Keywords: concrete gravity dams, optimal shape design, gravitational search algorithm, particle swarm optimization, weighted least squares support vector machine.

The economy and safety of concrete gravity dams depends on appropriate shape designs. To find a proper shape, several alternative schemes with various patterns should be selected and modified to obtain a number of feasible shapes. Therefore, the proper shape of a dam considering the economy and safety of design, structural criteria, etc. is selected as the final shape. In order to overcome these difficulties, optimization techniques can be effectively utilized [1].

In this paper, the optimal shape design of concrete gravity dams including dam-water-foundation rock interaction is proposed using a hybrid meta-heuristic optimization method and the weighted least squares support vector machine (WLS-SVM) approach. The linear dynamic behaviour of gravity dam-water-foundation rock system subject to earthquake ground motion is considered.

In recent years, the meta-heuristic optimization techniques in comparison with gradient-based methods have been shown to provide suitable tools for global searches. In order to utilise the advantages of these techniques, the hybrid meta-heuristic optimization method is proposed based on a combination of gravitational search algorithm (GSA) [2] and particle swarm optimization (PSO) [3], which is called GSA-PSO. In the first stage of GSA-PSO, a preliminary optimization is accomplished using GSA as a local search. An optimal initial swarm is produced using the optimum result of GSA in the second stage of GSA-PSO. Other particles of the initial swarm are randomly selected to complete the initial swarm. Finally, PSO is employed to find the optimum design using the optimal initial swarm.

In order to reduce the computational cost of the dam analysis subject to earthquake loading, the weighted least squares support vector machine approach [4] is employed. In this study, this method is utilized to accurately predict dynamic responses of gravity dams instead of using a time consuming finite element analysis in optimization procedure.

In order to investigate the computational efficiency of the hybrid meta-heuristic optimization method for the optimal shape of concrete gravity dams. The optimum design obtained using GSA-PSO is also compared with those achieved using GSA and PSO. Results of GSA-PSO show improvement in terms of computational efficiency, optimum solution, the number of function measurements and convergence history in the optimization process.

1

S.M. Seyedpoor, J. Salajegheh, E. Salajegheh, S. Gholizadeh, "Optimal Design of Arch Dams Subjected to Earthquake Loading by a Combination of Simultaneous Perturbation Stochastic Approximation and Particle Swarm Algorithms", Applied Soft Computing, 11(1), 39-48, 2011. doi:10.1016/j.asoc.2009.10.014

2

J. Kennedy, R.C. Eberhart, "Swarm Intelligence", Morgan Kaufman Publishers, San Francisco, 2002.

3

E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, "GSA: a Gravitational Search Algorithm", Information Science, 179(13), 2232-2248, 2009. doi:10.1016/j.ins.2009.03.004

4

J.A.K. Suykens, J.D. Brabanter, L. Lukas, J. Vandewalle, "Weighted Least Squares Support Vector Machines: Robustness and Sparse Approximation", Neurocomputing, 48, 85-105, 2002. doi:10.1016/S0925-2312(01)00644-0

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