Technical NoteFlow discharge prediction in compound channels using linear genetic programming
Highlights
► This study presents LGP approach to flow discharge estimation for compound channels. ► The published data were compiled for stage–discharge data sets for 394 laboratories, and field of 30 compound channels. ► The proposed GP approach produces satisfactory results compared to existing predictors.
Introduction
Flow discharge determination in rivers is one of the key elements in mathematical modelling in the design of river engineering projects. Rivers in their downstream reaches generally have wide floodplains that are inundated during high floods. In this case, due to the high differences of flow depths and Manning’s roughness coefficients in main channel and floodplains, a large gradient of velocity is generated across the channel. This leads to a strong lateral momentum transfer between subsections. The traditional methods such as Divided Channel Method (DCM) ignore this strong shear stress at interfaces and hence a large error may be occurred in flow discharge computations. In these methods, compound channels have analysed by simply dividing the cross section into three subsections with nearly uniform characteristics and then adding the subsection discharges. To modify these methods, many numerical and experimental studies have been carried out which led to some methods with more accuracy (e.g. Shiono and Knight, 1988, Wormleaton and Merrett, 1990, Wark et al., 1990, Ackers, 1992, Lambert and Myers, 1998, Bousmar and Zech, 1999, Ervine et al., 2000, Atabay and Knight, 2006). Among these different methods, the 1D coherence method (Ackers, 1992) and 2D analytical model (Shiono and Knight, 1988) have promising applications in flumes and natural rivers (Knight et al., 1989, Seckin, 2004); however extending them for all types of compound channels with different geometric and hydraulic conditions is certainly difficult. Furthermore, these methods usually have cumbersome computations or need numerical solutions. To overcome these difficulties, some approaches have been proposed, such as nonlinear regression methods (Ervine et al., 2000, Hosseini, 2004), artificial neural networks (MacLeod, 1997, Liu and James, 2000, Zahiri and Dehghani, 2009, Unal et al., 2010) and genetic algorithm (Sharifi, 2009).
GP is another approach for prediction problems in river engineering, especially for cases that involve complex and highly non-linear relationships between data. Azamathulla et al., 2010, Azamathulla et al., 2011 employed the GP technique to predict the scour depth around abutments and piers. They showed that GP was more accurate than the regression equations. It is well-known that the main advantage of the GP based approaches over regression and other soft computing techniques is their ability to generate simplified prediction equations without assuming a prior form of the existing relationships (Alavi et al., 2011).
In the previous studies, limited data have been used for calibration and verification. In this study, the main attempt is to derive a simple and dimensionless equation for flow discharge prediction in straight laboratory and river compound open channels using a new branch of GP, called linear genetic programming (LGP).
Section snippets
Divided channel method
In Fig. 1, a compound section with three subdivided sections is shown. Total flow discharge is the sum of discharges calculated separately in each subsection using an appropriate conventional friction formula, e.g. Manning equation (Chow, 1959):where Q is total flow discharge in compound channel, A is area, R is hydraulic radius, S0 is bed slope and n is manning roughness coefficient. In this equation, i refers to subsections (e.g. main channel and floodplains) and N
LGP model
In this study, LGP was underutilised to develop a dimensionless equation for the total flow discharge in compound channels with high accuracy. It was assumed, somewhat similar to Ackers (1992) approach, that discharge ratio in compound open channels depends on some dimensionless parameters as follows:where Dr is depth ratio (ratio of water depth in floodplain to that of main channel), COH is coherence parameter and QDCM is flow discharge calculated from Manning equation
Results and discussion
The Eq. (6) has been implemented for testing data. The computation results of DCM and Ervine et al. (2000) approach are presented in Fig. 3, Fig. 4, respectively. From Fig. 3 it is seen that the DCM in all variable ranges (laboratory and field data), over-predicts the discharges with large errors. This is due to ignoring the interaction effect or transfer momentum between main channel and floodplains. By the increase of flow depth and the resulting flow discharge, the errors increase.
Summary and conclusions
A new LGP-based model was developed to predict the values of the relative flow rate using the collected data. Based on the R2, RMSE and AE values, the LGP model appeared to be very precise. The LGP model has produced the best results compared with those of DCM and Ervine et al. (2000). This study reveals that LGP can be used to predict non-dimensional parameter with more accuracy for any condition without limitations.
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