A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves

Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Application of Maximum Entropy Principle to Studying the Distribution of Wave Heights in A Random Wave Field

Based on the maximum entropy principle, a probability density function (PDF) is derived for the distribution of wave heights in a random wave field, without any more hypothesis. The present PDF, being a non-Rayleigh form, involves two parameters: the average wave height H— and the state parameter γ. The role of γ in the distribution of wave heights is examined. It is found that γ may be a certain measure of sea state. A least square method for determining γ from measured data is proposed. In virtue of the method, the values of γ are determined for three sea states from the data measured in the East China Sea. The present PDF is compared with the well known Rayleigh PDF of wave height and it is shown that it much better fits the data than the Rayleigh PDF. It is expected that the present PDF would fit some other wave variables, since its derivation is not restricted only to the wave height.

Application of Maximum Entropy Distribution to the Statistical Properties of Wave Groups

The new distributions of the statistics of wave groups based on the maximum entropy principle are presented. The maximum entropy distributions appear to be superior to conventional distributions when applied to a limited amount of information. Its applications to the wave group properties show the effectiveness of the maximum entropy distribution. FFF filtering method is employed to obtain the wave envelope fast and efficiently. Comparisons of both the maximum entropy distribution and the distribution of Longuet-Higgins （1984） with the laboratory wind-wave data show that the former gives a better fit.

基于次序统计量的4鸭问题求解

次序统计量是数理统计基本概念章节的一个教学难点.通过4鸭问题,介绍次序统计量解决该问题的一种解题思路,融入次序统计量概率密度函数的梳理,为次序统计量内容的讲授丰富教学思路.

基于CB-RRT^(*)算法的滩涂履带车路径规划

针对滩涂履带车在受潮汐影响的滩涂环境中进行长时间勘测作业的需求,提出柯西贝塞尔快速搜索随机树星(Cauchy Bessel Rapidly-exploring Random Tree Star,CB-RRT^(*))算法进行路径规划。为规划出安全路径,基于全局地图和潮汐数据,并通过滩涂履带车到分界区的距离构建出滩涂预测模型;为提高滩涂履带车移动到目标点需进行多次路径规划的速度,对初始路径的关键树节点使用柯西概率密度函数进行采样缩小采样范围来提高节点的利用率,进而提高算法的收敛性;在重选父节点过程中考虑最大转角约束设定相应系数,并使用连续二次贝塞尔曲线进行拼接的方式来生成路径,达到提高路径平滑度的目的和解决平滑后路径与原路径偏差过大造成的安全性问题。仿真实验结果表明,CB-RRT^(*)算法在静态滩涂环境和动态滩涂环境中,能大大提高算法的收敛性和路径的平滑性,且保证路径长度最优,研究内容可以保证滩涂履带车在各种滩涂环境中进行长时间安全作业。

基于极大熵法的三峡水库洪水预报误差分布规律

深入研究洪水预报误差的分布规律具有很大的实用价值,可为水库调度决策的拟定提供辅助参考。通常的研究方法为正态分布法与对数正态分布法,但这类研究方法受人为主观性的影响较大。使用三峡水库2020-2022年入库洪水数据将洪水分为4个量级,建立三峡水库洪水洪量预报误差分布的极大熵模型,得出不同预见期下4个量级的洪水洪量预报相对误差的分布规律,结果表明:采用极大熵模型可以定量地获得三峡水库的洪水预报误差分布规律,具有较强的适用性且可进一步推广使用。

基于最大熵Copula方法的古黄河宿迁段流域月降雨量模拟

为了解决Copula函数方法在拟合过程中要先选择函数类型和多变量水文模拟中保留相关性的问题,基于最大熵原理(POME),直接构建Copula函数,而无需进行Copula函数类型的优选,简化了联合概率分布函数的拟合过程。以古黄河宿迁段流域的皂河站、金锁站和泗阳站3个雨量站点39年(1980~2018年)的月降雨量实测资料为研究对象,进行实例分析。通过建立不同站点间的降雨量联合分布,检验最大熵Copula方法的有效性,并利用Gibbs采样法对月降雨量进行随机模拟。结果表明,基于最大熵Copula方法能保留各站点降雨序列的统计特性,以及不同站点间的降雨相关性,验证了该方法的有效性,可为流域多站点间的降雨量相关性分析和水资源规划与利用提供参考。

