Optimizing Chute-Flip Bucket System Based on Meta

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Optimizing Chute-Flip Bucket System Based on Meta-Modelling Approach

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2018-0534.R2

Manuscript Type: Article

Date Submitted by the Author: 27-Jun-2019

Complete List of Authors: Bananmah, Mohammad ; Shiraz University, Department of Civil and Environmental EngineeringNikoo, Mohammad Reza; Shiraz University, Civil and Environmental EngineeringNematollahi, Banafsheh; Shiraz University, Department of Civil and Environmental EngineeringSadegh, Mojtaba ; Boise State University

Keyword: Chute-Flip Bucket system, Genetic Algorithm, Artificial Neural Network, Flow-3D numerical model

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

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Canadian Journal of Civil Engineering

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1 Optimizing Chute-Flip Bucket System Based on Meta-Modelling Approach

2 Mohammad Bananmah1, Mohammad Reza Nikoo2*, Banafsheh Nematollahi3, Mojtaba Sadegh4

3 1 Mohammad Bananmah

4 Research Assistant, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran.

5 Email Address: [email protected]

6

7 2 Mohammad Reza Nikoo (Corresponding Author)

8 Associate Professor, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran.


10 Phone: +98-713-613-3497

11 Fax: +98-713-647-3161

12

13 3 Banafsheh Nematollahi

14 Research Assistant, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran.


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17 4 Mojtaba Sadegh

18 Assistant Professor, Department of Civil Engineering, Boise State University.


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21 Word count: 5634

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28 Abstract: Optimal design of Chute-Flip Bucket (CFB) system depends on various

29 parameters, among which energy dissipation and cavitation prevention are the most

30 important. This study develops a simulation-optimization model based on a calibrated Flow-

31 3D numerical model, Multi-Layer Perceptron Artificial Neural Network (MLP-ANN), and

32 Genetic Algorithm (GA) optimization approach for determining the optimal geometry of the

33 CFB system. To alleviate the computational time burden of the Flow-3D numerical model, a

34 MLP-ANN meta-model is developed based on some limited simulations of Flow-3D. The

35 meta-model framework is then coupled with GA to provide an efficient design framework for

36 the CFB system. The proposed framework is employed to design optimal geometry of the

37 CFB system of the Jareh dam in Ahvaz, Iran. The results show that the obtained optimal

38 design increases the cavitation index up to 30% and energy dissipation up to 32% compared

39 to the old engineering design already in place.

40

41 Key words: artificial neural network, chute-flip bucket system, Flow-3D numerical model,

42 genetic algorithm

43

44 1. Introduction

45 Energy dissipation structures are installed to alleviate scouring and erosion in the downstream

46 of the dams (Shivashankara Rao 1982; Vischer and Hager 1995; Heller et al. 2005). Flip bucket

47 is an effective dissipation structure which is installed at the end of chute spillways to decrease

48 the kinematic energy of spill water. The chute spillway and the flip bucket can be considered a

49 unified energy dissipation structure, so-called Chute-Flip Bucket (CFB) system, due to their

50 interdependent performances. Avoiding cavitation on the chute spillway and maximizing

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51 energy dissipation in the system are the main considerations when optimizing the performance

52 of the CFB system (Vischer and Hager 1995; Heller et al. 2005). Several studies have focused

53 on developing and designing a range of experimentation and simulation models to satisfy the

54 design criteria for dissipation structures and spillways, including: experimental approach

55 (Falvey 1990; Heller et al. 2005; Steiner et al. 2008; Ashiq and Sattar 2010; Pfister and Hager

56 2010a; Pfister and Hager 2010b; Kumar and Sreeja 2012), numerical simulation using Flow-

57 3D numerical model (Savage and Johnson 2001; Hoo et al. 2004; Nohani et al. 2013; Parsaie

58 et al. 2018; Morovati and Eghbalzadeh 2018), and numerical simulation using Smoothed

59 Particle Hydrodynamics (SPH) approach (Ferrari 2010; González-Cao et al. 2018). Despite the

60 progress made, less attention has been paid to optimizing the geometric design of the CFB

61 system based on coupling optimization approaches with numerical simulation models. This

62 highlights the need for an integrated simulation-optimization model to obtain optimal geometry

63 of the CFB.

