Reliable method of determining stable threshold channel shape using experimental and gene expression programming techniques

The geometric dimensions and bank profile shape of channels with boundaries containing particles on the verge of motion (threshold channels) are significant factors in channel design. In this study, extensive experimental work was done at different flow velocities to propose a reliable method capable of estimating stable channel bank profile. The proposed method is based on gene expression programming (GEP). Laboratorial datasets obtained from Mikhailova et al. (Hydro Tech Constr 14:714–722, 1980), Ikeda (J Hydraul Div ASCE 107:389–406 1981), Diplas (J Hydraul Eng ASCE 116:707–728, 1990) and Hassanzadeh et al. (J Civil Environ Eng 43(4):59–68, 2014) were used to train, test, validate and examine the GEP model in various geometric and hydraulic conditions. The obtained results demonstrate that the proposed model can estimate bank profile characteristics with great accuracy (determination coefficient of 0.973 and mean absolute relative error of 0.147). Moreover, for practical calculations of channel dimensions, the model provides a specific mathematical relationship to solve problems with different discharge rates (Q) and particles with various median grain sizes (D50). The proposed model’s performance is compared with 8 relationships suggested previously by researchers (based on empirical and theoretical analyses) and a relationship obtained using a nonlinear regression model with different experimental data. The polynomial VDM and two exponential functions, i.e. IKM and DIM, are introduced as the superior existing models. According to the present study results, the proposed GEP model can predict the bank profile shape trend well and similar to the experimental datasets. Sensitivity analysis was also applied to assess the impact of each input variable (x, Q and D50) on the presented relationship. According to the current study, the GEP model provides a suitable equation for predicting the bank profile shape of stable channels.

[1]  Mahmut Firat,et al.  Estimating discharge coefficient of semi-elliptical side weir using ANFIS , 2012 .

[2]  A. Tahershamsi,et al.  An evaluation model of artificial neural network to predict stable width in gravel bed rivers , 2012, International Journal of Environmental Science and Technology.

[3]  J Stebbings,et al.  THE SHAPES OF SELF-FORMED MODEL ALLUVIAL CHANNELS. , 1963 .

[4]  Gregorio G. Vigilar,et al.  Stable Channels with Mobile Bed: Formulation and Numerical Solution , 1997 .

[5]  O. B. Shevchenko,et al.  Laboratory investigation of the formation of stable canal channels , 1980 .

[6]  Amir Hossein Gandomi,et al.  A new predictive model for compressive strength of HPC using gene expression programming , 2012, Adv. Eng. Softw..

[7]  Hassanzadeh Yousef,et al.  VALIDATION OF RIVER BANK PROFILES IN SAND-BED RIVERS , 2014 .

[8]  Robert E. Glover,et al.  Stable channel profiles , 1951 .

[9]  Mustafa Gunal,et al.  Genetic Programming Approach for Prediction of Local Scour Downstream of Hydraulic Structures , 2008 .

[10]  Hossein Bonakdari,et al.  Developing an expert group method of data handling system for predicting the geometry of a stable channel with a gravel bed , 2017 .

[11]  Özgür Kisi,et al.  River suspended sediment estimation by climatic variables implication: Comparative study among soft computing techniques , 2012, Comput. Geosci..

[12]  Amir Hossein Zaji,et al.  Improving the performance of multi-layer perceptron and radial basis function models with a decision tree model to predict flow variables in a sharp 90° bend , 2016, Appl. Soft Comput..

[13]  Hossien Riahi-Madvar,et al.  Developing an expert system for predicting alluvial channel geometry using ANN , 2011, Expert Syst. Appl..

[14]  Farhad Gharagheizi,et al.  Gene expression programming strategy for estimation of flash point temperature of non-electrolyte organic compounds , 2012 .

[15]  Amir Hossein Zaji,et al.  Gene expression programming to predict the discharge coefficient in rectangular side weirs , 2015, Appl. Soft Comput..

[16]  Asaad Y. Shamseldin,et al.  Statistical downscaling of watershed precipitation using Gene Expression Programming (GEP) , 2011, Environ. Model. Softw..

[17]  Lyman S. Willardson,et al.  Parabolic Canal Design and Analysis , 1984 .

[18]  Hossein Bonakdari,et al.  Comparative analysis of GMDH neural network based on genetic algorithm and particle swarm optimization in stable channel design , 2017, Appl. Math. Comput..

[19]  Ehsan Khadangi,et al.  Application of artificial neural networks in establishing regime channel relationships , 2009, 2009 2nd International Conference on Computer, Control and Communication.

[20]  Amir Hossein Zaji,et al.  New radial basis function network method based on decision trees to predict flow variables in a curved channel , 2017, Neural Computing and Applications.

