Evaluation of genetic programming-based models for simulating friction factor in alluvial channels

doi:10.1016/j.jhydrol.2014.06.047

Journal of Hydrology

Volume 517, 19 September 2014, Pages 1154-1161

https://doi.org/10.1016/j.jhydrol.2014.06.047 Get rights and content

Highlights

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We applied GP to simulate friction factor in alluvial channels.
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Data from a laboratory flume were used for simulation.
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GP outperform existence models in simulating friction factor.

Summary

The bed resistance is one of the most complex aspects of water flow studies in natural streams. Most of the existing non-linear formulas for describing alluvial channel flows are based on dimensional analysis and statistical fitting of data to the parameters considered in the functional relationships implicitly, which are partially valid. The present study aims at developing genetic programming (GP) – based formulation of Manning roughness coefficient in alluvial channels. The training and testing data are selected from original experiments, performed in a hydraulic flume using a sand mobile bed. A comparison was also made between GP and traditional nonlinear approaches of resistance modeling. The obtained results revealed the GP capability in modeling resistance coefficient of alluvial channels’ bed.

Introduction

There are multitudes of bed forms for alluvial channels, namely ripples (at low shear stress with progressive developments of dunes), washed out dunes (transition), flat bed, anti-dunes, and standing waves with increasing shear stresses or velocities. The corresponding resistance (which depends on their dimensions as well as flow and sediment characteristics), is significant in some cases. Accurate estimation of this resistance in alluvial channels is important for watershed and flood studies, river engineering and planning issues and designing hydraulic structures. Due to the importance of the bed form resistance in determining the overall resistance of sand-bed flows, the prediction of bed-from geometry as an essential component of flow resistance and water level estimation during flood periods is of crucial importance. Early important works on dune geometry carried out by Yalin, 1964, Raudkivi, 1998, Ranga-Raju and Soni, 1976 and Allen (1978) considering dune height as a function of bed shear stress and other variables according to experimental and field data. van Rijn (1984) expressed shape resistance as equivalent sand diameter and derived an exponential relation based on dune height and flow depth. Bruschin stated Manning coefficient as a function of sediment diameter, hydraulic radius and energy slope (Raudkivi, 1998). Karim and Kennedy (1990) derived friction factor ratio f/f₀ (f₀: grain friction factor and f: total friction factor), as a function of relative dune height. Karim (1999) applied regression and dimensional analysis for computing the Manning coefficient as a function of mean grain size (d₅₀) and f/f₀. The complexity of the underlying physical process can be attributed to several factors, e.g. a large number of interrelated governing variables, three-dimensional (3D) nature of bed-form development, lag in bed-form adjustment in response to variable flow conditions, and practical difficulties in measuring bed-flow dimensions particularly in field conditions. Recognizing that continuing research efforts will be needed for the accurate formulation of this complex process, a new method is proposed in this paper as a modest but incremental step toward achievement of this goal. This study employs heuristic genetic programming (GP) technique for modeling bed resistance.