基于Copula函数和风速正交分量的风矢量联合概率密度研究

准确地表示风矢量联合概率密度对于风能的评估和风机结构设计具有重要意义,本文将围绕提升风矢量联合概率密度表示结果准确性展开研究。首先,将风矢量表示为风速正交分量,采用混合Normal分布分别对边缘概率密度进行表示,并提出了估计混合Normal分布参数的方法。然后,基于Copula函数考虑风速正交分量间的相关性,从而得到二者的联合概率密度,其中Copula参数通过最小二乘法估计,紧接着通过雅可比变换得到风矢量联合概率密度。最后,采用印度风能研究所的测点S3和S7的每小时平均风速和风向数据,与以往基于Copula函数和风速、风向变量得到的风矢量联合概率密度结果进行对比。结果表明,与以往方法相比,所提方法得到的风矢量联合概率密度结果准确性有很大的提升,本文可为风能的开采和利用提供理论依据。

结合Kriging模型权重信息熵函数的结构可靠性研究

为提高基于Kriging模型信息熵函数(Information Entropy Function,H)的可靠性计算效率,考虑样本点与极限状态曲面的空间距离和随机变量的概率密度函数,通过对样本点的信息熵赋予不同的权值,提出权重信息熵函数(Weight Information Entropy Function,WH)。该学习函数选择更接近极限状态曲面且概率密度函数值较大的样本点更新Kriging模型,从而减少对功能函数的调用次数,有效提高可靠性计算效率。通过算例表明:与其他学习函数相比,WH学习函数在建立Kriging模型过程中所需要的样本点更少,收敛速度更快,计算效率更高。

基于三种不同分布函数的西藏东部地区极大风速估算研究

基于西藏东部地区9个站点40~67 a的长期观测数据(最早自1953年起)与61个站点2014年后的短期观测数据,利用三种不同概率密度分布函数,估算西藏东部地区极大风速并研究其时空分布情况。结果表明:长期来看,西藏东部地区位于西风带与季风共同影响区域,主要以西北风(频率达27%)为主,99%的样本风速不超过9.0 m/s,风速超过15.0 m/s的仅占万分之1.6;对实测极大风速分别进行极值Ⅰ型、极值Ⅱ型和极值Ⅲ型分布函数拟合,发现不同时期数据拟合后的参数无显著差异;利用最小二乘法进行检验订正,可使估算的极大风速的平均绝对偏差和均方根误差大幅降低,观测数据时间序列越长整体估算效果越好;基于极值Ⅱ型函数估算的西藏东部地区极大风速分布能更好地表征该地区实际极大风速的空间分布,极大风速变化范围为13.2~30.9 m/s。

Wigner-Hough transform based on slice's entropy and its application to multi-LFM signal detection

To enhance the capacity of the radar-reconnaissance interception receiver recognizing linear frequency modulated (LFM) at a low signal-noise ratio, this paper presents WignerHough transform (WHT) of the LFM signal and its corresponding characteristics, derives the probability density functions of the LFM signal and Gaussian white noise within WHT based on entropy (WHTE), dimension under different assumptions and puts forward a WHT algorithm based on entropy of slice to improve the capacity of detecting the LFM signal. Entropy of the WHT domain slice is adopted to assess the information size of polar radius or angle slice, which is converted into the weight factor to weight every slice. Double-deck weight is used to weaken the influences of noise and disturbance terms and WHTE treatment and signal detection procedure are also summarized. The rationality of the algorithm is demonstrated through theoretical analysis and formula derivation, the efficiency of the algorithm is verified by simulation comparison between WHT, fractional Fourier transform and periodic WHT, and it is highlighted that the WHTE algorithm has better detection accuracy and range of application against strong noise background.

南水北调中线工程冬季输水冰情风险研究

针对南水北调中线工程冬季输水冰情的安全运行问题,以南水北调中线工程河北段为研究对象,以热平衡理论为出发点推导出目标单元渠段的整体总热量变化公式;采用单因素局部分析法选出风险评价指标,基于概率论构建了风险评价指标之间的联合概率密度函数,将气象事件发生概率、热量变化率与冰情风险等级一一对应,从而对渠道冰情进行风险评估。对2021年1月6—8日南水北调中线工程河北段输水渠道冰情风险分析结果表明:在整个热交换过程中,短波辐射、蒸发和对流热交换是影响热量变化的主要因素,且夜间渠道的热量散失明显大于白天,加大了夜间发生冰情的风险;沙河节制闸—渠末段虽然与其他渠段风险等级一样,但其单位面积热量损失明显高于其他渠段,接近于极高风险,应加强对该渠段的实时监测并做好冰情防护。

