scholarly journals Comparison of Conventional Deterministic and Entropy-Based Methods for Predicting Sediment Concentration in Debris Flow

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 439 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Bo Pang ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Debris Flow ◽  
Maximum Entropy ◽  
Shannon Entropy ◽  
Sediment Concentration ◽  
Tsallis Entropy ◽  
Principle Of Maximum Entropy ◽  
General Index ◽  
Deterministic Methods ◽  
The Mean ◽  
Principle Of Maximum

In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.

scholarly journals An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 522 ◽  
Author(s):  
Zhongfan Zhu ◽  
Jingshan Yu ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Maximum Entropy ◽  
Shannon Entropy ◽  
Open Channel ◽  
Tsallis Entropy ◽  
Channel Flows ◽  
Test Cases ◽  
Deterministic Models ◽  
Open Channel Flows ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

In the context of river dynamics, some experimental results have shown that particle velocity is different from fluid velocity along the stream-wise direction for uniform sediment-laden open-channel flows; this velocity difference has been termed velocity lag in the literature. In this study, an analytical expression for estimating the velocity lag in open-channel flows was derived based on the Tsallis entropy theory together with the principle of maximum entropy. The derived expression represents the velocity lag as a function of a non-dimensional entropy parameter depending on the average and maximum values of velocity lag from experimental measurements. The derived expression was tested against twenty-two experimental datasets collected from the literature with three deterministic models and the developed Shannon entropy-based model. The Tsallis entropy-based model agreed better with the experimental datasets than the deterministic models for eighteen out of the twenty-two total real cases, and the prediction accuracy for the eighteen experimental datasets was comparable to that of the developed Shannon entropy-based model (the Tsallis entropy-based expression agreed slightly better than the Shannon entropy-based model for twelve out of eighteen test cases, whereas for the other six test cases, the Shannon entropy-based model had a slightly higher prediction accuracy). Finally, the effects of the friction velocity of the flow, the particle diameter, and the particles’ specific gravity on the velocity lag were analyzed based on the Tsallis entropy-based model. This study shows the potential of the Tsallis entropy theory together with the principle of maximum entropy to predict the stream-wise velocity lag between a particle and the surrounding fluid in sediment-laden open-channel flows.

scholarly journals Principle of maximum entropy in the estimation of suspended sediment concentration

RBRH ◽  
2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Patrícia Diniz Martins ◽  
Cristiano Poleto
Keyword(s):  
Maximum Entropy ◽  
Probabilistic Method ◽  
Sediment Concentration ◽  
Global Scale ◽  
Computational Effort ◽  
River Channels ◽  
Monitoring And Control ◽  
Water Contaminants ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

ABSTRACT The concern with water quality has been promoting development of better monitoring and control techniques every day. As sediments transport most of water contaminants, their study is fundamental. Given the large number of variables for estimating sediment concentration and high costs of monitoring campaigns, it becomes necessary to develop more accessible methods which bring satisfactory practical results. Therefore, this work deals with application of the principle of maximum entropy, a probabilistic method to determine concentration of sediments in river channels with various concentrations and particle sizes. For this purpose, it was proposed a relationship between the theory of entropy parameters in order to reduce the computational effort. The results were satisfactory at concentrations above 10 g/L with R2 greater than 0.88. The calculated squared errors in this study were lower than those found when using the theory of entropy by Tsallis and the equation of Rouse, classic models for determining the sediment concentration profile. The applicability of the proposed model and the ease of using the probabilistic method, since it reduces the amount of data needed to perform the estimate, makes it feasible on a global scale.

scholarly journals O Princípio da Máxima Entropia e a Moderna Teoria das Carteiras

2003 ◽  
Vol 1 (2) ◽  
pp. 271
Author(s):  
Ailton Cassetari
Keyword(s):  
At Risk ◽  
Maximum Entropy ◽  
Value At Risk ◽  
Capital Allocation ◽  
Systematic Comparison ◽  
Principle Of Maximum Entropy ◽  
The Mean ◽  
Mean Variance ◽  
Principle Of Maximum ◽  
Risk Concept

In this work, a capital allocation methodology base don the Principle of Maximum Entropy was developed. The Shannons entropy is used as a measure, concerning the Modern Portfolio Theory, are also discuted. Particularly, the methodology is tested making a systematic comparison to: 1) the mean-variance (Markovitz) approach and 2) the mean VaR approach (capital allocations based on the Value at Risk concept). In principle, such confrontations show the plausibility and effectiveness of the developed method.

scholarly journals To Be or to Have Been Lucky, That Is the Question

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 57
Author(s):  
Antony Lesage ◽  
Jean-Marc Victor
Keyword(s):  
High Risk ◽  
Maximum Entropy ◽  
Chronic Diseases ◽  
Statistical Test ◽  
Low Risk ◽  
Principle Of Maximum Entropy ◽  
Ex Ante ◽  
Social Opportunities ◽  
Global Population ◽  
Principle Of Maximum

Is it possible to measure the dispersion of ex ante chances (i.e., chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex ante chances in various areas, with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk of becoming ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk, like the overwhelming majority of the population, but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

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