COMPARISON OF TWO DATA-DRIVEN ...

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E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the

COMPARISON OF TWO DATA-DRIVEN APPROACHES IN ESTIMATION OF SEDIMENT TRANSPORT IN SEWER PIPE (1)

HOSSEIN BONAKDARI , ISA EBTEHAJ (1)

(2)

Associate Professor, Department of Civil Engineering, Razi University, Kermanshah, Iran, e-mail: [email protected] (2)

Ph.D. Candidate, Department of Civil Engineering, Razi University, Kermanshah, Iran, e-mail: [email protected]

ABSTRACT Correct prediction of sediment transport to prevent of deposition in sewer pipes is very important for designing of sewer network. The application of two different data-driven approaches, gene expression programming (GEP), which is an extension of genetic programming (GP) and group method of data handling (GMDH) for bed load sediment transport estimation, is compared in this paper. Also GEP and GMDH were compared with the other existing sediment transport equations, which were obtained using nonlinear regression analysis. Using non-dimensional parameters affecting sediment transport at sewer pipe, different models to determine minimum velocity have been provided. The nondeposition sediment transport data for bed load sediment transport from two different references are used. The root mean square error (RMSE), mean average percentage error (MAPE) and determine of coefficient (R2) are used for evaluating of the accuracy of the models. As the comparisons demonstrated, the GEP (RMSE = 0.14, MAPE = 2.82 R2 = 0.99) and GMDH (RMSE = 0.35, MAPE = 5.1, R2 = 0.95) models are more accurate than existing equations and could be successfully employed in forecasting minimum velocity. However, GEP is superior to GMDH in giving explicit expressions for the problem. Keywords: bed load, Gene Expression Programming (GEP), Group Method of Data Handling (GMDH), sediment, sewer 1.

INTRODUCTION

One extant problem in sewer pipe is the deposition of sediment at different sections. In sewer systems, the occurrence of sedimentation of suspended solids is because of the reduction of flow velocity at different periods especially during wet weather flow (WWF). The presence of sediments can alter the hydraulic capacity of the pipe in two ways: 1- reducing the cross section of the flow due to existence of sediments on the bed of the pipe; 2- increasing the hydraulic roughness experience by the flow (increased flow resistance) due to sediments. In traditional method, for estimations in preventing sedimentation at different flow sections, two simple criteria, based on the minimum velocity or minimum shear stress at a specified depth of flow or period, have been defined. Different shear stress and velocity values have been presented in Vongvisessomjai et al. (2010) for different areas and different flow conditions. Taking into account the fact that these fixed values do not consider the channel and sediment specifications, they do not present similar results under different flow conditions. This leads to underdesign and overdesign (Ebtehaj et al., 2014; Bonakdari and Ebtehaj, 2014). Therefore, to design the proper velocity, characteristics of sediment and flow should be considered in order to allow the designer to obtain the minimum velocity to economical design without sedimentation. Several researchers have studied the parameters influencing the prediction of minimum velocity and presented different equations to determine it (Mayerle et al., 1991; Nalluri and Ab Ghani, 1996; Ota and Nalluri, 2003; Vongvisessomjai et al., 2010; Ebtehaj et al., 2014). May et al. (1996) presented their semi experimental equation using different data sets as following:

C V  3.03  10 2 (D 2 /A)d/D 

0.6

Vt  0.125 g(s  1)d y/d 

0.47

V /(g(s  1)D) 1  (V /V) 2

1.5

4

t

[1] [2]

Where CV is the volumetric sediment concentration, A is the cross-sectional area of the flow, D is the pipe diameter, V is the flow velocity, d is the median diameter of particles, y is the flow depth, s is the specific gravity of sediment (ρs/ρ) and Vt is the velocity required for incipient motion of the sediment (Equation 2). Nalluri and Ota (2000) presented a model for transporting sediment at limit of deposition through the use of the physical concept of transportation. Considering the fact sediment transport equations at limit of deposition does not lead to economical results in large-diameter channels, Ota and Nalluri (2003) used a similar method but this time, with a model for sediment transport in large channels. Banasiak (2008) conducted a number of experiments on the movement of noncohesive and semi-cohesive sediment and examined the behavior of sediment deposited in the channel besides its effect on the pipe’s hydraulic performance. He showed that a transport regime occurs for Froude numbers higher than 0.5, accompanied by a wash-out bed form. Almedeij and Almohsen (2010) offered some remarks on Camp’s criterion and 1

E-proceedings of the 36th IAHR World Congress, 28 June – 3 July, 2015, The Hague, the Netherlands

proposed a lower limit of flow strength above which the method may warrant developing of a more efficient storm sewer system. Azamathulla et al. (2012) presented their equation as follows, to modify Ab Ghani’s (1993) equation:

Fr  V/ g(s  1)d  0.22C V

λ s  0.851λ c

0.86

CV

0.04

D gr

0.16

D gr

0.14

(d/R) 0.29 λ s

0.03

0.51

[3] [4]

Where λc is the clear water friction factor of the channel. Bong et al. (2013) confirmed the existing equations for incipient motion for a rigid rectangular channel, proposing a new equation by incorporating the factor of sediment deposit thickness. Ebtehaj et al. (2014) using wide range of data from three different reference modified Vongvisessomjai et al.’s (2010) equation as following:

Fr  V/ g(s  1)d  4.49C V

0.21

(d/R) 0.54

[5]

