Efficient slope reliability analysis under soil spatial variability using maximum entropy distribution with fractional moments

Spatial variability of soil properties imposes a challenge for practical analysis and design in geotechnical engineering.The latter is particularly true for slope stability assessment,where the effects of uncertainty are synthesized in the so-called probability of failure.This probability quantifies the reliability of a slope and its numerical calculation is usually quite involved from a numerical viewpoint.In view of this issue,this paper proposes an approach for failure probability assessment based on Latinized partially stratified sampling and maximum entropy distribution with fractional moments.The spatial variability of geotechnical properties is represented by means of random fields and the Karhunen-Loève expansion.Then,failure probabilities are estimated employing maximum entropy distribution with fractional moments.The application of the proposed approach is examined with two examples:a case study of an undrained slope and a case study of a slope with cross-correlated random fields of strength parameters under a drained slope.The results show that the proposed approach has excellent accuracy and high efficiency,and it can be applied straightforwardly to similar geotechnical engineering problems.

Delineation of Prospecting Prospect Area Based on Maximum Entropy Model

Taking the Dapingzhang copper-polymetallic deposit in Yunnan Province, China as the research object, the maximum entropy model was used to extract the mining information, and the mineral resource prediction model was established by using the exploration data of the deposit and related regions in this area, so as to determine the prospecting prospect area in the study area. In this paper, the Jacknife analysis module of maximum entropy model is used to quantitatively rank the importance of 39 geochemical element variables, and finally obtain the prospecting prospect map of the study area. The research results show that the Dapingzhang mining area has the potential to find hidden ore in the deep and surrounding areas, and the northern and southern ends and western sides of the rock ore control structural belt in the eastern region of the mining area have good prospecting prospects. The research results provide an important basis for the deployment of follow-up exploration work in the study area, and the maximum entropy model has a good application effect in mineral resources exploration.

基于MaxEnt模型的公路项目环评中重要物种适宜生境评价及预测

公路建设项目属于线性项目,其对生态环境的主要影响是对物种生境的阻隔和切割,致使物种适宜生境面积减少,并伴有光污染、声环境质量下降。基于拟建的穿越国家一级保护动物黑嘴松鸡生境的公路,以MaxEnt为预测模型,模拟公路建设前后黑嘴松鸡适宜生境的分布变化。结果显示:基于最大熵模型的黑嘴松鸡受试者工作特征曲线AUC值为0.945,可信度较高。适生区分析显示:黑嘴松鸡集中分布在保护区核心区和缓冲区,项目建设后不适生区面积大幅度增加。研究认为,最大熵模型能很好地模拟项目建设前后研究区黑嘴松鸡适生区的分布,明确公路项目建设对黑嘴松鸡分布的影响,研究结果可为环评中对适宜生境的评价及预测提供参考。

基于MaxEnt模型的石柱县马尾松毛虫害风险空间分布估测

【目的】精准掌握重庆市石柱土家族自治县马尾松毛虫害的风险范围,为及时有效地防治虫灾提供有力依据。【方法】选取60个马尾松毛虫分布点的数据,结合该县马尾松区域的地形、气候和人为因子,用MaxEnt模型估测该县的马尾松毛虫害风险。通过环境因子的百分比贡献率、置换重要性和环境因子响应曲线,探讨该县马尾松毛虫适宜生境条件。利用该模型的“训练遗漏、预测面积和阈值达到平衡”的阈值和“阈值熵与原始分布熵相等”的阈值对风险区进行风险分级,将该区域的马尾松毛虫害风险等级划分为低风险、中风险和高风险,并通过地理信息系统统计各个风险区的区域面积。通过该模型AUC均值验证估测精度,以及对比该县2022年马尾松毛虫飞防的区域内各风险区面积占比,对风险分级效果进行验证。【结果】1)年均降水量、月均潜在蒸散发量、距居民点距离和海拔为影响该县马尾松毛虫生存的主要环境因子。2)MaxEnt模型的训练和测试的AUC均值分别为0.92与0.87,标准差为0.013,小于0.05,表明模型的结果为优,预测结果的可靠性高,可用于该县马尾松毛虫害风险估测;通过对比2022年石柱县春季马尾松毛虫的飞防区域,面积占比高达99.05%,表明高风险区分布与其实际分布高度一致,分级效果好。3)该县马尾松毛虫害高风险区主要集中于临溪镇、悦崃镇、鱼池镇、河嘴乡和万朝镇等;王场镇、龙沙镇、王家乡、西沱镇、黎场乡、沿溪镇和万朝镇的高风险区面积占各自乡镇马尾松区域面积高达90%以上。【结论】研究表明,石柱县的马尾松毛虫害高风险区主要集中在西部和北部的乡镇,通过对乡镇间与乡镇内高风险区分布的统计分析,更全面地了解了马尾松毛虫的风险区分布,可为马尾松毛虫的针对性防治与监管提供科学依据。

