Elsevier

Journal of Hydrology

Volumes 460–461, 16 August 2012, Pages 156-159
Journal of Hydrology

Technical Note
Gene expression programming for prediction of scour depth downstream of sills

https://doi.org/10.1016/j.jhydrol.2012.06.034Get rights and content

Summary

Local scour is crucial in the degradation of river bed and the stability of grade control structures, stilling basins, aprons, ski-jump bucket spillways, bed sills, weirs, check dams, etc. This short communication presents gene-expression programming (GEP), which is an extension to genetic programming (GP), as an alternative approach to predict scour depth downstream of sills. Published data were compiled from the literature for the scour depth downstream of sills. The proposed GEP approach gives satisfactory results (R2 = 0.967 and RMSE = 0.088) compared to the existing predictors (Chinnarasri and Kositgittiwong, 2008) with R2 = 0.87 and RMSE = 2.452 for relative scour depth.

Highlights

► This study presents GEP to predict scour depth downstream of sills. ► Published data were compiled from the literature for the scour depth downstream of sills. ► The proposed GEP approach gives satisfactory results.

Introduction

Local scour modelling is an important issue in environmental/water resources engineering in order to prevent degradation of river bed and protect the stability of grade control structures (Laucelli and Giustolisi, 2011). In a river, a sill is the initial foundation or the lower part of structure that has to be constructed on a bed of alluvial material. The river bed in the vicinity of a hydraulic structure is generally protected against current, waves, and eddies (Mason and Arumugam, 1985, Shields et al., 1995, Hoffmans and Verheij, 1997, Rosgen, 2001, Azamathulla, 2006, Guven and Gunal, 2008a, Guven and Gunal, 2008b, Scurlock et al., 2011). Scour occurs both upstream and downstream of the point of impingement. The scouring continues up to the point where the impinging jet energy is insufficient to exert breaking pressure on the rock or where the secondary currents produced are not strong enough to remove the rock blocks (Mason and Arumugam, 1985).

The length of the bed protection depends on the permissible scour depth. Local scour is the erosion of a bed surface and the hydraulic structures due to the impact of flowing water. Grade-control structures are built to prevent excessive channel-bed degradation in alluvial channels. However, local scour downstream of grade-control structures occurs due to erosive action of the overflowing water, and this action may undermine these structures (Bormann and Julien, 1991). Hydraulic grade-control structures have been widely used to increase slope stability and control scour in mountain streams (Chinnarasri and Kositgittiwong, 2008). They are built across the rivers in low-stability areas, or in areas that have to be adjusted from steeper slopes to less severe slopes (Gaudio et al., 2000, Lenzi et al., 2002, Marion et al., 2004).

Most of the previous researchers focused on local scouring at isolated drop structures by free jets through experimental studies (Volkart et al., 1973, Whittaker, 1987). Various investigators have given empirical formulae based on laboratory as well as prototype observations to predict the scour depth downstream of the sills (Azmathullah et al., 2005). The problem of single, isolated drop structures were reported by Lenzi et al. (2002); however much less is known about the case of a staircase-like sequence of grade control structures (Gaudio and Marion, 2003, Lenzi et al., 2002, Lenzi et al., 2003). The principle of grade-control structures is to decrease the bed slope by dividing it into partitions. Initial steep bed slope is scoured greatly; but when there are grade-control structures, longitudinal channel slope is decreased to a lower value called an ultimate slope, representing a dynamic equilibrium between bed scouring and aggradation (Lenzi et al., 2003).

The governing parameters of flow and local scouring downstream of bed sills include critical specific energy (Hs), maximum depth of the scour hole at the equilibrium condition (Ys), initial bed slope (So), equilibrium bed slope (Seq), sill spacing (L), median sediment size (D50), morphological jump a = (S0-Seq)L which is equivalent to head drop (Gaudio et al., 2000) density of water (ρw), submerged density of sediment (ρs), sorting index (SI) and acceleration due to gravity (g) as shown in Fig. 1. The effect of sediment sorting can be described by a reference size, (D50), and a geometric standard deviation (σg) of the particles. The sorting index (SI), is not considered in the present study since equations proposed by Chinnarasri and Kositgittiwong (2008) showed that SI is inversely related with the relative scour depth, with the negative powers. Scour can be expressed asYs=f[Hs,S0,a,L,D50,ρw,ρs,SI,g]

A dimensional analysis of Eq. (1) givesYsHs=f[aHs,D50HsaΔD50,LHs,S0]

where Δ = (ρsρw)/ρw is the relative submerged density of sediment and which is constant for a given bed material sample being used in the experiments and can be eliminated from the analysis. Lenzi et al. (2002) carried out local scouring studies in high gradient streams where the initial bed slopes were 0.0785 m/m, 0.1145 m/m and 0.1480 m/m, respectively. They found that the maximum scour depth on low- and high-gradient streams could be expressed with the non-linear equation as (valid for 0.16  aD95  1.15):YsHs=1.453(aHs)0.863+0.06(aΔD50)1.491

