The artificial neural network is now one of the most rapidly expanding area of research across many disciplines [1,2]. In mathematical fields the neural network is an effective mapping tool-mapping an input vector to an output vector. The application areas are classification, pattern recognition and function approximation. The author has used a neural network to detect the damage of the structural element [3].

On the other hand, the identification technique for support conditions of continuous bodies is becoming important, with increasing size and complexity of machines and vessels. Yasuda and Goto [4] and Kamiya, et al. [5] proposed the experimental identification technique for boundary conditions of the beam. Yasuda, et al. [6] presented the identification of non-linear support systems by using transient response. Takahashi [7,8,9] proposed the identification method for the axial force (or critical force) and boundary conditions of a beam using the neural networks.

In this paper the possibility of using a Multilayer Perceptron Network trained with the Backpropagation Algorithm for identifying the critical flutter load and support conditions (or shape parameters) of the cracked L-shaped shaft is studied. The natural frequecies which are the most fundamental and simplest in the modal parameters are adopted here to estimate the flutter load and support conditions (or shape parameters). The basic idea is to train a neural network with simulated patterns of the relative changes in natural frequencies and corresponding critical flutter loads and support conditions of shafts in order to recognize the vibrating behavior of them. Subjecting this neural network to un-learning natural frequencies should imply information about the support condition (or shape parameters) and critical flutter load of shafts. The training data are obtaining by the values using the transfer matrix method. By a trial-and-error approach, with a view of simplify the network structure and speed up the convergence of the algorithm, we defined the network of three layers. The neural networks were trained with numerical values of the relative changes of the lowest four frequency parameters of shafts. The response surface approximation method is applied to the same problems and then the advantages and disadvantages of two methods are compared.

From the results of the numerical examples we can draw the following conclusions. First, the critical flutter load and support conditions (or shape paramaters) can be predicted by the change of frequency parameters. Second, the one hidden layer of trained network is sufficient to identify them. However, the generalization capability is insufficient for identifying the crack position.

1

Master, T., "Neural, Novel & Hybrid Algorithms for Time Series Prediction", John Wiley & Sons, Inc.1995.

2

Hassoun, M.H., "Artificial Neural Networks", The MIT Press.1995.

3

Takahashi, I. and Yoshioka ,T., "Use of neural networks for fault identification in a beam structure", Proceedings of CIVIL-COMP 1995, Developments in Neural Networks and Evolutionary Computing for Civil and Structural Engineering, pp.15-23, 1995.

4

Yasuda ,K. and Goto, Y., "Experimental identification technique for boundary conditions of a beam", Bulletin of JSME , 570, C, pp.118-125, 1994.

5

Kamiya ,K., Yasuda, K.and Miya, H., "Experimental identification of a nonlinear beam(when boundary conditions are linear)", Bulletin of JSME , 587, C, pp.212-219, 1995.

6

Yasuda, K. , Goto, Y. and Hirose, Y ., "Experimental identification technique for boundary conditions of a beam(when boundary conditions are non-linear)", Bulletin of JSME , 599, C, pp.2599-2605, 1996.

7

Takahashi, I., "Identification for axial force and boundary conditions of a beam using neural networks", Proceedings of the 1997 International Conference on Engineering Applications of Neural Networks, Neural Networks in Engineering Systems , pp.253-256, 1997.

8

Takahashi, I., "Identification for critical force and boundary conditions of a beam using neural networks ", J. Sound Vibr, 228, pp.857-870, 1999. doi:10.1006/jsvi.1999.2451

9

Takahashi, I., "Neural identification for critical flutter load of a cracked shaft simultaneously subjected to a follower force with an axial force", Proceedings of the 3rd. International Conference on Engineering Computational Technology, CD-ROM, 2002. doi:10.4203/ccp.76.80

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