## Random Wave(随机波)研究综述

Random Wave 随机波 - Detection of wave groups from random waves may be a key step in predicting the occurrence of extreme events.^{[1]}In this study, the Amir-Kabir semi-submersible platform has been modeled which is installed in 700 m’ depth of the Caspian Sea, and random waves have been generated towards the structure in the form of the JONSWAP wave spectrum according to the conditions of the Caspian Sea.

^{[2]}After CS reconstruction, the spectrum acquisition rate is equal to the random wavelength modulation rate, up to 10 MHz in this Letter, providing an attractive alternative to laser-based dynamic interferometry.

^{[3]}For a realistic approach of the dynamic response, the oil-tanker is considered under random waves’ loads, requiring several steps in the process of the short-term and long-term global structural analysis.

^{[4]}Different from traditional 2D SR based range-Doppler imaging method which assumes a repetitive transmit waveform, the proposed method can deal with the random waveforms varying among different pulses in noise radar.

^{[5]}This study is concerned with time domain fatigue analysis of offshore structures subjected to random waves.

^{[6]}The hydrodynamic performance characteristics of an oscillating water column (OWC) device mounted on a pile-supported breakwater (OWC-PSB) exposed to action of regular and random waves is investigated.

^{[7]}We consider two types of operations in the scheme: firstly, a input signal treatment phase—the awake phase—and, secondly, a reorganizing phase of the random wavelet coefficients obtained in the previous awake phase—the asleep phase.

^{[8]}The system is then used to detect a modulation of the optical beam through a random wavefront profile.

^{[9]}To adaptively adjust the collective pitch control parameters according to random wave and wind speed disturbances, the barrier function method was used to conceive adaptive sliding mode control gains.

^{[10]}The said multi-purpose option, termed as OWCBW system is investigated for optimizing the spacing between an array of OWC devices subjected to regular and random waves in normal and oblique wave incidences.

^{[11]}The interactions of random waves with a cluster of structures positioned in a gridded array are investigated through a series of experiments and high-fidelity RANS and LES simulations.

^{[12]}In this work, we show that mixing noisy optical modes of various complexity in a second-order nonlinear medium can be used for efficient and straightforward filtering of a random wavefront under sum-frequency generation processes without utilizing correlation-based calculations.

^{[13]}The performance of an OWC device placed over stepped bottom is analyzed in random waves environment.

^{[14]}Firstly, a dynamic model of C11 roll in random waves is improved, and it is verified by the model test and numerical simulation.

^{[15]}An application of the mathematical model to a real scale U-OWC subject to random waves compatible with a JONSWAP spectrum is presented.

^{[16]}In this study, unlike most previous investigations have limited to the regular wave conditions or combined wave and current conditions, a numerical model for seabed response around a pipeline in a trenched layer due to random waves is established.

^{[17]}Recently, random waveform electric vestibular stimulation has become an increasingly common means of probing the vestibular system.

^{[18]}The CO-TENG has been successfully applied to harvest the energy of random waves, wind, and water flows, through the adjustment of the input gear train and energy collection parts, such as water turbine, wind scoop, and oscillating buoy.

^{[19]}This chapter details a comprehensive experimental investigation to understand the dynamic pressures on the different components of the OWC including the total force on the structure induced by both regular and random waves.

^{[20]}A general approach that utilizes both spectral and extremal statistical methods are utilized to investigate the time series of flow-induced response behavior of a flexible horizontal cylinder subject to both random waves and constant current conditions.

^{[21]}Because the high order harmonics may possess random amplitudes and phase shifts in relation to components at fundamental frequency, it is important that the meter’s performance is verified with random waveforms as well.

^{[22]}Due to the stochastic nature of wave loads, random wave and constrained new-wave theories are utilized in the generation of the wave records.

^{[23]}A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves.

^{[24]}It demonstrates that when pretension is not large enough during the tests, the mooring will experience slack configuration during the random waves.

^{[25]}These resonances are created by the existence of the region where the second mode can propagate in the random waveguide.

^{[26]}(2020) can be extended to random wave-induced pipeline scour.