基于MaxEnt与ArcGIS的中国角茴香生态适宜性区划研究

利用最大熵模型(MaxEnt)和地理信息系统(ArcGIS),结合相关生态因子,对角茴香的生态适宜性范围进行预测和分析。收集角茴香在中国的205个经纬度信息,结合19项生态因子应用MaxEnt模型和ArcGIS对角茴香的潜在适生分布区进行分析。影响角茴香潜在分布的主要生态因子包括,最冷季节降水量、最冷季节平均温度、最暖季节降水量、昼夜温差与年温差比值等。当前气候条件下,角茴香高度适宜生长的区域主要集中在北京、河北北部、山西、河南、陕西和内蒙古南部等,面积约为77.4×104 km2;未来气候条件下,适生区将向东北部和西部扩张。该研究预测的结果与角茴香实际分布区域相符,为角茴香的可持续利用和角茴香的引种栽培提供重要的理论依据。

基于MaxEnt模型预测未来气候变化情境下红树秋茄(Kandelia obovata)在中国潜在适生区的变化

红树秋茄为自然分布于我国南方热带与亚热带潮间带的木本植物群落,是淤泥质滩涂上特有的植被类型,由其构成的红树林生境在维持海岸生态系统平衡、湿地生物多样性等方面具有重要作用。全球气候变化影响了红树秋茄的地理分布范围,尤其是其分布北界的变化一直是当前红树研究领域的争论焦点之一。基于MaxEnt模型,筛选了141个秋茄现有分布点,并结合筛选后的14个陆地气候变量和2个海洋表层海洋环境因子,模拟了秋茄种群在不同碳排放情景下的潜在适生分布区域。分析了影响秋茄自然分布的主要环境因子,揭示了其在中国内地分布北界的演化趋势。根据模型结果,当前模拟的潜在分布区与现有分布范围吻合度较高,受试者工作特征曲线下面积(AUC值)为0.990,预测结果优良。通过广义加性模型回归验证表明,主要环境因子与秋茄的生境适生性指数呈显著相关,整体方差解释率为94.7%(R^(2)=0.915),说明MaxEnt模型预测结果可靠稳定。基于环境变量贡献率和刀切法的结果表明海洋表层平均水温、等温性、最暖季度降水量、年平均气温、最热月份最高温度等可能是影响秋茄分布的主要环境因子;等温性(bio_03)为23.43—33.99,最热月份最高温度(bio_05)>31.7℃,最暖季度降水量(bio_18)>740.61mm,海洋表层平均水温(temperature)>24.9℃,将有利于秋茄种群的发育与扩散。根据模型预测,在21世纪中叶和21世纪末,秋茄的潜在分布区发生集中变化的区域在浙江与江苏一带,以秋茄自然分布区域北界变化最为显著。不同代表性浓度路径(Representative Concentration Pathways, RCPs2.6、4.5、8.5)下,秋茄高适生区域均发生北移,低适生区域可至长江口附近,甚至到达江苏沿岸。这为上述区域未来利用红树秋茄进行生态系统修复和增加碳汇储备提供了理论依据。

基于MaxEnt模型的湖北烟区潜在适宜性分布及其环境特征分析

为全面评价生态气候因子对湖北省烟叶生长发育的影响,利用2008—2020年中国气象局陆面数据同化系统(CMA land data assimilation system,CLDAS)数据集和其他环境因子,基于最大熵模型(MaxEnt),利用湖北省西部烟区实际种植点位模拟湖北省烟区的潜在适宜性分布,并评估影响适宜性分布的主导环境因子。结果显示:MaxEnt模型对烟草适宜性分布的模拟预测精度较高(AUC=0.854)。海拔(650~1750 m)、土壤类型(黄壤)、团棵期平均最低气温(8.9~15.0℃)、旺长期平均气温(16.0~22.9℃)、成熟期平均气温(18.8~25.6℃)是影响湖北烟草分布的主导环境因子。烟草的高适生区主要分布在恩施、十堰和襄阳南部及宜昌东南部,占湖北省总面积的18.2%,80%区域的海拔为700~1350 m、团棵期平均最低气温11.2~14.5℃、旺长期平均气温19.2~22.8℃、成熟期平均气温22.0~25.4℃。在所有环境因子中,海拔高度起决定性作用,温度则是影响烟草生长发育的重要气象因子。研究表明,本研究结果与湖北烟区实际空间分布基本相符。

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

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.