64 Implementation of an integrated optimal design of the chute spillway and the flip bucket is

65 challenging. In this study, a simulation-optimization model for the CFB system of the Jareh

66 dam in Ahvaz, Iran is proposed based on calibrated Flow-3D numerical model, Multi-Layer

67 Perceptron Artificial Neural Network (MLP-ANN), and GA optimization approach. The main

68 decision variables for this simulation-optimization model are bottom slopes of the chute

69 spillway, curvature radius, and deflection angle of the flip bucket (Pfister et al. 2014).

70 This paper develops the proposed simulation-optimization model in three major steps. First,

71 the flow characteristics through the CFB system are simulated using a calibrated Flow-3D

72 numerical model, which is validated based on experimental data. The calibrated Flow-3D

73 numerical model is executed for different values of curvature radius and deflection angle of the

74 flip bucket as well as various slopes of the chute spillway to obtain a comprehensive scenario

75 database. Second, a meta-model based on MLP-ANN is trained and validated with the chute

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76 spillway slope, curvature radius, and deflection angle of the flip bucket as its inputs, and the

77 cavitation index and energy dissipation derived from the calibrated Flow-3D numerical model

78 as its outputs. Finally, the optimal CFB geometry is delineated by coupling MLP-ANN model

79 and GA optimization approach. To show the efficiency and applicability of the proposed

80 framework, the developed simulation-optimization model is applied to the Jareh dam CFB

81 system, which is located in Khuzestan province, Southern part of Iran. In the following,

82 methodology, case study, results, and summary and conclusion sections of this paper are

83 presented.

84

85 2.Methodology

86 The proposed simulation-optimization framework for the Chute-Flip Bucket (CFB) system

87 comprises three main stages, which are summarized in Fig. 1.

88 In the first stage (steps 1 and 2), essential data including surface roughness, water depth, flow

89 velocity, and pressure, as well as CFB geometric parameters (i.e. curvature radius and

90 deflection angle of the flip bucket, and bottom slopes of the chute spillway) are gathered, which

91 are then used for developing the numerical Flow-3D numerical model. In the second step, the

92 geometric information and hydraulic properties of the flow are utilized to calibrate the Flow-

93 3D numerical model for efficient simulation of the CFB. It should be noted that this model is

94 calibrated based on the data gathered from Khuzestan Water and Power Authority (KWPA).

95 Then, the calibrated Flow-3D numerical model is executed for different geometric scenarios of

96 the CFB.

97 In the next stage (step 3), an MLP-ANN meta-model is trained and validated using the

98 input/output database generated by the calibrated Flow-3D numerical model.

99 Finally, in stage 3 (steps 4 and 5), this meta-model is coupled with the GA optimization

100 approach to obtain the optimal geometry of the CFB system with two objectives: 1. controlling

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101 the cavitation problem, and 2. maximizing the energy dissipation of the system. In the

102 following sections, the main stages of the proposed framework are described in more details.

103

104 2. 1. Numerical simulation with the Flow-3D numerical model

105 Flow-3D is a superlative software for computational fluid dynamics problems with ability to

106 simulate 1-D, 2-D and 3-D fluid dynamics (Hirt and Nichols 1981; Hirt and Sicilian 1985).

107 One of the significant features of this software used in the analysis of the hydraulic structures

108 is its ability to model open-channel flow using Volume Of Fluid (VOF) model (Hirt and

109 Nichols 1981). This numerical model is developed based on the Navier-Stokes equations (Hirt

110 and Nichols 1981; Hirt 1990). In order to calculate the volume ratio of each fluid cell,

111 momentum equations for air and flow are solved by volume-fluid model, simultaneously. In

112 each cell, the summation of the volume ratio for the air and for the water is equal to one. The

113 volume ratio of the fluid q(αq) can be defined as (Hirt and Nichols 1981):

114 The cell is devoid of fluid q. αq=0

115 The cell is full of fluid q. αq=1

116 The cell is filled by fluid q and other fluid (s). 0<αq<1

117 The Flow-3D numerical model can be developed with the assumption that CFB is a rigid body

118 with known geometry. For more details about the Flow-3D software, refer to the Flow-3D user

119 manual (Flow Science Inc. 2011). In this study, a computer model of the CFB system for the

120 Jareh dam is constructed by the Rhinoceros software with scale of 1:1 (Fig. 2). This computer

121 model provides the CFB geometric with the information needed by the Flow-3D numerical

122 model. Calibration of the Flow-3D numerical model and mesh sensitivity analysis is then

123 performed using hydraulic information from the KWPA reports. This provides a suitable mesh

124 size.

