Numerical experiments on an ill-posed inverse problem for a given velocity around a hydrofoil by iterative and noniterative regularizations

For a given velocity distribution around a hydrofoil, the inverse problem of the hydrofoil is studied. The inverse problem is formulated by representing the hydrofoil in terms of vortices within the framework of linear potential theory. From the mathematical formulation, it is known that the inverse problem turns out to be ill-posed in the usual topology. In this paper, iterative and noniterative regularizations are applied to solve the problem and to find their suitability for the two-dimensional inverse hydrofoil problem. Numerical experiments demonstrate that the regularization methods are accurate and suitable for the inverse mathematical formulation for a given velocity distribution around a hydrofoil. Received: June 6, 2000 / Accepted: December 8, 2000     

基于反向方法的船体冰载荷研究

船舶碰撞海冰引起的冰载荷分布是十分复杂的。文章选取Thikhonov正则化这一反向方法,根据极地科考补给船S.A Agulhas II号于2013-2014年间南极航行时实测的数据,分析得到了船体艉肩部的冰载荷。通过应用三种独立的冰载荷离散方式来模拟海冰的自然特性,在有限元中得到模型的影响矩阵,并应用Matlab对Thikhonov正则化方程进行了优化。研究结果表明,反向方法可以克服数据处理过程中的不适定性,并计算得到船体冰载荷。     

Application of stochastic inverse theory to marine hydrodynamics

The objective of this article is to give an overview about the stochastic inverse method and its application to an ill-posed inverse problem in marine hydrodynamics. In stochastic inversion, it is possible to take into account inherent measurement and system uncertainties in the solution of an inverse problem in a very simple manner. The stochastic inverse method transforms the original inverse problem into the problem of a probabilistic question. Thus, the solution to an inverse problem is described by a distribution of the unknown parameters. These are some main differences with the deterministic inverse method. Stochastic inversion also provides lots of advantages over deterministic inverse methods such as quantitative parameter estimates, determination of confidence intervals, treatments of arbitrary forward maps, error estimates, or parameter estimates given noisy measurement data. In this work, the robust solution procedure from the perspective of the stochastic inverse method is discussed with two different ill-posed inverse problems in marine hydrodynamics.     

大幅船舶横摇运动非线性附加质量惯性矩和阻尼矩特性的非参数识别（英文）

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.     

基于Winding number积分方法求解输流管特征方程

Winding number积分方法是一种用于求解复特征值问题的有效方法。在用传递矩阵法分析输流管道的稳定性时,最终需要求解临界流速的特征方程。该特征方程属于复特征值问题,可应用Winding number积分方法来很好的处理。本文以输流直管为例,阐述了该方法的基本思想和计算的方法及步骤,并对典型边界条件下的特征方程进行求解,验证了Winding number积分方法在求解复数方程根时的有效性。最后,在此基础上研究了弹性支撑的刚度系数对输流管道稳定性的影响。     

一种高效的舰船磁性定位方法

为有效解决现有磁性定位方法定位精度不高的问题,提出了基于磁偶极子阵列模型的磁定位方法.为求解模型参数,根据磁场测量数据建立了定位参数反演模型.针对实际舰船磁性检测中所得磁场信息的局部性而引起反演模型病态不适定问题,应用Tikhonov正则化方法优化求解模型参数.船模实验证明,该方法对船模进行定位计算,定位精度高,结果稳...     

Dullin-Gottwald-Holm方程的1-孤子解

研究了一类由Dullin,Gottwald和Holm提出的新的含线性和非线性色散项的完全可积型浅水波方程(称为Dullin-Gottwald-Holm方程)的反散射问题。首先利用反散射方法建立了DGH方程的反散射方程以及一系列求解方程,并且给出了解的一般形式,然后利用散射数据以参数形式给出了DGH方程的1-孤子解,最后画出了几个取特殊值时解的侧面图。     

Solution of an unstable inverse problem: wave source evaluation from observation of velocity distribution

This paper illustrates how to estimate a wave source generating a wave system, including local waves, with the assumption of linear dispersive waves of two dimensions. The estimation of wave source is realized by using an inverse problem. Unfortunately, the inverse problem is ill-posed in the sense of stability, since the wave source information included in local waves diminishes as the distance from the wave source increases. In the area of applied mathematics, there are well-developed methods to tackle ill-posed problems, which are called regularizations. In this paper, three different regularizations which are well known in applied mathematics are introduced and investigated to learn whether they are applicable to the present problem of the estimation of wave source. From the numerical experiments, it is shown that the estimation is realized by the regularizations introduced in this study, so that they can be applied to the determination of a wave source generating a wave system including local waves. Received: June 6, 2000 / Accepted: February 7, 2001     

