Keywords: earthquake, time history analysis, neural networks, intelligent neural system, approximation.

Time history dynamic analysis of structures subject to earthquakes is usually carried out by step-by-step processes. Increasing the number of structural degrees of freedom causes the time history method to require enormous computational effort. Therefore, approximation methods must be considered to reduce the computational burden. In the last decade neural network techniques were widely utilized for the simplification of complex problems in a broad range of scientific and engineering applications. Such applications have been described in references [1,2]. Some neural networks such as the radial basis function (RBF) and the competitive (COM) have been widely used in civil and structural engineering problems [3,4]. RBF neurons have a significant response to the inputs only over a range of data called the receptive field. In a single RBF network all of the hidden layer neurons have the same receptive field. If the distribution of RBF neurons over input space locates them into some clusters, the accuracy of network outputs over the clusters will be indeed better than over regions with a low density of neurons. To cover vacant regions, the magnitude of the RBF neurons receptive field must be increased but this may cause an overlap between various cluster neurons and in this case the network outputs accuracy will be deviated.

In the present investigation we introduce a new system by combining RBF and COM networks, called an intelligent neural system (INS), to access the efficient approximate dynamic analysis of structures under earthquake loading. In this new system, the generated input-target training pairs are classified in some classes based on a specific criterion. In other words, the input and target spaces are divided into some subspaces as the data located in each subspace have identical properties. Now a RBF network can be trained for each subspace using its assigned training data. In the simple strategy a single global RBF network which is trained for all over the input space is substituted with a set of parallel local RBF networks as each of which is trained for one part of the classified input space. INS has four main advantages: appropriate generality, high speed training, logical validation and high speed approximation. Also INS has two limitations: criterion specification and determination of the number of the classes. In the full length paper the advantages and limitations of an INS are clearly explained.

As numerical examples a three story steel frame with rigid diaphragms and a 10 bar steel truss was selected. The structures are considered under the Naghan (1977-Iran) and El Centro (S-E 1940) earthquakes respectively. To design the INS, a COM network is trained to classify the input space based on the some significant periods of the structures. Therefore, similar structures over the input space are located in some separated clusters. After the clusters are determined, we can train a specific RBF network to approximate time history response of structures located in each cluster. Substituting a large single RBF network with a set of properly trained small specific RBF networks appropriately covers the input space. In this case RBF neurons appear with various magnitudes of receptive fields. In the normal mode by presenting some virgin input samples to the INS the natural periods of the presented structures are determined. Then trained COM network predicts their location in classified input space and then the corresponding specific RBF networks will be excited. Thus approximated time history responses of the structures can be rapidly and accurately determined spending less effort. As revealed in reference [5] there are no explicit methods for selecting training samples and this job is usually achieved on a random basis. Authors have demonstrated in the full length paper that employing INS appears an effective method for logical sampling and validation of neural networks with high scientific insight. Comparison of the INS results with an exact analysis obtained by SAP2000 and ANSYS indicates that the suggested system is rapid, accurate and a powerful tool for approximating the dynamic analysis of structures against earthquakes with low computational burden.

1

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

2

N.D. Lagaros, M. Papadrakakis, "Learning Improvement of Neural Networks used in Structural Optimisation", Advances in Engineering Software, 35, 9-25, 2004. doi:10.1016/S0965-9978(03)00112-1

3

A. Zhang, L. Zhang, "RBF Neural Networks for the Prediction of Building Interference Effects", Computers & Structures, 82, 2333-2339, 2004. doi:10.1016/j.compstruc.2004.05.014

4

A. Meyer-Bäse, S. Pilyugin, A. Wismüller, S. Foo, "Local Exponential Stability of Competitive Neural Networks with Different Time Scales", Engineering Applications of Artificial Intelligence, 17, 227-232, 2004. doi:10.1016/j.engappai.2004.02.010

5

M.Y. Rafiq, G. Bugmann, D.J. Easterbrook, "Neural Network Design for Engineering Applications", Computers & Structures, 79, 1541-1552, 2001. doi:10.1016/S0045-7949(01)00039-6

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