基于机器学习的脉动源格林函数预报初探

自由面格林函数是边界元法求解海洋工程水动力学问题的基础,如何精确而快速地计算格林函数及其导数是水动力求解的难题。对无因次化表达的脉动点源格林函数计算建立的数据库,采用深度学习函数库Keras,对数据库进行学习,建立了神经网络预报模型,探讨了全局和局部学习及预报精度,研究了模型预报效率。研究表明机器学习模型预报的格林函数能够保证较高的精度,计算效率高于数值积分计算,低于解析函数为主的多项式逼近,为提高水动力问题求解效率,解决传统计算难题提供了新的思路。     

Study on HOBEM Based on Analytical Panel Integrals Related to Translating-Pulsating Source for Hydrodynamic Responses of Vessels Sailing in Waves

China Ocean Engineering - A higher-order boundary element method (HOBEM) incorporated with analytical panel integrals related to translating-pulsating source Green’s function is proposed for...     

Numerical Treatments and Applications of the 3D Transient Green Function

How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain.Based on the Bessel function,an Ordinary Differential Equation(ODE)was derived for time-domain Green function and its gradients in this paper.A new efficient calculation method based on solving ODE is proposed.It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function.Numerical research indicates that it is efficient to solve the hydrodynamic problems.     

有航速浮体时域分析的混合边界元法

给出了一种联合瞬态格林函数和Rankine源进行有航速浮体时域水动力分析的混合——边界元方法。在三维混合边界元方法中,通过一个匹配面将流体域划分为内域和外域,在内域中使用Rankine源以模拟直壁或非直壁船体及线性或非线性自由面条件,在外域中使用瞬态格林函数以满足自由面条件和远方辐射条件。使用该方法计算了一个有航速潜没圆球的波浪力,和解析结果的比较证明了该方法的正确性。进一步给出了一个有航速Wigley船的水动力结果,计算结果稳定,没有外传波向内反射的现象发生。     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

Fast Evaluation of Time-Domain Green Function for Finite Water Depth

1 .IntroductionShipsrestrainedbycablesandfendersinfrontofdocksundergolargeamplitudenon harmonicmotionsinwaves.Forthiskindofnon harmonicproblem ,atime domainmethodmustbeapplied .LinandYue ( 1 990 )usedanintegralequationwiththetime domainGreenfunctionforinfinitewaterdepthtocomputetheshipmotionindeepwater.Butforthepresentproblem ,theintegralequationwiththetime domainGreenfunctionforfinitewaterdepthmustbeapplied .TheGreenfunctionisafieldwithacertainboundaryandinitialconditionsproducedbyasourceat…     

Consistent expressions for the free-surface Green function in finite water depth

Fast and accurate computation of the free-surface Green function is of key importance for the numerical solution of linear and second-order wave-structure interaction problems in three dimensions. Integral and series expressions for the Green function are derived for which the limiting values for zero and infinite frequency are consistent with the zero and infinite frequency Green function defined in terms of infinite series of Rankine image sources. The integral expressions presented here have the advantage that they are slowly varying with the non-dimensional wave frequency, making them more efficient to approximate compared with previous expressions.     

有限水深中零航速浮体波浪力计算奇点积分的数值处理方法

使用三维源汇分布法Ⅲ计算有限水深中零航速浮体所受到的波浪力,对两种不同形式的格林函数中所共同存在的奇点问题分别进行了处理。公式推导表明,使用级数形式的格林函数可以使计算更加快捷。最后,对不同尺度的圆柱体进行了验算,在对计算结果与解析解进行了比较之后,工程计算也证明选择格林函数级数计算公式是更令人满意的方案。     

Hydroelastic analysis of cantilever plate in time domain

Numerical solutions for the hydroelastic problems of bodies are studied directly in the time domain using Neumann–Kelvin formulation. In the hydrodynamic part of problem, the exact initial boundary value problem is linearized using the free stream as a basis flow, replaced by the boundary integral equation applying Green theorem over the transient free surface Green function. The resultant boundary integral equation is discretized using quadrilateral elements over which the value of the potential is assumed to be constant and solved using the trapezoidal rule to integrate the memory or convolution part in time. In the structure part of the problem, the finite element method is used to solve the hydroelastic problem. The Mindlin plate as a bending element, which includes transverse shear effect and rotary inertia effect are used. The present numerical results show acceptable agreement with experimental, analytical, and other published numerical results.     