Maximum Entropy Estimation of n-Year Extreme Waveheights

A new method for estimating the n (50 or 100) -year return-period waveheight, namely, the extreme waveheight expected to occur in n years, is presented on the basis of the maximum entropy principle. The main points of the method are as follows: (1) based on the Hamiltonian principle, a maximum entropy probability density function for the extreme waveheight H, f(H)=αHγ e -βH4 is derived from a Lagrangian function subject to some necessary and rational constraints; (2) the parameters α, β, and γ in the function are expressed in terms of the mean , variance V= (H-)2 and bias B= (H-)3 ; and (3) with , V and B estimated from observed data, the n -year return-period wave height H n is computed in accordance with the formula 11-F(H n)=n , where F(H n) is defined as F(H n)=∫ H n 0f(H) d H. Examples of estimating the 50 and 100-year return period waveheights by the present method and by some currently used method from observed data acquired from two hydrographic stations are given. A comparison of the estimated results shows that the present method is superior to the others.

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 Distribution Function and Uncertainty Evaluation Criteria

Marine environmental design parameter extrapolation has important applications in marine engineering and coastal disaster prevention.The distribution models used for environmental design parameter usually pass the hypothesis tests in statistical analysis,but the calculation results of different distribution models often vary largely.In this paper,based on the information entropy,the overall uncertainty test criteria were studied for commonly used distributions including Gumbel,Weibull,and Pearson-III distribution.An improved method for parameter estimation of the maximum entropy distribution model is proposed on the basis of moment estimation.The study in this paper shows that the number of sample data and the degree of dispersion are proportional to the information entropy,and the overall uncertainty of the maximum entropy distribution model is minimal compared with other models.

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.

MAXIMUM ENTROPY RESTORATION METHOD OF LINEARLY DEGRADED BINARY IMAGE

This paper investigates the maximum entropy restoration of blurred binary image.In concerning with the binary property of image,a new maximum entropy restoration methodwith binary constraint is proposed.The properties of existence and uniqueness of solution arediscussed.The problem of maximum of entropy with two constraints is solved and the corre-sponding algorithm is given.In this paper,the maximum bounded entropy principle is employedconcerning the prior knowledge of binary image,and the maximum bounded entropy restora-tion method with binary constraint is put forward.The proposes methods,Wiener filter(WF)restoration method and maximum entropy restoration method are compared.The experimen-tal results show that the maximum entropy restoration method and maximum bounded entropyrestoration method with binary constraint can improve the quality of restored image.

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.

Foreign Fiber Image Segmentation Based on Maximum Entropy and Genetic Algorithm

In machine-vision-based systems for detecting foreign fibers, due to the background of the cotton layer has the absolute advantage in the whole image, while the foreign fiber only account for a very small part, and what’s more, the brightness and contrast of the image are all poor. Using the traditional image segmentation method, the segmentation results are very poor. By adopting the maximum entropy and genetic algorithm, the maximum entropy function was used as the fitness function of genetic algorithm. Through continuous optimization, the optimal segmentation threshold is determined. Experimental results prove that the image segmentation of this paper not only fast and accurate, but also has strong adaptability.

Receiver function estimated by maximum entropy deconvolution

Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

PHASE EXTENSION AND STRUCTURE ANALYSIS BY THE MAXIMUM ENTROPY METHOD

Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.

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.

The deconvolution of lunar brightness temperature based on the maximum entropy method using Chang'e-2 microwave data

A passive and multi-channel microwave sounder onboard the Chang＇e-2 orbiter has successfully acquired microwave observations of the lunar surface and subsurface structure. Compared with the Chang＇e-1 orbiter, the Chang＇e-2 orbiter obtained more accurate and comprehensive microwave brightness temperature data, which are helpful for further research. Since there is a close relationship between mi- crowave brightness temperature data and some related properties of the lunar regolith, such as the thickness, temperature and dielectric constant, precise and high resolution brightness temperature data are necessary for such research. However, through the detection mechanism of the microwave sounder, the brightness temperature data ac- quired from the microwave sounder are weighted by the antenna radiation pattern, so the data are the convolution of the antenna radiation pattern with the lunar brightness temperature. In order to obtain the real lunar brightness temperature, a deconvolution method is needed. The aim of this paper is to solve the problem associated with per- forming deconvolution of the lunar brightness temperature. In this study, we introduce the maximum entropy method （MEM） to process the brightness temperature data and achieve excellent results. The paper mainly includes the following aspects： first, we introduce the principle of the MEM; second, through a series of simulations, the MEM has been verified as an efficient deconvolution method; and third, the MEM is used to process the Chang＇e-2 microwave data and the results are significant.