sideweir discharge coefficient evaluation.pdf

International Journal of Agriculture and Crop Sciences. Available online at www.ijagcs.com IJACS/2013/5-23/2804-2811 ISSN 2227-670X 2013 IJACS Journal

Development and evaluating of two-neural network model (MLP

1 and SVM

2) to estimate the Side weir

discharge coefficient

Abbas Parsaie1 , Amir Hamzeh Haqiabi2

1. Ph.D. student of hydro structures, Department of water Engineering, Lorestan University 2. Associate professor of water Engineering Lorestan University ([email protected])

Corresponding author email: [email protected]

ABSTRACT: Prediction and modeling of hydraulic phenomenon is an important part of hydraulicengineering activities. One of the applications of Prediction and modeling is to estimate the dischargecoefficient for hydraulic structures.Side weirs are widely used for flow diversion in irrigation, land drainage, urban sewage systems and alsoin intake structures. There are many ways to calculate flow dischargecoefficient As experimental methods and computational intelligence. Experimental methods have been considered due to error. Therefore using of soft computing methods to estimate the flow rate is inevitable. In this study to estimate the side weir flow coefficient two model of neural network (MLP and SVM) has been developed.Training and simulation process of these models have been conducted in the Matlabsoftware environment. The results show that the MLP and SVM developed models in comparison with other empiricalequations, has accuracy is very favorable.the performance of MLP model is better than SVM model. Keywords: Side weir discharge coefficient,MLP,SVM.

INTRODUCTION

A side weir is an overflow and set into the side of a channel)chow,1959). This structure is used to remove excess flow therefore it used in most water engineering project such as irrigation network, land drainage, urban sewage systems and Sometimes used as an overflow dam(Ghodsian,2004). When the water level reaches above the side weir crest its divert a certain amount of discharge(May et al, 2003).like all typical weir, side weir can be , sharp, broad crested with various geometric and also the flow in the main channel can be sub-critical and supercritical(Subramanyaand Awasthy, 1976). many studies have been done on defining the hydraulic behavior of this type ofweir, which are often experimental method(Borghei and Parvaneh, 2011; Kumar et al, 2011; Kaya,2011). The flow over a side weir is a typical case of spatially varied flow(SVF) with decreasing discharge (AL-TAEE., 2011) .De Marchi with assuming constant energy, obtained equation of the (SVF)and to calculate the outflow discharge form the side, he solved analytically the (SVF) Finally, he proposed anequation for side weir discharge coefficient that today is known as the De Marchi coefficient (Haddadi and Rahimpour, 2012). Sharp crested rectangular side weirs have been studied extensively by many researchers and usually used in water engineering project(Emiroglu et al, 2011).more recently, Laboratory Studies have on various types of this structure and also to improve the performance of these structures have been done. Rahimpour et al(2011)and Haddadi and Rahimpour and et al.(2012) done An experimental and Theoreticalinvestigation on the flow over trapezoidal sharp an broad-crested side weir in rectangular channels under subcritical flow conditions.They shows that discharge coefficient is related to the Froude number at the upstream of the weir, ratiosof weir height to depth of flow, weir length to width of main channel and length of broad-crested weirto width of main channel . Additionally, finally they

