# Predictive modeling of discharge in compound open channel by support vector machine technique

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## Abstract

Modeling of river phonemes is one of the main parts in Hydraulic engineering studies. Predicting the discharge in the compound open channel is the main subject of the river engineer researches. In this study the support vector machine (SVM) technique is used to predict the discharge in the compound open channel. The result of the error indexes shows that the best accuracy of the SVM by correlation coefficient 0.99 is related to the SVM model which includes the radial basis function (RBF) as kernel function. During the SVM model process obtained 0.00005 for the gamma coefficient, epsilon is equal to 0.1 and C = 1.

## Keywords

Compound open channel Support vector machine Discharge prediction River hydraulic## Introduction

_{mc}and n

_{fp}sequentially. This difference between the roughness leads to create a momentum transferring and appearance an interaction area between main channel and floodplains (Myers 1987; Ackers 1993; Al-Khatib et al. 2012). Flow structure in compound open channel is fully turbulence and 3D dimensionality especially in flooding condition, so calculating the discharge by classical formulas such as Manning and Chezy makes to appearance the incredible error in river engineering studies (Wormleaton and Hadjipanos 1985; Stephenson and Kolovopoulos 1990).

Several ways as analytical approaches and artificial intelligent (AI) techniques have been proposed to achieve more accuracy in rivers discharge prediction. In this regards the Single-Channel Method, Divided-Channel Method, and Coherence Method can be mentioned as analytical approaches (Yang et al. 2014; Bousmar et al. 2004; Huthoff et al. 2008; Yonesi et al. 2013; Al-Khatib et al. 2012; Mohanty and Khatua 2014; Hosseini 2004; Naot et al. 1993; Al-Khatib et al. 2013; Liao and Knight 2007; Atabay and Knight 2006). Recently by advancing the data mining approaches, some artificial intelligence models such as artificial neural network; Genetic Programing, and M5 tree models was applied to predict the flow discharge in compound open channel. Based on the scientific reports the performances of the Artificial intelligence (AI) models are better than the analytical approaches (Sahu et al. 2011; Seckin 2004; Unal et al. 2010; Zahiri and Azamathulla 2014). Using the AI model AI models together numerical methods in a computer simulation of the hydraulic phonemes leads to increase the accuracy of the numerical modeling (Parsaie and Haghiabi 2015). Sahu et al. (2011) predicted the discharge in compound open channel by using the neural network technique and state that the ratio of the depth of the flow in the main channel to the depth of the flow in the floodplains \( \left( {D_{r} } \right) \), ratio of the area of the main channel to the floodplains \( \left( {A_{r} } \right) \) and ratio of the hydraulic radius of the main channel to the floodplains \( \left( {R_{r} } \right) \) are the most influence parameters for predicting the flow discharge in the compound open channel. Zahiri and Azamathulla (2014) by applying the genetic programing technique on the single-channel method results proposed an equation to predict the discharge in compound open channel. In this paper another types of AI models which is named support vector machine (SVM) is used for predicting the flow discharge in the compound open channel.

## Support vector regression

- (i)
Linear kernel: \( k\left( {x_{i} , x_{j} } \right) = x_{i}^{T} x_{j} \)

- (ii)
Polynomial kernel: \( k\left( {x_{i} , x_{j} } \right) {\kern 1pt} = {\kern 1pt} \left( {\gamma x_{i}^{T} x_{j} + r} \right)^{d} ,\quad \gamma > 0 \)

- (iii)
RBF kernel: \( k\left( {x_{i} , x_{j} } \right) = { \exp } \left( { - \gamma \left\| {x_{i} - x_{j} } \right\|} \right)^{ 2} ,\quad \gamma > 0 \)

- (iv)
Sigmoid kernel: \( k\left( {x_{i} , x_{j} } \right) = { \tanh } \left( {\gamma x_{i}^{T} x_{j} + r} \right), \quad \gamma > 0 \)

Here C, γ and r and d are kernel parameters. It is well known that SVM generalization performance (estimation accuracy) depends on a good setting of meta-parameters parameters *C*, \( \gamma \) and *r* and the kernel parameters. The choices of *C*, \( \gamma \) and *r* control the prediction (regression) model complexity. The problem of optimal parameter selection is further complicated because the SVM model complexity (and hence its generalization performance) depends on all three parameters. Kernel functions are used to change the dimensionality of the input space to perform the classification.

## Analytical approach

*n*

_{ i }is the roughness coefficient (Manning coefficient) of the subsections.

