Next Article in Journal
Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations
Next Article in Special Issue
Data Science: Measuring Uncertainties
Previous Article in Journal
The Gender Productivity Gap in Croatian Science: Women Are Catching up with Males and Becoming Even Better
Previous Article in Special Issue
Application of Cloud Model in Qualitative Forecasting for Stock Market Trends
Open AccessArticle

A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle

1
Department of Soils and Agri-Food Engineering, Université Laval, Québec, QC G1V0A6, Canada
2
Environmental Research Centre, Department of Civil Engineering, Razi University, Kermanshah 6714414971, Iran
3
Faculty of Civil Engineering, Technische Universität Dresden, 01069 Dresden, Germany
4
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
5
School of Economics and Business, Norwegian University of Life Sciences, 1430 Ås, Norway
6
Department of Civil Engineering, Lakehead University, 955 Oliver Rd, Thunder Bay, ON P7B 5E1, Canada
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(11), 1218; https://doi.org/10.3390/e22111218
Received: 31 July 2020 / Revised: 14 October 2020 / Accepted: 23 October 2020 / Published: 26 October 2020
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
This paper presents an extensive and practical study of the estimation of stable channel bank shape and dimensions using the maximum entropy principle. The transverse slope (St) distribution of threshold channel bank cross-sections satisfies the properties of the probability space. The entropy of St is subject to two constraint conditions, and the principle of maximum entropy must be applied to find the least biased probability distribution. Accordingly, the Lagrange multiplier (λ) as a critical parameter in the entropy equation is calculated numerically based on the maximum entropy principle. The main goal of the present paper is the investigation of the hydraulic parameters influence governing the mean transverse slope (St¯) value comprehensively using a Gene Expression Programming (GEP) by knowing the initial information (discharge (Q) and mean sediment size (d50)) related to the intended problem. An explicit and simple equation of the St¯ of banks and the geometric and hydraulic parameters of flow is introduced based on the GEP in combination with the previous shape profile equation related to previous researchers. Therefore, a reliable numerical hybrid model is designed, namely Entropy-based Design Model of Threshold Channels (EDMTC) based on entropy theory combined with the evolutionary algorithm of the GEP model, for estimating the bank profile shape and also dimensions of threshold channels. A wide range of laboratory and field data are utilized to verify the proposed EDMTC. The results demonstrate that the used Shannon entropy model is accurate with a lower average value of Mean Absolute Relative Error (MARE) equal to 0.317 than a previous model proposed by Cao and Knight (1997) (MARE = 0.98) in estimating the bank profile shape of threshold channels based on entropy for the first time. Furthermore, the EDMTC proposed in this paper has acceptable accuracy in predicting the shape profile and consequently, the dimensions of threshold channel banks with a wide range of laboratory and field data when only the channel hydraulic characteristics (e.g., Q and d50) are known. Thus, EDMTC can be used in threshold channel design and implementation applications in cases when the channel characteristics are unknown. Furthermore, the uncertainty analysis of the EDMTC supports the model’s high reliability with a Width of Uncertainty Bound (WUB) of ±0.03 and standard deviation (Sd) of 0.24. View Full-Text
Keywords: water resources; channel; mathematical entropy model; bank profile shape; gene expression programming (GEP); entropy; genetic programming; artificial intelligence; data science; big data water resources; channel; mathematical entropy model; bank profile shape; gene expression programming (GEP); entropy; genetic programming; artificial intelligence; data science; big data
Show Figures

Figure 1

MDPI and ACS Style

Bonakdari, H.; Gholami, A.; Mosavi, A.; Kazemian-Kale-Kale, A.; Ebtehaj, I.; Azimi, A.H. A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle. Entropy 2020, 22, 1218. https://doi.org/10.3390/e22111218

AMA Style

Bonakdari H, Gholami A, Mosavi A, Kazemian-Kale-Kale A, Ebtehaj I, Azimi AH. A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle. Entropy. 2020; 22(11):1218. https://doi.org/10.3390/e22111218

Chicago/Turabian Style

Bonakdari, Hossein; Gholami, Azadeh; Mosavi, Amir; Kazemian-Kale-Kale, Amin; Ebtehaj, Isa; Azimi, Amir H. 2020. "A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle" Entropy 22, no. 11: 1218. https://doi.org/10.3390/e22111218

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop