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Genetic Programming Approach for Estimating Energy Dissipation of Flow over Cascade Spillways

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Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

Abstract

In this study, the hydraulics of cascade spillways were investigated by conducting a series of laboratory experiments; twenty different cascade spillways tested in a horizontal laboratory flume. A wide range of discharge values, three weir slope angles (15, 25 and 45 degrees), and different step numbers ranged from 3 to 50 on ogee surface were considered. Some data-based models were developed to explain the relationships between hydraulic parameters. Multiple regression equations were developed based on dimensional analysis theory to compute energy dissipation over cascade spillways. For testing the robustness of developed data-based models, genetic programming (GP) was used as a new computing technique. A GP approach was developed to relate the input and output (energy dissipation) variables. It was found that formulation based on the GP approach in solving energy dissipation problems over cascade spillways is more successful than the method based on the regression equation.

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Abbreviations

B :

Spillway width

E 1 :

Energy at the downstream of spillway before hydraulic jump

E 0 :

Total energy at the upstream of spillway

ΔE :

Difference between energy at the upstream and at downstream of the spillway (ΔE = E0 − E1)

F r :

Supercritical Froude number = \(V_{1} /\sqrt {gy_{1} }\)

g :

Acceleration due to gravity

h:

Each step height

H w :

Total spillway height from flume bed

l:

Each step length

q :

Discharge per unit width

Q :

Discharge

S :

Spillway slope (V: H)

V a :

Approach velocity = q/y

V 1 :

Velocity at the toe of the spillway

y 0 :

Depth of flow about 0.60 m distance from upstream in spillway above the spillway crest

y 1 :

Depth before hydraulic jump at the spillway toe

y2 :

Depth after hydraulic jump

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Correspondence to Farzin Salmasi.

Appendix: Experimental Results

Appendix: Experimental Results

The number of data points are totally 154. A decision was made to use 110 data points for training and 44 data points for testing the model in its prediction model.

See Table 7.

Table 7 Experimental results of stepped spillway

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Salmasi, F., Sattari, M.T. & Nurcheshmeh, M. Genetic Programming Approach for Estimating Energy Dissipation of Flow over Cascade Spillways. Iran J Sci Technol Trans Civ Eng 45, 443–455 (2021). https://doi.org/10.1007/s40996-020-00541-3

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  • DOI: https://doi.org/10.1007/s40996-020-00541-3

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