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.

The Impact of Changing Climate on Agroforestry Tree Distribution across Agroecological Zones of Nigeria: MaxEnt Modelling Perspective

The survival of agroforestry tree species in sub-Saharan Africa is essential for sustainable livelihoods, particularly in the semi-arid environment. Drought in the Agroecological zones (AEZ) of Nigeria is one of the environmental factors limiting parkland tree regeneration. Species distribution modelling offers the opportunity to predict future distributions of plant species based on current distribution data and bioclimatic variables. Maxent (maximum entropy) model was employed to predict the future tree distribution in AEZ parklands, under the four Representative Concentration Pathway (RCP) climate change prediction using current tree distribution (presence-only data) along a transect across three agroecological zones. The spatial data used were 19 bioclimatic variables and presence-only data for the two most important tree species—Parkia biglobosa and Vitellaria paradoxa. The result showed a drastic reduction (>45%) in the suitability of farmlands across predictions observed in the studied agroecological zones. The 2050 scenario in both species predicted areas had an increasing mid-range potential, over 44% lower suitability in sampled AEZ distribution predictions. The future prediction potential distribution maps for year 2070 of both species displayed large variations in suitability compared to 2050, showing a significant increase (up to 53%) in areas climatically suitable for both species to regenerate and thrive. This is attributed to over increased annual evapotranspiration, despite increasing seasonal precipitation. This study highlights the need for more climate-smart regeneration and improved restoration strategies to reduce land degradation as climate conditions change over time.

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.

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.

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.

Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

A Novel Modified Alpha Power Transformed Weibull Distribution and Its Engineering Applications

This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.

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.

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.

Thermodynamic properties at the kinetic freeze-out in the Au + Au and Cu + Cu collisions at the RHIC using the Tsallis distribution

The thermodynamic properties of charged particles,such as the energy density,pressure,entropy density,particle density,and squared speed of sound at the kinetic freeze-out in the Au+Au collisions from the relativistic heavy ion collider (RHIC)beam energy scan program √S_(NN) and in the Cu+Cu collisions at √S_(NN),200 GeV are studied using the thermodynamically consistent Tsallis distribution.The energy density,pressure,and particle density decrease monotonically with the collision energy for the same collision centrality;These properties also decrease monotonically from the central to peripheral collisions at the same collision energy.While the scaled energy densityε∕T^(4) and scaled entropy density s∕T^(3) demonstrate the opposite trend with the collision energy for the same collision centrality.There is a correlation betweenε∕T^(4) and s∕T^(3) at the same centrality.In addition,the squared speed of sound was calculated to determine that all the collision energies share nearly the same value at different collision centralities.

Estimation of Design Sea Ice Thickness with Maximum Entropy Distribution by Particle Swarm Optimization Method

The maximum entropy distribution, which consists of various recognized theoretical distributions, is a better curve to estimate the design thickness of sea ice. Method of moment and empirical curve fitting method are common-used parameter estimation methods for maximum entropy distribution. In this study, we propose to use the particle swarm optimization method as a new parameter estimation method for the maximum entropy distribution, which has the advantage to avoid deviation introduced by simplifications made in other methods. We conducted a case study to fit the hindcasted thickness of the sea ice in the Liaodong Bay of Bohai Sea using these three parameter-estimation methods for the maximum entropy distribution. All methods implemented in this study pass the K-S tests at 0.05 significant level. In terms of the average sum of deviation squares, the empirical curve fitting method provides the best fit for the original data, while the method of moment provides the worst. Among all three methods, the particle swarm optimization method predicts the largest thickness of the sea ice for a same return period. As a result, we recommend using the particle swarm optimization method for the maximum entropy distribution for offshore structures mainly influenced by the sea ice in winter, but using the empirical curve fitting method to reduce the cost in the design of temporary and economic buildings.