Analysis of Wave Loads on A Semi-Submersible Platform

For the global and structural fatigue strength analysis of a semi-submersible platform, wave loads under design conditions are calculated by use of the three-dimensional boundary element method. Methods for calculating the forward-speed free-surface Green function are discussed and a computer program with this Green function is developed. According to the special rules, the wave loads under several typical design conditions of the platform are calculated. The maximum vertical bending moment, torsion moment and horizontal split force are determined from a series of contour maps of wave loads for the wave period of 5 to 18 seconds at a certain interval and the wave phase of 0°to 360°at a certain interval. The wave height is determined by the function of wave period with a given exceedance probability. The maximum wave loads under the combination of wave parameters are used as the input of hydrodynamic pressure in the three-dimensional finite element analysis process. The transfer functions of wave loads     

New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.     

Dynamic response of a large-diameter pile with variable section in layered saturated soil considering construction disturbance effect

ABSTRACT

An analytical solution is developed in this paper to investigate the vertical time-harmonic response of a large-diameter variable-section pile, and it considers the radial inhomogeneity of the surrounding soil caused by construction disturbance. First, the saturated soil surrounding the pile is described by Biot’s poroelastic theory and a series of infinitesimally thin independent layers along the shaft of the pile, and the pile is represented by a variable-section Rayleigh–Love rod. Then, the dynamic equilibrium equations of the soil and pile are solved to obtain an analytical solution for the impedance function at the pile top using the complex stiffness transfer method and impedance function transfer method. Finally, the proposed solution is compared with previous solutions to verify its reliability, and a parameter study is conducted to provide insights into the sensitivity of the vertical dynamic impedance of the pile and velocity response in low-strain integrity testing on defective piles.     

A new ordinary differential equation for the evaluation of the frequency-domain Green function

Clément (2013) derived a second order ordinary differential equation (ODE) satisfied by the free-surface Green function in the frequency domain. Since then, similar ODEs for the gradient of the Green function have been developed. Unfortunately, all these ODEs degenerate at zero frequency. Therefore, it is not possible to initialize the numerical solution of these ODEs from this zero frequency. Alternative methods based on the shifting of the initial condition to frequencies strictly greater than zero have then been developed.The present paper describes an alternative approach to address this issue. It involves a new function which is the solution of a modified ODE which can be solved from the zero frequency.Finally, comparisons with evaluations of the Green function using the classical direct integration method are provided. They show that the new ODE can provide accurate estimates of the Green function.     

Green functions with pulsating sources in a two-layer fluid of finite depth

The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.     

Numerical Investigation on Submerged Horizontal Plate

Hydrodynamic characters on a horizontal, thin, rigid plate located beneath the free surface are numerically investigated. Assuming a linear, time-harmonic potential flow and utilizing Green identity, the governing Laplace equation can be simplified into Fredholm integral equation ofthe second kind. Supposing linear-order discontinuous elements along intersecting vertical boundaries, and by use of the boundary element method, numerical solution about source strength distribution on the plate can be changed into a series of algebraic equations. The 3D Green function is introduced to set up the integral equations, and the GMRES solver is performed for solving the large dense linear system of equations. The added-mass, damping force and exciting force are evaluated directly from the equations. It is found that the added-mass coefficient becomes negative for a range of frequencies when the plate is sufficiently close to the free surface.     

