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

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...

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Veröffentlicht in:Entropy (Basel, Switzerland) Jg. 22; H. 11; S. 1218
Hauptverfasser: Bonakdari, Hossein, Gholami, Azadeh, Mosavi, Amir, Kazemian-Kale-Kale, Amin, Ebtehaj, Isa, Azimi, Amir Hossein
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Switzerland MDPI 26.10.2020
MDPI AG
Schlagworte:
bank profile shape
channel
entropy
gene expression programming (GEP)
mathematical entropy model
water resources
genetic programming
entropy
water resources
bank profile shape
data science
channel
gene expression programming (GEP)
big data
artificial intelligence
mathematical entropy model
ISSN:1099-4300, 1099-4300
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1099-4300
1099-4300
DOI:10.3390/e22111218