Application of novel data mining algorithms in prediction of discharge and end depth in trapezoidal sections

Highlights

• Discharge and end depth in free overfall flow were estimated by data driven models.

• Hydraulic and geometric parameters were used as inputs.

• Several input combinations were used for modeling of discharge and end depth.

• The DENFIS provided the best estimates.

Abstract

Flow measurement in irrigation and drainage networks and water conveyance channels have particular importance. Direct methods of flow measurement are costly, time-consuming and are generally associated with losses of energy in flow. In this study, estimation of discharge and end depth of free overfall flows in trapezoidal channels section were investigated. For this purpose, data-driven techniques including dynamic evolving neural-fuzzy inference system (DENFIS), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) were developed. 189 laboratory data experiments, six different scenarios based on geometric variables including side slope (m), bed width (B), bed slope (S₀), and hydraulic variables including critical depth (Y_c), critical slope (S_c) and end depth (Y_E) or discharge (Q) were applied. The model’s performance was evaluated thorough several statistical indicators and graphical presentations. The accuracy of all three models were apparent in estimation of the discharge and the end depth for most of the scenarios. The results showed that the DENFIS model for the input combination of all variables (Y_c, Y_E, B, S₀, m, S_c) with the maximum values of R² and Nash-Sutcliffe efficiency coefficient (NSE) that were equal to 0.976 and 0.975, respectively, and the minimum values of RMSE, MAE, PBIAS and RSR, that were equal to 0.0015, 0.0989, −1.5906, and 0.1574, respectively, showed the highest estimation accuracy. Regarding the end depth estimation, DENFIS model for the input combination including the variables Y_c, Q, S_c, m, B with the highest values of R² and NSE equal to 0.993 and 0.992 respectively, and the lowest values of RMSE, MAE, PBIAS and RSR equal to 0.0028, 0.1628, 0.7383 and 0.0883, respectively, had a better performance compared to other MARS and M5Tree. The results of this study suggest DENFIS as a suitable and powerful model for estimation of discharge in irrigation and drainage networks.

Introduction

Measuring and controlling the inflow discharge to fields is one of the important issues in the management and planning of agricultural water resources. Free overfall flow in open channels is used as a method for measuring discharge in irrigation and drainage networks. The method is based on end depth or brink depth measurement (Ramamurthy et al., 2006). The advantage of the mentioned method is that the flow energy dissipation is minimized compared to the other methods used in the discharge measurement structures. Furthermore, discharge measurements using instruments are costly and time-consuming (Badar and Ghare, 2012). Fig. 1 shows the free overfall in channel with the trapezoidal section. With regard to the formation of water surface profiles, the researchers attempt to find the end depth discharge relation (EDR) into trapezoidal and rectangular channels.