## Model development

*A*

_{ fp }and

*A*

_{ mc }is the area of main channel and floodplains,

*R*

_{ fp }and

*R*

_{ mc }is the hydraulic radius of main channel and floodplains, S is the longitudinal slope of compound open channel, H is the depth of flow in the main channel and h is the depth of the flow in the floodplains. Based on the researches which implement the neural network techniques to predict the flow discharge in the compound open channel, developing the AI models based on the dimensionless parameter leads to prepare an optimal structure of the model. Based on these researches the most popular dimensionless parameters aregiven in the Eq. (10).

*R*

_{ r }is defined as \( \frac{{R_{mc} }}{{R_{fp} }} \),

*D*

_{ r }is defined \( \frac{H - h}{H} \), and

*Q*

_{ m }is the measured discharge. For developing the SVM the

*n*

_{ r },

*A*

_{ r },

*R*

_{ r }, S and

*D*

_{ r }is considered as inputs parameters and

*Q*

_{ m }is considered as outputs parameter.

Range of data collection related to the discharge

| | | S | | | |
---|---|---|---|---|---|---|

Min | 1.000 | 0.047 | 0.020 | 0.000 | 0.041 | 0.005 |

Max | 6.408 | 2.909 | 0.195 | 0.002 | 0.773 | 1.114 |

Avg | 1.306 | 0.651 | 0.066 | 0.001 | 0.303 | 0.144 |

STDEV | 0.999 | 0.424 | 0.038 | 0.001 | 0.167 | 0.218 |

## Results and discussion of SVM

*R*

^{2}) and root mean square (RSME)of error was applied. It should be noted that all the data collection (202 data set) is used for assessing the performance of the DCM method. As shown in the Fig. 2, the results of the DCM method in low values of the discharge especially values which are less than the 0.1 (cms) is more than the measured data and it is related to increase the area of the flow cross section in compare to hydraulic radius. The accuracy of the DCM method in the values between the 0.2 and 1 is suitable. By increasing the value of the discharge [values more than the 1(cms)] due to increase the intensity of the momentum transferring between the main channel and floodplains, usually the accuracy of the other analytical approaches are decreases but as shown in the Fig. 2 the performance of the DCM method is suitable and it is related to the considering the effect of the momentum transferring in the method development. As shown in the Fig. 2, the correlation coefficient of the DCM method is equal to (0.87) and RMSE is (0.05) and in overall the performance of the DCM is suitable.

## Conclusions

Prediction of flow discharge in the natural stream flows is the main parameter in the flood management problems. The compound channel concept is the accurate approach for the simulation of the river problems. Predicting the flow discharge in compound open channels by classical formulas such as Manning and Chezy lead to appearance the incredible error in compare to the measured data, so researcher revised these approaches and proposed more advanced analytical approaches such as Divided Channel method. Although the revised approaches have been increased the accuracy of flow discharge calculation but flood management needs to implement more accurate approaches in the river engineering problems. Recently by advancing the AI models in water engineering problems, the artificial neural network models have been used widely for flow discharge prediction. Based on the results of this study, the maximum accuracy (correlation coefficient) of the analytical approaches is about 0.87 but a new model of the ANN such as support vector machine can easily obtain the accuracy about 0.99. The main points of the AI models developing are preparing a suitable set data collection which has suitable distribution along the range of the data collection. In addition to have a suitable data collection, considering the suitable kernels functions and correct setting the coefficients which uses in the kernel functions is necessary.

