满足给定数字特征和谱的随机信号的产生

本文给出了满足给定数字特征和谱的随机序列的产生方法，即用无记忆非线性变换实现非正态随机信号的模拟，该法与Ｇｕｊａｒ法相比较，放宽了变量概率分布的限制，只要求变量矩的存在，同时考虑无记忆非线变换对谱的影响，用异于Ｌｉｕ的方法在频域上求解输入正态分布随机序列的谱。     

实测海浪数据的最大熵谱估计

一.前言 多年来,估算平稳随机过程的功率谱常用的方法是FTA(自相关函数的福氏变换)法和FFT(快速福氏变换)法.FTA法,是通过随机过程样本序列的自相关函数乘以某些窗函数,然后经过福氏变换及某种平滑而得到功率谱估计值.FFT法,是通过样本序列乘以某种数据窗,经过快速福氏变换和频率平滑而得到功率谱估计值.这两种谱分析法实际上对样本序列作了如下不切实际的假定:(1)过程是以样本长度为其周期之一的周     

三阶Stokes型随机波浪载荷谱研究

应用非线性谱分析理论，对三阶Stokes型随机波浪载荷谱进行了分析，将波面方程及海水质点的水平速度用一阶波面的非线性组表示，导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱，将阻力项展开为幂级数式，并应用非线性谱分析理论，确定了幂级数的系数，进而将波浪载荷表示为一阶波面及其导数的非线性组合，最后得出波浪载荷谱密度的表达式，并应用数值分析方法，得出单位桩柱波浪力及总波浪力谱密度。     

一般格子方程新的无穷序列精确解

为了获得非线性差分微分方程的无穷序列精确解,引入一种双曲函数型辅助方程,并给出该方程解的Bcklund变换和解的非线性叠加公式.在此基础上,利用辅助方程与函数变换相结合的方法,借助符号计算系统Mathematica,用一般格子方程为应用实例,获得了无穷序列精确解.     

非线性随机波的数值模拟

本文根据作者提出的非线性不规则波四阶近似理论解,首先导出二阶非线性谱和线性谱的关系式,并应用非线性有约束最优化方法建立了从靶谱分解线性谱和二阶非线性谱的数学模式,进而建立非线性随机波数值模拟的数学模型及其快速傅里叶交换算式,从而大大地缩短计算机时。由于采用从靶谱分解出的线性谱,模拟的非线性随机波现实谱和靶谱符合一致。最后通过算例,对模拟的非线性及线性随机波的谱估计及波面统计特性进行初步分析,本方法为浅水不规则波与水流及建筑物相互作用的研究提供随机模拟基础。     

COD浓度非线性检验与预测

采用 BDS、Box-Pierce 和 Ljung-Box 方法对 1995-2005 年渤海化学耗氧量(COD) 浓度历史监测数据的独立性进行了检验,采用代替数据检验 IAAFT、White 和 Terasvirta 人工神经网络弱非线性检验、Hinich 双谱检验以及无 Fourier 变换检验进行了相关性的非线性检验,判断出渤海 COD 不独立且线性相关.综合比较线性 ARMA、局部线性、规则集成、随机森林、随机梯度Boosting、支持向量、人工神经网络、自适应样条 8 种预测方法,结果表明线性 ARMA 模型误差均值和方差最小,证明线性 ARMA模型更适合分析渤海 COD 数据,同时证实了前述各种非线性检验结果的可靠性.     

基于Beta波面分布的非线性海浪波高分布

基于非线性Beta波面分布,采用经验变换,导出1种仅用随机波面偏度λ3和尖度λ4 2个参数表示的非线性海浪波高概率统计分布--波高类Beta分布.此分布发展了线性窄谱假定下的Rayleigh分布.就所用实验室资料验证而言,本文推导的波高类Beta分布要优于几种工程上常用的波高分布.     

Stokes波的谱特性分析

应用理论推导及数值计算方法，对Stokes随机波的谱特性进行了分析。首先将波面方程，海水质点水平速度用一阶波面分量的非线性组合表示，应用平稳随机高阶短的降阶计算法则，得到了波面方程及海水质点水平速度与一阶波面分量的自相关函数之间的关系，从而确定了Stokes随机波浪的波浪谱密度及海水质点水平速度和加速度谱密度，进而求得有关波浪要素的均方根值。文章还应有数值计算方法，分析了波浪基本参数对均方根值的影响。     

广东阳西近岸海域海浪谱分析

根据广东阳西近岸海域测站1a实测共4 949组的原始随机波面观测记录,用自相关函数法和快速傅里叶变换法进行谱估计,得到波谱各特征参数,并与实测波面统计的特征值进行比较,经分析,选用快速傅里叶变换法估计研究海域的实测谱,对粗谱进行平滑和分析,筛选出研究海域海浪的样本谱498个,将平滑后的谱形无维量化,得到广东阳西海域海浪无维量平均谱曲线并求出对应谱参数,计算得到谱峰频率f0为0.121,特征频率μ10、μ20分别为1.929、2.733,谱宽度ε、ν为0.83、1.39.采用5种理论频谱模式对实测无维量谱进行拟合,根据拟合结果推荐γ=1.920 5的JONSWAP谱或者b=5.7、δ=6.0、k=0.5的莆田谱作为广东阳西近岸海域的海浪谱型,对该海区的工程建设、海浪预报警报和海浪理论研究具有较好的参考作用,对我国其他类似海域也有一定的参考价值.     

