Probability Density Analysis of Nonlinear Random Ship Rolling

Ship rolling in random waves is a complicated nonlinear motion that contributes substantially to ship instability and capsizing.The finite element method(FEM)is employed in this paper to solve the Fokker Planck(FP)equations numerically for homoclinic and heteroclinic ship rolling under random waves described as periodic and Gaussian white noise excitations.The transient joint probability density functions(PDFs)and marginal PDFs of the rolling responses are also obtained.The effects of stimulation strength on ship rolling are further investigated from a probabilistic standpoint.The homoclinic ship rolling has two rolling states,the connection between the two peaks of the PDF is observed when the periodic excitation amplitude or the noise intensity is large,and the PDF is remarkably distributed in phase space.These phenomena increase the possibility of a random jump in ship motion states and the uncertainty of ship rolling,and the ship may lose stability due to unforeseeable facts or conditions.Meanwhile,only one rolling state is observed when the ship is in heteroclinic rolling.As the periodic excitation amplitude grows,the PDF concentration increases and drifts away from the beginning location,suggesting that the ship rolling substantially changes in a cycle and its stability is low.The PDF becomes increasingly uniform and covers a large region as the noise intensity increases,reducing the certainty of ship rolling and navigation safety.The current numerical solutions and analyses may be applied to evaluate the stability of a rolling ship in irregular waves and capsize mechanisms.

Nonparametric Identification of Nonlinear Added Mass Moment of Inertia and Damping Moment Characteristics of Large-Amplitude Ship Roll Motion

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of largeamplitude ship roll motion based on transient motion data through the nonparametric system identification method.An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data.However,this numerical approach leads to solution instability due to noisy data.Regularization is a technique that can overcome the lack of stability;hence,Landweber’s regularization method was employed in this study.The L-curve criterion was used to select regularization parameters(number of iterations)that correspond to the accuracy of the inverse solution.The solution of this method is a discrete moment,which is the summation of nonlinear restoring,nonlinear damping,and nonlinear mass moment of inertia.A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship,and the detections are matched with the inverse solution at the same discrete times.The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy.Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Non-linearity Analysis of Ship Roll Gyro-stabilizer Control System

A gyro-stabilizer is the interesting system that it can apply to marine vessels for diminishes roll motion.Today it has potentially light weight with no hy­drodynamics drag and effective at zero forward speed.The twin-gyroscope was chosen.Almost,the modelling for designing the system use linear model that it might not comprehensive mission requirement such as high sea condition.The non-linearity analysis was proved by comparison the re­sults between linear and non-linear model of gyro-stabilizer throughout fre­quency domain also same wave input,constrains and limitations.Moreover,they were cross checked by simulating in time domain.The comparison of interested of linear and non-linear close loop model in frequency domain has demonstrated the similar characteristics but gave different values at same frequency obviously.The results were confirmed again by simulation in irregular beam sea on time domain and they demonstrate the difference of behavior of both systems while the gyro-stabilizers are switching on and off.From the resulting analysis,the non-linear gyro-stabilizer model gives more real results that correspond to more accuracy in a designing gyro-sta­bilizer control system for various amplitudes and frequencies operating condition especially high sea condition.

Probability density function solution to nonlinear ship roll motion excited by external Poisson white noise

The stationary probability density function (PDF) solution to nonlinear ship roll motion excited by Poisson white noise is analyzed. Subjected to such random excitation, the joint PDF solution to the roll angle and angular velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. To solve this equation, the exponential-polynomial closure (EPC) method is adopted. With the EPC method, the PDF solution is assumed to be an exponential-polynomial function of state variables. Special measure is taken such that the generalized FPK equation is satisfied in the average sense of integration with the assumed PDF. The problem of determining the unknown parameters in the approximate PDF finally results in solving simultaneous nonlinear algebraic equations. Both slight and high nonlinearities are considered in the illustrative examples. The analysis shows that when a second-order polynomial is taken, the result of the EPC method is the same as the one given by the equivalent linearization (EQL) method. The EQL results differ significantly from the simulated results in the case of high nonlinearity. When a fourth-order or sixth-order polynomial is taken, the results of the EPC method agree well with the simulated ones, especially in the tail regions of the PDF. This agreement is observed in the cases of both slight and high nonlinearities.

Roll stability catastrophe mechanism of a flooded ship on regular sea waves

Based on a typical one-free-degree ship roll motion equation, the cusp catastrophe model is built including the bifurca- tion set equation, splitting factor ＇u＇ and regular factor ＇v＇, where both ＇u＇ and ＇v＇ are further expressed with typical flooded ship parameters. Then, the roll catastrophe mechanism is analyzed mainly by means of ＇u＇, under the given parameters of a typical trawler boat. The aim of this research is to reveal the mutagenic mechanism of the roll stability and provide a reference for improving ship roll stability.

Approximation Method for Flare Slamming Analysis of Large Container Ships in Parametric Rolling Conditions

Since the research of flare slamming prediction is seldom when parametric rolling happens, we present an efficient approximation method for flare slamming analysis of large container ships in parametric rolling conditions. We adopt a 6-DOF weakly nonlinear time domain model to predict the ship motions of parametric rolling conditions. Unlike previous flare slamming analysis, our proposed method takes roll motion into account to calculate the impact angle and relative vertical velocity between ship sections on the bow flare and wave surface. We use the Wagner model to analyze the slamming impact forces and the slamming occurrence probability. Through numerical simulations, we investigate the maximum flare slamming pressures of a container ship for different speeds and wave conditions. To further clarify the mechanism of flare slamming phenomena in parametric rolling conditions, we also conduct real-time simulations to determine the relationship between slamming pressure and 3-DOF motions, namely roll, pitch, and heave.

Energy Optimization of the Fin/Rudder Roll Stabilization System Based on the Multi-objective Genetic Algorithm （MOGA）

Energy optimization is one of the key problems for ship roll reduction systems in the last decade. According to the nonlinear characteristics of ship motion, the four degrees of freedom nonlinear model of Fin/Rudder roll stabilization can be established. This paper analyzes energy consumption caused by overcoming the resistance and the yaw, which is added to the fin/rudder roll stabilization system as new performance index. In order to achieve the purpose of the roll reduction, ship course keeping and energy optimization, the self-tuning PID controller based on the multi-objective genetic algorithm （MOGA） method is used to optimize performance index. In addition, random weight coefficient is adopted to build a multi-objective genetic algorithm optimization model. The objective function is improved so that the objective function can be normalized to a constant level. Simulation results showed that the control method based on MOGA, compared with the traditional control method, not only improves the efficiency of roll stabilization and yaw control precision, but also optimizes the energy of the system. The proposed methodology can get a better performance at different sea states.

The Applicability of Hydrofoils as a Ship Control Device

Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim to prevent capsizing and to increase ship maneuverability in high-speed water craft. This model can be used to develop algorithms for control system improvement. The mathematical model presented in this paper optimized the use of multipurpose hydrofoils to reduce heeling and the trimming moment, maintaining an upright ship’s position and lessening the resistance via transverse force. Conventionally, the trimming and heeling of a ship are controlled using ballast water;however, under variable sea conditions it is sometimes difficult to control a ship’s motion using ballast water. In this case, a hydrofoil would be more stable and maneuverable than a ballast tank controlled vessel. A movable hydrofoil could theoretically be adapted from moveable aerofoil technology. This study proves the merit of further investigation into this possibility.

Design of Fin-propeller Test Set-up and Analysis of Roll Stabilization Ability

Presents the fin-propeller test set-up to solve the problem of roll stabilization with ships in full speed range, withwhich, tests were run in water rank for acquisition of data, and concludes from data acquired that the fin-propeller test set-up produces more lift than simple fin, and provides lateral thrust as well, and it is therefore an effective roll stabilization devicefor ships in full speed range.

船模静水参激横摇阻尼测量实验研究

针对船舶参数横摇独特的运动特征,设计激励稳性参数的船模静水参激横摇实验,研究与船舶参数横摇特征吻合的横摇阻尼测量方法.基于船舶参数横摇机理,设计了由激励船模重心高度的激振器,控制电机与测量船模运动的测控仪为主要设备组成的实验系统.由阻尼耗散、激励释放和复原力矩三项能量的平衡,推导了横摇阻尼系数的计算公式.露天船模水池的静水参激横摇阻尼测量实验.结果表明:稳态响应的横摇幅值持续稳定,大幅横摇阻尼可测,实验测量的重复性好.

基于联邦泛化的非平稳船舶横摇运动预测方法

船舶易受到风浪干扰而影响海上风力发电机的安装精度和维护安全性,其中长峰波随机波浪谱下的非平稳横摇运动影响最大。为保证海上作业在复杂海况下的稳定性,需要提高预测模型的泛化性,故本文提出基于联邦泛化的非平稳船舶横摇运动预测方法。首先,利用变模态方法分解非平稳船舶横摇运动为多分量平稳序列,进而采用注意力机制的长短期记忆神经网络建立本地多维多步预测模型,并进行误差校正;其次,为了提高复杂海况下遇到新类型船舶横摇运动时的预测效果,在不共享数据的前提下联合多家船舶横摇运动数据持有方进行择优联邦建模;最后,使用最大均值差异方法选择特征相似度高的数据进行加权平均联邦训练。实验结果表明,经过联邦学习后的模型具有更高的预测精度,以及更好的泛化能力,有助于风电安装时的波浪补偿稳定控制。