## References

- Ackers P (1993) Flow formulae for straight two-stage channels. J Hydraul Res 31(4):509–531. doi: 10.1080/00221689309498874 CrossRefGoogle Scholar
- Al-Khatib IA, Dweik AA, Gogus M (2012) Evaluation of separate channel methods for discharge computation in asymmetric compound channels. Flow Meas Instrum 24:19–25. doi: 10.1016/j.flowmeasinst.2012.02.004 CrossRefGoogle Scholar
- Al-Khatib I, Hassan H, Abaza K (2013) Application and validation of regression analysis in the prediction of discharge in asymmetric compound channels. J Irrig Drain Eng 139(7):542–550. doi: 10.1061/(ASCE)IR.1943-4774.0000579 CrossRefGoogle Scholar
- Atabay S, Knight DW (2006) 1-D modelling of conveyance, boundary shear and sediment transport in overbank flow. J Hydraul Res 44(6):739–754. doi: 10.1080/00221686.2006.9521725 CrossRefGoogle Scholar
- Bousmar D, Wilkin N, Jacquemart J, Zech Y (2004) Overbank flow in symmetrically narrowing floodplains. J Hydraul Eng 130(4):305–312. doi: 10.1061/(ASCE)0733-9429(2004)130:4(305) CrossRefGoogle Scholar
- Greco M, Carravetta A, Morte RD (2004) River flow 2004. In: Balkema AAGoogle Scholar
- Hosseini SM (2004) Equations for discharge calculation in compound channels having homogeneous roughness. Iran J Sci Technol Trans B EngGoogle Scholar
- Huthoff F, Roos P, Augustijn D, Hulscher S (2008) Interacting divided channel method for compound channel flow. J Hydraul Eng 134(8):1158–1165. doi: 10.1061/(ASCE)0733-9429(2008)134:8(1158) CrossRefGoogle Scholar
- Khatua K, Patra K, Mohanty P (2012) Stage-discharge prediction for straight and smooth compound channels with wide floodplains. J Hydraul Eng 138(1):93–99. doi: 10.1061/(ASCE)HY.1943-7900.0000491 CrossRefGoogle Scholar
- Knight D, Shamseldin A (2005) River basin modelling for flood risk mitigation. CRC Press, UKGoogle Scholar
- Knight DW, Demetriou JD, Hamed ME (1984) Stage discharge relationships for compound channels. In: Smith KVH (ed) Channels and channel control structures. Springer, Berlin pp 445–459. doi: 10.1007/978-3-662-11300-4_35
- Liao H, Knight D (2007) Analytic stage-discharge formulas for flow in straight prismatic channels. J Hydraul Eng 133(10):1111–1122. doi: 10.1061/(ASCE)0733-9429(2007)133:10(1111) CrossRefGoogle Scholar
- Mohanty PK, Khatua KK (2014) Estimation of discharge and its distribution in compound channels. J Hydrodyn Ser B 26(1):144–154. doi: 10.1016/S1001-6058(14)60017-2 CrossRefGoogle Scholar
- Myers W (1987) Velocity and discharge in compound channels. J Hydraul Eng 113(6):753–766. doi: 10.1061/(ASCE)0733-9429(1987)113:6(753) CrossRefGoogle Scholar
- Naot D, Nezu I, Nakagawa H (1993) Calculation of compound-open-channel flow. J Hydraul Eng 119(12):1418–1426. doi: 10.1061/(ASCE)0733-9429(1993)119:12(1418) CrossRefGoogle Scholar
- Parsaie A, Haghiabi A (2015) The effect of predicting discharge coefficient by neural network on increasing the numerical modeling accuracy of flow over side weir. Water Resour Manage 29(4):973–985. doi: 10.1007/s11269-014-0827-4 CrossRefGoogle Scholar
- Sahu M, Khatua KK, Mahapatra SS (2011) A neural network approach for prediction of discharge in straight compound open channel flow. Flow Meas Instrum 22(5):438–446. doi: 10.1016/j.flowmeasinst.2011.06.009 CrossRefGoogle Scholar
- Seckin G (2004) A comparison of one-dimensional methods for estimating discharge capacity of straight compound channels. Can J Civ Eng 31(4):619–631. doi: 10.1139/l04-053 CrossRefGoogle Scholar
- Stephenson D, Kolovopoulos P (1990) Effects of momentum transfer in compound channels. J Hydraul Eng 116(12):1512–1522. doi: 10.1061/(ASCE)0733-9429(1990)116:12(1512) CrossRefGoogle Scholar
- Tang X, Knight DW, Samuels PG (1999) Variable parameter Muskingum-Cunge method for flood routing in a compound channel. J Hydraul Res 37(5):591–614. doi: 10.1080/00221689909498519 CrossRefGoogle Scholar
- Te Chow V (2009) Open-channel hydraulics. Blackburn PressGoogle Scholar
- Unal B, Mamak M, Seckin G, Cobaner M (2010) Comparison of an ANN approach with 1-D and 2-D methods for estimating discharge capacity of straight compound channels. Adv Eng Softw 41(2):120–129. doi: 10.1016/j.advengsoft.2009.10.002 CrossRefGoogle Scholar
- Wormleaton P, Hadjipanos P (1985) Flow distribution in compound channels. J Hydraul Eng 111(2):357–361. doi: 10.1061/(ASCE)0733-9429(1985)111:2(357) CrossRefGoogle Scholar
- Yang K, Liu X, Cao S, Huang E (2014) Stage-discharge prediction in compound channels. J Hydraul Eng 140(4):06014001. doi: 10.1061/(ASCE)HY.1943-7900.0000834 CrossRefGoogle Scholar
- Yonesi HA, Omid MH, Ayyoubzadeh SA (2013) The hydraulics of flow in non-prismatic compound channels. J Civil Eng Urban 3(6):342–356Google Scholar
- Zahiri A, Azamathulla HM (2014) Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels. Neural Comput Applic 24(2):413–420. doi: 10.1007/s00521-012-1247-0 CrossRefGoogle Scholar