Entropy Bayesian Analysis for the Generalized Inverse Exponential Distribution Based on URRSS

This paper deals with the Bayesian estimation of Shannon entropy for the generalized inverse exponential distribution.Assuming that the observed samples are taken from the upper record ranked set sampling(URRSS)and upper record values(URV)schemes.Formulas of Bayesian estimators are derived depending on a gamma prior distribution considering the squared error,linear exponential and precautionary loss functions,in addition,we obtain Bayesian credible intervals.The random-walk Metropolis-Hastings algorithm is handled to generate Markov chain Monte Carlo samples from the posterior distribution.Then,the behavior of the estimates is examined at various record values.The output of the study shows that the entropy Bayesian estimates under URRSS are more convenient than the other estimates under URV in the majority of the situations.Also,the entropy Bayesian estimates perform well as the number of records increases.The obtained results validate the usefulness and efficiency of the URV method.Real data is analyzed for more clarifying purposes which validate the theoretical results.

Droplets diameter distribution using maximum entropy formulation combined with a new energy-based sub-model

The maximum entropy principle(MEP) is one of the first methods which have been used to predict droplet size and velocity distributions of liquid sprays. This method needs a mean droplets diameter as an input to predict the droplet size distribution. This paper presents a new sub-model based on the deterministic aspects of liquid atomization process independent of the experimental data to provide the mean droplets diameter for using in the maximum entropy formulation(MEF). For this purpose, a theoretical model based on the approach of energy conservation law entitled energy-based model(EBM) is presented. Based on this approach, atomization occurs due to the kinetic energy loss. Prediction of the combined model(MEF/EBM) is in good agreement with the available experimental data. The energy-based model can be used as a fast and reliable enough model to obtain a good estimation of the mean droplets diameter of a spray and the combined model(MEF/EBM) can be used to well predict the droplet size distribution at the primary breakup.

Alternative Optimal Activity Distribution to the Classical Optimal Distribution in Catalyst Pellets with Exergy and Entropy Consideration

It is generally recognized that the optimal distribution of catalyst activity in a spherical catalyst is a Dirac d-function. However, catalyst with other alternative distribution may accomplish the same reaction task without necessarily concentrating the catalyst activity in an inside thin layer. Moreover, the alternative with activity on catalyst surface may offer higher reaction rate and better utilization of reaction heat (higher exergy output). Simple cases of first-order exothermal reactions, in particular when the catalyst is limited by the maximum working temperature, are presented to demonstrate the above advantages and to show the importance of studying the optimal activity distribution with the consideration on exergy maximization and entropy production minimization.

INVESTIGATION OF THE SPATIAL AND TEMPORAL DISTRIBUTION OF EXTREME HIGH TEMPERATURE IN CHINA WITH DETRENDED FLUCTUATION AND PERMUTATION ENTROPY

With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.

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.

The Burr XII Distribution Family and the Maximum Entropy Principle: Power-Law Phenomena Are Not Necessarily “Nonextensive”

In this paper, we recall for physicists how it is possible using the principle of maximization of the Boltzmann-Shannon entropy to derive the Burr-Singh-Maddala (BurrXII) double power law probability distribution function and its approximations (Pareto, loglogistic.) and extension (GB2…) first used in econometrics. This is possible using a deformation of the power function, as this has been done in complex systems for the exponential function. We give to that distribution a deep stochastic interpretation using the theory of Weron et al. Applied to thermodynamics, the entropy nonextensivity can be accounted for by assuming that the asymptotic exponents are scale dependent. Therefore functions which describe phenomena presenting power-law asymptotic behaviour can be obtained without introducing exotic forms of the entropy.

Maximum Entropy and Maximum Likelihood Estimation for the Three-Parameter Kappa Distribution

The two statistical principles of maximum entropy and maximum likelihood are investigated for the three-parameter kappa distribution. These two methods become equivalent in the discrete case with x, β>0 where 0<α=1/(2k+1)≤1, k=0,1,2…or the maximum entropy method.