1Multilayer Perceptron

2Support vector machine

Intl J Agri Crop Sci. Vol., 5 (23), 2804-2811, 2013

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proposed three equation for side slope(1:1,1:1.5,1:2) to calculate the discharge coefficient of trapezoidal broad-crested side weirs. Emiroglu(2011) Laboratory studied on Discharge coefficient of a semi-elliptical , triangular labyrinth side weir in subcritical flow, they studied on the hydraulic effects of semi-elliptical side weirs to increase their discharge capacity. They shows that semi-elliptical and triangular labyrinth side weir the discharge coefficient, is related to the dimensionless weir length L/B, the dimensionless effective length L/,the dimensionless weir height p/h1, the dimensionless ellipse radius b/a, and upstream Froude number. they founded that the discharge coefficient of semi-elliptical side weirsis higher than that of classical side weirs. And finally they proposed a reliable equation for calculating the dischargecoefficient of semi-elliptical side weirs. In Table (1) Some of the empirical equation that have been proposed for the Sharp crested rectangular side weir Is collected. The study is based on mathematical modeling and artificial intelligencehas also been done. in Artificial Intelligence Studies Instead of a relationship that results from the linear or nonlinear regression, a network has been development.The ANN,ANFIS,GP , In the field of artificial intelligence techniques that have been used to calculate the side weir discharge coefficient (Bilhan et al,2011; Emiroglu,2010) .The based on the reported accuracy of all these methods are much more than empiricalequation. The conclusion that can be derived from a review of research is that study on hydraulic of side weir started with Laboratory investigation and recently the intelligent method have been usedfor prediction of side weir discharge coefficient. In this study, the MLP and SVM models have been developed to predict the of side weir discharge coefficient.

Table1. Some empirical formulas that presented to the calculation of side weir dischargecoefficient Equation Author row

(

)

Nandesamoorthy et al. 1

(

)

Subramanya et al 2

Yu-Tech 3 Ranga Raju et al 4

(

)

Hager 5

Cheong 6

(

)

Singh et al 7

(

)

Jalili et al 8

(

) (

)

Borghei 9

METHODOLOGY

First, using dimensional analysis to extract important dimensionless factors influencing in the side weir discharge coefficient.Then to assessment of the empirical equation,some data that published in Articles in reputable journals was collected in table(2).the number of these data is about 140. the Following The MLP and SVM has been developed. The training and testing process of these model(MLP and SVM) has been done with the same data collected. for developing the MLP and SVM model,

Table2. Range of data collected

F1 p/h1 L/b L/h1 C_d

min 0.09 0.34 0.30 0.35 0.28

max 0.83 0.91 3.00 10.71 1.75

mean 0.41 0.77 1.60 3.99 0.57

stdv 0.20 0.14 1.11 3.10 0.26

Dimensional analysis Referring to Fig. 1 the discharge coefficient (Cd) can be writtenas a function of width of channel (b), flow depth in the main channel (h1), mean velocity of flow at upstream end of side weir (V1),length of side weir (L), acceleration due to gravity (g), slope of mainchannel bed (So), deviation angle of flow ( ), Using the Buckingham theorem, nondimensional equations in functional forms can be obtained as below:


2806

(

)

(

)

El-Khashab also mentioned that the dimensionless length of the side weir (L/b) includes theeffect of the deviation angle on the discharge coefficient. Therefore, the deviation angle is not existed in the side weir discharge coefficient equations in the literature. Thus The discharge coefficient (Cd) depends on the following dimensionless parameters.

(

)

Figure 1. Definition sketch of subcritical flow over a rectangular side weir.

Artificial neural network (ANN) The ANN is a nonlinear mathematical model that is able to simulate arbitrarily complex nonlinear processes that relate the inputs and outputs of any system. In many complex mathematical problems that leads to solve complex nonlinearequations, A Multilayer Perceptron network with definition of Appropriate functions, weights and bias can used. Due to the nature of the problem, different Activity functions in neurons that can be used. An ANN has one or more hidden layers. Fig. 2 demonstrates a three-layer neural network consisting of inputs layer, hidden layer(layers) and outputs layer. As shown in the fig.2 the wi is the weights and bi is the bias for each neuron.Initial assigned weight values are progressivelycorrected during a training process that compares predicted outputs to known outputs. Such networks are often trained using back propagation algorithm. In the current study, the ANN was trained using LevenbergMarquardt technique because this technique is more powerful and faster than the conventional gradient descent technique.


2807

Figure2. A three-layer ANN architecture.

Support vector machine SVMs are set of related supervised learning methods used for classification and regression. In many applications a non-linear classifier provides better accuracy. In SVR, the input x is first mapped onto a m-dimensional feature space using some fixed (nonlinear) mapping, and then a linear model is constructed in this feature space. The naive way of making a non-linear classifier out of a linear classifier is to map our data from the input space X to a feature space F using a non-linear function In the space F the discriminant function is: Using mathematical notation, the linear model (in the feature space) f(x, w) is given by

In the feature space, F this expression takes the form:

( )

There are many kernel functions in SVM, so how to select a good kernel function is also a research issue.However, for general purposes, there are some popular kernelfunctions.