So far, GP has been applied for rainfall- runoff modeling (e.g. Kisi et al., 2013a, Savic et al., 1999), derivation of unit hydrographs of urban basins (Rabunal et al., 2006), suspended sediment modeling (e.g. Kisi and Shiri, 2012, Kisi et al., 2012a), velocity prediction in compound channels (Harris et al., 2003), modeling vegetation resistance (Rodrigues et al., 2007), determining chezy resistance factor (Giustolisi, 2004), predicting longitudinal dispersion coefficients in streams (Azamathulla and Ghani, 2011), analyzing real time operation of reservoir systems (Fallah-Mehdipour et al., 2012), predicting groundwater level fluctuations (Fallah-Mehdipour et al., 2013, Shiri and Kisi, 2011, Shiri et al., 2013), development of stage-discharge curve (Azamathulla et al., 2011), modeling evaporation rates (Izadifar and Elshorbagy, 2010, Shiri et al., 2012, Shiri et al., 2014a, Shiri et al., 2014b), precipitation forecasting (Kisi and Shiri, 2011), forecasting urban water demand (Nasseri et al., 2011), flood routing (Sivapragasam et al., 2008), lake water level forecasting (Kisi et al., 2012b), forecasting discharge time series (Wang et al., 2009) and modeling flow and water quality variables in watersheds (Kisi et al., 2013a, Kisi et al., 2013b, Preis and Otsfeld, 2008) as well as modeling energy dissipation over spillways (Roushangar et al., 2014a) and modeling total bed material load (Roushangar et al., 2014b). The literature survey by the authors showed that only limited studies (e.g. Azamathulla, 2012, Azamathulla and Jarrett, 2013, Azamathulla et al., 2013, Giustolisi, 2004) deal with modeling friction factor in alluvial channels with unstable bed materials. The present paper aims at GP-based modeling of friction factor in alluvial channel through application of some dominant factors governing the flow on dunes. Consequently, different input configurations of dominant factors were built and applied as GP inputs for simulating the friction factor. Nevertheless, the object function (targets) in this paper were defined as observed manning’s coefficients as well as its modified versions, which makes it possible to compare the models accuracies for modeling friction factor.

Section snippets

Experimental setup

Sediment and flow variables comprising flow depth and velocity, water surface gradient, sediment diameter, distribution and type are the main parameters influencing the bed forms. A 5 m long, 0.15 wide, and 0.25 m tall rectangular pollex glass flume located in the hydraulic laboratory of Caen University was utilized as shown in Fig. 1.

Sediment particles used in the experiments were natural quartz sand with specific gravity of 2.65 and uniform average diameters of 0.15 mm and 0.4 mm. Water flow was

Application and results

In this research, four function sets comprising different combinations of mathematical operators are defined. The objective functions are divided to dimensional Manning roughness coefficient (n) or GP and dimensionless Manning roughness coefficient $n^{'} = \frac{n \sqrt{g}}{{(R)}^{\frac{1}{6}}}$ or $G^{'} P$

F₁:(+, −, *, /) F₂:(+, −, *, /, Power, Sqrt, log, Ln)

F₃:(+, −, *, /, Power, Sqrt, sin, cos) F₄:(+, −, *, /, Power, Sqrt, sin, cos, log, Ln)

The applied Input combinations (terminals) are summarized in Table 2. In the proposed models,

Conclusions

A modeling study was reported here based on Genetic Programming (GP) for the formulation of friction factor of alluvial channels. The original experiment data (356 tests) were used as training (250 patterns) and testing (106 patterns) blocks for development and validation of GP. The optimal model found to comprise three input variables, namely, S_w, Re and $\frac{R}{D_{50}}$ . Also, a comparison between obtained results by GP and existing equations in the literature confirms the capability and workability of

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Evaluation of genetic programming-based models for simulating friction factor in alluvial channels

Highlights

Summary

Introduction

Section snippets

Experimental setup

Application and results

Conclusions

Sediment. Geol.

J. Hydro-Environ. Res.

Comput. Geosci.

Comput. Geosci.

Comput. Geosci.

Expert Syst. Appl.

J. Hydrol.

J. Hydrol.

J. Hydrol.

Comput. Geosci.

J. Hydrol.

Comput. Geosci.

J. Hydrol.

J. Hydrol.

Gene-expression programming to predict friction factor of Southern Italian Rivers

Neural Comput. Appl.

Genetic programming for predicting longitudinal dispersion coefficients in streams

Water Resour. Manage.

Use of gene-expression programming to estimate manning’s roughness coefficient for high gradient streams

Water Resour. Manage,

Gene-expression programming for the development of a stage-discharge curve of the Pahang River

Water Resour. Manage.

An expert system for predicting Manning roughness coefficient in smooth open channels by using GEP

Neural Comput. Appl.

Bed–form development

J. Hydraul. Eng.