^{[27]}The establishment of a theoretical distribution model of the number of typhoon occurrences and random waves is of great theoretical and practical significance for the study of the number of storm surge impacts and damage to marine engineering as well as the safety evaluation of offshore engineering.

^{[28]}Based on the high-order spectral (HOS) numerical model, both the characteristics of Bragg resonance induced by the regular waves and random waves are investigated.

^{[29]}In the experiments, the wave sequences with and without the freak wave are defined as freak and random waves, respectively.

^{[30]}On the basis of the wave turbulence theory, we derive nonequilibrium kinetic equations describing the random waves in a regime where disorder dominates nonlinear effects.

^{[31]}A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume.

^{[32]}The motion characteristics of the tunnel at zero-freeboard and immersion rigs are compared under regular and random waves.

^{[33]}In this study, experiments on rogue wave events under a background of random waves were conducted in the wave basin.

^{[34]}Their contours were placed in a background of random wavelets.

^{[35]}In this paper, three types of road profile inputs (bump, sine wave, random wave) are introduced to excite the suspension system.

^{[36]}The overall performance, heaving performance, power output and wave energy conversion efficiency of the pilot APR WEC running under random waves are reported and analyzed in detail.

^{[37]}However, in the existing GAFDEM systems using a square wave or a 2n pseudorandom wave, the ground source needs to transmit more sets of waveforms with different fundamental frequencies in more flights to improve the vertical resolution for the same observed line, which will seriously reduce the exploration efficiency.

^{[38]}In actual conditions during the installation process, tensions applied along the pipeline as effect from random waves.

^{[39]}For isotropic ensembles of random waves, the probability distributions of the different wavevectors are estimated by codimension arguments and calculated exactly for statistically isotropic superpositions of plane waves.

^{[40]}In this study, a comprehensive experimental investigation is carried out in order to examine the effect of perforations on a submerged artificial reef exposed to regular and random waves.

^{[41]}Laboratory and numerical experiments on stem waves due to random waves.

^{[42]}Consistently in all patients, the stereotypical high-frequency oscillations with the highest degree of waveform similarity were localized within the seizure onset zones only, whereas the channels generating high-frequency oscillations embedded in random waveforms were found in the functional regions independent of the epileptogenic locations.

^{[43]}Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra.

^{[44]}Regular and random waves are tested and three water depths are considered to account for the influence of variable mangroves frontal area along the vertical.

^{[45]}This article provides a simple analytical method for giving estimates of random wave-driven drag forces on near-bed vegetation in shallow water from deepwater wind conditions.

^{[46]}After detection at a photodetector, an electrical waveform with the time shift information encoded in the random waveform is obtained, which is further compressed by correlation to increase the time resolution.

^{[47]}This paper considers the problem of estimating the response of an array of Oscillating Water Columns (OWCs) installed in a vertical breakwater and exposed to the action of random waves.

^{[48]}We study the effects of both skirt and internal radius dimensions on the power extraction efficiency for monochromatic and random waves.

^{[49]}Physical models were developed to compare the wave reflection from vertical plane, semi-porous, and porous seawalls caused by both regular and random waves.

^{[50]}

从随机波中检测波群可能是预测极端事件发生的关键步骤。

^{[1]}在本研究中，模拟了安装在里海 700 m' 深度的 Amir-Kabir 半潜式平台，并根据条件以 JONSWAP 波谱的形式向结构产生了随机波。里海。