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125 In the next step, different scenarios of the geometric properties corresponding to the CFB

126 system were simulated using the Flow-3D numerical model. Estimated values of the cavitation

127 index in specific checkpoints and the energy dissipation of the entire system are calculated for

128 each scenario. Cavitation occurs when the cavitation index is less than or equal to the critical

129 cavitation index. Following the common guidelines for concrete-based hydraulic structures,

130 the critical cavitation index is considered in the range of 0.2 to 0.25. Cavitation index as a

131 hydrodynamic parameter that describes the cavitation process is defined as,

132

0

212

k VP P

V

for: k=1, 2, …, np (1)

133

134 Where,

Pv Vapor pressure (kPa),

P0 Reference pressure (kPa),

V Fluid velocity (m/s),

ρ Fluid density (kg/m3),

k Checkpoint's number,

σk The cavitation index at kth checkpoint,

Np Total number of checkpoints,

135 2. 2. Multi-Layer Perceptron-Artificial Neural Network (MLP-ANN)

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136 Artificial Neural Networks are intelligent models based on the neural structure of the human

137 brain. This intelligent model can be coupled with other numerical and/or optimization models

138 in engineering problems that require high computational efficiency (Schalkoff 1997). In this

139 study, Multi-layer Perceptron-Artificial Neural Network (MLP-ANN) is coupled as a meta-

140 model with GA optimization approach for efficient computational speed. MLP-ANN contains

141 feedforward networks of simple processing units with at least one “hidden” layer, wherein

142 each processing unit is similar to a perceptron with non-linear functionality (Schalkoff 1997).

143 There is neither a specific rule to determine the optimum number of hidden layers and

144 neurons, nor a definite guidance to the effective choice of transfer functions in the MLP-

145 ANN models. Therefore, aforementioned parameters are defined through a trial and error

146 process. In this study, MLP-ANN model is utilized with 3 layers (one hidden) and 7 neurons

147 in the hidden layer. Four decision variables (i.e., the bottom slopes of the chute spillway,

148 curvature radius, and deflection angle of the flip bucket) are inputs to this meta-model, and

149 energy dissipation and the cavitation index are model outputs. In order to train the meta-

150 model, the available dataset (generated by Flow3D scenario simulation) is randomly divided

151 into two groups of training and testing validation categories. It is, however, important to

152 avoid extrapolation in any Neural Network modeling. Hence, it has been checked to ensure

153 the range of validation data is covered by the train data. To delineate the procedure in

154 selecting the training and testing data, upper and lower boundaries of data as well as average

155 and their standard deviations are presented in Table 3. The values of the average and standard

156 deviation for all training and testing data are close to each other

157 Finally, to evaluate performance of the MLP-ANN model, multiple statistical error indices

158 (i.e., Bias, Scatter Index (SI), Root Mean Square Relative Error (RMSRE), Mean Absolute

159 Relative Error (MARE), and Correlation Coefficient (CC)) are calculated for training and

160 validating data. These indices are defined as,

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161

*

1 1

1 1n n

i ii i

Bias w wn n

(2)

2* *

1

1 ( )n

i ii

w W w WnSI

W

(3)

2*

*1

1 100%n

i i

i i

w wRMSREn w

(4)

*

*1

1 100%n

i i

i i

w wMAREn w

(5)

*

1

2 *2

1 1

n

i ii

n n

i ii i

w wCC

w w

(6)

162

163 Where,

w Values of the calculated cavitation and energy dissipation using the Flow-3D

numerical model,

w* Values of the calculated cavitation and energy dissipation from the ANN meta-

model,

W Average of ,w

W * Average of ,*w

n Number of total data points used in the training and validation processes of ANN

164

165 2. 3. Genetic Algorithm (GA) optimization

166 Genetic Algorithm (GA) is an efficient method for solving optimization problems (Khorshidi

167 et al. 2019). Once the fitness functions of the GA approach and optimization constraints are

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168 defined, this algorithm makes an iterative effort to update a population of solutions using

169 selection, cross over, and mutation operators, until convergence to a global optimum is reached

170 (Kumar 2012). In each iteration (generation) of the GA optimization, individuals are randomly

171 selected from the current population with weights according to the fitness function. Superior

172 solutions according to the fitness function and optimization constraints are more likely to be

173 chosen. The mentioned process is repeated until some specific termination criteria are satisfied

174 and the optimized solutions are achieved (Davis 1991).

