Keywords: arch dam, natural frequency, optimum design, evolutionary algorithm, genetic algorithm, wavelet, back propagation, neural network.

Natural frequencies are fundamental parameters which affect the dynamic behaviour of arch dams. Therefore, some limitations must be considered on the natural frequency range so the dynamic response of arch dams may be modified and so that the deteriorative resonance phenomenon is eliminated. Analysis and design of arch dams is a complicated procedure which contains many trial and error steps [1]. The process can be easily and reliably implemented by employing optimisation algorithms. Determination of the natural frequencies of arch dams using finite element methods will result in the corresponding eigen problem to be time consuming. This drawback is resonated when optimizing an arch dam with frequency constraints using time consuming algorithms. In this case, to reduce the computational effort we must inevitably employ some efficient approximating techniques. In recent years the ability of neural network techniques to solve many rigorous problems has been demonstrated.

In this study, an efficient method is introduced to find the optimal shape of arch dams on the basis of constrained natural frequencies utilizing evolutionary algorithms based on employing real values of design variables. The arch dam cost including concrete volume and the casting areas, is considered as an objective function in the optimisation process. The design variables are the principal geometric parameters of the arch dam and the design constraints are taken as the limited frequencies as well as some geometric requirements.

The evolutionary algorithm used in this investigation is based on the virtual sub population (VSP) method [2]. The standard GA is not good at finding solutions for the problems with a great number of design variables. While the VSP method as an evolutionary algorithm creates a robust tool for this type of problem. In this method all the necessary mathematical models of the natural evolution operations are implemented on the small initial population to determine an optimal solution on iterative basis.

The stochastic nature of evolutionary algorithms makes the convergence of the process slow, furthermore evaluating the natural frequencies in the framework of the optimisation procedure can impose a great number of computations and slow down the convergence. Evaluating the arch dam natural frequencies is achieved by using properly trained back propagation (BP) and wavelet back propagation (WBP) neural networks [3,4]. The wavelet network is now the most popular mapping neural network. Activation functions of hidden layer neurons behave as daughter wavelets with a fixed position and dilation and the weights of the network are adjusted using optimisation algorithms. In the full length paper, the evolutionary algorithm and the trained BP and WBP neural networks are explained in detail.

The numerical results reveal the robustness and high performance of the suggested method for the optimum design of arch dams.

1

J. Abrishami, N.V. Rajaee, "Concrete Arch Dam: Design and Construction", Astan Ghods Rzavi Publications, Mashhad, Iran, 2001.

2

E. Salajegheh, S. Gholizadeh, "Optimum Design of Structures by an Improved Genetic Algorithm and Neural Networks", Advances in Engineering Software. 36, 757-767, 2005. doi:10.1016/j.advengsoft.2005.03.022

3

E. Salajegheh, A. Heidari, "Optimum Design of Structures against Earthquake by Wavelet Neural Network and Filter Banks", Earthquake Engineering and Structural Dynamics, 34, 67-82, 2005. doi:10.1002/eqe.417

4

E. Salajegheh, S. Gholizadeh, "Comparison of RBF, GR and BP with Wavelet Back Propagation Networks in Approximation Dynamic Analysis of Structures", 7th ICCE, Tehran, Iran, 2006. (Accepted)

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