^{[2]}在 CS 重建之后，光谱采集速率等于随机波长调制速率，在本信中高达 10 MHz，为基于激光的动态干涉测量提供了一个有吸引力的替代方案。

^{[3]}对于动态响应的现实方法，油轮被考虑在随机波浪载荷下，在短期和长期整体结构分析过程中需要几个步骤。

^{[4]}与传统的基于二维 SR 的距离多普勒成像方法假设重复发射波形不同，该方法可以处理噪声雷达中不同脉冲之间变化的随机波形。

^{[5]}本研究涉及受随机波影响的海上结构的时域疲劳分析。

^{[6]}研究了安装在桩支撑式防波堤 (OWC-PSB) 上的振荡水柱 (OWC) 装置在规则和随机波浪作用下的水动力性能特征。

^{[7]}我们在该方案中考虑了两种类型的操作：首先，输入信号处理阶段——清醒阶段——以及其次，在前一个清醒阶段获得的随机小波系数的重组阶段——睡眠阶段。

^{[8]}然后使用该系统通过随机波前轮廓检测光束的调制。

^{[9]}为根据随机波浪和风速扰动自适应调整集体变桨控制参数，采用障碍函数法构建自适应滑模控制增益。

^{[10]}研究了称为 OWCBW 系统的所述多用途选项，以优化 OWC 设备阵列之间的间距，这些设备在正常和斜波入射中受到规则波和随机波的影响。

^{[11]}通过一系列实验和高保真 RANS 和 LES 模拟，研究了随机波与位于网格阵列中的一组结构的相互作用。

^{[12]}在这项工作中，我们表明，在二阶非线性介质中混合各种复杂度的噪声光学模式可用于在和频生成过程下对随机波前进行有效且直接的滤波，而无需使用基于相关的计算。

^{[13]}在随机波环境中分析了放置在阶梯底部的 OWC 器件的性能。

^{[14]}首先改进了C11在随机波中横摇的动力学模型，并通过模型试验和数值模拟进行了验证。

^{[15]}提出了将数学模型应用于受与 JONSWAP 频谱兼容的随机波影响的真实尺度 U-OWC。

^{[16]}在这项研究中，与大多数先前的研究仅限于常规波浪条件或波浪和海流组合条件不同，建立了随机波引起的沟槽层中管道周围海床响应的数值模型。

^{[17]}最近，随机波形电前庭刺激已成为探测前庭系统越来越普遍的手段。

^{[18]}CO-TENG通过调整输入齿轮系和能量收集部件，如水轮机、风勺和摆动浮标，成功地应用于收集随机波浪、风和水流的能量。

^{[19]}本章详细介绍了全面的实验研究，以了解 OWC 不同组件上的动态压力，包括由规则波和随机波引起的结构上的总力。

^{[20]}一种利用光谱和极值统计方法的通用方法用于研究受随机波和恒流条件影响的柔性水平圆柱体的流动诱导响应行为的时间序列。

^{[21]}由于高次谐波可能具有与基频分量相关的随机幅度和相移，因此使用随机波形验证仪表的性能也很重要。

^{[22]}由于波浪载荷的随机性，随机波和受约束的新波理论被用于波浪记录的生成。

^{[23]}通过一系列数值模拟研究了随机波浪作用下伞吸锚地基（USAF）周围的局部冲刷。

^{[24]}它表明，在测试过程中，当预紧力不够大时，系泊在随机波浪中会出现松弛配置。

^{[25]}这些共振是由于第二模式可以在随机波导中传播的区域的存在而产生的。

^{[26]}（2020）可以扩展到随机波引起的管道冲刷。

^{[27]}建立台风发生次数和随机海浪次数的理论分布模型，对于研究风暴潮对海洋工程的影响次数和破坏次数以及海洋工程的安全评价具有重要的理论和实践意义。

^{[28]}基于高阶谱（HOS）数值模型，研究了规则波和随机波引起的布拉格共振特性。

^{[29]}在实验中，将有和没有反常波的波序列分别定义为反常波和随机波。

^{[30]}在波浪湍流理论的基础上，我们推导了描述无序支配非线性效应的随机波的非平衡动力学方程。

^{[31]}提出了一种流氓波的统计理论，并针对在长水箱中收集的实验数据进行了测试，在该水箱中，具有不同程度非线性的随机波是机械产生的，并且可以沿着水槽自由传播。

^{[32]}比较了规则波和随机波下隧道在零干舷和浸没钻机下的运动特性。

^{[33]}在这项研究中，在波浪盆地中进行了随机波背景下的流氓波事件实验。

^{[34]}它们的轮廓被放置在随机小波的背景中。

^{[35]}在本文中，引入了三种类型的道路轮廓输入（颠簸、正弦波、随机波）来激励悬架系统。

^{[36]}对APR WEC在随机波浪下运行的综合性能、起伏性能、功率输出和波浪能转换效率进行了详细的报告和分析。

^{[37]}然而，在现有的使用方波或2n伪随机波的GAFDEM系统中，地源需要在更多的飞行中传输更多组不同基频的波形，以提高同一观测线的垂直分辨率，这将严重降低勘探效率。

