a real ship are used to verify the reasonableness and feasibility of NSA model. Then, virtual fuzzy observers (VFOs) for both fault-free and faulty systems are proposed to estimate the unmeasured states and unknown fault simultaneously, and compensate for the faulty system by using the fault estimates. Accordingly, the VFO-based H∞ robust controller (VFO-HRC) and fault-tolerant controller (VFO-HFTC) are designed. Subsequently, a smoothed Z-score-based fault detection and alarm (FDA) is developed to provide switching signals for which the controller and its corresponding observer should be invoked. Finally, simulation results on the “Yulong” ship demonstrate the effectiveness of the developed control method.

First passage times for nonlinear ship dynamics using Gaussian random fields and effective waves

It is important to know the mean time until critical roll motion occurs in various operating and sea conditions, in order to determine and ensure the safety of ship designs and operating ships. Since typical ocean waves are irregular, the forcing and roll response of the ship is considered to be a stochastic process of colored noise type. However, the simulation of the corresponding first passage times is very time consuming. Therefore, an approach for the determination of mean first passage times of critical roll motion of ships is proposed in this paper which needs much less computation time. This approach is based on explicit formulas for the roll energy of the ship. These formulas are used to determine the mean first passage times based on integral expressions, which were previously obtained. The resulting integral expressions can be computed very fast using standard quadrature formulas. Moreover, the underlying model for ship dynamics is extended by introducing a new effective wave for short-crested sea states. This is an extension to the improved Grim’s effective wave concept.

Ship Collision Avoidance Based on the Vulnerability Assessment for Small Vessels in Bad Weather

In the conditions of bad weather, the small vessels maneuvering ability of collision avoidance is seriously reduced and the vulnerability to maritime accidents increases due to the influence of strong wind and wave. This paper proposes a collision avoidance decision-making and control method for small vessels using the integrated collision risk assessment based on fuzzy logic. First, the speed of wind and height of wave in the bad weather conditions are fuzzified. Then, the collision risk indices are selected for fuzzy inference to get the basic collision risk which will be integrated with the vulnerability to collision accidents and it helps to improve the accuracy of collision risk assessment. According to the current multi-ships encounter situations, the similar cases are retrieved from the case database, and the collision avoidance decision is given after fuzzy adjustments. To implement collision avoidance actions, a fuzzy algorithm for nonlinear ship heading dynamic surface control (DSC) control considering input saturation and uncertainties is designed. The problem of "computational expansion" that may occur in high-order systems is avoided by using DSC technology. Finally, simulation experiments are implemented to verify the effectiveness of the collision avoidance method.

Towards improved understanding of naval ship structural performance via virtual hull monitoring

Weight-optimised ships, such as High Speed Light Craft (HSLC), are operated by navies around the world. Naval ships must perform in harsh and contested ocean environments. Operations in high sea states result in large linear and nonlinear ship motions which in turn, induce significant loads on ship structures and accelerate structural fatigue. Monitoring and assessment of fatigue on ship structures is important for navies, to understand the performance, limitations, and life-cycle costs of their ships. An established method for monitoring structural responses is via long-term measurements, using Instrumented Hull Monitoring (IHM). However, this approach is generally too resource-intensive to be implemented on a broad scale. Virtual Hull Monitoring (VHM) is a technique to couple on-board ship data, such as Global Positioning System (GPS) data, with hindcast wave data. The resulting enriched dataset enables robust numerical fatigue analysis, because the structural responses are related to the encountered wave environment, rather than based on global wave statistics. Thus, the concept of VHM is receiving increased attention in both commercial and military sectors. This is due to its low cost and the relative ease of implementation compared to IHM. Using a Royal Australian Navy HSLC as the test bed, this study presents an investigation into the feasibility of VHM by comparing results with available IHM data. An efficient framework was developed in PythonTM to extract and couple hindcast wave data to ship speed and position, calculating the resultant stresses on the ship structure, and comparing with the measured stresses from IHM. The novel aspects of this work include the use of a semi-displacement hullform, and the utilisation of both sea-trials and long-term measurements. The study shows promising results for VHM. Finally, recommendations for further work are provided.

Nonlinear Ship Wake Detection in SAR Images Based on Electromagnetic Scattering Model and YOLOv5

Traditional wake detection methods have been successfully applied to the detection of a simple linear ship wake. However, they cannot effectively detect nonlinear wake and weak wake under high sea state conditions, whereas the deep-learning-based detection method could play to its strengths in this respect. Due to the lack of sufficient measured SAR images of ship wake to meet the training requirement for deep learning method, this paper explores the method to detect the nonlinear ship wake by combining electromagnetic scattering model with deep learning technique. The composite scene model of the sea surface and its wake is established first, then the facet scattering distribution of the ship wake and the sea background is analyzed with the help of the electromagnetic scattering model, and the simulation of the wake SAR images under the sea background is finally accomplished based on the modulation model. Combined with the simulation results and measured wake SAR images, the sample database is constructed. The You Only Look Once Version five algorithm (YOLOv5) based on deep learning techniques is applied to detect the wake target in complex conditions such as different sea states, multiple targets, curvilinear wakes, and weak wakes. The result show that the YOLOv5 leads to an obvious higher detection efficiency with satisfactory accuracy. Moreover, the comparison between YOLOv5 and the traditional Radon transform method for detecting nonlinear wakes in a strong noise background shows that the proposed method is better than the traditional object detection model. Thus, the proposed scheme would be a practical tool to deal with the detection of nonlinear ship wake and weak wake in complex scenarios, which will be helpful to the further remote sensing investigation of the ship.