Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

A modified method to calculate reliability index using maximum entropy principle

Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.

Extraction of Information from Crowdsourcing: Experimental Test Employing Bayesian, Maximum Likelihood, and Maximum Entropy Methods

A crowdsourcing experiment in which viewers (the “crowd”) of a British Broadcasting Corporation (BBC) television show submitted estimates of the number of coins in a tumbler was shown in an antecedent paper (Part 1) to follow a log-normal distribution ∧(m,s2). The coin-estimation experiment is an archetype of a broad class of image analysis and object counting problems suitable for solution by crowdsourcing. The objective of the current paper (Part 2) is to determine the location and scale parameters (m,s) of ∧(m,s2) by both Bayesian and maximum likelihood (ML) methods and to compare the results. One outcome of the analysis is the resolution, by means of Jeffreys’ rule, of questions regarding the appropriate Bayesian prior. It is shown that Bayesian and ML analyses lead to the same expression for the location parameter, but different expressions for the scale parameter, which become identical in the limit of an infinite sample size. A second outcome of the analysis concerns use of the sample mean as the measure of information of the crowd in applications where the distribution of responses is not sought or known. In the coin-estimation experiment, the sample mean was found to differ widely from the mean number of coins calculated from ∧(m,s2). This discordance raises critical questions concerning whether, and under what conditions, the sample mean provides a reliable measure of the information of the crowd. This paper resolves that problem by use of the principle of maximum entropy (PME). The PME yields a set of equations for finding the most probable distribution consistent with given prior information and only that information. If there is no solution to the PME equations for a specified sample mean and sample variance, then the sample mean is an unreliable statistic, since no measure can be assigned to its uncertainty. Parts 1 and 2 together demonstrate that the information content of crowdsourcing resides in the distribution of responses (very often log-normal in form), which can be obtained empirically or by appropriate modeling.

Tree Network Formation in Poisson Equation Models and the Implications for the Maximum Entropy Production Principle

This paper presents not only practical but also instructive mathematical models to simulate tree network formation using the Poisson equation and the Finite Difference Method (FDM). Then, the implications for entropic theories are discussed from the viewpoint of Maximum Entropy Production (MEP). According to the MEP principle, open systems existing in the state far from equilibrium are stabilized when entropy production is maximized, creating dissipative structures with low entropy such as the tree-shaped network. We prepare two simulation models: one is the Poisson equation model that simulates the state far from equilibrium, and the other is the Laplace equation model that simulates the isolated state or the state near thermodynamic equilibrium. The output of these equations is considered to be positively correlated to entropy production of the system. Setting the Poisson equation model so that entropy production is maximized, tree network formation is advanced. We suppose that this is due to the invocation of the MEP principle, that is, entropy of the system is lowered by emitting maximal entropy out of the system. On the other hand, tree network formation is not observed in the Laplace equation model. Our simulation results will offer the persuasive evidence that certifies the effect of the MEP principle.

A microscopic ancient river channel identification method based on maximum entropy principle and Wigner-Ville Distribution and its application

In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.

Maximum Entropy and Bayesian Inference for the Monty Hall Problem

We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian inference results in an “irrelevant, therefore invariant” hypothesis. We discuss the advantages of Bayesian inference over the frequentist inference in tackling the uneven prior probability Monty Hall variant. We demonstrate that the use of Bayesian statistics conforms to the Maximum Entropy Principle in information theory and Bayesian approach successfully resolves dilemmas in the uneven probability Monty Hall variant. Our findings have applications in the decision making, information theory, bioinformatics, quantum game theory and beyond.

基于Copula-POME的负荷与气象因素相关性度量研究

负荷与气象因素的关系是非线性且模糊的,针对传统的线性相关系数不能准确刻画负荷与其气象成因的相依结构。在分析负荷对气象因素响应的基础上,提出了结合Copula函数与最大熵原理(POME)的负荷与气象因素相关性度量方法,该方法基于POME建立了负荷与气象因素的边缘分布,利用Copula函数拟合了负荷与气象多变量系统中的非线性相依结构,并推导了度量相关性的Kendall秩相关系数、Spearman秩相关系数和Copula熵。在实际的负荷和气象系统中的应用表明,Copula-POME方法在分析负荷与其气象成因关系时无先验分布假定,具有灵活的函数形式,能准确表达多变量系统的相依结构;秩相关系数和Copula熵弥补了线性相关系数在度量尾部相关中的不足,能准确度量负荷与气象因素的相关性。

Principle of maximum entropy for reliability analysis in the design of machine components

We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy(PME).We used PME to select the statistical distribution that best fits the available information.We also established a probability density function(PDF)and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME.We obtained the first four moments of the state function for reliability analysis and design.Furthermore,we attained an estimate of the PDF with the fewest human bias factors using the PME.This function was used to calculate the reliability of the machine components,including a connecting rod,a vehicle half-shaft,a front axle,a rear axle housing,and a leaf spring,which have parameters that typically follow a non-normal distribution.Simulations were conducted for comparison.This study provides a design methodology for the reliability of mechanical components for practical engineering projects.

