Keywords: neural networks, backpropagation, shell, impact, identification.

This paper shows that identifications of loading characteristics can be performed by neural networks trained by strain outputs when impact loads were given to the composite cylindrical shell. Design and application on composite materials have been developed in fields of aerospace engineering. Christoforou and Swanson announced a closed solution of composite cylindrical shells with simple supports under impact loads [1]. Gong, Shim and Toh expanded closed solutions that impact loading points can be varied. Berke and Hajela introduced artificial neural networks in mechanical engineering. Identification of loading characteristics is important techniques. Cao, Sugiyama and Mitsui researched application of artificial neural networks to load identification. Jones and Sirikis found loading characteristics of the plate that strain gauges were attached [2]. Waszczyszyn and Zienmianski introduced statistical analysis in neural networks [3].

Analytical solutions of the CFRP cylindrical shell with lateral impact loads that satisfies simply supports at both ends has been known by Christoforou, and others. The solutions can show displacements on the central point of the impact area. But displacements of the lateral strains are far from impact area can not be obtained by analytical procedures. On this study, PATRAN and NASTRAN were used to find the maximum displacements and strains. The shell was loaded from 445N to 8,900N by increasing 445N (20 loading cases). Impact points varied from one end to the other end by moving every grid point (49 impact points). Loading type is a half sine wave that frequency varies from 100Hz to 1,000Hz by increasing 100Hz (10 frequencies). Finally these 9,800 results fo transient analysis were used for patterns of neural networks. Full patterns needed 9,800 NASTRAN executions. All of patterns need large computer resources.

Momentum backpropagation was used as basic neural networks on this study. Neural networks for the identification of loading characteristics of the composite shell under impact loads consist of 9 inputs, 3 outputs, and 3 hidden layers. Input patterns are 9 strains on the side of the shell. 3 output patterns are major loading characteristics, loads, impact points, maximum displacements at the impact point. 9 strains from the side of a shell were obtained from structural analysis. Each distance between measuring points is equal. Number of hidden layers varies from 5 elements to 30 elements by increasing 5 elements.

Momentum backpropagation algorithm has been well known as a robust technique. But fixed coefficients lead to limitations of the learning. Learning results of momentum backpropagation are dependent on the momentum coefficient and learning rate. Till now there are several tries for the improvements of learning. On this study, modified momentum backpropagation algorithm was re-modified. Especially learning rate and momentum coefficient can be changed by defined iterations. Developed algorithm can overcome the limitations of the learning into deep levels successfully. Developed algorithm uses sigmoid function as a transfer function. Momentum coefficient and learning rate were modified after ever 30 million iterations. Training of neural networks was performed until iterations met 300 million iterations while momentum coefficient and learning rate was changed continuously by 30 million iterations.

Two types of patterns were performed. One case was trained by using 100Hz only. The other case was trained by using all 9,800 patterns. Two types of neural networks were trained. One case has 1 output layer that each loading characteristic was learned one by one independently. The other has 3 output layers that three loading characteristics were trained simultaneously. When neural networks has 1 output layer and was trained by 980 patterns loaded by 100Hz only, the learning is almost exact.

Most of the learning and identifications of loading characteristics were succeeded. In the case of training with neural networks having 1 output layer which used 9,800 patterns of impact loading, identifications of loading characteristics are available with 99.7% confidence interval, 11.6% on impact loads, 4.2% on loading points, 17.8% on maximum displacements. Loading points can be identified almost exactly. Used method was variable momentum backpropagation which was developed for this study. Developed algorithm was proved that it is efficient for ultimate learning. As a result of this study, inverse engineering of the composite laminated cylindrical shell was proved. Even though real strain gauges are used for preparing patterns of the same study, similar results will be obtained. This study on applications of neural networks of the cylindrical shell is the first one in this research field.

1

A.P. Christoforou, S.R. Swanson, "Analysis of Simply Supported Orthotropic Cylindrical Shells Subjected to Lateral Impact Loads", Journal of Applied Mechanics, Transactions of the ASME, 57, 376-382, 1990. doi:10.1115/1.2892000

2

Richard T. Jones, James S. Sirkis, E.J. Friebele, "Detection of Impact Location and Magnitude for Isotropic Plates Using Neural Networks", Journal of Intelligent Material Systems and Structures, 8(1), 90-99, 1997. doi:10.1177/1045389X9700800109

3

Z. Waszczyszyn, L. Zienmianski, "Neural Networks in Mechanics of Structures and Materials � New Results and Prospects of Applications", Computers and Structures, 79, 2261-2276, 2001. doi:10.1016/S0045-7949(01)00083-9

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