^{[38]}在安装过程中的实际情况下，管道沿线施加的张力是随机波的影响。

^{[39]}对于随机波的各向同性集合，不同波矢量的概率分布由余维参数估计，并针对平面波的统计各向同性叠加精确计算。

^{[40]}在这项研究中，为了检验射孔对暴露于规则和随机波的水下人工鱼礁的影响，进行了一项全面的实验研究。

^{[41]}随机波引起的干波的实验室和数值实验。

^{[42]}一致地，在所有患者中，具有最高波形相似性的定型高频振荡仅位于癫痫发作起始区域内，而产生嵌入随机波形的高频振荡的通道则在独立于致癫痫位置的功能区域中发现.

^{[43]}我们之前的工作研究了泰勒机制所起的作用，这是由于波浪引起的漂移剖面导致污染物在水平方向上的纵向分散，在规则正弦波和具有单峰光谱的随机波下。

^{[44]}测试了规则波和随机波，并考虑了三个水深来解释沿垂直方向可变红树林正面区域的影响。

^{[45]}本文提供了一种简单的分析方法，用于估算深水风条件下浅水中近床植被的随机波浪驱动阻力。

^{[46]}在光电探测器检测后，得到一个电波形，其时移信息编码在随机波形中，并通过相关进一步压缩以提高时间分辨率。

^{[47]}本文考虑估计安装在垂直防波堤中并暴露于随机波作用的振荡水柱 (OWC) 阵列的响应问题。

^{[48]}我们研究了裙边和内半径尺寸对单色和随机波的功率提取效率的影响。

^{[49]}开发了物理模型来比较由规则波和随机波引起的垂直平面、半多孔和多孔海堤的波反射。

^{[50]}

## significant wave height 有效波高

In the current analysis, two spectrum estimation techniques, based on the Welch and Thomson methods, were applied to a set of random wave signals generated from a theoretical wave spectrum obtained by combining wind sea and swell components with the same prevailing direction but different combinations of significant wave heights, peak periods, and peak enhancement factors.^{[1]}Random waves of significant wave height between 0.

^{[2]}In addition to conventional altimeter-derived parameters such as significant wave height (SWH) and the normalized radar cross-section (NRCS) sigma0, the spatial (along-track) SWH gradient and SWH standard deviation (STD) for standard 1-s altimetry data are assumed to be responsible for random wave field dynamics and, thus, for the observed characteristic mean wave period.

^{[3]}The significant wave height over rugged topography is a standardized statistics to denote the characteristic height of the random waves in a sea state.

^{[4]}Thirty six different wave barrier configurations (10%, 20%, 30%, 40%, 50% and 60% porosities and 1 to 6 numbers of slotted walls) were tested in random wave fields of JONSWAP spectra for different combinations of significant wave heights and peak periods.

^{[5]}

在当前的分析中，基于 Welch 和 Thomson 方法的两种频谱估计技术被应用于一组随机波信号，这些随机波信号由理论波谱产生，该理论波谱是通过组合具有相同盛行方向但不同组合的风海和涌浪分量获得的。有效波高、峰值周期和峰值增强因子。

^{[1]}有效波高在 0 之间的随机波。

^{[2]}除了有效波高 (SWH) 和归一化雷达截面 (NRCS) sigma0 等传统高度计衍生参数外，标准 1 秒高度计的空间（沿航迹）SWH 梯度和 SWH 标准偏差 (STD)假设数据负责随机波场动力学，因此负责观察到的特征平均波周期。

^{[3]}nan

^{[4]}nan

^{[5]}

## Unidirectional Random Wave

Model tests with unidirectional random wave fields are common for coastal engineering purposes.^{[1]}In this study, a series of experiments with several bathymetry configurations from deep to shallow water were conducted for unidirectional random waves.