[21]  Cândida Ferreira,et al.  Gene Expression Programming: A New Adaptive Algorithm for Solving Problems , 2001, Complex Syst..

[22]  Gregorio G. Vigilar,et al.  Stable Channels with Mobile Bed: Model Verification and Graphical Solution , 1998 .

[23]  H. Bonakdari,et al.  No-deposition Sediment Transport in Sewers Using of Gene Expression Programming , 2017 .

[24]  Van Rijn,et al.  Sediment transport; Part I, Bed load transport , 1984 .

[25]  D. W. Knight,et al.  GEOMETRY OF SELF-FORMED STRAIGHT THRESHOLD CHANNELS IN UNIFORM MATERIAL. , 1998 .

[26]  Yi-Fei Pu,et al.  Using gene expression programming to infer gene regulatory networks from time-series data , 2013, Comput. Biol. Chem..

[27]  G. Parker,et al.  Stable width and depth of straight gravel rivers with heterogeneous bed materials , 1988 .

[28]  H. Md. Azamathulla,et al.  Gene-Expression Programming for Sediment Transport in Sewer Pipe Systems , 2011 .

[29]  James E. Pizzuto,et al.  Numerical simulation of gravel river widening , 1990 .

[30]  Amir Hossein Zaji,et al.  Simulation of open channel bend characteristics using computational fluid dynamics and artificial neural networks , 2015 .

[31]  H. Md. Azamathulla,et al.  Development of GEP-based functional relationship for sediment transport in tropical rivers , 2012, Neural Computing and Applications.

[32]  Saeed Reza Khodashenas.  Threshold gravel channels bank profile: a comparison among 13 models , 2016 .

[33]  Hazi Mohammad Azamathulla,et al.  Estimation of dimension and time variation of local scour at short abutment , 2013 .

[34]  Gregorio G. Vigilar,et al.  Hydraulic Geometry of Threshold Channels , 1992 .

[35]  Amir Hossein Alavi,et al.  A new prediction model for the load capacity of castellated steel beams , 2011 .

[36]  Mohammad Najafzadeh,et al.  GMDH based back propagation algorithm to predict abutment scour in cohesive soils , 2013 .

[37]  Amir Hossein Zaji,et al.  Adaptive neuro-fuzzy inference system multi-objective optimization using the genetic algorithm/singular value decomposition method for modelling the discharge coefficient in rectangular sharp-crested side weirs , 2016 .

[38]  John Pitlick,et al.  Width adjustment in experimental gravel‐bed channels in response to overbank flows , 2013 .

[39]  Amir Hossein Zaji,et al.  Design of modified structure multi-layer perceptron networks based on decision trees for the prediction of flow parameters in 90° open-channel bends , 2016 .

[40]  Amir Hossein Zaji,et al.  Predicting the velocity field in a 90° Open channel bend using a gene expression programming model , 2015 .

[41]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[42]  Elham Sadat Mostafavi,et al.  Gene expression programming as a basis for new generation of electricity demand prediction models , 2014, Comput. Ind. Eng..

[43]  Amir Hossein Gandomi,et al.  Design equations for prediction of pressuremeter soil deformation moduli utilizing expression programming systems , 2012, Neural Computing and Applications.

[44]  Syunsuke Ikeda,et al.  Self-Formed Straight Channels in Sandy Beds , 1981 .

[45]  Cândida Ferreira,et al.  Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence , 2014, Studies in Computational Intelligence.

[46]  Graham H. Macky.  Large flume experiments on the stable straight gravel bed channel , 1999 .

[47]  Fevzi Onen.  GEP prediction of scour around a side weir in curved channel , 2014 .

[48]  Hossein Rezaei,et al.  Application of ANFIS and MLR models for prediction of methane adsorption on X and Y faujasite zeolites: effect of cations substitution , 2017, Neural Computing and Applications.

[49]  Hossein Bonakdari,et al.  Design of an adaptive neuro-fuzzy computing technique for predicting flow variables in a 90° sharp bend , 2017 .

[50]  S. Cao,et al.  Design for Hydraulic Geometry of Alluvial Channels , 1998 .

[51]  Subhasish Dey.  Bank profile of threshold channels : A simplified approach , 2001 .

[52]  G. Parker.  Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river , 1978, Journal of Fluid Mechanics.

[53]  P. Diplas.  Characteristics of Self‐Formed Straight Channels , 1990 .

[54]  H. Md. Azamathulla,et al.  Gene-expression programming for transverse mixing coefficient , 2012 .

[55]  Chun Kiat Chang,et al.  Gene expression programming for total bed material load estimation--a case study. , 2010, The Science of the total environment.