Application of Wavelet Neural Networks in Optimization of Skeletal Buildings under Frequency Constraints

The main goal of the present work is to decrease the computational burden for optimum design of steel frames with frequency constraints using a new type of neural networks called Wavelet Neural Network. It is contested to train a suitable neural network for frequency approximation work as the analysis program. The combination of wavelet theory and Neural Networks (NN) has lead to the development of wavelet neural networks. Wavelet neural networks are feed-forward networks using wavelet as activation function. Wavelets are mathematical functions within suitable inner parameters, which help them to approximate arbitrary functions. WNN was used to predict the frequency of the structures. In WNN a RAtional function with Second order Poles (RASP) wavelet was used as a transfer function. It is shown that the convergence speed was faster than other neural networks. Also comparisons of WNN with the embedded Artificial Neural Network (ANN) and with approximate techniques and also with analytical solutions are available in the literature.

Authors:

• Mohammad Reza Ghasemi
• Amin Ghorbani

Keywords:

• Weight Minimization
• Frequency Constraints
• Steel Frames
• ANN
• WNN
• RASP Function.

References:

[1] TH. Haftka and Z. Gurdal, Elements of structural optimization. 3rd ed.
Netherlands: Kluwer Academic Publishers, 1992.W.-K. Chen, Linear
Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993,
pp. 123-135.
[2] R.V. Grandhi, Structural optimization with frequency constraints-a
review. AIAA J., 1993, 31:2296-22303.
[3] H. Adeli, Neural networks in civil engineering:1989-2000.
Comp-Aided Civil and Infrastructures Eng. J., 2001, 6:126-
142.
[4] B. Muller and J.Reinhardt, Neural Networks. Spring Verlag.1990, Berlin.
[5] R. Lippmann, An Introduction to Computing with Neural Networks.
IEEE ASSP Mag., April 1987, pp 4-22.
[6] A. Grossmann and J. Morlet, Decomposition of Hardy Functions into
Square Integrable Wavelets of Constant Shape. SIAM J., Math. Anal.,
v15, n4, 1984, pp. 723-736.
[7] G. Lekutai, Adaptive self-tuning neuro wavelet network controllers. PhD
thesis, Elec Eng, 1997, Virginia, 24061-01115.
[8] A. D. Belegundu and T. R. Chandrupatla, Optimization Concepts and
Applications in Engineering, 1999, Prentice Hall, Upper Saddle River,
New Jersey 07451.
[9] O. G. McGee and K. F. Phan, A robust optimality criteria procedure for
cross-sectional optimization of frame structures with multiple frequency
limits. Comp Struct J., 1991, 38:485-500.
[10] E. Salajegheh, Optimum design of structures with high-quality
approximation of frequency constraints. Advances in Engineering
Software J., 2000, 31:381-384.
[11] O. G. McGee and K. F. Phan, On the convergence quality of minimum
weight design of large space frames under multiple dynamic constraints.
Struct Opt J., 1992, 4:156-164.