Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method
Entropy models have been recently adopted in many studies to evaluate the shear stress distribution in open-channel flows. Although the uncertainty of Shannon and Tsallis entropy models were analyzed separately in previous studies, the uncertainty of other entropy models and comparisons of their rel...
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MDPI AG
2021-07-01
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| author | Amin Kazemian-Kale-Kale Azadeh Gholami Mohammad Rezaie-Balf Amir Mosavi Ahmed A. Sattar Amir H. Azimi Bahram Gharabaghi Hossein Bonakdari |
| author_facet | Amin Kazemian-Kale-Kale Azadeh Gholami Mohammad Rezaie-Balf Amir Mosavi Ahmed A. Sattar Amir H. Azimi Bahram Gharabaghi Hossein Bonakdari |
| author_sort | Amin Kazemian-Kale-Kale |
| collection | DOAJ |
| description | Entropy models have been recently adopted in many studies to evaluate the shear stress distribution in open-channel flows. Although the uncertainty of Shannon and Tsallis entropy models were analyzed separately in previous studies, the uncertainty of other entropy models and comparisons of their reliability remain an open question. In this study, a new method is presented to evaluate the uncertainty of four entropy models, Shannon, Shannon-Power Law (PL), Tsallis, and Renyi, in shear stress prediction of the circular channels. In the previous method, the model with the largest value of the percentage of observed data within the confidence bound (N<sub>in</sub>) and the smallest value of Forecasting Range of Error Estimation (FREE) is the most reliable. Based on the new method, using the effect of Optimized Forecasting Range of Error Estimation (FREE<sub>opt</sub>) and Optimized Confidence Bound (OCB), a new statistic index called FREE<sub>opt</sub>-based OCB (FOCB) is introduced. The lower the value of FOCB, the more certain the model. Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, and had the highest certainty, followed by <i>ρ</i>gRs and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy, with the value of FOCB equal to 57.726, had less certainty. |
| first_indexed | 2024-03-10T08:47:08Z |
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| issn | 2076-3263 |
| language | English |
| last_indexed | 2024-03-10T08:47:08Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Geosciences |
| spelling | doaj.art-b89d54946235422eaa4a4ed800109e182023-11-22T07:47:32ZengMDPI AGGeosciences2076-32632021-07-0111830810.3390/geosciences11080308Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel MethodAmin Kazemian-Kale-Kale0Azadeh Gholami1Mohammad Rezaie-Balf2Amir Mosavi3Ahmed A. Sattar4Amir H. Azimi5Bahram Gharabaghi6Hossein Bonakdari7Environmental Research Centre, Razi University, Kermanshah 6718773654, IranEnvironmental Research Centre, Razi University, Kermanshah 6718773654, IranDepartment of Water Engineering, Graduate University of Advanced Technology, Kerman 7631818356, IranDepartment of Mathematics, J. Selye University, 94501 Komarno, SlovakiaDepartment of Irrigation & Hydraulics, Faculty of Engineering, Cairo University, Cairo 12613, EgyptDepartment of Civil Engineering, Lakehead University, Thunder Bay, ON P7B 5E1, CanadaSchool of Engineering, University of Guelph, Guelph, ON NIG 2W1, CanadaDepartment of Soils and Agri-Food Engineering, Laval University, Quebec City, QC G1V 0A6, CanadaEntropy models have been recently adopted in many studies to evaluate the shear stress distribution in open-channel flows. Although the uncertainty of Shannon and Tsallis entropy models were analyzed separately in previous studies, the uncertainty of other entropy models and comparisons of their reliability remain an open question. In this study, a new method is presented to evaluate the uncertainty of four entropy models, Shannon, Shannon-Power Law (PL), Tsallis, and Renyi, in shear stress prediction of the circular channels. In the previous method, the model with the largest value of the percentage of observed data within the confidence bound (N<sub>in</sub>) and the smallest value of Forecasting Range of Error Estimation (FREE) is the most reliable. Based on the new method, using the effect of Optimized Forecasting Range of Error Estimation (FREE<sub>opt</sub>) and Optimized Confidence Bound (OCB), a new statistic index called FREE<sub>opt</sub>-based OCB (FOCB) is introduced. The lower the value of FOCB, the more certain the model. Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, and had the highest certainty, followed by <i>ρ</i>gRs and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy, with the value of FOCB equal to 57.726, had less certainty.https://www.mdpi.com/2076-3263/11/8/308water resourcesuncertaintyshear stress distributioncircular channelentropyShannon |
| spellingShingle | Amin Kazemian-Kale-Kale Azadeh Gholami Mohammad Rezaie-Balf Amir Mosavi Ahmed A. Sattar Amir H. Azimi Bahram Gharabaghi Hossein Bonakdari Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method Geosciences water resources uncertainty shear stress distribution circular channel entropy Shannon |
| title | Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method |
| title_full | Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method |
| title_fullStr | Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method |
| title_full_unstemmed | Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method |
| title_short | Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method |
| title_sort | uncertainty assessment of entropy based circular channel shear stress prediction models using a novel method |
| topic | water resources uncertainty shear stress distribution circular channel entropy Shannon |
| url | https://www.mdpi.com/2076-3263/11/8/308 |
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