Evolution of Quantum State for Mesoscopic Circuits with Dissipation

Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially.

Application of MEP Method to the Study of statistical Properties of Random Waves

The maximum entropy principle (MEP) method and the corresponding probability evaluation method are introduced, and the maximum entropy probability distribution expression is deduced in moment of the second order. Fully developed wave height distribution in deep water and wave height and period distribution for different depths in wind wave channel experiment are obtained from the MEP method, and the results are compared with the distribution and the experimental histogram. The wave height and period distribution for the Lianyungang port is also obtained by the MEP method, and the results are compared with the Weibull distribution and the field histogram.

APPLICATION OF MAXIMUM ENTROPY PRINCIPLE METHOD TO THE STUDY OF WAVE CLIMATE STATISTICAL CHARACTERISTICS

The Maximum Entropy Principle (MEP) method is elaborated, and thecorresponding probability density evaluation method for the random fluctuation system is introduced,the goal of the article is to find the best fitting method for the wave climate statisticaldistribution. For the first time, a kind of new maximum entropy probability distribution (MEPdistribution) expression is deduced in accordance with the second order moment of a random process.Different from all the fitting methods in the past, the MEP distribution can describe theprobability distribution of any random fluctuation system conveniently and reasonably. If themoments of the random signal is limited to the second order, that is, the ratio of theroot-mean-square value to the mean value of the random variable is obtained from the random sample,the corresponding MEP distribution can be computed according to the deduced expression in thisessay. The concept of the wave climate is introduced here, and the MEP distribution is applied tofit the probability density distributions of the significant wave height and spectral peak period.Take the Mexico Gulf as an example, three stations at different locations, depths and wind wavestrengths are chosen in the half-closed gulf, the significant wave height and spectral peak perioddistributions at each station are fitted with the MEP distribution, the Weibull distribution and theLog-normal distribution respectively, the fitted results are compared with the field observations,the results show that the MEP distribution is the best fitting method, and the Weibull distributionis the worst one when applied to the significant wave height and spectral peak period distributionsat different locations, water depths and wind wave strengths in the Gulf. The conclusion shows thefeasibility and reasonability of fitting wave climate statistical distributions with the deduced MEPdistributions in this essay, and furthermore proves the great potential of MEP method to the studyof wave statistical properties.

Motoyosi Sugita—A “Widely Unknown” Japanese Thermodynamicist Who Explored the 4th Law of Thermodynamics for Creation of the Theory of Life

The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as detailed as possible. And also I have put short history of Motoyosi Sugita’s personal life in order for you to know him well. I hope that this article helps you to know this wonderful man and understand what he did in the past, which was totally forgotten in the world and even in Japan.

基于能量系数的电力变压器热故障严重性评估方法

运行电力变压器内部的热点温度直接影响其使用寿命和运行可靠性。为准确评估电力变压器内部过热故障的严重程度,文章借助焓变理论提出一种计算故障能量系数的方法,为故障赋予一定的权值系数;并基于能量系数这一概念,以电力变压器各类不同程度的热故障为研究对象,建立其严重程度分级评估基准,此基准是以563组电力变压器热故障油色谱分析数据所计算出的能量系数值作为样本数据,利用最大熵原理得出最符合实际分布的电力变压器热故障能量系数概率分布函数,并求取其分位值Q_(20)、Q_(70)和Q_(95)作为热故障严重程度的分级评估值。经实际算例分析,采用文中所提方法,不仅可以实现对热故障严重程度的量化评估,还可以合理地划分其严重等级,可为检修人员制定和执行维护计划提供参考。

基于最大熵原理的光伏接入配网系统电压风险评估

在国家能源战略的推动下,未来光伏等新能源接入配网的情况将日益增加,准确评估其接入配网后的越限风险具有重要意义。为了合理评估光伏并网后产生的影响,文中在考虑光伏发电的随机性及负荷波动性的前提下,提出基于最大熵原理求解含光伏配网系统的概率潮流,并结合效用偏好指数型函数表征越限严重度,构建起电压越限风险综合评估模型。以IEEE 33节点系统为例,对比蒙特卡洛模拟法求解概率潮流,最大熵原理在拟合电压概率密度具有准确性及高效性。同时通过仿真结果表明合理选择接入点及接入容量能有效降低整个配网的越限风险,提高了配网的安全稳定运行能力,为今后新能源并网风险评估提供参考。