175 The objective function and constraints of the developed GA-based simulation-optimization

176 model are presented in the following. In the present framework, the decision variables are

177 slopes of the chute spillway (S1 and S2), deflection angle (θ), and curvature radius (R) of the

178 flip bucket. Furthermore, the objective functions are maximizing cavitation index and

179 maximizing energy dissipation, as defined by:

Maximize 1 21

npknorm norm

kf wt wt E

(7)

0 1 2( , , , , , , , )kVL V P P R S S for: k=1, 2, …, np (8)

1 2 1 2( , , , , , , , , , )E e V R S S y y g (9)

180 Subject to:

0.2k for: k=1, 2, …, np (10)

20 40 (11)

and = fixed at specified elevation1y 2y (12)

181 Where,

wt1 Importance weight of cavitation index objective,

wt2 Importance weight of energy dissipation objective,

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σknorm Normalized cavitation index in the kth checkpoint,

ΔEnorm Normalized energy dissipation,

L MLP-ANN meta-model used to predict the cavitation index,

E MLP-ANN meta-model used to estimate energy dissipation,

R Curvature radius of the flip bucket,

Θ Deflection angle of the flip bucket,

S1 The bottom slopes of the first section of the chute spillway,

S2 The bottom slopes of the second section of the chute spillway,

y1 Upstream elevation of the chute spillway,

y2 Downstream elevation of the chute spillway,

G Gravitational acceleration,

µ Fluid viscosity,

182

183 3. Case Study

184 The Jareh dam is located at 49°43' East and 31°26' North on the Zard river, 35 kilometer

185 Northeast of Ramhormoz in Khuzestan province, southern part of Iran (Fig. 3). The main

186 purpose of this earthen dam is supplying agricultural water demand. Total reservoir volume of

187 the Jareh dam in the normal water level is 180 MCM (106 m3), and it's elevation from sea level

188 is 497 meters. CFB of the Jareh dam consists of a chute spillway with 325.65 m horizontal

189 length, which is located in the elevation range of 481.07 meters to 429.4 meters and the flip

190 bucket with a curvature radius of 25 meters and deflection angle of 45.5° at the end of the chute

191 spillway in the elevation of 429.4 meters (KWPA 2009).

192

193 3. 1. Experimental procedure

194 The main governing forces in some hydraulic structures such as spillways are gravity and

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195 inertia forces. To this end, the Froude similarity law can be utilized to determine model scale

196 for such hydraulic structures in the laboratory (Novak and Cabelka 1981). The scale

197 considered for modeling hydraulic structures should consider several guidelines to minimize

198 scale effects. For example, the scaling factor for a model should not be less than a specific

199 value to avoid viscosity effects. Another important limitation is created by surface tension

200 and the corresponding Weber number. In more details, the water elevation in the model

201 should not be less than a specific value, usually determined through experience (about 3 cm)

202 (Kobus 1980). This approximate minimum value is 1.5 cm to 2 cm in some references. There

203 are some other limitations in selecting the similarity law and scale factor that can be studied

204 in source references (Novak and Cabelka 1981). As mentioned earlier, the Froude number

205 similarity was chosen in this study, and after careful consideration of the limiting factors, a

206 scale of 1:50 is chosen to construct the experimental model of the Jareh dam.

207 The experimental model is constructed with transparent Plexiglas with 3 main sections:

208 1. Upstream reservoir: as a sub-section of the lake, dam body, channel connected to the main

209 spillway, and the entrance of the emergency spillway,

210 2. The components of the CFB system including gated spillway, chute and flip bucket,

211 3. Outlet tank including outlet channel and a river section.

212 The details of constructed experimental model of the Jareh dam and its CFB in the laboratory of

213 Khuzestan Water and Power Authority is shown in Figs. 4 and 5.

214

215 3. 2. Measurement point selection

216 Twenty-three points (A to W) are selected along the experimental model of the Jareh dam to

217 calculate the hydraulic parameters, including velocity and water depth, in which 11 points are

218 placed on the CFB system (Fig. 6). In this study, 8 of the 11 points were selected as the

219 checkpoints to calibrate and analyze the mesh grid used in the Flow-3D numerical model (Fig.

