scholarly journals Significance of higher moments for complete characterization of the travel time probability density function in heterogeneous porous media using the maximum entropy principle

2010 ◽  
Vol 46 (5) ◽  
Author(s):  
Hrvoje Gotovac ◽  
Vladimir Cvetkovic ◽  
Roko Andricevic
Keyword(s):  
Porous Media ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Maximum Entropy Principle ◽  
Complete Characterization ◽  
Heterogeneous Porous Media ◽  
Higher Moments ◽  
Entropy Principle

Notes on Bell-Sejnowski PDF-Matching Neuron

2002 ◽  
Vol 14 (12) ◽  
pp. 2847-2855 ◽  
Author(s):  
Simone Fiori
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Single Unit ◽  
Neuron Model ◽  
Maximum Entropy Principle ◽  
Entropy Principle ◽  
Single Input ◽  
Pdf Matching

This article investigates the behavior of a single-input, single-unit neuron model of the Bell-Sejnowski class, which learn through the maximum-entropy principle, in order to understand its probability density function matching ability.

Some Results on the Random Wear Coefficient of the Archard Model

2012 ◽  
Vol 79 (5) ◽  
Author(s):  
Fabio Antonio Dorini ◽  
Rubens Sampaio
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Maximum Entropy Principle ◽  
Linear Wear ◽  
Wear Depth ◽  
Wear Coefficient ◽  
Wear Process ◽  
Entropy Principle ◽  
Wear Law

The most used model for predicting wear is the linear wear law proposed by Archard. A common generalization of Archard’s wear law is based on the assumption that the wear rate at any point on the contact surface is proportional to the local contact pressure and the relative sliding velocity. This work focuses on a stochastic modeling of the wear process to take into account the experimental uncertainties in the identification process of the contact-state dependent wear coefficient. The description of the dispersion of the wear coefficient is described by a probability density function, which is performed using the maximum entropy principle using only the information available. Closed-form results for the probability density function of the wear depth for several situations that commonly occur in practice are provided.

Online Variable Kernel Estimator

2017 ◽  
Vol 8 (1) ◽  
pp. 58-92
Author(s):  
Yissam Lakhdar ◽  
El Hassan Sbai
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Maximum Entropy Principle ◽  
Kernel Estimation ◽  
Simulated Data ◽  
Kernel Estimator ◽  
Variable Kernel ◽  
Entropy Principle ◽  
And Performance

In this work, the authors propose a novel method called online variable kernel estimation of the probability density function (pdf). This new online estimator combines the characteristics and properties of two estimators namely nearest neighbors estimator and the Parzen-Rosenblatt estimator. Their approach allows a compact online adaptation of the estimated probability density function from the new arrival data. The performance of the online variable kernel estimator (OVKE) depends on the choice of the bandwidth. The authors present in this article a new technique for determining the optimal smoothing parameter of OVKE based on the maximum entropy principle (MEP). The robustness and performance of the proposed approach are demonstrated by examples of online estimation of real and simulated data distributions.

Study on Determining Safety-Monitoring Index for Concrete Dam Based on Cloud Model

2012 ◽  
Vol 226-228 ◽  
pp. 1106-1110 ◽  
Author(s):  
Dong Qin ◽  
Xue Qin Zheng ◽  
Song Lin Wang
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cloud Model ◽  
Safety Monitoring ◽  
Monitoring Data ◽  
Concrete Dam ◽  
Deterministic Function ◽  
Monitoring Index

The paper, based on analyzing original monitoring data, employs forward and backward cloud algorithm in studying determining safety-monitoring index for concrete dam ,which integrates randomness and fuzziness into of qualitative concept of digital features. By means of above monitoring data, its digital characteristics can be easily transformed to the “quantitative-qualitative- quantitative” change. The final generated quantitative value constitutes the cloud diagram where each droplet demonstrates the characterization of raw monitoring data. At the same time, it also shows the randomness and fuzziness of monitored value. we can study out the safety monitoring indexes according to different remarkable levels by using the probability density function and deterministic function which completed by cloud algorithm. In the end, it is obtained with practice that this method is more suitable and reliability.

scholarly journals Probability density function approach for modelling multi-phase flow with ganglia in porous media

2011 ◽  
Vol 688 ◽  
pp. 219-257 ◽  
Author(s):  
Manav Tyagi ◽  
Patrick Jenny
Keyword(s):  
Porous Media ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Transport Equations ◽  
Kolmogorov Equation ◽  
Phase Flow ◽  
Correlation Times ◽  
Multi Phase Flow ◽  
Multi Phase

AbstractA probabilistic approach to model macroscopic behaviour of non-wetting-phase ganglia or blobs in multi-phase flow through porous media is proposed. The key idea is to consider a set of stochastic Markov processes that can mimic the microscopic multi-phase dynamics. These processes are characterized by equilibrium probability density functions (PDFs) and correlation times, which can be obtained from micro-scale simulation studies or experiments. A Lagrangian viewpoint is adopted, where stochastic particles represent infinitesimal fluid elements and evolve in the physical and probability space. Ganglion mobilization and trapping are modelled by a two-state jump process with transition probabilities given as functions of ganglion size. Coalescence and breakup of ganglia influence the ganglion size distribution, which is modelled by a Langevin type equation. The joint probability density function (JPDF) of the chosen stochastic variables is governed by a high-dimensional Chapman–Kolmogorov equation. This equation can be used to derive moment (e.g. saturation, mean mobility etc.) transport equations, which in general do not form a closed system. However, in some special cases, which arise in the limit of one time scale being smaller or larger than the others, a closed set of moment transport equations can be obtained. For slowly varying and quasi-uniform flows, the saturation transport equation appears in closed form with the mean mobility fully determined, if the equilibrium PDFs are known. Furthermore, it is shown how statistical parameters such as mobilization and trapping rates and equilibrium PDFs can be obtained from the birth–death type approach, in which ganglia breakup and coalescence are explicitly considered. A two-equation transport model (one equation for the total saturation and one for the trapped saturation) is obtained in the limit of very fast coalescence and breakup processes. This model is employed to mimic hysteresis in relative permeability–saturation curves; a well known phenomenon observed in the successive processes of imbibition and drainage. For the general case, the JPDF-equation is solved using the stochastic particle method, which was proposed in our previous paper (Tyagi et al. J. Comput. Phys. 227, 2008, 6696–6714). Several one- and two-dimensional numerical simulation results are presented to show the influence of correlation times on the averaged macroscopic flow behaviour.

A note on the characterization of a U-shaped probability density function

1972 ◽  
Vol 9 (03) ◽  
pp. 684-685
Author(s):  
P. Ghosh ◽  
D. N. Shanbhag
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Characteristic Property

In this note a characterization for a U-shaped probability density function is given using a well-known result for unimodal distributions due to Khinchine. As a corollary of this result, a characteristic property based on moments is found.

Sign in / Sign up

Export Citation Format

Share Document