A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle
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- @Article{bonakdari:2020:Entropy,
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author = "Hossein Bonakdari and Azadeh Gholami and
Amir Mosavi and Amin Kazemian-Kale-Kale and Isa Ebtehaj and
Amir Hossein Azimi",
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title = "A Novel Comprehensive Evaluation Method for Estimating
the Bank Profile Shape and Dimensions of Stable
Channels Using the Maximum Entropy Principle",
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journal = "Entropy",
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year = "2020",
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volume = "22",
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number = "11",
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keywords = "genetic algorithms, genetic programming, gene
expression programming",
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ISSN = "1099-4300",
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URL = "https://www.mdpi.com/1099-4300/22/11/1218",
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DOI = "doi:10.3390/e22111218",
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abstract = "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 used 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 models high reliability with a
Width of Uncertainty Bound (WUB) of ±0.03 and
standard deviation (Sd) of 0.24.",
-
notes = "also known as \cite{e22111218}",
- }
Genetic Programming entries for
Hossein Bonakdari
Azadeh Gholami
Amir Mosavi
Amin Kazemian-Kale-Kale
Isa Ebtehaj
Amir Hossein Azimi
Citations