A time-domain mode-expansion method for calculating transient elastic responses of a pontoon-type VLFS

A time-domain calculation method is described for elastic responses to arbitrary time-dependent external loads, on the basis of a general differential equation of second order including the convolution integral related to memory effects in the hydrodynamic forces. The time-dependent elastic deflection of a structure is represented by a superposition of mathematical modal functions, and a Galerkin scheme is employed to obtain a linear system of simultaneous differential equations for the amplitude of modal functions assumed. Special care is paid to numerical accuracy in computing the memory-effect function and the added mass at infinite frequency. The validity of the numerical results was confirmed through a comparison with time histories of the vertical deflection measured in an impulsive weight-drop test conducted at the Ship Research Institute and a comparison with existing numerical results for the same problem. To check the necessity of memory-effect terms, computations using a constant value for the hydrodynamic damping coefficient were also performed, and practical measures for reducing the computation time are discussed. Received: April 12, 2000 / Accepted: August 24, 2000     

Variational principle for determining the unknown wetted surface of a planing ship

A variational principle is presented to solve the problem of determining the unknown wetted surface of a planing ship on still water under gravity. The functional associated with the variational principle is expressed by the unknown wetted length distribution, the vortex line function, and the circulation distribution around the longitudinal sections, not by the bottom pressure distribution. In addition, the variational principle is adjoined with pseudoflow, here called reverse flow. The extremal of the functional satisfy the hull boundary integral equation in a similar way to that of lifting-surface theory and the elevated water surface condition along the spray root line. Both are sufficient to determine the wetted surface. A method of high aspect ratio approximation is also investigated. A simple relation is obtained between the wetted surface when moving and at standstill. The calculated shapes of the wetted surface of a planing plate agreed well with experimental results. Received for publication on Nov. 11, 1999; accepted on April 4, 2000     

有限水深中垂直下潜弹性薄板的水波散射(英文)

The problem of water wave scattering by a thin vertical elastic plate submerged in uniform finite depth water is investigated here.The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate.Using the Green’s function technique,from this boundary condition,the normal velocity of the plate is expressed in terms of the difference between the velocity potentials(unknown)across the plate.The two ends of the plate are either clamped or free.The reflection and transmission coefficients are obtained in terms of the integrals’involving combinations of the unknown velocity potential on the two sides of the plate,which satisfy three simultaneous integral equations and are solved numerically.These coefficients are computed numerically for various values of different parameters and depicted graphically against the wave number in a number of figures.     

自升式平台桩腿海上对接过程中的碰撞问题

碰撞现象在海上作业中时有发生,给人员和财产安全带来极大威胁。本文基于非线性有限元理论,研究自升式平台桩腿吊装过程中浮吊船与平台的碰撞问题以及桩腿移动就位时对平台上层建筑的碰撞问题;分析撞击过程中平台的变形与应力变化及结构失效等情况,给出使平台不同区域发生破坏的临界碰撞速度;给出了浮吊船在就位过程中的安装制动距离以及移动过程中与上层建筑间的安全距离和移动速度限制,为桩腿海上吊装作业方案设计提供参考。     

基于多次透射公式和无奇异边界元法模拟全非线性数值波浪水池

文章基于势流理论对全非线性的三维数值水池进行了模拟,其控制方程由无奇异边界积分方程法(Desingularized Boundary Integral Equation Method,DBIEM)进行离散求解,在求解全非线性的自由面微分方程时,文中采用混合欧拉—拉格朗日法(Mixed Eulerian-Lagrangian,MEL)和四阶Adams-Bashforth-Moulton(ABM4)预报—修正方法,为了避免结果发散即增强数值稳定性,文中采用B样条法来光顺波面.同时,在远方辐射控制面上采用多次透射公式方法(Multi-transmitting Formula,MTF)来进行消波,文中得到的结果与理论解进行了比较,结果表明该方法可用来有效模拟全非线性的数值波浪水池.     

