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.

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.

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

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.

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.

On the Distribution of the Minimum or Maximum of a Random Number of i.i.d. Lifetime Random Variables

Statisticians are usually concerned with the proposition of new distributions. In this paper we point out that a unified and concise derivation procedure of the distribution of the minimum or maximum of a random number N of indepen-dent and identically distributed continuous random variables Yi,{i = 1,2,…,N} is obtained if one compounds the probability generating function of N with the survival or the distribution func-tion of Yi. Expressions are then derived in closed form for the density, hazard and quantile func-tions of the minimum or maximum. The methodology is illustrated with examples of the distributions proposed by Adamidis and Loukas (1998), Kus (2007), Tahmasbi and Rezaei (2008), Barreto-Souza and Cribari-Neto (2009), Cancho, Louzada, and Barriga (2011) and Louzada, Roman and Cancho (2011).

On the Generalized Theory of Atmospheric Particle Systems

Unification is both necessary and challenging for studying atmospheric particle systems, which are polydispersesystems containing particles of different sizes and shapes. A general framework is proposed to realize the first order generalization. Within this generalized framework, (1) atmospheric particle shapes are unified into self-similar fractals; (2) a self-similar particle is characterized by various power-law relationships; (3) by combining these power-law relationships for a single particle with Shannon's maximum entropy principle and some concepts in statistical mechanics, unified maximum likelihoood number size distributions are of the Weibull form for atmospheric particle systems. Frontier disciplines (e. g., scaling,fractal,chaos and hierarchy) are argued to provide potential 'tools' for such unification. Several new topics are raised for future research.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

Design of a Level-3 electric vehicle charging station using a 1-MW solar system via the distributed maximum power point tracking technique

Solar power is mostly influenced by solar irradiation,weather conditions,solar array mismatches and partial shading conditions.Therefore,before installing solar arrays,it is necessary to simulate and determine the possible power generated.Maximum power point tracking is needed in order to make sure that,at any time,the maximum power will be extracted from the photovoltaic system.However,maximum power point tracking is not a suitable solution for mismatches and partial shading conditions.To overcome the drawbacks of maximum power point tracking due to mismatches and shadows,distributed maximum power point tracking is util-ized in this paper.The solar farm can be distributed in different ways,including one DC-DC converter per group of modules or per module.In this paper,distributed maximum power point tracking per module is implemented,which has the highest efficiency.This technology is applied to electric vehicles(EVs)that can be charged with a Level 3 charging station in<1 hour.However,the problem is that charging an EV in<1 hour puts a lot of stress on the power grid,and there is not always enough peak power reserve in the existing power grid to charge EVs at that rate.Therefore,a Level 3(fast DC)EV charging station using a solar farm by implementing distributed maximum power point tracking is utilized to address this issue.Finally,the simulation result is reported using MATLAB®,LTSPICE and the System Advisor Model.Simulation results show that the proposed 1-MW solar system will provide 5 MWh of power each day,which is enough to fully charge~120 EVs each day.Additionally,the use of the proposed photovoltaic system benefits the environment by removing a huge amount of greenhouse gases and hazardous pollutants.For example,instead of supplying EVs with power from coal-fired power plants,1989 pounds of CO_(2) will be eliminated from the air per hour.

The Maximum Surplus Distribution before Ruin in an Erlang（n） Risk Process Perturbed by Diffusion

In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang（n） risk process （i.e., convolution of n exponential distributions with possibly different parameters） perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.