Obtaining the EDR in free overfall flow for rectangular channels was widely investigated (Rouse, 1936, Rajaratnam and Muralidhar, 1968, Hager, 1983, Marchi, 1993, Khan and Steffler, 1996, Ferro, 2000, Mohapatra et al., 2001, Ahmad, 2003, Liu et al., 2014). Investigation on free overfall flow in trapezoidal channels is limited while for the most of irrigation and drainage networks, the channel with trapezoidal section is used in practice. The first laboratory study was conducted on free overfall flow in the trapezoidal channel by Diskin (1961). He used momentum presented EDR for subcritical and supercritical flow conditions by assuming hydrostatic pressure distribution in the end section. Several scholars such as Replogle, 1962, Rajaratnam, 1962, Hamid, 1962, and Kar (1962) discussed the finding of Diskin (1961) and improved the obtained results. Rajaratnam and Muralidhar (1970) conducted experiments on various side slopes to achieve the hydraulic flow characteristics and EDR in free overfall flow through trapezoidal channels. Keller and Fong (1989) showed that assuming a pressure distribution of the quadratic parabolic at free overfalls for trapezoidal channels increases accuracy of the relationship for discharge estimation. To this end, they contributed the end depth pressure force in the momentum equation. Gupta et al., 1993, Ahmad, 2001 designed a calibrated curve on zero, negative, and positive slopes of channel bed based on the measured values of end depth and discharge of the trapezoidal channels. Anastasiadou-Partheniou and Hatzigiannakis (1995) obtained EDR for subcritical and supercritical flows in trapezoidal channels. Moreover, Ramamurthy et al. (2004) gauged water surface profiles, the velocity, and pressure distribution in the free overfall flow in trapezoidal channels and then, calculated EDR. Ramamurthy et al. (2006) simulated the free overfall flow in trapezoidal channels using k-ɛ turbulence model on the basis of solving the Reynolds averaged Navier-Stokes equations. Ahmad and Azamathulla (2012), assuming a quadratic parabola for pressure distribution at the brink, provided a theoretical method based on the sharp-crested weir theory for sub-critical flow regimes of trapezoidal free overfall flows to compute the EDR for supercritical flow regimes. Vatankhah (2013) presented a theoretical EDR for free overfall in a horizontal open channel with the generalized trapezoidal section based on sharp crested weir theory with zero crest height and zero brink pressure for a subcritical flow regime. Abrari et al. (2018) assumed the streamline curvature and pressure distributions at the brink, used continuity and energy equations as a new theoretical approach to utilize the free overfall as a flow-gauging toolkit into the generalized trapezoidal channel cross sections.

Recently, the application of soft computing techniques has been utilized by researchers as a powerful tool for modeling complex nonlinear systems and has been widely used to predict various responses in hydraulic, hydrological and agricultural sciences e.g., scour depth (Onen, 2014, Raikar et al., 2016), computation of discharge coefficient of side weir (Bilhan et al., 2011, Ebtehaj et al., 2015), estimation of suspended load in rivers (Lafdani et al., 2013, Kisi and Ozkan, 2017), modelling nutrient requirements (Kovalchuk et al., 2017, Akin et al., 2016) rainfall-runoff modeling (Nourani et al., 2009, He et al., 2014), estimation of flow characteristics in hydraulic structures (Donmez, 2011, Juma et al., 2014, Parsaie et al., 2016).

Regarding the estimation of EDR in free overfall for rectangular and trapezoidal channels, some limited studies based on soft computing methods are available. Raikar et al. (2004) applied ANN to estimate the end depth ratio (EDR) or critical depth for an inverted semicircular channel on the basis of the measured experimental values of Dey (2003). Ozturk (2005) used the multi-layered feed-forward backpropagation algorithm for anticipating discharge for various roughnesses in rectangular channel. Pal and Geol (2006) used SVM for determining the EDR and discharge of a free overfall happening on an inverted smooth semicircular channel and a circular channel. The results showed that SVM can perform better than the empirical equations. In another study, Pal and Goel (2007) examined support vector machine and radial basis function models function to estimate the discharge and end depth in trapezoidal channels with negative, zero or horizontal, and positive bottom slopes. It was found that the SVM and RBF can be used effectively for simulating free overfalls in a trapezoidal shaped channel in comparison to empirical relationships reported by Ahmad (2001). Sharifi et al. (2011) employed genetic programming (GP) for estimating EDR in rectangular, circular, and trapezoidal channels with a flat bed. Results indicated that its general performance was higher than the other suggested empirical relationships. Hong et al. (2011) applied artificial neural network for predicting features of free overfalls. Simulation outputs showed that artificial neural network may accurately determine the effect force and location of free overfalls in the channel down-stream.

The literature review showed that few researches have been done regarding the use of soft computing to predict the free overfalls in open channels (i.e. trapezoidal part). Hence, the aim of this study is estimating end-depth and discharge to calculate discharge into trapezoidal channels using parameters as brink depth, side slope, channel bed slope and width. DENFIS, MARS, and M5 tree were utilized for modeling.