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CFD and VIV

An Application of Evolutionary Optimization Algorithms for Determining Concentration and Velocity Profiles in Sheet Flows and Overlying Layers

[+] Author and Article Information
R. Bakhtyar1

 Laboratoire de Technologie Écologique Institut d’Ingénierie de l’environnement, Faculté de L’environnement Naturel, Architectural et Construit, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerlandroham.bakhtyar@epfl.ch

S. H. Meraji

 Laboratoire de Technologie Écologique Institut d’Ingénierie de l’environnement, Faculté de L’environnement Naturel, Architectural et Construit, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerlandhamed_meraji@iust.ac.ir

D. A. Barry

 Laboratoire de Technologie Écologique Institut d’Ingénierie de l’environnement, Faculté de L’environnement Naturel, Architectural et Construit, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerlandandrew.barry@epfl.ch

A. Yeganeh-Bakhtiary

Civil Engineering Department,  Iran University of Science and Technology, Tehran, Iranyeganeh@iust.ac.ir

L. Li

 School of Civil Engineering, University of Queensland, Brisbane, Australial.li@uq.edu.au

1

Author to whom all correspondence should be addressed.

J. Offshore Mech. Arct. Eng 134(2), 021802 (Dec 02, 2011) (10 pages) doi:10.1115/1.4004516 History: Received January 22, 2010; Revised December 20, 2010; Published December 02, 2011; Online December 02, 2011

The particle swarm optimization (PSO) method and the genetic algorithm (GA) were used to derive formulas for determining the velocity and concentration profiles in sheet flows. Specifically, these evolutionary optimization algorithms were used in conjunction with experimental data to determine coefficients and identify parameters for preselected formulas. The objective function, defined as the sum-of-squared errors between observed and predicted values of sediment velocity and concentration, was minimized by adjusting the parameter values in the formulas. Two well-known empirical formulas were also applied to the same data. The bias, root mean square error and scatter index were used to evaluate the comparison between predictions and measurements. The results indicated that the errors based on the PSO and GA approaches to predicting sediment parameters were less than those of the existing empirical formulas. Overall, both evolutionary approaches provided formulas that were in good agreement with the experimental data, giving improved descriptions of the vertical distribution of velocity and sediment concentration in the sheet flow for practical purposes. These models also described well the behavior of the velocity and sediment concentration above the sheet flow layer; in contrast with most existing formulas that are applicable only to the sheet flow layer.

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References

Figures

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Figure 3

Rate of convergence of maximum, minimum and average values of fitness function for different values of (a) Scale, (b) Shrink, and (c) population sizes in the GA model

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Figure 1

Vertical distribution of the particle velocity profile using (a) empirical formulas, (b) quadratic EAs (Eqs. 5,6), and (c) exponential EAs (Eqs. 7,8). Right panels show the results for 0.30-mm and left panels for 0.56-mm sand. Solid symbols are the experimental data [12] and lines are the formulas. Panels (b) and (c) show one curve: This is because the formulas derived by PSO and GA are very similar.

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Figure 2

Vertical distribution of the particle velocity profile under oscillatory sheet flow conditions for the (a) GA, and (b) PSO methods (Eqs. 9,10). Solid symbols are the experimental data [22,28] and lines are the EAs formulas.

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Figure 4

Maximum, minimum and average values of the objective function over 20 runs for different inertia weights using the PSO model, with a constant minimum inertia weight

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Figure 5

Maximum, minimum and average values of the objective function over twenty runs of the PSO model

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Figure 6

Vertical distribution of the concentration profile for (a) GA (Eqs. 12,13,14) and (b) PSO [Eqs. 15,16,17]. Right panels show the results for 0.30-mm sand and left panels for 0.56-mm sand. Solid symbols are the experimental data [12] and lines are the model predictions.

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Figure 7

Vertical distribution of the sediment concentration profile at (a) t/T = 0; (b) 0.08; (c) 0.21; (d) 0.33; (e) 0.42; (f) 0.56; (g) 0.72 and (h) 0.89. Solid symbols are the experimental data [22,28] and lines are given by the GA formula [Eq. 18].

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Figure 8

Vertical distribution of the sediment concentration profile at (aa) t/T = 0; (b) 0.08; (c) 0.21; (d) 0.33; (e) 0.42; (f) 0.56; (g) 0.72 and (h) 0.89. Solid symbols are the experimental data [22,28] and lines are given by the PSO formula [Eq. 19].

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