GMDH to predict scour depth around a pier in cohesive soils

doi:10.1016/j.apor.2012.12.004

Applied Ocean Research

Volume 40, March 2013, Pages 35-41

https://doi.org/10.1016/j.apor.2012.12.004 Get rights and content

Abstract

This study presents new application of group method of data handling (GMDH) to predict scour depth around a vertical pier in cohesive soils. Quadratic polynomial was used to develop GMDH network. Back propagation algorithm has been utilized to adjust weighting coefficients of GMDH polynomial thorough trial and error method. Parameters such as initial water content, shear strength, compaction of cohesive bed materials, clay content of cohesive soils, and flow conditions are main factors affecting cohesive scour. Performances of the GMDH network were compared with those obtained using several traditional equations. The results indicated that the proposed GMDH-BP has produced quite better scour depth prediction than those obtained using traditional equations. To assign the most significant parameter on scour process in cohesive soils, sensitivity analysis was performed for the GMDH-BP network and the results showed that clay percentage was the most effective parameter on scour depth. The error parameter for three classes of IWC and C_p showed that the GMDH-BP model yielded better scour prediction in ranges of IWC = 36.3–42.28% and C_p = 35–100%. In particular application, the GMDH network was proved very successful compared to traditional equations. The GMDH network was presented as a new soft computing technique for the scour depth prediction around bridge pier in cohesive bed materials.

Highlights

▸ Quadratic polynomial was used to develop GMDH network. ▸ The GMDH network provided significantly accurate outcomes compared to ones of traditional equations. ▸ Debnath and Chaudhuri equation provided quite better scour depth than other traditional equations. ▸ Results of sensitivity analysis showed that clay percent was the most effective parameter.

Introduction

Scouring phenomena is a significant problem for bridge engineering. There are several ocean and coastal structures located in rivers, sea and streams that may be prone to erosion due to combinations of scouring factors. It is believed that erosion in cohesive bed materials occurs when the fluid shear stress is sufficient to overcome the tensile strength of the bed material and submerged unit weight of the soil.

Investigations on scour depth in non-cohesive materials have been extensively carried out in the last few decades [[1], [2], [3], [4], [5]]. In contrast, few researchers have studied scouring in cohesive soils [[6], [7], [8], [9], [10], [11], [12], [13], [14], [15]]. Most of the investigations resulted traditional equations based on regression models in limited experimental conditions [11,12,14,15]. Each of the traditional equations has focused on special parameters. Conditions of laboratory and field are limiting factors that can be caused to provide the prediction of scour depth with low accuracy.

Recently, various artificial intelligence approaches such as artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), genetic programming (GP), linear genetic programming (LGP), data mining, and machine learning method were applied to develop the modeling of problems in scour prediction [[16], [17], [18], [19], [20], [21], [22], [23]]. Among these methods, the GMDH network is known as a system identification method which is employed in various fields in order to model and forecast the behaviors of unknown or complex systems based on given input–output data pairs [24]. Recently, GMDH network has been utilized to predict scour depth around bridge piers, abutments, and pipelines in coarse bed sediment [[25], [26], [27], [28],29]. Results of performances indicated that combinations of iterative and evolutionary algorithms with GMDH network provided quite better prediction than those obtained using traditional equations and soft computing tools.

In addition, the GMDH approach has been used in different researches such as energy conservation, control engineering, system identification, marketing, economics and engineering geology [24,[30], [31], [32], [33]].

The main objective of this study is to investigate the efficiency of the GMDH network and traditional equations in the prediction of scour depth in cohesive soils. Furthermore, influence of the effective parameters on the scour depth would be considered. In this way, GMDH network has been improved using back propagation (BP) technique, and a programming code was introduced.