Lenzi et al. (2002) concluded that their formula overestimates compare to the observed scour. (Chinnarasri and Kositgittiwong, 2008) proposed five equations that had high relative error. However the present study considers four independent parameters such as aHs,D50Hs,LHs,S0 with the consideration that these parameters govern the scour depth. Table 1 summarizes the ranges of dimensionless parameters (Chinnarasri and Kositgittiwong, 2008) used in this study. The objective of this study is to predict scour depth using GEP. The performance of the proposed GEP model is compared with that of Chinnarasri and Kositgittiwong (2008).

During the last two decades, researchers have used soft computing techniques such as genetic programming (GP) for solving civil engineering problems (Gandomi and Alavi 2011). The results were demonstrated to be significantly better than those from conventional statistical methods (Giustolisi, 2004, Azmathullah et al., 2005, Guven and Gunal, 2008a, Guven and Gunal, 2008b, Azamathulla et al., 2010a, Azamathulla et al., 2010b). Recently, gene-expression programming (GEP) has attracted attention in the prediction of hydraulic characteristics. However, the use of GEP for hydraulic applications is limited and needs further exploration. This study presents GEP as an alternative tool for estimating scour downstream of sills.

Section snippets

Overview of GEP

GEP, which is an extension of (GP (Koza, 1992), is a search technique that evolves computer programs (e.g., mathematical expressions, decision trees, polynomial constructs, and logical expressions). Computer programs generated by GEP computer programs are encoded in linear chromosomes and are then expressed or translated into expression trees (ETs) Readers can refer to Ferreira (2001) or Teodorescu and Sherwood (2008) for further information about GEP.

GEP is a full-fledged genotype/phenotype

GEP for relative scour depth modelling

In this section, the scour depth downstream of sills is modeled using the GEP approach. Initially, the “training set” is selected from the entire data set, and the rest is used as the “testing set”. Once the training set is selected, one could say that the learning environment of the system is defined. The modeling also includes five major steps to use GEP. The first is to choose the fitness function. For this problem, the fitness, fi, of an individual program, i, is measured by:f=j=1Ci(M-C(i,j

Training and testing results of GEP modeling

The performance of GEP in training and testing sets is evaluated in terms of four common statistical measures such as R2 and RMSE, which are expressed as follows:R2=1-i=1N(oi-ti)2i=1N(oi-o¯i)2RMSE=i=1N(oi-ti)2Nwhere ti denotes the target values of YsHs, while oi and o¯i denotes the observed and averaged observed values of YsHs, respectively, and N is the number of data points. The functional set and operational parameters used in the present GEP modeling are listed in Table 2.

Results and discussion

The results obtained by the GEP model and equation (8) proposed by Chinnarasri and Kositgittiwong (2008) are computed for the collected testing data set (see Fig. 2.). The reason behind selecting Eq. (8) from Chinnarasri and Kositgittiwong (2008) is that it has produced the lowest error compared to the other equations. Lenzi et al., 2002, Lenzi et al., 2004 concluded that their formula for scour depth prediction was not well and greatly over estimated, the reason of which was not clarified. It

Conclusions

A GEP approach is used to derive a new model for the prediction of scour downstream of sills. Based on the results, the proposed equation is found to be useful to estimate scour depth for Mountain Rivers for various bed slopes. The comparative study shows that the GEP expression outperforms the existing models. The expression is found to be particularly suitable for bed slopes where predictions are very close to the measured scour depth. The future studies in the future may involve estimation

Acknowledgements

The writer thankful to the all reviewers and Professor Z. Ahmad, IIT Roorkee, India for their suggestions in preparation of this manuscript and also reviews. The author wish to express his sincere gratitude to Universiti Sains Malaysia for funding a short term grant to conduct this on-going research (304.PREREDAC.6035262). Author also wishes to acknowledge the Professor Chinnarasri and Ms. Kositgittiwong for their data.

References (29)

  • C. Ferreira

    Gene expression programming: a new adaptive algorithm for solving problems

    J. Complex Syst.

    (2001)
  • R. Gaudio et al.

    Time evolution of scouring downstream of bed sills

    J. Hydraul. Res.

    (2003)
  • R. Gaudio et al.

    Morphological effects of bed sills in degrading rivers

    J. Hydraul. Res.

    (2000)
  • O. Giustolisi

    Using genetic programming to determine Chèzy resistance coefficient in corrugated channels

    J. Hydroinformatics

    (2004)
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