熵权模糊改进法在宁夏黄河水质评价中的应用

为了解宁夏境内黄河流域的水质状况,选取银古公路桥、平罗黄河大桥、中卫香山湖、吴忠金沙湾、固原沟圈5个监测断面在2021年4月、6月、8月、12月4个时期的溶解氧、高锰酸盐指数、氨氮、总磷、总氮5项评价指标,共获得80组水样。针对熵权模糊评价法在权重趋于1时其微小变化会引起熵权成倍变化的病态问题和由于最大隶属度原则不能普遍适用而导致评价失效的问题,提出了一种熵权模糊改进的评价方法,通过改进熵权法确定权重和加权等级,建立改进的模糊综合评价模型,对水质样品进行水质分析和综合评价。结果表明,在权重分配方面,相比于隶属度法和传统的熵值法,改进熵权法分配的权重更为合理;在水质评价方面,加权等级法评定出的结果更符合研究区域的真实水质状况;宁夏境内黄河流域Ⅰ类和Ⅱ类水质占比超过90%,水质状况良好,5个断面4个时期的水质综合评价结果显示,12月份的水质最优,Ⅰ类水质占比85%;对水质的时空分析显示氨氮为全局性污染因子,溶解氧为区域性污染因子。改进的模糊综合评价模型对宁夏黄河水质的评价结果更为客观合理。

可靠性的科学探索:从经典到量子

作为设备稳定服役能力的一种衡量,可靠性对工程技术发展和创新十分重要。基于物理、信息论和统计方法的耦合,可靠性研究正逐步发展并有望成为一门新的科学。同时随着量子技术的发展,量子相干器件及设备将会被大量地植入到传统装备系统中。这不仅给可靠性自身的研究带来新的机遇和挑战,也会使量子物理和可靠性研究交叉起来,导致交叉领域思想上的原始创新。文章首先介绍可靠性研究从工程向科学迈进的历程,然后从可靠性工程需求的视角介绍量子可靠性的基本概念和逻辑,强调量子自洽历史对寿命统计的内在描述,最后结合目前量子技术所面临的退相干挑战,展望可靠性工程对量子技术的潜在应用。

基于Copula函数的区域雨潮遭遇风险概率分析

随着气候变化、人类活动影响加剧以及城市化进程等一系列事件的加快,我国的城市内涝问题日渐突出。以扬州市仪邗区域为例,由于扬州南濒长江,受长江洪水、潮水顶托,当面临暴雨等灾害时,仪邗区域无法快速外排,进而增大了内涝风险,针对内涝灾害的研究也因此成为了重要内容。本文利用Copula函数构建了研究区域最大三日面雨量和长江最大三日平均潮位的联合概率分布函数,并对不同雨潮组合情况下的遭遇概率进行分析,最终得到了雨潮的联合风险概率和同现风险概率。最终结果显示,Copula函数在雨潮联合概率分布方面拟合良好。这一拟合结果不仅可以为解决仪邗山洪在长江高水位时出路不足的问题提供一定的理论支持和科学依据,也可以为其他感潮河段的防洪决策提供参考。

基于最大熵原理的谐波评估指标研究

随着新型电力系统的加速构建,电网的谐波特性日益复杂,研究谐波数据的有效统计管理,对评估电网电能质量好坏具有重要意义。提出一种基于最大熵原理的谐波评估指标统计方法,通过记录并保存谐波数据的平均值、中心距等数字特征,使用最大熵原理对谐波进行概率分布拟合,达到保存并识别谐波特征的目的,方便数据储存;利用拟合的概率分布获取谐波95%概率值和99%概率值两种谐波评估标准,保证了指标的准确性和一致性。最后通过谐波实测数据进行算法实例分析,验证了所提方法的有效性。

基于单线激光雷达的道路区域分割

针对单线激光雷达在进行道路区域分割时出现的识别不准确以及精度问题,研究一种基于最大熵原理提取自适应阈值,并通过滑动窗口法实现道路区域分割的方法。利用中值滤波对原始点云数据进行预处理,以减少噪声和异常值产生的影响;结合最大熵原理提取的自适应阈值和滑动窗口算法完成对道路区域点云的分割;最后基于概率论的方法确定道路边界点云。通过对3种不同类型的结构化道路进行实验,得到路面、障碍物以及路沿的识别准确率依次为96.88%、86.82%、95.50%,证明了该方法的有效性和适用性。