间歇式空气辅助喷雾的时变特性研究

基于间歇式空气辅助喷射系统,采用高速相机和相位多普勒粒子分析仪对时变条件下的喷雾特性展开试验.对比分析了不同喷射控制参数以及空间采样位置的液滴尺寸-速度联合概率密度分布函数(JPDF)、液滴平均直径与速度,并对喷雾场的气流速度和相间滑移速度进行计算.结果表明:油、气喷射脉宽比大于8时,喷雾的投影面积随喷射时间保持递增趋势;不同工况下的液滴直径-速度的联合概率密度均呈单峰分布特征;液滴直径主要分布在0~40μm范围,而液滴速度分布范围为0~150 m/s;喷油脉宽的增加会显著增大喷雾液滴直径并降低液滴运动速度;气、油喷射脉宽比大于0.25会导致喷雾发展后期的液滴被进一步加速;不同油、气喷射脉宽比下的相间滑移速度不受喷射时间的影响,而不同气、油喷射脉宽比下的相间滑移速度则受到喷气脉宽与喷射时间的共同影响.

柔性作业车间调度与视情维修的联合决策

针对设备状态可直接或间接检测获得的生产系统,提出柔性作业车间调度和视情维修的联合策略,决策变量分别为调度序列与视情维修序列,并建立两者的联合决策模型。进而根据联合策略,推导了相应的概率密度函数。通过数值分析,对比联合决策与独立决策的优化结果,表明了所建模型的有效性,并进行设备劣化参数的敏感度分析,验证了模型的正确性。

基于高斯函数-最大熵展开的风电并网系统概率潮流计算

为有效计及风电出力随机性对电网运行状态的影响,在风电并网系统中提出一种基于高斯函数-最大熵原理的改进半不变量概率潮流计算方法。首先,以高斯函数为风速分布信息的载体,在此基础上采用改进反射核密度估计,建立计及风速有界性的风电出力概率模型,以便精确地求取描述风电出力随机性的各阶矩、半不变量等数字特征。然后,基于节点电压、支路功率等状态变量的数字特征,采用高斯函数改进最大熵模型进行状态变量的分布展开,由高斯函数的数量和性质来计及输入侧风速分布形状对输出侧状态变量分布的影响。同时将所提改进最大熵模型的约束由积分形式转为代数形式,提升计算效率。最后,以IEEE30节点系统对所提方法进行测试,结果证明了所提方法的有效性、准确性。

杂波环境下基于最大熵模糊聚类的JPDA算法

针对杂波环境下的多目标跟踪数据关联存在跟踪精度低、实时性差的问题,提出了一种基于最大熵模糊聚类的联合概率数据关联算法(joint probabilistic data association algorithm based on maximum entropy fuzzy clustering,MEFC-JPDA)。首先,采用最大熵模糊聚类求得的隶属度初步表征目标与有效量测之间的关联概率。其次,采用基于目标距离的量测修正因子对关联概率进行调整,并建立关联概率矩阵。最后,结合卡尔曼滤波算法,对目标的状态进行加权更新。仿真结果表明,所提算法在杂波环境下的跟踪性能相比现有的两种关联算法有较大提升,是一种有效的多目标跟踪数据关联算法。

Method for extracting geometrical characteristics of joint probability density based on contour lines

This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.

用电压暂降严重程度和最大熵评估负荷电压暂降敏感度

现有负荷敏感度随机估计法以电压暂降的物理特征为基础,用主观概率模型描述负荷电压耐受曲线(voltage tolerance curve,VTC)的随机分布规律,所需样本量大,在实际中难以实现且可能引入主观误差。将电压暂降特征转换为电压暂降严重性指标,在负荷VTC曲线分布规律未知和样本数较少的情况下,根据最大熵原理确定VTC曲线的概率密度函数,用累计求和法计算负荷故障率,提出一种适合于小样本的随机评估方法。对评估原理、最大熵模型、约束条件、求解算法与评估过程等进行详细研究。对个人计算机(personal computers,PC)进行仿真并与现有4种评估方法比较,结果证明,该方法对样本量依赖性小,无需主观假设,在未知VTC曲线随机分布规律时,评估结果准确,适应性强。

最大熵原理在交通流统计分布模型中的应用

交通流统计分布函数的形式具有多样性 ,选择把数据套到一个适合的分布上去常常是困难的。为此 ,寻求一种简便的产生概率密度函数的统一方法是十分必要的。运用最大熵原理不仅导出了几个科学实践中常见的概率分布密度函数 ,而且在分析物理学中已有的导出公式的基础上给出了交通工程实践中产生概率密度函数的统一方法及其实用的数值算法。