^{[2]}

具有单向随机波场的模型测试在海岸工程中很常见。

^{[1]}在这项研究中，对单向随机波进行了一系列从深水到浅水的测深配置的实验。

^{[2]}

## Nonlinear Random Wave

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering.^{[1]}The methodology is also fit with a 2nd order correction for generating nonlinear random wave series.

^{[2]}

非线性随机波的统计分析在海岸和海洋工程中很重要。

^{[1]}该方法还适用于生成非线性随机波序列的二阶校正。

^{[2]}

## Arithmetic Random Wave

the spatial variable, or in a random Gaussian scenario (‘arithmetic random waves’).^{[1]}The square billiard is studied, where the high spectral degeneracies allow for the introduction of a Gaussian ensemble of random Laplace eigenfunctions (“boundary-adapted arithmetic random waves”).

^{[2]}

## Order Random Wave

The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.^{[1]}The wave amplification effect is predicted using second-order random wave theory together with linear diffraction/radiation analysis, and the drag forces are linearized.

^{[2]}

## Incident Random Wave

In this paper, three new technologies are presented, i) real-time inverse estimate of incoming incident random wave by using adaptive Kalman filter, ii) real-time estimate of line profiles and stresses by using multiple inclinometers and robust algorithm, iii) real-time estimate of line profiles and stresses by using minimal number of inclinometers and ANNbased machine-learning algorithm.^{[1]}Here, the effect of incident wave randomness on subharmonic edge wave excitation is explored following a weakly nonlinear stability analysis under the assumption of narrow-band incident random waves.

^{[2]}

## random wave field 随机波场

However, the feedback of the soliton on the background wave eventually leads to the destruction of the coherent structure and energy dispersion in a quasi-random wave field.^{[1]}In addition to conventional altimeter-derived parameters such as significant wave height (SWH) and the normalized radar cross-section (NRCS) sigma0, the spatial (along-track) SWH gradient and SWH standard deviation (STD) for standard 1-s altimetry data are assumed to be responsible for random wave field dynamics and, thus, for the observed characteristic mean wave period.

^{[2]}Model tests with unidirectional random wave fields are common for coastal engineering purposes.

^{[3]}The wave induced dynamic pressures under the deck and the global wave forces and moments on an offshore platform model were measured for three different model orientations and for partial and full green water conditions in random wave fields of different energy levels.

^{[4]}The reflections from irregular walls and scatterers superimpose and lead to speckle like, random wave fields.

^{[5]}Thirty six different wave barrier configurations (10%, 20%, 30%, 40%, 50% and 60% porosities and 1 to 6 numbers of slotted walls) were tested in random wave fields of JONSWAP spectra for different combinations of significant wave heights and peak periods.

^{[6]}Numerical simulation shows that as sea wave conditions are getting harsh, a non-negligible probability mass shifts toward the low transmittance coefficients due to long waves appearing in the random wave field by sub-harmonic resonance wave-wave interaction, which is well-known after the studies of Hasselmann(1967) and Phillips(1980) on the development of wind waves.

^{[7]}Using short time asymptotic expansions and taking advantage of the scale separation in the semi-classical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the "tailedness" of the probability density function.

^{[8]}Here we present measurements of the velocity field of oscillatory flows, which are induced by mechanically generated random wave fields in a large scale experimental facility.

^{[9]}The background spectrum is used to generate random wave field, simulate the real sea surface, and use singular spectrum.

^{[10]}high amplitude fluctuations in random wave fields, have been studied in several contexts, ranging from optics via acoustics to the propagation of ocean waves.

^{[11]}Using a statistical equation that describes weakly nonlinear interactions in a random wave field, we perform analytical and numerical stability analyses for a modulating wave train.

^{[12]}Using short time asymptotic expansions and taking advantage of the scale separation in the semiclassical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the "tailedness" of the probability density function.

