Keywords: optimum design, earthquake, neural networks, evolutionary algorithm.

Optimum design of structures is usually achieved by selecting the design variables such that an objective function is minimised while all of the design constraints are satisfied. Structural optimisation requires the structural analysis to be performed many times for the specified external loads. This makes the optimal design process inefficient, especially when a time history analysis is considered. This difficulty will be resonated when the optimisation method employed has the stochastic nature such as evolutionary algorithms.

In this investigation, in order to eliminate this drawback, the dynamic responses of the structures have been approximated using an intelligent neural system (INS) [1]. By such approximation the exact dynamic analysis of the structure is not necessary during the optimisation process. In the INS, the input and target spaces are divided into some subspaces as the data located in each subspace have identical properties. These properties may be taken as some natural periods of the structures. Then a distinct radial basis function (RBF) network is trained for each subspace using its assigned training data. Therefore the INS consists of some parallel RBF networks with proper generality properties over the corresponding subspaces.

In all the examples, the input space includes natural periods of the structures and the target space consists of corresponding responses of selected nodes and element stresses for the earthquake loading. To provide training data, ANSYS [2] is employed. To train and test the networks, MATLAB [3] is utilized.

The evolutionary algorithm used in this study is based on the virtual sub-population (VSP) method [4]. A standard GA is not good at finding the solutions in the problems with an enormous number of design variables, but the VSP method as an evolutionary algorithm can create a robust tool for this problem. In this method all the necessary mathematical models of the natural evolution operations are implemented on the small initial population to access optimal solutions on an iterative basis. In summary, the VSP is a repeated application of the standard GA with smaller population and some similar members in each iteration.

In the present work, a two dimensional truss structure and a 25 bar space tower subjected to the El Centro (S-E 1940) and Naghan (1977 Iran) earthquakes are selected as the two numerical examples. The numerical results of the optimisation show that these approximation techniques in the framework of a VSP can create a powerful tool for optimum design of structures for earthquake loading and reduce the computational effort.

Optimum design of structures for earthquake loading using a VSP requires less effort with respect to a standard GA but the overall optimisation time is still too much. In the present paper, a RBF neural network and INS are employed to approximate the necessary time history responses of structures. The numerical results show that in the proposed method, the time of optimisation is reduced to about 0.001 of the time required for exact optimisation; however, the average RMS error is about 0.24.

1

S. Gholizadeh, E. Salajegheh, "An Intelligent Neural System for Predicting Structural Responses Subject to Earthquake Loading", The Fifth International Conference on Engineering Computational Technology, Civil-Comp Press, UK, 2006. doi:10.4203/ccp.84.63

2

ANSYS Incorporated, "ANSYS Release 8.1", 2004.

3

The Language of Technical Computing, "MATLAB", Math Works Inc, 2004.

4

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

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