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220 7).

221 It is notable to mention that, one of the main reasons for utilizing deflector is avoiding cavitation at

222 the end of the chute using a technique that is so-called as constant cavitation number (Bingnan et al.,

223 1982; Falvey, 1990). With this in mind, the cavitation index increased in the deflector because of

224 surplus of the flow depth and pressure. The possibility of cavitation occurrence in the deflector is very

225 little, and hence, no point is chosen on the deflector as a potential point for cavitation.

226

227 3. 3. Experimental data uncertainties

228 As mentioned, experimental data for this study are collected from the experimental model

229 constructed by Khuzestan Water and Power Authority. In the available reports presented by this

230 organization, some uncertainties corresponding to the experimental data are mentioned, which

231 are summarized as:

232 Error in designing and constructing the experimental model:

233 This error is related to the level evaluation of the different sections corresponding to a dam such

234 as dam spillway, which is reported as ± 0.025 (m), approximately.

235 Error in water level measurement:

236 This error is considered due to measuring instruments and human errors, which is reported as ±

237 0.050 (m), approximately.

238 Error in water velocity measurement:

239 This error is considered approximately about ± 0.048 (m/s) for Pitot tube in high velocity

240 region and about ± 0.35 (m/s) for Current in low velocity region.

241 Error in flow discharge measurement:

242 This error is related to the errors in constructing the model, reading the water level, and model

243 leakage, which is about ± 2.79%.

244 Experimental data uncertainties are inevitable in any experimental study, which should be

245 considered in calibration of the numerical models. Minimizing uncertainties during laboratory

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246 recording, such as error in reading flow characteristics and measurement instruments, is critical

247 for successful design.

248

249 4. Results

250 First step of the proposed methodology involves developing and calibrating the Flow-3D

251 numerical model of the CFB system. The proper mesh grid is acquired and Flow-3D

252 numerical model is calibrated by comparing the hydraulic parameters, including water

253 velocity and flow depth of the experimental and numerical simulations in 8 checkpoints along

254 the CFB system. Figs. 8 and 9 demonstrate this comparison for the values of water depth and

255 flow velocity with different mesh dimensions.

256 Figs. 8 and 9 show that 1-meter network dimension can be considered appropriate, because

257 further refining the mesh dimensions beyond 1-meter considerably increases the

258 computational time with no significant accuracy gain.

259 Furthermore, the MARE statistical error index in numerical model for 1-meter mesh

260 dimension is equivalent to 7 and 3 percent for depth and velocity compared to the

261 experimental data, respectively. Therefore, this mesh dimension is acceptable given the

262 efficient computational speed and appropriate accuracy.

263 Subsequently, the cavitation index for 6 critical checkpoints (Fig. 7) was calculated to check

264 the cavitation phenomenon and evaluate the risks associated with different geometric scenarios

265 of the CFB system (Ball 1976; Falvey 1990). The energy dissipation was also calculated for

266 different geometric scenarios using Bernoulli’s equation.

267 After estimating cavitation index and energy dissipation values, a meta-model based on 3 layers

268 perceptron artificial neural network is trained and validated using several statistical error

269 indices (Eq. 2- Eq. 6). This meta-model is subsequently used for predicting the cavitation index

270 and energy dissipation of the CFB. Table 1 shows the results of different statistical error indices

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271 used in the validation stage of the MLP-ANN meta-model. It should be noted that all indices

272 are dimensionless.

273 As mentioned earlier, the optimal geometry of the CFB system was obtained through a MLP-

274 ANN meta-model coupled with a GA optimization model. This simulation-optimization model

275 optimizes the objective function while satisfying the design constraints presented in section 2

276 (Eq. 7- Eq. 12). Furthermore, this coupling leads to maximizing the cavitation index and energy

277 dissipation for the CFB system by determining the optimal slopes for the chute spillway and

278 optimal curvature radius and deflection angle for the flip bucket (Bananmah 2016). In the

279 developed GA optimization framework, the number of population and generation are set to 40

280 and 100, respectively, based on a trial and error procedure. Furthermore, the optimization