On the side wall effects upon bodies of arbitrary geometry in wave tanks

A numerical model based on using a tank Green function, has been developed to compute the side wall effects on first- and second-order loadings upon bodies of arbitrary geometry in wave tanks. This tank Green function (TGF) is composed of a finite series of open-sea Green functions and an asymptotic part represented by two single integrals whose kernels decrease exponentially with the integral variable. This consistent expression of the TGF permits one to highlight the side wall effects and to give some criteria for the choice of tank width and the measurement duration to limit the reflection of diffraction and radiation waves.

The efficiency of the developed model is shown in the application to hemispheres and a box-shaped barge placed in the center of the wave tanks. The numerical results explain well the irregularities in the experimental measurements and show that the side walls have important effects on the first-order quantities. These effects are much more pronounced on the second-order drift loads.     

时间不连续压力序列的傅立叶分析方法

提出了一种用于对不连续压力采样序列的傅立叶分析方法.此方法将周期函数展开成傅立叶级数,但在数值积分时取函数周期内有采样值的区间作为积分域,然后求解线性方程组得到傅立叶级数的系数值.为了检验本方法的有效性,利用此方法对解析函数进行了拟合,当一个周期内的取样时间大于1/2周期时,利用此方法能够得到满意的结果.利用实验方法研究了波浪作用下截断圆柱表面的压力分布.在波浪作用下静水面附近的测点在露出水面时没有压力值.利用所提出的傅立叶分析方法对略低于静水面位置的实测压力进行了分析,拟合结果与实测结果吻合很好,说明此方法在处理物理模型实验中间断采样得到的数据是有效的.利用数值方法对波浪压力进行了计算,并将一阶和二阶波压力的数值结果与实测值进行了比较.     

大深度分层流体中二维淹没浮体的波浪力分析

研究了大深度分层流体中二维任意形状淹没浮体的波浪力特性。首先基于一种合适的格林函数,采用边界积分方程法研究了流体中浮体对水波散射问题,然后通过单个淹没圆柱体的透射能和反射能与解析方法结果的比较,对所提出的方法进行了验证,最后分析了在不同的几何和物理条件下几种形状的浮体对波浪力的特有影响,得到了一些有意义的结果,这对分层海洋中淹没浮体的设计具有重要的参考价值。     

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

1 .IntroductionRecentlygreatinteresthasbeenshowninthedevelopmentofverylargefloatingstructuressuchasMegaFloatofJapan (Isobe ,1 999)andMOBofUSA (Remmers ,1 999) .Owingtotheirextremelargesizeandgreatflexibility ,thecouplingbetweenthestructuraldeformationandfluidmotionissignifi cant.Thisisatypicalproblemofhydroelasticity .Efficientandaccurateestimationofthehydroelasticresponseofverylargefloatingstructuresinwavesisveryimportantfordesign .Manymethodshavebeenproposedinliteratureforthepredictiono…     

Towards sustainable fisheries subsidies: Entering a new round of reform under the Common Fisheries Policy

On 22 April 2009 the European Commission published its ‘Green Paper on the Reform of the Common Fisheries Policy’. The Green Paper points out a contradiction in policy, noting on one hand that public financial support to the Community's fisheries sector is substantial, but on the other hand such support is often incompatible with other Common Fisheries Policy (CFP) objectives, particularly the need to reduce overcapacities. Providing an analytical framework to better understand the effects of subsidies as well as an overview of existing funding schemes under the CFP, this article aims at answering some of the questions posed by the European Commission within its Green Paper. Answers are based on two ideas: the exploitation of marine capture resources ultimately depends on the level of available fish stocks and that a large share of subsidies fuels the race to fish by inducing investment incentives for the fisheries sector. Policies that have ignored this tend to encourage inefficient and unsustainable fishing as well as the misallocation of public funds. Although support schemes under the CFP have changed in recent years, some problematic support schemes persist. A future reform will have to continue the course taken towards sustainable and efficient approaches to supporting the fisheries industry.