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.

Maximum entropy principle and statistical distribution of ocean wave heights

This paper concerns an application of a popular existing law, the maximum entropy principle, to the study of statistical distribution of the ocean wave heights. Under two proper premisses. a conclusion that the wave heights obey the Weibull distribution is drawn by making use of the maximum entropy principle. From this result, we hold that the intnnsic departures using the Rayleigh distribution to describe The realistic wave height must exist, and the Weibull distribution usually used as an empirical one has profound origin in physics. The Gluhovskli's empirical wave heights distribution relying on water depth is also discussed briefly, and a possible physical explanation associated with the maximum entropy principle is carried out.

Statistical Inference of Truncated Weibull-Rayleigh Distribution: Its Properties and Applications

In this paper, we derived a new distribution named as truncated Weibull Rayleigh (TW-R) distribution. Its characterization and statistical properties are obtained, such as reliability function, hazard function, reversed hazard rate function, cumulative hazard rate function, quantile function, rth moment, incomplete moments, Rényi and q entropies and order statistic. Parameter estimation is implemented using method of maximum-likelihood estimation and Fisher information matrix is derived. Finally, application of the presented new distribution to a real data representing the failure times of 63 airbcraft Windshield is given and its goodness-of-fit is demonstrated. In addition to, comparisons to other models are implemented to show the flexibility of the presented model.

熵损失下Rayleigh分布尺度参数倒数的Bayes估计

在熵损失函数下研究Rayleigh分布的尺度参数倒数在不同先验分布下的Bayes估计并且讨论了其多层Bayes估计并证明该参数的Bayes估计是可容许的.

最大熵原理应用于海浪波高分布的研究

利用最大熵原理从理论上推导出波高的最大熵分布,在此基础上研究了状态参量对波高分布和波高熵的影响。影响最大熵分布的因子是平均波高和状态参量,不同海况对应的状态参量是不同的。利用波高实测资料,得出3种不同海况下的最大熵分布,通过比较发现最大熵分布很好地符合实测数据。把最大熵分布与目前广泛应用的瑞利分布作了比较,结果表明,最大熵分布有2个优点:没有对波高作出任何限制性假定和能够描述不同海况下的波高分布。

基于高阶傅里叶同步挤压变换与希尔伯特变换的次同步振荡分析

针对次同步振荡分量提取存在噪声干扰和模态混叠问题,提出一种结合高阶傅里叶同步挤压变换(high-order Fourier synchrosqueezed transform,HFSST)与希尔伯特变换(Hilbert transform,HT)的次同步振荡分析方法。该方法在傅里叶同步挤压变换(Fourier syn-chrosqueezed transform,FSST)基础上,通过信号幅值和相位的高阶泰勒展开,定义一种调制算子对瞬时频率估计进行修正,从而提高信号时频分布的能量聚集程度和重构精度。然后,将所提方法应用于次同步振荡分析中,利用该方法对次同步振荡进行时频分析和模态分解,并与HT结合得到各分量振荡参数。通过仿真实验和实测数据分析,并与短时傅里叶变换(short-time Fourier transform,STFT)、重排方法(reassignment method,RM)、经验模态分解(empirical mode decomposition,EMD)等对比,结果表明:所提方法能抑制噪声干扰,得到更好的次同步振荡时频分布,同时可实现多分量的次同步振荡模态分解,准确辨识次同步振荡参数,对电力系统安全稳定运行具有一定的参考意义。

Detection method of forward-scatter signal based on Rényi entropy

The application scope of the forward scatter radar(FSR)based on the Global Navigation Satellite System(GNSS)can be expanded by improving the detection capability.Firstly,the forward-scatter signal model when the target crosses the baseline is constructed.Then,the detection method of the for-ward-scatter signal based on the Rényi entropy of time-fre-quency distribution is proposed and the detection performance with different time-frequency distributions is compared.Simula-tion results show that the method based on the smooth pseudo Wigner-Ville distribution(SPWVD)can achieve the best perfor-mance.Next,combined with the geometry of FSR,the influence on detection performance of the relative distance between the target and the baseline is analyzed.Finally,the proposed method is validated by the anechoic chamber measurements and the results show that the detection ability has a 10 dB improvement compared with the common constant false alarm rate(CFAR)detection.

定时截尾瑞利分布的Bayes估计

在定时截尾取损失函数为熵损失函数情形下,给出了瑞利分布参数θ的Bayes估计的一般形式,在给出先验分布的条件下得出了参数θ的Bayes估计的精确形式,最后证明了Bayes的可容许性.

基于时频能量谱特征的跳频电台个体识别

针对于跳频电台的细微特征分类识别问题,提出基于跳频信号时频能量谱的细微特征提取算法。首先,利用跳频信号在时频域的稀疏特性,通过稀疏重构方法得到跳频信号时频能量谱;然后,在不同尺度条件下对时频能量谱进行分割,分别提取时频能量谱瑞利熵、多重分形维数和差分盒维数三种特征;最后,通过支持向量机分类器对提取特征集进行训练、分类和识别,实现跳频电台个体识别。利用四部电台的跳频信号,验证对比了本文算法与另外两种算法的识别性能。实验结果表明,本文方法所提取的细微特征集具有较强的分辨能力,避免了由单一特征的相似性而引起的误判问题,能够在少量训练样本条件下,保持较高的识别正确率。

黑体辐射公式的多种推导及其在近代物理构建中的意义(Ⅰ)

黑体辐射是近代物理史上一只会下金蛋的鹅,是近代物理的摇篮。黑体辐射研究的意义还在于这是唯一一个涉及c,k,h三个普适常数的物理情景。黑体辐射谱抗测量误差的特性带来了辐射标准和绝对温度参照,谱分布公式对模型的不敏感则使得黑体辐射成为独特的物理研究母题。黑体辐射谱分布公式,普朗克多角度推导过,德拜推导过,艾伦菲斯特推导过,劳厄推导过,洛伦兹和庞加莱深入讨论过,泡利推导过,玻色推导过,爱因斯坦在20多年的时间里多角度推导过且产出最为丰硕,近代还有从相对论角度的推导,每一个角度的推导都带来了物理学的新内容,这包括量子力学、固体量子论、受激辐射、量子统计、相对论统计,等等。认真回顾黑体辐射研究的历史细节,考察其中的思想概念演化,不啻于体验一次教科书式的学(做)物理之旅,比如也可以尝试给出能量局域分立化的简单新证明。

熵损失函数下幂函数分布和瑞利分布参数的Bayes估计

【目的】研究熵损失函数下幂函数分布和瑞利分布参数的Bayes估计并对它的可容许性进行验证。【方法】以幂函数分布及瑞利分布为基础,以熵损失函数为主要的损失函数通过参数估计的方法和性质进行证明和研究。【结果】证明得到任意分布在熵损失函数下参数的Bayes估计、先验分布为伽马分布熵损失函数下两个分布参数的Bayes估计,得到参数可容许性。【结论】得到参数的Bayes估计,同时得到两个分布的参数在熵损失函数下的Bayes估计是可容许的。