In order to reduce the computational work of the structural time history analysis, a discrete wavelet transform (DWT) is used by means of which the number of points in the earthquake record is decreased. In this work, Daubechies [1] wavelet function (Db2) is selected to decompose the earthquake record. The DWT process is repeated in two stages, and the number of points of the original record is reduced to 0.25 of the primary points.

Despite the major reduction in the computational effort of the time history analysis, the optimisation process requires a great number of such analyses; thus the overall time of the optimisation process is still very long. In this work to overcome this difficulty, a metamodel, called self-organizing generalized regression (SOGR), is proposed to accurately predict the time history response of the structures. Training the SOGR is performed in two phases. In the first phase, the input and target spaces are classified as the similar data is located in some subspaces. The classification is performed by a self-organizing map (SOM) neural network. In the second phase, a distinct generalized regression (GR) neural network is trained for each subspace using its training data. Therefore, the SOGR consists of a classifying unit and a set of parallel GR neural networks which are locally trained on the input space.

A slight modification is performed on the virtual sub-population (VSP) [2] algorithm to more efficiently achieve the optimisation task. In this modified VSP the probability of the mutation and crossover are determined adaptively. This evolutionary algorithm is called adaptive virtual sub-population (AVSP) algorithm.

In order to investigate the efficiency of the proposed methodology, a six-storey space frame structure is designed for optimal weight for the El Centro earthquake. The numerical results demonstrate the efficiency and computational advantages of the proposed methodology. It is impressive to say that in this paper the time of optimisation employing neural networks, including data generation, training and testing is about 0.12 times of exact optimisation while, the errors of approximation are insignificant.

1

I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis", IEEE Transactions on Information Theory, 36, 961-1005, 1990. doi:10.1109/18.57199

2

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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