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.

Two-dimensional horizontal visibility graph analysis of human brain aging on gray matter

Characterizing the trajectory of the healthy aging brain and exploring age-related structural changes in the brain can help deepen our understanding of the mechanism of brain aging.Currently,most structural magnetic resonance imaging literature explores brain aging merely from the perspective of morphological features,which cannot fully utilize the grayscale values containing important intrinsic information about brain structure.In this study,we propose the construction of two-dimensional horizontal visibility graphs based on the pixel intensity values of the gray matter slices directly.Normalized network structure entropy(NNSE)is then introduced to quantify the overall heterogeneities of these graphs.The results demonstrate a decrease in the NNSEs of gray matter with age.Compared with the middle-aged and the elderly,the larger values of the NNSE in the younger group may indicate more homogeneous network structures,smaller differences in importance between nodes and thus a more powerful ability to tolerate intrusion.In addition,the hub nodes of different adult age groups are primarily located in the precuneus,cingulate gyrus,superior temporal gyrus,inferior temporal gyrus,parahippocampal gyrus,insula,precentral gyrus and postcentral gyrus.Our study can provide a new perspective for understanding and exploring the structural mechanism of brain aging.

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.

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.

Maximum entropy spectral characteristics of seismic activity for great earthquakes in China

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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.

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.

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.

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.

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-2orbiter 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 microwave 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 acquired 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 performing 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.

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.

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. Laboratory 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.

Predicting Potential Distribution of Tibetan Spruce (Picea smithiana) in Qomolangma (Mount Everest) National Nature Preserve Using Maximum Entropy Niche-based Model

Tibetan spruce (Picea smithiana) is an endemic species of the Himalayas,and it distributes only in a re-stricted area with very low number.To address the lack of detailed distributional information,we used maximum en-tropy (Maxent) niche-based model to predict the species' potential distribution from limited occurrence-only records.The location data of P.smithiana,relative bioclimatic variables,vegetation data,digital elevation model (DEM),and the derived data were analyzed in Maxent.The receiver operating characteristic (ROC) curve was applied to assess the prediction accuracy.The Maxent jackknife test was performed to quantify the training gains from data layers and the response of P.smithiana distribution to four typical environmental variables was analyzed.Results show that the model performs well at the regional scale.There is a potential for continued expansion of P.smithiana population numbers and distribution in China.P.smithiana potentially distributes in the lower reaches of Gyirong Zangbo and Poiqu rivers in Gyirong and Nyalam counties in Qomolangma (Mount Everest) National Nature Preserve (QNNP),China.The species prefers warm temperate climate in mountain area and mainly distributes in needle-leaved evergreen closed to open forest and mixed forest along the river valley at relatively low altitudes of about 2000-3000 m.Model simulations suggest that distribution patterns of rare species with few species numbers can be well predicted by Max-ent.

A Microcomputer Fitted Method for Determination of the True ODF of Hexagonal Materials according to the Maximum-Entropy Estimate

A method which is especially suitable for microcomputer calculation of the true orientation distribution function(ODF) according to the maximum-entropy estimate is proposed for hexagonal system polycrystalline materialswith physical symmetry.The resultant computational software system has been also designed and first carried outin a microcomputer PANAFACOM-U1200 being on line with the X-ray diffractometer D/max-3A.The simu-lated calculation shows that the method is concisely pragmatic and easily popularized,while the results obtainedare trust worthy.

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.

An Interval Maximum Entropy Method for Quadratic Programming Problem

With the idea of maximum entropy function and penalty function methods, we transform the quadratic programming problem into an unconstrained differentiable optimization problem, discuss the interval extension of the maximum entropy function, provide the region deletion test rules and design an interval maximum entropy algorithm for quadratic programming problem. The convergence of the method is proved and numerical results are presented. Both theoretical and numerical results show that the method is reliable and efficient.

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.