滚装船载运的锂电池汽车仿真模拟研究

为应对船舶运输中锂电池汽车火灾带来的严重后果,构建滚装船甲板上的锂电池汽车火灾仿真模型。首先,利用锂电池汽车全尺寸火灾试验数据,验证单辆和双辆锂电池汽车火灾仿真模型准确性。随后,应用经验证的仿真模型对滚装船甲板上的锂电池汽车火灾模拟仿真,分析不同车辆间距下火灾热释放速率、温度和辐射热等变化特征。结果表明:在锂电池汽车火灾初期,火焰会先蔓延至并排停放的车辆,特别是受到喷射火影响的一侧车辆,然后再扩展至前后两侧的车辆,且前方车辆遭受的火灾损毁程度明显大于后方车辆。同时,喷射火会加剧锂电池汽车火灾的蔓延和发展,有喷射火区域的温度显著高于无喷射火区域,而受到喷射火影响的邻近车辆则最先被引燃。通过数值仿真手段可有效模拟船舶载运锂电池汽车火灾发展及蔓延过程。

基于LSTM模型的船舶材料成本滚动预测

船舶建造周期长、材料成本占比大,易受大宗商品价格指数和汇率等多个因素的影响,造成实际完工成本与报价估算存在较大误差的情况。采用灰色关联分析(Grey Correlation Analysis,GCA)方法识别材料成本的影响因素,基于长短期记忆网络(Long Short-Term Memory,LSTM)模型构建船舶材料成本滚动预测模型,并使用某造船企业53艘64000 t散货船63个月的材料成本数据和对应的影响因素数据进行试验分析。结果表明,预测数据与实际数据误差在可接受范围内,可证明所选择方法和构建模型的有效性。研究结果对制造过程的成本实时预测和控制具有现实意义。

一种海洋自升式修井平台船型分析

针对渤海海域油气开发中自升式修井平台的船型设计,进行系统分析。从桩腿数量维度出发,考虑波流载荷、风载荷和平台重力的共同作用,通过有限元数值模拟软件,建立自升式修井平台的仿真模型,计算不同方向角下平台的波流载荷、桩腿位移和抗倾力矩等评价指标,综合对比分析三桩腿和四桩腿两种不同船型的设计特点,以揭示各自在平台方案、预压载能力和稳定性等方面的特点。研究结果发现,四桩腿平台在舱内设备布置、预压载能力和抗倾稳性方面具有明显优势,特别是在单桩失效情况下,四桩腿平台的稳定性和安全性更高。研究结论对自升式修井平台的设计优化具有重要的指导意义,为进一步提升平台的安全性和高效性提供理论依据。

基于VOF方法的规则波下破舱进水数值模拟

文中以某理想客滚船舱段模型为研究对象,基于VOF方法建立两相流体积模型,采用重叠网格和交界面网格技术,分析规则波下不同破口形状舱室模型破舱进水下的运动响应.结果表明:不同破口形状对破舱进水过程的影响主要表现为横摇时域的高频成分,且不同破口形状导致的流量不同.

随机激励作用下船舶横摇运动的奇异非混沌动力学

基于一类规则横浪作用下的单自由度船舶横摇运动模型,考虑恢复力矩和阻尼力矩的非线性因素,以一低干舷船模为例,利用龙格库塔法求解了横摇运动方程,通过时间庞加莱截面绘制了系统的分岔图;考虑其受随机风荷载扰动下不同周期吸引子演变成奇异非混沌吸引子的具体过程,发现周期激励系统在随机激励扰动下同样存在奇异非混沌吸引子,且当分岔参数离混沌区域越远,所需要随机激励的幅值越大才能诱发奇异非混沌吸引子.通过最大李雅普诺夫指数验证吸引子的非混沌性;采用奇异连续谱和分形图刻画吸引子的奇异性.

基于扩张状态观测器的滑模预测串级舵减摇控制

针对在定权重模型预测舵减摇控制下的欠驱动船舶转向响应较慢的问题,提出一种基于模糊扩张状态观测器(FESO)的滑模预测串级舵减摇控制方法。建立线性三自由度欠驱动船舶运动模型,设计FESO来估计船舶状态和外部扰动,设计离散自适应滑模控制(DASMC)作为串级外环航向控制,以外环控制作为预期控制律,设计模型预测控制(MPC)作为串级内环减摇控制。通过分析船舶的航向误差和航行情况,设计模糊规则在不同航行情况下改变MPC目标函数的状态权重和控制输入权重,理论证明了所设计观测器的收敛性和控制方法的闭环稳定性。通过对一艘多用途海军舰艇进行数值仿真分析,在航向改变的情况下,所设计的控制器减摇率在保证减摇效果的同时,相比固定权重线性MPC在30°的转向的响应时间更少,证明了所提方法能有效提升欠驱动船舶减摇时对转向的响应。