281 function weights are set to 0.7 for cavitation index (wt1) and 0.3 for energy dissipation (wt2). It

282 is notable that the aforementioned weights significantly influenced to the optimal design of the

283 CFB system. The results show that the optimal slopes of the first and second sections of the

284 chute spillway are 3.27% and 23%, respectively. Moreover, the optimal curvature radius and

285 deflection angle of the flip bucket are 25.46 meters and 56.57 degrees, respectively. In addition,

286 after obtaining optimal geometric parameters, the proposed CFB system was simulated by

287 Flow-3D numerical model to check the performance of the optimal CFB system in terms of

288 cavitation and energy dissipation. This procedure shows that the proposed optimization-

289 simulation model increases the cavitation index and energy dissipation up to 30% and 32%,

290 respectively, compared to the actual constructed CFB system of the Jareh dam. Fig. 10 presents

291 comparison results of the cavitation indices of the optimal CFB system proposed in this study

292 with the actual CFB system in 6 critical checkpoints. Performance of the proposed CFB system

293 has improved in all critical checkpoints compared to the actual CFB system.

294 Moreover, in this study, the objective function is optimized using different weighting scenarios

295 (Fig. 11). With this in mind, the utilized weighting scenarios are clarified in more details in

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296 Table 2. In addition, the minimum, average, and maximum values of the cavitation indices at

297 critical checkpoints along the CFB system for different weighting scenarios are shown in Fig.

298 12. This is the result of a sensitivity analysis on different weighting scenarios, and includes

299 comparison of the calculated cavitation indices and energy dissipation through the proposed

300 framework using different weights for each objective function. In other words, different

301 weighting scenarios are utilized in the proposed model to investigate the impact of each

302 weighting scenarios on the optimal decision variables and obtained objective functions.

303 Finally, the geometric parameters corresponding to the CFB system is stated in Table 2 for

304 different weights obtained from sensitivity analysis (Table 2).

305

306 4. Summary and Conclusion

307 In this study, a simulation-optimization model based on a calibrated Flow-3D numerical

308 model, Multi-Layer Perceptron Artificial Neural Network (MLP-ANN), and GA optimization

309 approach is proposed to determine the optimal geometry of the Chute-Flip Bucket (CFB)

310 system of the Jareh dam. Given the acceptable performance of the proposed methodology in

311 simulating the flow characteristics of the CFB system, it can be concluded that the

312 simulation-optimization model proposed in this study is an acceptable alternative for

313 experimental method with suitable accuracy and computational speed. Furthermore, the

314 results show that using a MLP-ANN meta-model is appropriate for predicting cavitation

315 index and energy dissipation in the CFB systems. This robust framework leads to increasing

316 cavitation index up to 30% and energy dissipation up to 32%, compared to the actual

317 constructed system already in place. The proposed framework tackles computational issues

318 by training a meta-model that can closely emulate the response of the CFB system as well as

319 the Flow-3D numerical model. Although the computational burden is decreased using the

320 proposed framework containing 4 state variables, the computational speed for a larger set of

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321 decision variables is still challenging. The computational burden for modeling the CFB

322 system due to a wide variety of decision variables can be addressed in the future studies to

323 find more efficient solutions. Furthermore, this research is underway to implement the

324 developed simulation-optimization solution considering flood uncertainty using Fuzzy Set

325 theory. Moreover, the proposed framework also can be applied to other dissipation structures.

326

327 Conflict of Interest: The authors declare no conflict of interest.

328

329 References

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381 83-90

382 Parsaie, A., Moradinejad, A., and Haghiabi, A.H. 2018. Numerical modeling of flow pattern

383 in spillway approach channel. Jordan Journal of Civil Engineering, 12(1).

384 Pfister, M., and Hager, W.H. 2010a. Chute aerators. II: Hydraulic design. Journal of Hydraulic

385 Engineering, 136(6): 360-367.

386 Pfister, M., and Hager, W.H. 2010b. Chute aerators. I: Air transport characteristics. Journal of

387 Hydraulic Engineering, 136(6): 352-359.

388 Pfister, M., Hager, W.H., and Boes, R.M. 2014. Trajectories and air flow features of ski jump-

389 generated jets. Journal of Hydraulic Research, 52(3): 336-346.