Linear kernel: ( )

Polynomial kernel: ( )

RBF kernel : ( )

Sigmoid kernel: ( )

Here C, and r and d are kernel parameters .It is well known that SVM generalization performance (estimationaccuracy) depends on a good setting of meta-parametersparameters and and the kernel parameters. The choices of and control the prediction (regression) model complexity. The problemof optimal parameter selection is further complicated becausethe SVM model complexity (and hence its generalization performance)depends on all three parameters.Kernel functions are used to change the dimensionality of the inputspace to perform the classification. Evaluation of empirical equation To evaluation of empirical equation that collected in table(1). approximately 140 data has been used that published in journal by researchers.The error indexes calculated and shown in table(3). As shown in Figure(3) and table(2) is shown the Borghei equation has suitable results.


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Figure3. Compression between and empirical equation result and observation data

Table3. The RMSE, MAE,AP and R

2 statistics of the empirical equations.

Development and Validation of MLP model The MLP model that developed to predict the Side weir discharge coefficient included tow layer(fig:2), one layer to hidden layer and also one layer to Output Variable. The MLP model was trained with levenberg_marquardt Algorithm. The 65 percent of data used to training and 35 percent also used to model testing. Characteristics of MLP model such as number of the neurons in each layers, transform functionis presented in Table 4.The inputs

parameter for MLP is the dimensionless parameter that extract in Dimensional Analysis stage is (

) and

out puts is .the result of the MLP model in training and testing process shown in the figures(5,6). To assessment the performance of the MLP model the statistical index such as RSME and has been calculated and the shown in the Table 5. the accuracy of the MLP model is very suitable and in compare with empirical formulas, the MLP model is more accurate.

Table 4.characteristics of MLP model Layer Number of neurons Transform function

hidden layer 4 tansig Outputs Layer 1 tansig

Equation R^2 RSME MAE APE

Nandesamoorthy 0.29 0.315 0.205 32.53

Subramanya 0.34 0.315 0.207 33.88

Yu-Tech 0.277 0.285 0.192 32.23

RangaRaju 0.277 0.336 0.237 41.72

Hager 0.17 0.312 0.19 25.53

Cheong 0.34 0.325 0.194 25.89

Singh 0.12 0.273 0.209 40.86

Jalili 0.337 0.372 0.235 32.41

Borghei 0.834 0.288 0.247 51.79

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 20 40 60 80 100 120 140 160

Dis

char

ge

Co

eff

Data number

Present

studyNandesamoorthy

Subramanya

Yu-Tech

Ranga Raju

Hager

Cheong

Singh

Jalili

Borghei


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Figure4. structure of MLP model

Figure5. Performance of MLP models during the training Stage

Figure6. Performance of MLP models during the Test Stage

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

0 20 40 60 80

Dis

char

ge

Coef

f

Data Namber

Data_Real

MLP_model

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 10 20 30 40

Dis

char

ge

Co

eff

Data Number

Data_Real

MLP_model


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Table5. The RMSEand R2 statistics indexes of the MLP model stage R^2 RSME APE MAE

Train 0.99 0.029 2.26 0.02 Test 0.93 0.05 4.32 0.03

Development and Validation of SVM model To development and validation of SVM model the same that collected in table(2) has been used. 70 percent of these data used for training process and 30 percent used for Validation and testing the SVM model. TheSigmoidfunction had implement for kernel function. the parameter that used in SVM model is (sigma=1),(C=10),epsilon(0.2). The performance of the SVM model during the Training and testing stage plotted in the figure(7,8).As shown in Figure (7,8) is the accuracy of the model is suitable and in compare with empirical equation results are much better.