用波面高度分布的非正态特征反演非线性随机海浪

本文不依据波动的非线性方程,而是利用波面高度分布的非正态特征反演非线性随机海浪.在窄谱条件下,论述了反演的非线性波面、谱及波面极大(小)值分布同现有某些非线性理论结果的一致性,以深水正态海浪过程用浅水非正态特征反演浅水非线性海浪过程及其谱作为算例,并用实测资料检验,结果表明,其同实测值符合较好,从而说明本文方法是可行的.     

Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a second-order nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.     

Invariants of Spectral Moments and their Degeneracy for a Gaussian Surface

The transformation and symmetry properties of surface derivatives and spectral moments under rotation of the coordinate axes are examined. It is shown that the moments as well as the derivatives are generally represented in terms of their rotational invariants. For a Gaussian surface, which is characterized by additional symmetry of correlation matrices, the even moments higher than the second order are degenerate; i.e., only three of them are independent, and only two invariants are nonzero. Specific properties of spectrum symmetry and the joint statistical distribution of the mean and differential curvatures are found in this case. As an application of these results to observation of the sea surface, a simple optical method is suggested for simultaneous remote-sensing measurement of the second- and fourth-order moments. This method is based on the count of reversely reflected light impulses, arising from sea-surface scanning by the continuous laser radiation.     

Statistical characteristics of long waves nearshore

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width.     

Accuracy improvement of the radar backscatter simulation from sea surface covered by oil slick using fetch-dependent waveheight spectrum: Comparison with the 2007 <Emphasis Type="Italic">Heibei Spirit</Emphasis> Case in the Yellow Sea

In this paper, results are presented on the comparison of X-band radar backscattering coefficient (RBC) from an oilcovered sea surface that features the Elfouhaily and Durden-Vesecky waveheight spectra. The Durden-Vesecky spectrum applies to a fully-developed sea, while the Elfouhaily spectrum accounts for the fetch of arbitrary length. Using these two waveheight spectra, a one-dimensional random rough surface is simulated by the Monte Carlo method, and the method of moments (MoM) is applied to yield the RBC. Comparison of the results with TerraSAR-X synthetic aperture radar (SAR) data acquired over the coastal waters polluted by the Hebei Spirit oil tanker shows that the Elfouhaily spectrum yields better agreement than the Durden-Vesecky spectrum for the fully-developed sea, and that the fetch-dependent Elfouhaily spectrum improves the agreement with SAR data in comparison with the fetch-independent spectrum for the fully developed sea. A possible application to estimate the amount of spilled oil is also suggested.     

Numerical simulation of a random sea: a common error and its effect upon wave group statistics

A commonly used method of simulating ocean waves from a specified frequency spectrum is shown to be incorrect. The method consists of adding numerous sine curves with random phases; and the error arises from assuming that the amplitudes of these component sine waves are deterministic, when they are in fact random variables. Methods of using random amplitudes are described and only one is found to be satisfactory. In this method the number of random values simulated — and then transformed with an inverse FFT — equals the required number of simulated data points. So simulation in the frequency domain can only give relatively short runs; it is necessary to work in the time domain if arbitrarily long runs are required.Errors in wave group statistics derived from the incorrect simulation method are discussed and related to discrepancies reported between groupiness in simulated data and ocean measurements.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.     

畸形波作用下半潜式平台波浪爬升与气隙响应特性

半潜平台的波浪爬升与气隙响应是设计过程中的重要考量因素。为探究随机波浪场中畸形波对半潜平台波浪爬升及气隙响应的影响,将含畸形波的随机波浪试验与一般随机波浪试验结果进行了对比研究分析。对模型试验测得的运动以及监测点处的波浪爬升及气隙进行频谱分析以及极值统计分析。研究发现,纵荡和纵摇的极大值主要受畸形波的影响而显著增大,纵荡、垂荡以及纵摇响应谱几乎不受单个畸形波影响;波浪爬升与气隙的极大值受到畸形波的影响而增大,同时,畸形波对气隙响应谱造成极大影响,增强了波浪爬升与气隙响应的非线性性。     

On the Spectral Moments of Wind Waves

In order to obtain high order spectral moments, the residual moment , as proposed by De-nis, is presented for approximate estimation of spectral moment Glazman's partial averaging idea isdiscussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to es-timate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as is related to wind speed. The0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.     

Probability distribution of random wave–current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied.     

An Application of Direct Ritz Method for Random Seismic Responses of Jacket Platforms

1 .IntroductionNowadays tremendous efforts have been devotedtothe analysis of randomseismic responses .Forexample ,American PetroleumInstitute (API) has declared that the analysis of randomseismic re-sponsesis a useful tool for safety inspection. Owing to the complexity of platformand randomness ofload,it is difficult to carry out the randomresponse analysis of a jacket platform. The conventionalrandomvibration methods ,such as square root of the sumof squares (SRSS) and complete quadratic…