Because of the complex sediment transport mechanism in various geometrical and hydraulical conditions, soft computing methods have been widely applied for sediment transport prediction. Numerous research works have also been conducted in the field of sediment deposition as one of the crucial topics of water engineering through the soft computing such as genetic programming, artificial neural networks, evolutionary algorithms, adaptive neuro fuzzy inference system (Aytek and Kisi, 2008; Ebtehaj and Bonakdari, 2013, 2014, 2015; Azamathulla et al., 2012). One of the major problem of these methods are not providing a certain equation to the target parameter estimation. Therefore in recent years genesis prediction methods that provide a parametric relationship such as GMDH and GEP, has been considered by many researchers. (Aminifarad et al., 2008; Kalantary et al., 2009; Khan et al., 2012; Chang et al., 2012; Azamathulla et al. 2012; Najafzadeh et al., 2013; Abdolrahimi et al., 2014). The main aim of this study is to develop two explicit formulations based on GEP and GMDH for accurately estimation of minimum velocity at sewer pipe. The parameters affecting the minimum velocity prediction are first determined by examining the influential factors in sediment transport. Thereafter, different models will be presented to examine their respective effect on predicting minimum velocity. The accuracy of GEP and GMDH are compared with existing sediment transport equation. 2.

GENE EXPRESSION PROGRAMMING

Gene expression programming is a developed form of genetic programming (Koza, 1992). Gene expression programming belongs to evolutionary algorithms family and is closely related to genetic algorithm and genetic programming. It has inherited linear chromosomes with fixed lengths from genetic algorithm and it has inherited tree analysis with varied lengths and shapes from genetic programming (Ferreira, 2001) Gene expression programming presents computer programs such as mathematical models, decision trees, multi- sentence structures and logarithmic expressions or different types of models. These models have complex tree structure and training and conforming them according to their sizes, shapes and their combination is very much like that of a living thing while as living organisms, gene expression programming computer programs are also coded in simple linear chromosomes with the same length. Therefore, gene expression programming is a genotype-phenotype system which utilizes a simple genome to preserve and transfer genetic information and is a complex phenotype for discovering the environment and adapting to it. In comparison to GP in which phenotype and genotype are combined in a simple replicator system, GEP is an evolved genotype-phenotype system in which genotype is usually completely separated from phenotype. Therefore, the evolved genotype/phenotype system in GEP causes superiority with a factor as large as 100 to 60000 times more than the GP system (Ferreira, 2001). The gene expression programming firstly includes selecting the essential function for creating a model and then the terminal set is selected. In the following stage the present set of data are called upon to estimate the intended parameters and compare them with the real value. Then the chromosomes are produced in order to randomly present the initial population. In the following stage the program is run for the produced population through using the present chromosomes and the suitability of the target function is studied. In case we reach the finishing point of the program we will end it, otherwise the target function will be evaluated again using modified genetic operators and the new population. This process will continue to the point where the conditions for stopping the program are provided. Figure 1 shows the schematics for GEP modeling process. The detailed theoretical information about GEP can be found in the Ferreira (2001).

3.

Group Method Of Data Handling (GMDH)

GMDH algorithm was first used by Ivakhnenko (1971) in order to model complex systems, which included a set of data with a number of inputs and one output. The main purpose of the GMDH network is actually the constructing a function in a feed-forward network on the basis of second degree transfer function. The number of layers and neurons within the hidden layers, the effective input variables and the optimal structure of the model are automatically determined in this algorithm. The mapping between the input and output variables that is done through GMDH neural network is a nonlinear function called Volterra series, known as equation (6). Analyzing Volterra series into a two-variable seconddegree polynomial is done using Equation (7): 2

E-proceedings of the 36th IAHR World Congress 28 June – 3 July, 2015, The Hague, the Netherlands

 y  a0 

m

 i 1

a ixi 

m

m

i 1

j1



a ij x i x j 

m

m

i 1

j1 k 1

m

 x a

j ijk

G(x i , x j )  a 0  a 1 x i  a 2 x j  a 3 x i2  a 1 x 2j  a 5 x i x j

x i x j x k  ...

[6] [7]

The aim of the GMDH algorithm is to find the αi unknown coefficients in Volterra series. And the αi coefficients are solved with regression methods for each pair of xi and xj input variables (Iba and Sato, 1995). On this basis, taking into consideration the principle of least squares error (Nariman-Zadeh et al., 2005) as follows: M 1 y i  G i O2 i 1 M y i  f(x i1 , x i2, , x i3 ,..., x im ) i  1,2,3,...,m

E



[8] [9]

Since the search area was not differentiable, GA was used in the neural network training for optimizing the weights or the coefficients in this study. The GA is better capable of optimizing weights in comparison to the classical gradient methods (Nariman-Zadeh and Jamali, 2007). 4.

Data Used

For this research project, laboratory outcomes of Vongvisessomjai et al. (2010) and Ota and Nalluri (1999) were utilized. For the purpose of their tests at limit of deposition, Ota et al. (1999) used 6 different dimensions of d (ranging from 0.71 mm to 5.61 mm). They conducted 24 tests in total. Moreover, to test the impact of granulation on sediment transport, they conducted 20 further experiments using 5 different ranges of sediments with an average diameter of d = 2 mm. The range of the data applied in the experiments was as follows: 0.39