Keywords: neural networks, backpropagation, cold-formed steel, Z-profile, compression member, finite strip analysis.

The various types of cold-formed steel sections with their flexibility in the fabrication process require extensive optimization for different structural functions. The difficulties of the design of these sections, due to their complex stability behaviour, local, distortional and global buckling [1], require an advanced design methodology. In an ongoing research program at the Department of Structural Engineering of Budapest University of Technology and Economics the aim is to develop optimized cold-formed steel sections by the application of improved design tools.

The first phase of the research is to develop an advanced design process based on nonlinear finite element simulations in parallel with laboratory tests. In the second phase of the research - discussed in this paper - the purpose is to develop a neural network to predict the critical and ultimate load of cold-formed profiles. By the trained neural network the critical and ultimate load can be determined very fast, which can be the basis of a genetic algorithm (GA) based optimization process [2].

In the paper the prediction of the critical load of steel cold-formed Z-profile compression members are discussed, using neural network. To predict the critical force a backpropagation neural network is developed with two hidden layers and sigmoid activation functions in the hidden layer and linear function in the output layer [3]. The input parameters of the network are the geometrical data of the cold-formed Z-sections and the length of the compression member, as output data the critical load is considered. Therefore the nodes at the input and the output layer are 6 and 1, respectively. The number of nodes in the hidden layers is chosen to 6 and 2 using the recommendations of [4].

The training patterns are selected from a set of real fabricated sections. There are 30 Z-profiles given with 15 sort of lengths and 130 of the 450 combinations are selected for the training patterns. After pre-processing the input and output data, the network is trained and generalized for test patterns not included in training patterns. The errors between the critical load estimated by the neural network and calculated by the finite strip program CUFSM [5] are investigated.

Parallel networks are applied to eliminate the inaccuracy of the results, that come from the badly structured input data. Considering the median of the different estimates given by the parallel network the value of the error can be reduced under 10 %. The predicted results by the trained neural network have a maximum error about 5-7 % and about 1 % error on average.

The trained network gives very fast results and with some further analysis the uncertainties can be decreased and make the network accurate enough for the practical application. Therefore this procedure can be the basis of a GA-based optimization method for cold-formed compression members.

1

B.W. Schafer, "Local, distortional and Euler buckling in thin-walled columns", ASCE Journal of Structural Engineering, 128(3), 289-299, 2002. doi:10.1061/(ASCE)0733-9445(2002)128:3(289)

2

W. Lu, "Optimum design of cold-formed steel purlins using genetic algorithms", Helsinki University of Technology, Laboratory of Steel Structures, Publications 25, 2003.

3

W. Lu, "Neural network model for distortional buckling behaviour of cold- formed steel compression members", Helsinki University of Technology, Laboratory of Steel Structures, Publications 16, 2000.

4

H. Demuth, M. Beale, "Matlab Neural Networks Toolbox, User's Guide", Copyright 1992-2001, The MathWorks, Inc., http://www.mathworks.com.

5

B.W. Schafer, "Elastic buckling of thin-walled structures", http://www.ce.jhu.edu/bschafer/, 2002.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £95 +P&P)