390 Savage, B.M., and Johnson, M.C. 2001. Flow over ogee spillway: Physical and numerical

391 model case study. Journal of Hydraulic Engineering, 127(8): 640-649.

392 Schalkoff, R.J. 1997. Artificial neural networks. McGraw-Hill Higher Education.

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393 Shivashankara Rao, K.N. 1982. Design of energy dissipators for large capacity spillways.

394 In Proc., Brazilian Committee on Large Dams, pp. 311-328.

395 Steiner, R., Heller, V., Hager, W.H., and Minor, H.E. 2008. Deflector ski jump

396 hydraulics. Journal of Hydraulic Engineering, 134(5): 562-571.

397 Vischer, D.L., and Hager, W.H. 1995. Energy dissipators, hydraulic structures design

398 manual. IAHR, Balkema, Rotterdam, Netherlands.

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414 Figure Captions:

415 Fig. 1. Flowchart of the proposed simulation-optimization framework for optimal design of the CFB

416 Fig. 2. Geometric model of the Jareh dam constructed by Rhinoceros software with a scale of 1:1

417 Fig. 3. The plan view of the Jareh dam (Google earth 7.3.2.5776 2019)

418 Fig. 4. The experimental model of the CFB system of the Jareh dam (KWPA 2009)

419 Fig. 5. The experimental model of the Jareh dam in details (KWPA 2009)

420 Fig. 6. Measurement points on the experimental model of the Jareh dam (KWPA 2009)

421 Fig. 7. Selected critical checkpoints from cavitation point of view and measurement checkpoints for calibration

422 of the Flow-3D model on the CFB system

423 Fig. 8. Comparison of the calculated velocity by Flow-3D numerical model and the experimental data for different

424 mesh dimensions

425 Fig. 9. Comparison of the calculated water depth by Flow-3D numerical model and the experimental data for

426 different mesh dimensions

427 Fig. 10. Comparison of the cavitation indices of the proposed model and the actual model of the Jareh dam

428 Fig. 11. Sensitivity analysis for the cavitation index and energy dissipation of different weighting scenarios

429 Fig. 12. Sensitivity analysis for cavitation index of different weighting scenarios

430

431

432

433

434

435

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437

438

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439 Symbols:

440 CFB Chute-Flip Bucket

441 GA Genetic Algorithm

442 MLP-ANN Multi-Layer Perceptron Artificial Neural Network

443 SPH Smoothed Particle Hydrodynamics

444 VOF Volume Of Fluid

445 αq the volume ratio of the fluid q

446 Pv vapor pressure (kPa)

447 P0 reference pressure (kPa)

448 V fluid velocity (m/s)

449 ρ fluid density (kg/m3)

450 k checkpoint's number

451 σk the cavitation index at kth checkpoint

452 np total number of checkpoints

453 SI Scatter Index

454 RMSRE Root Mean Square Relative Error

455 MARE Mean Absolute Relative Error

456 CC Correlation Coefficient

457 w values of the calculated cavitation and energy dissipation using the

458 Flow-3D numerical model

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459 w* values of the calculated cavitation and energy dissipation from the

460 ANN meta-model

461 W average of w

462 W * average of *w

463 n number of total data points used in the training and validation

464 processes of ANN

465 S1 the bottom slopes of the first section of the chute spillway

466 S2 the bottom slopes of the second section of the chute spillway

467 θ deflection angle of the flip bucket

468 R curvature radius of the flip bucket

469 wt1 importance weight of cavitation index objective

470 wt2 importance weight of energy dissipation objective

471 σknorm normalized cavitation index in kth checkpoint

472 ΔEnorm normalized energy dissipation

473 L MLP-ANN meta-model used to predict the cavitation index

474 e MLP-ANN meta-model used to estimate energy dissipation

475 µ fluid viscosity

476 y1 upstream elevation of the chute spillway

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477 y2 downstream elevation of the chute spillway

478 h flow depth

479 g gravitational acceleration.

