Abstract
Stepped spillway is an effective approach to remove the potential occurrences of cavitation in chute of spillways and also to significantly reduce the size of energy dissipators at the toe of dam. In this study, to predict the energy dissipation ratio of flow over stepped spillways, artificial neural network, support vector machine, genetic programming (GP), group method of data handling (GMDH), and multivariate adaptive regression splines (MARS) were developed. MARS, GMDH, and GP are smart function fitting methods that assign more weight to the most effective parameters on the output. These models, in addition to predicting the desired phenomena, present a mathematical expression between independent and dependent variables. Results of applied models indicated that all models have suitable performance; however, MARS model with coefficient of determination close to 0.99 in training and testing stages is more accurate compared to others. This model also has a high ability to present the mathematical expression between involved parameters in energy dissipation. To derive the most influential parameters on efficiency of stepped spillways in terms of energy dissipation of flow, a review on the structure of models derived from GP, GMDH, and MARS was carried out. Results indicated that drop number, ratio of critical depth to the height of steps, and Froude number are the most effective parameters on energy dissipation of flow over stepped spillways.
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- ANFIS:
-
Adaptive neuro-fuzzy inference system
- ANN:
-
Artificial neural network
- AVEG:
-
Average
- bi:
-
Bias
- DN:
-
Drop number
- E :
-
Specific energy
- EDR:
-
Energy dissipation ratio
- Fr :
-
Froude number
- g :
-
Gravity acceleration
- GA:
-
Genetic algorithm
- GEP:
-
Gene expression programming
- GMDH:
-
Group method of data handling
- GP:
-
Genetic programming
- h :
-
Height of steps
- H w :
-
Dam height
- l :
-
Length of steps
- LM:
-
Least square
- MARS:
-
Multivariate adaptive regression splines
- Max:
-
Maximum
- Min:
-
Minimum
- MLP:
-
Multilayer perceptron neural networks
- PSO:
-
Partcle swarm optimization
- RBF:
-
Radial basis function
- S :
-
Slope of stepped spillway
- STDEV:
-
Standard deviation
- SVM:
-
Support vector machine
- V :
-
Flow velocity
- wi:
-
Weight
- y :
-
Flow depth
- Y c/h :
-
Critical depth to the height of steps
- C :
-
Error penalty factor
- w :
-
Normal vector
- ε :
-
Loss function
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Parsaie, A., Haghiabi, A.H., Saneie, M. et al. Prediction of Energy Dissipation of Flow Over Stepped Spillways Using Data-Driven Models. Iran J Sci Technol Trans Civ Eng 42, 39–53 (2018). https://doi.org/10.1007/s40996-017-0060-5
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DOI: https://doi.org/10.1007/s40996-017-0060-5