^{[13]}

然而，孤子对背景波的反馈最终导致准随机波场中相干结构和能量色散的破坏。

^{[1]}除了有效波高 (SWH) 和归一化雷达截面 (NRCS) sigma0 等传统高度计衍生参数外，标准 1 秒高度计的空间（沿航迹）SWH 梯度和 SWH 标准偏差 (STD)假设数据负责随机波场动力学，因此负责观察到的特征平均波周期。

^{[2]}具有单向随机波场的模型测试在海岸工程中很常见。

^{[3]}在不同能量水平的随机波场中，针对三种不同的模型方向以及部分和全部绿水条件，测量了甲板下的波浪引起的动态压力以及海上平台模型上的全局波浪力和力矩。

^{[4]}来自不规则墙壁和散射体的反射叠加并导致散斑状随机波场。

^{[5]}nan

^{[6]}nan

^{[7]}使用短时间渐近展开并利用半经典状态下的尺度分离，我们得到了一个简单的显式公式，描述了随机波场幅度四阶矩演化的早期阶段，即“尾度”的定量测量的概率密度函数。

^{[8]}在这里，我们展示了振荡流速度场的测量结果，这些振荡流是由大型实验设施中机械产生的随机波场引起的。

^{[9]}nan

^{[10]}nan

^{[11]}nan

^{[12]}nan

^{[13]}

## random wave excitation 随机波激发

The established model coincides with the experimental and SIMO results in terms of barge motion responses both at regular and random wave excitations.^{[1]}The numerical example consists of a jacket platform subjected to random wave excitation.

^{[2]}To achieve the goal, ship structural response under random wave excitation was assumed to be linear one and represented by linear Volterra series, which is expanded by linear combination of Laguerre polynomials.

^{[3]}The numerical example of a jacket-type offshore platform under random wave excitation is applied to verify the applicability of convolutional neural network (CNN), long short-term memory (LSTM) networks, and CNN-LSTM method.

^{[4]}Beginning with fundamental test cases, such as static equilibrium, eigen-analysis, and free-decay simulations, the scenarios advance in complexity to include current loading, regular and random wave excitation, in conjunction with both steady and turbulent wind inflow.

^{[5]}The random wave excitation is described by a spectrum which is depended on the wave energy spectrum and the amplitude of the moment of roll.

^{[6]}Afterwards, two modal analysis methods, the eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI), were used to obtain the modal parameters of the tested structure using the vibration signal under artificial excitation and random wave excitation, respectively.

^{[7]}This paper is devoted to analyzing the inelastic impacted ship roll motion under random wave excitations by path integration (PI) method.

^{[8]}

建立的模型与规则和随机波激励下的驳船运动响应方面的实验和 SIMO 结果一致。

^{[1]}数值示例由一个受到随机波激发的夹套平台组成。

^{[2]}为实现该目标，随机波激励下的船舶结构响应被假定为线性的，并由线性沃尔泰拉级数表示，该级数通过拉盖尔多项式的线性组合展开。

^{[3]}应用随机波激励下的导管架式海上平台数值算例，验证了卷积神经网络（CNN）、长短期记忆（LSTM）网络和CNN-LSTM方法的适用性。

^{[4]}nan

^{[5]}随机波激励由一个取决于波能谱和横摇力矩幅度的谱来描述。

^{[6]}之后，分别利用人工激励和随机波激励下的振动信号，采用本征系统实现算法（ERA）和随机子空间识别（SSI）两种模态分析方法获得被测结构的模态参数。

^{[7]}nan

^{[8]}

## random wave model 随机波模型

First, the cloud data of the river are generated based on the random wave model and an electromagnetic calculation model is established.^{[1]}Methods First, the spectral density of random waves, spectral density of wave inclination and spectrum of waves acting on ships are calculated using a random wave model with long peak waves.

^{[2]}Numerous numerical and experimental investigations show that rogue waves present much larger probabilities of occurrence than predicted by the linear random wave model, i.

^{[3]}The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.

^{[4]}Finally, we clarified the basic hydrodynamic characteristics of the composite bucket foundation in the frequency domain and adopted multiple random wave models to investigate the effects of different wave heights, periods, and spectral peak factors on the towing motion characteristics of composite bucket foundation.

^{[5]}We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry’s random wave model to a finite collection of (possibly overlapping) smooth compact subsets of $${\mathbb {R}}^2$$ R 2.