480

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499 Tables:

500

501 Table 1. Statistical error indices based on the results of the MLP-ANN meta-model

Statistical error index Bias SI RMSRE MARE CCTrain -0.0082 0.0793 8.0832 6.4968 0.9971Dissipation of

energy (%) Test -0.7034 0.0441 8.8375 6.9182 0.9961Train 0.0004 0.0603 8.1404 5.0833 0.9985Cavitation

index Test -0.0002 0.0597 7.9973 5.1459 0.9983502

503 Table 2. Sensitivity analysis results for different weight scenarios

Decision variablesWeight scenario's number

1wt 2wtS1 S2 R θ

1 0.1 0.9 7 23 25.72 56.572 0.3 0.7 6.99 23 25.72 56.573 0.5 0.5 4.83 23 25.51 56.574 0.7 0.3 3.27 23 25.46 56.575 0.9 0.1 3.01 23.01 25.45 56.57

504

505 Table 3. The values of average and standard deviation of training and testing procedure

Variables

Proc

edur

e

S1 S2 R θ σ ΔE

Data ranges [3* - 7**] [20 - 50] [20 - 35] [20 - 40] [5.44 - 4.67] [22 - 43]

Average 5 35 28 30 4.87 36

Tra

in

Standard deviation 1.63 10 5.61 7.91 0.25 10.25

Data ranges [3 - 7] [20 - 50] [20 - 35] [25 - 35] [5.55 – 4.62] [28 – 41]

Average 5 35 27.5 30 4.86 37.65Tes

t

Standard deviation 1.63 10 5.59 6.83 0.23 8.54

506 * Lower bound of data507 ** Upper bound of data508

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1

Start

Geometry parameters of the Chute-Flip Bucket (CFB) system

including slopes of the chute spillway as well as deflection angle

and curvature radius of the flip bucket

Gathering hydraulic parameters of the Chute-Flip

Bucket (CFB) system including water depth, velocity

and pressure

Creating the main model of the CFB using Rhinoceros as an input for the Flow-3D model

Mesh sensitivity analysis to reach best mesh dimension Decreasing

the mesh

dimension

Are the results

suitable compared to

experimental data?

Flow-3D numerical model is calibrated and ready to use

No

Yes

No

Yes

Determining the requirement time to reach steady state condition Mesh assignment and imposing boundary conditions

Is the flow steady?

Running the calibrated Flow-3D model for various scenarios with different decision variables to obtain the

input/output database for training and validating MLP-ANN meta-model

Training and validating the MLP-ANN meta-model to predict the flow characteristics

Calculating the cavitation index and energy dissipation for different scenarios

Determining the objective function and constraints with respect to design criteria of the CFB

Coupling developed GA optimization model with validated MLP-ANN meta-model

Choosing the best geometry of the CFB using developed simulation-optimization model

End

Step 1: Collecting data

Step 2: Numerical simulation using calibrated Flow-3D numerical

model

Step 3: Developing MLP-ANN meta-Model based on input/output results of the calibrated Flow-3D numerical

model for different scenarios

Step 4: Developing simulation-optimization model by coupling MLP-ANN meta-model to Genetic Algorithm

(GA) optimization

Step 5: Determining the optimal dimensions of the CFB

Increasing the simulation time

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Fig. 2. Geometric model of the Jareh dam constructed by Rhinoceros software with a scale of 1:1

209x115mm (300 x 300 DPI)

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Fig. 3. The plan view of the Jareh dam (Google earth 7.3.2.5776 2019)

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Fig. 4. The experimental model of the CFB system of the Jareh dam (KWPA 2009)

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Fig. 5. The experimental model of the Jareh dam in details (KWPA 2009)

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Fig. 6. Measurement points on the experimental model of the Jareh dam (KWPA 2009)

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Fig. 7. Selected critical checkpoints from cavitation point of view and measurement checkpoints for calibration of the Flow-3D model on the CFB system

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Fig. 8. Comparison of the calculated velocity by Flow-3D numerical model and the experimental data for different mesh dimensions

210x159mm (300 x 300 DPI)

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Fig. 9. Comparison of the calculated water depth by Flow-3D numerical model and the experimental data for different mesh dimensions

210x159mm (300 x 300 DPI)

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Fig. 10. Comparison of the cavitation indices of the proposed model and the actual model of the Jareh dam

217x159mm (300 x 300 DPI)

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Fig. 11. Sensitivity analysis for the cavitation index and energy dissipation of different weighting scenarios

217x159mm (300 x 300 DPI)

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Fig. 12. Sensitivity analysis for cavitation index of different weighting scenarios

217x159mm (300 x 300 DPI)

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Optimizing Chute-Flip Bucket System Based on Meta