Relation between the lifting surface theory and the lifting line theory in the design of an optimum screw propeller

A theory on an optimum screw propeller is described. The optimum means optimum efficiency of a propeller, that is, maximizing thrust horse power for a given shaft horse power. The theory is based on the propeller lifting surface theory. Circulation density (lift density) of the blade is determined by the lifting surface theory on a specified condition in general. However, it is shown that, in the case of optimum condition, the circulation density is not determined by the lifting surface theory, although the circulation distribution which is the chordwise integral of the circulation density is determined. The reason is that the governing equation of the optimization by the lifting surface theory is reduced to that by the lifting line theory. This theoretical deduction is the main part of this paper. The importance of the lifting line theory in the design of the optimum propeller is made clear. Numerical calculations support the conclusion from the deduction. This is shown in the case of freely running propellers and in the case of wake adapted propellers.     

基于无奇异边界元法模拟三维全非线性液舱晃荡

文章基于全非线性势流理论对三维液舱晃荡进行了数值模拟,其控制方程由无奇异边界积分方程法(Desingular-ized Boundary Integral Equation Method,DBIEM)进行离散求解,在求解全非线性的自由面微分方程时,文中采用混合欧拉—拉格朗日法(Mixed Eulerian-Lagrangian,MEL)和四阶Adams-Bashforth-Moulton(ABM4)预报—修正方法,为了避免结果发散即增强数值稳定性,文中采用B样条法来光顺自由面.在微幅水平激励下,该文中得到的结果与解析解吻合较好.     

基于矩量法对线天线辐射特性的仿真研究

采用全域基、点匹配法的矩量法对Hallen积分方程求解，以半波线天线为例，求得其电流分布，并与King的三项理论及Mack实验数据曲线比较，仿真结果较好，对进一步研究船舶系统中电磁兼容问题预测有指导意义。     

动态载荷识别的自适应延迟逆模型方法

为减小载荷识别问题对原系统先验知识的依赖,采用系统的自适应延迟逆模型识别时域载荷。采用自适应算法辨识延迟逆模型,代替了一般识别方法中的系统特性矩阵求逆过程,避免了病态问题。随后将工作状态下的响应作为逆模型的输入,则其输出就是时域载荷的延迟估计。通过对两端简支梁结构进行载荷识别的仿真研究,以及对双层隔振试验台架的试验研究,识别了稳态激励和瞬态激励,验证了该方法的有效性。该方法不需要了解系统的数学模型及参数,因此能够应用于工程实践中。     

On the realization of nonlinear wave profiles using the Banach fixed-point theorem: Stokes wave in a finite depth

A new mathematical formulation for the realization of nonlinear wave profiles and its nonlinear solution procedure, based on the Banach fixed-point theorem, is proposed. To apply the formulation, a nonlinear equation for the Stokes wave in a finite depth was derived, and some numerical solutions are given. A numerical study showed that the proposed iteration method, based on linear progressive wave potential only, enabled us to realize the Stokes nonlinear wave profiles in a finite depth. The nonlinear strategy of iteration has a very fast convergence rate, i.e., only about 6–10 iterations are required to obtain a numerically converged solution.     

螺旋桨扰动速度场数值预报

本文给出了螺旋桨周围流场的预报方法及其数值计算结果。本方法以具有涡分布和源汇分布的升力面来构造螺旋桨对流场的状动。升力面取奖叶拱弧面。根据桨叶表面流动不穿透条件解出升力面奇点后，然后再求它们对流场的扰动。敞水螺旋桨的脉动速度计算结果与试验结果吻合良好。     

Nonlinear hydroelastic behavior of propellers using a finite-element method and lifting surface theory

A finite-element method coupled with analysis of a noncavitating lifting surface was used to assess the performance of a marine propeller, including the thrust, torque, efficiency coefficients, and deflections. The formulation used displacements as unknowns in the structural part and the strength of the vortex as unknowns in the fluid part. A coupled matrix derived from the Bernoulli equation and hydrostatic pressure in terms of the strength, of the vortex enforced coupling between the fluid and the structure. The resulting matrix equation was unsymmetric and nonlinear; a Newton-Raphson procedure was used to solve this equation. The numerical results were compared with test data; computed and measured values agreed satisfactorily. We also investigated the effect of blade thickness on the performance and strength of the propeller. We did not consider the fatigue strengh of the propeller in this analysis.