^{[6]}

首先，基于随机波模型生成河流云数据，建立电磁计算模型。

^{[1]}方法首先，利用长波峰随机波模型计算随机波谱密度、波倾谱密度和作用于船舶的波谱。

^{[2]}nan

^{[3]}nan

^{[4]}最后，在频域阐明了复合桶形基础的基本水动力特性，采用多种随机波模型研究了不同波高、周期、谱峰因子对复合桶形基础拖曳运动特性的影响。

^{[5]}我们考虑随机变量的向量，通过将 Berry 随机波模型的节点集的长度限制为 $${\mathbb {R}}^2$$ R 2 的（可能重叠的）光滑紧致子集的有限集合而获得。

^{[6]}

## random wave equation 随机波方程

In this article, we study Goursat problem for fuzzy random wave equations in the framework of generalized complete metric spaces in the sense of Luxemburg.^{[1]}This paper deals with the random wave equation on a bounded domain with Dirichlet boundary conditions.

^{[2]}The first mathematical papers were written in the 60’s by Keller [1964] who connected radiative transport theory and random wave equations.

^{[3]}

在本文中，我们研究了卢森堡意义上的广义完全度量空间框架下的模糊随机波动方程的 Goursat 问题。

^{[1]}本文研究了具有 Dirichlet 边界条件的有界域上的随机波动方程。

^{[2]}第一篇数学论文是 60 年代由 Keller [1964] 撰写的，他将辐射传输理论和随机波动方程联系起来。

^{[3]}

## random wave condition

The significant hydrodynamic performance of the introduced novel concept has been proven in the wide range of wave frequencies for both regular and random wave conditions.^{[1]}This paper presents results from an experimental work to investigate wave loading on the main column of a tripod offshore wind turbine in regular and random wave conditions in the Large Wave Flume in Hannover, Germany.

^{[2]}Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions.

^{[3]}

所引入的新颖概念的显着流体动力学性能已在规则和随机波条件的宽波频率范围内得到证明。

^{[1]}本文介绍了一项实验工作的结果，该实验研究了在德国汉诺威的大波浪槽中，在规则和随机波浪条件下三脚架海上风力涡轮机主柱上的波浪载荷。

^{[2]}当新解决方案与涉及双色和随机波条件的高分辨率实验室数据进行比较时，获得了强烈的一致性。

^{[3]}

## random wave energy

This article addresses the random wave energy dissipation due to submerged aquatic plants in shallow water based on deep water wave conditions including estimation of wave damping.^{[1]}Triggered by water waves, the ball revolves in the torus shell for triboelectric power generation, and the TS-TENG can harvest random wave energy from all directions.

^{[2]}Many mechanisms have been invented to absorb the random wave energy.

^{[3]}

本文基于深水波浪条件（包括波浪阻尼估计）解决了浅水中淹没水生植物引起的随机波浪能量耗散问题。

^{[1]}在水波的触发下，球在圆环壳中旋转摩擦发电，TS-TENG可以从各个方向收集随机波能。

^{[2]}已经发明了许多机制来吸收随机波能量。

^{[3]}

## random wave train

In the model, an extreme transient wave is embedded into a random wave train based on a partitioning of the total wave energy: with one part of the energy going into the underlying random sea, and another part going into the focused transient wave.^{[1]}Advanced analysis and hindcasting of real-world ocean wave data have revealed the central role of directionality and the superposition of random wave trains in the formation of ocean rogue waves.

^{[2]}Random wave trains with various periods and wave heights are generated by a wave maker using the improved JONSWAP spectrum.

^{[3]}

在该模型中，根据总波浪能量的划分，将极端瞬态波嵌入到随机波列中：一部分能量进入下方的随机海，另一部分进入聚焦瞬态波。

^{[1]}对现实世界海浪数据的高级分析和后报揭示了方向性和随机波列叠加在海洋流氓波形成中的核心作用。

^{[2]}nan

^{[3]}

## random wave load 随机波载荷

This paper is devoted to the dynamic reliability analysis of jacket platforms subjected to random wave loads with Monte-Carlo simulation (MCS), in which a sample size of the order of magnitude of 104 to 105 for repeated time–history analyses is required for small failure probability problems, and a duration time up to three hours needs to be considered in the time–history analyses for a specific sea condition.^{[1]}This paper presents an efficient fragility analysis approach for offshore structures subjected to random wave load considering parameter uncertainty.

