Abstract
The objective of this study is to employ support vector machine as a machine learning technique to improve flow discharge predictions in compound open channels. Accurate estimation of channel conveyance is a major step in prediction of the flow discharge in open-channel flow computations (e.g., river flood simulations, design of canals, and water surface profile computation). Common methods to estimate the conveyance are highly simplified and are a main source of uncertainty in compound channels, since popular river/canal models still incorporate 1-D hydrodynamic formulations. Further, the reliability of using a specific method (e.g., vertical divided channel method, the coherence method) over other methods for different applications involving various geometric and hydraulic conditions is questionable. Using available experimental and field data, a novel method was developed, based on SVM, to compute channel conveyance. The data included 394 flow rating curves from 30 different laboratory and natural compound channel sections which were used for the training, and verification of the SVM method. The data were limited to straight compound channels. The performance of SVM was compared with those from other commonly used methods, such as the vertical divided channel method, the coherence method and the Shiono and Knight model. Additionally, SVM estimations were compared with available data for River Main and River Severn, UK. Results indicated that SVM outperforms traditional methods for both laboratory and field data. It is concluded that the proposed SVM approach could be applied as a reliable technique for the prediction of flow discharge in straight compound channels. The proposed SVM can be potentially incorporated into 1-D river hydrodynamic models in future studies.
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Abbreviations
- A :
-
Cross-sectional area
- b :
-
Bias term
- C :
-
Penalty parameter
- COH:
-
Coherence parameter
- D(α):
-
Dual function
- D r :
-
Relative depth (ratio of floodplain depth to main channel depth)
- DISADF:
-
Discharge adjustment factor
- DISDEF:
-
Discharge deficit
- f :
-
SVM function
- h :
-
Bank-full depth
- H :
-
Flow depth
- K :
-
Conveyance parameter
- K(x i, x j):
-
Kernel function
- L :
-
Lagrange function
- L ɛ :
-
Loss function
- MAPE:
-
Mean absolute percentage error
- n :
-
Manning coefficient
- P :
-
Wetted perimeter
- Q b :
-
Bank-full discharge
- Q m :
-
Measured flow discharge
- Q p :
-
Predicted flow discharge
- Q t :
-
Total flow discharge
- Q VDCM :
-
Discharge calculated by VDCM
- r :
-
Lagrangian multiplier
- R :
-
Risk function
- R 2 :
-
Coefficient of determination
- Residual:
-
Difference between predicted and observed results
- RMSE:
-
Root mean square error
- SVM:
-
Support vector machine
- s :
-
Channel side slope
- S 0 :
-
Longitudinal slope
- s f :
-
Friction slope
- U d :
-
Depth-averaged velocity
- w :
-
Weight parameter
- x :
-
Difference of observed data and mean observed data
- X :
-
Observed data
- \( \bar{X} \) :
-
Mean observed data
- X i :
-
Data used to build the SVM model
- X max :
-
Maximum of data values
- X min :
-
Minimum of data values
- X n :
-
Normalized data
- y :
-
Difference of predicted data and mean predicted data
- Y :
-
Predicted data
- \( \bar{Y} \) :
-
Mean predicted data
- y i :
-
Target values
- α :
-
Lagrangian multiplier
- \( \varGamma \) :
-
Secondary flow parameter
- ɛ :
-
Parameter of insensitive loss function
- λ :
-
Dimensionless eddy viscosity
- ξ :
-
Slack variable
- ψ :
-
Higher-dimensional space map function
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Farhadi, H., Zahiri, A., Hashemi, M.R. et al. Incorporating a machine learning technique to improve open-channel flow computations. Neural Comput & Applic 31, 909–921 (2019). https://doi.org/10.1007/s00521-017-3120-7
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DOI: https://doi.org/10.1007/s00521-017-3120-7