Figure7. Performance of SVM models during the training Stage

Figure8. Performance of SVM models during the Test Stage

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 20 40 60 80 100

Dis

char

ge C

oef

f

Data number

Real Data

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 10 20 30 40 50

Dis

char

ge C

oef

f

Data number

Real data

SVM model


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Table6. The RMSE, MAE and R

2 statistics indexes of the SVM model

stage R^2 RSME APE MAE

Train 0.92 0.07 3.52 0.05 Test 0.9 0.08 9.64 0.05

CONCLUSION

Side weirs are widely used for flow diversion in irrigation, land drainage, urban sewage systems and alsoin intake structures.There are many ways to calculate flow dischargecoefficient As experimental methods and computational intelligence. The accurate estimates of this parameter helps to better manage water engineering projects.in this paper the accuracy of empirical equation has be evaluated,in the among of empirical equation the

Borghei is suitable( ) and Other formulas may contain significant error. for betterof the estimation of side weir discharge the SVM and MLP model has been development .the dimensionless parameter that extract with dimensional analysis Have been considered as model inputs parameters. The final result shows that the accuracy of the SVMand MLP models in Comparewith the almost empirical equations is more better and in compare with Borghei equation is more accurate. The compare of the accuracy of the MLP and SVM the MLP model is more a curated because in the SVM model some parameters (such as sigma, C) that must be set by human and the control of these parameters is not automatic.

REFERENCES AL-TAEE A.2011. theoretical analysis of flow over the side weir using Runge kutta method. annals of faculty engineering hunedoara

International Journal of Engineering Azamathulla HM, Wu FC.2011. Support vector machine approach for longitudinal dispersion coefficients in natural streams. Appl. Soft Comp.,

11(2), 2902-2905. Bilhan O, Emiroglu ME, Kisi O.2011.Use of artificial neural networks for prediction of discharge coefficient of triangular labyrinth side weir in

curved channels. Advances in Engineering Software ,Vol(42), 208214. Borghei SM, Parvaneh A.2011. Discharge characteristics of a modified oblique side weir in subcritical flow. . Journal of Flow Measurement and

Instrumentation ,vol(22) ,370376. Chow VT. 1959. Open channel hydraulics. McGraw Hill Book Company, New York Emiroglu ME, Agaccioglu H, Kaya N.2011. Discharging capacity of rectangular side weirs in straight open channels.Journal of Flow

Measurement and Instrumentation(22), 319330, Emiroglu ME, Kisi O, Bilhan O.2010. Predicting discharge capacity of triangular labyrinth side weir located on a straight channel by using an

adaptive neuro-fuzzy technique. Journal of Advances in Engineering Software,vol (41),154160. Ghodsian M.2004. Flow over triangular side weir, Journal Scientia Iranica Transaction on Civil Engineering, 11(1), pp 11420. Haddadi H, Rahimpour M.2012. A discharge coefficient for a trapezoidal broad-crested side weir in subcritical flow, Journal of Flow

Measurement and Instrumentation, v(26) , 6367. Kayaa N, Emiroglu ME, Agaccioglu H.2011. Discharge coefficient of a semi-elliptical side weir in subcritical flow. Journal of Flow Measurement

and Instrumentation V (22), 2532. Kumar S, Ahmada Z, Mansoorb T.2011. A new approach to improve the discharging capacity of sharp-crested triangular plan form weirs,

Journal of Flow Measurement and Instrumentation, vol(22) , 175180. May RWP, Bromwich BC, Gasowich Y, Rickard CE.2003. hydraulic design of side weir, Thomas Telford publishing, London Rahimi A.2012.Hydraulic Design of Side Weirs by Alternative Methods. Australian Journal of Basic and Applied Sciences, 6(6): 157-167, Rahimpour M, Keshavarz Z, Ahmadi MM.2011. Flow over trapezoidal side weir. Journal of Flow Measurement and Instrumentation, 22, 507

510. Robinson DI, Mcghee TJ. 1993. Computer modeling of side-flow weirs. J of Irrigation and Drainge Engineering, vol. 119, No. 6. Subramanya K, Awasthy SC. 1972. Spatially varied flow over side weirs. J. Hydr. Eng. ASCE.

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