^{[2]}A Ritz method combined with a pseudo-excitation method is then used to analyze the responses of the jacket platform under random wave loads with the associated power spectral densities, variances and higher spectral moments.

^{[3]}

本文致力于使用蒙特卡罗模拟 (MCS) 对承受随机波载荷的导管架平台进行动态可靠性分析，其中需要 104 到 105 个数量级的样本量进行重复时程分析故障概率问题，并且在特定海况的时程分析中需要考虑长达三个小时的持续时间。

^{[1]}本文提出了一种考虑参数不确定性的海上结构在随机波浪载荷下的有效脆弱性分析方法。

^{[2]}nan

^{[3]}

## random wave simulation

Monochromatic and random wave simulations are conducted to examine the combined effect of currents, mud-induced wave dissipation and modulation, and nonlinear wave-wave interactions on surface wave spectra.^{[1]}Cnoidal and random wave simulations are conducted.

^{[2]}Wave energy transfer through a shallow water region, produced by nonlinearity, was investigated using random wave simulations based on JONSWAP spectra in a physical experiment.

^{[3]}

进行单色和随机波模拟以检查电流、泥浆引起的波耗散和调制以及非线性波波相互作用对表面波谱的综合影响。

^{[1]}进行了 Cnoidal 和随机波模拟。

^{[2]}在物理实验中使用基于 JONSWAP 光谱的随机波模拟研究了由非线性产生的通过浅水区域的波能传递。

^{[3]}

## random wave conjecture

Šeba proposed that the eigenfunctions of toral point scatterers should also satisfy Berry’s random wave conjecture, which implies that the value distribution of the eigenfunctions ought to be Gaussian.^{[1]}The random wave conjecture suggests that in certain situations, the value distribution of $f$ under $\sigma$ is approximately Gaussian.

^{[2]}

Šeba 提出环点散射体的本征函数也应满足 Berry 随机波猜想，这意味着本征函数的值分布应为高斯分布。

^{[1]}随机波猜想表明，在某些情况下，$\sigma$ 下 $f$ 的值分布近似为高斯分布。

^{[2]}

## random wave loading

Random wave loadings are estimated by wave spectrum analysis and Morison’s equations.^{[1]}ABSTRACT The most reliable technique for predicting the statistical properties of the response of an offshore structure to random wave loading is the conventional time simulation method (CTS).

^{[2]}

通过波谱分析和 Morison 方程估计随机波载荷。

^{[1]}摘要 预测海上结构对随机波浪载荷响应的统计特性最可靠的技术是传统的时间模拟方法（CTS）。

^{[2]}

## random wave force

Firstly, the offshore platform is modeled as a system with time-varying control delay under random wave forces.^{[1]}The focus is on the effect of the correlation of the two random wave forces.

^{[2]}

## random wave number

Synthetic turbulence generators based on Fourier reconstruction of the fluctuating velocity field using random wave number vectors are, by definition, not periodic in a given direction.^{[1]}The response of random wave number and transmission distance to amplitude fluctuation and phase fluctuation is discussed respectively.

^{[2]}

根据定义，基于使用随机波数矢量对波动速度场进行傅里叶重建的合成湍流发生器在给定方向上不是周期性的。

^{[1]}分别讨论了随机波数和传输距离对幅度波动和相位波动的响应。

^{[2]}

## random wave packet 随机波包

Based on stochastic solutions, the dynamical evolution of solitons produce random wave packets.^{[1]}These differences were triggered by the presence of probability plateau formed in wave slope distribution whenever infra-gravity waves appear in random wave packet due to the resonant wave-wave interaction.

^{[2]}

基于随机解，孤子的动态演化产生随机波包。

^{[1]}当次重力波由于共振波-波相互作用而出现在随机波包中时，波斜率分布中形成的概率平台会触发这些差异。

^{[2]}