Section snippets

Review on pier scour in cohesive soils

The scour of cohesive materials is fundamentally different from that of non-cohesive materials. It involves not only complex mechanical phenomena, including shear stress and shear strength of soils, but also the chemical and physical bonding of individual particles and properties of the eroding fluid [34]. Also, scouring process in cohesive soils is more complicated than that of non-cohesive soils. A few investigators have studied scour in cohesive soils. Molinas and Honsy [35] carried out

Data collection

Based on the previous studies, the scour depth around a vertical pier in cohesive soils depends on initial water content of soil, compaction of cohesive soils, clay percentage, shear strength of bed soil [[6], [7], [8],[10], [11], [12],14,15]. Therefore, the following equation can be used for cohesive soils: $d_{s} = f (ρ, μ, U, d_{50}, y, g, D, I W C, C_{p}, S)$ where d_s, ρ, μ, U, d₅₀, y, g, D, IWC, C_p, and S are scour depth, mass density of water, fluid dynamic viscosity, flow velocity, medium diameter of bed material,

Principle of the GMDH network

GMDH is a learning machine based on the principle of heuristic self-organizing, proposed by Ivakhnenko in the 1960s. It is an evolutionary computation technique, which has a series of operations such as seeding, rearing, crossbreeding, and selection and rejection of seeds corresponding to the determination of the input variables, structure and parameters of model, and selection of model by principle of termination [24,39,40]. In fact, the GMDH network is a very flexible algorithm and it can be

Results and discussion

The results of GMDH network and traditional equations are presented in this section. In addition, influences of the non-dimensional parameters on the scour depth have been considered. In this way, correlation coefficient (R), root mean square error (RMSE), scatter index (SI), BIAS, and mean absolute percentage of error (MAPE) are the commonly used prediction error indicators in the training and testing stage [16,22,25].

Sensitivity analysis

To determine the importance of each input variable on scour depth, sensitivity analysis was performed on the GMDH-BP. In the analysis, one parameter of Eq. (4) was eliminated each time to evaluate its effect on the output. In this way, the RMSE values are characterized as common statistical errors. Accordingly, the clay percentage (C_p) was found to be the most effective parameter (R = 0.7, RMSE = 0.528, MAPE = 1.38, BIAS = 0.267, and SI = 0.77) on the scour depth and whereas the non-dimensional

Conclusion

The GMDH-BP network was proposed as a new soft computing tool for the scour depth prediction around a vertical pier in cohesive soils. The GMDH network was developed using quadratic polynomial neurons. Also, back propagation algorithm was utilized to yield correction of weighting coefficients in the training stage. The crucial parameters on the scour depth were considered using dimensional analysis. Clay percentage, initial water content, non-dimensional shear strength of bed soil, and the

Acknowledgement

The authors are grateful to Prof. Jean-Louis Braiud, Texas A&M University for his guidance and contributions to this paper.

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GMDH to predict scour depth around a pier in cohesive soils

Abstract

Highlights

Introduction

Section snippets

Review on pier scour in cohesive soils

Data collection

Principle of the GMDH network

Results and discussion

Sensitivity analysis

Conclusion

Acknowledgement

Engineering Geology

Ocean Engineering

Engineering Geology

Advances in Engineering Software

Applied Ocean Research

Applied Ocean Research

Ocean Engineering

Energy Conversion and Management

Scientia Iranica, Transactions A: Civil Engineering

Neurocomputing

Control Engineering Practice

Expert Systems with Applications

Engineering Geology

Simulation Modelling Practice and Theory

Neurocomputing

Temporal variation of scour around circular bridge piers

Journal of Hydraulic Engineering

Large scale clear-water local pier scour experiments

Journal of Hydraulic Engineering

SRICOS: prediction of scour rate in cohesive soils at bridge piers

Journal of Geotechnical and Geoenvironmental Engineering

Erosion function apparatus for scour rate predictions

Journal of Geotechnical and Geoenvironmental Engineering

SRICOS-EFA method for complex piers in fine grained soils

Journal of Geotechnical and Geoenvironmental Engineering