Keywords: damage identification, artificial neural network, modal parameters, finite element method, natural frequencies, damage size precision.

A method for damage localization based on modal parameters is presented in this paper. It has been developed using THE finite element method (FEM) and artificial neural networks (ANNs). The study has been applied to a problem of a cantilever beam with a small damaged area (1×1 cm²). The ANNs have been trained with the results obtained in numerical simulations using the FEM. These numerical simulations have been done by introducing damage with different localization in the beam. The mesh of the beam has the size of the damage size in order to have exceptional precision quality. In order to reduce the computational cost that a fine mesh represents, the natural frequencies have been calculated with a reduced number of master degrees of freedom (MDF). Once the ANN is trained, it has been evaluated as a tool to predict the position of the damage when the natural frequencies are provided.

The main objective of this study is to calibrate different networks for the ANN and different training algorithms in order to achieve the following three requirements: the capacity of the ANN to reproduce the results obtained using the FEM; the capacity of the ANN to generalize and predict; and the capacity for noise filtering [1,2]. The robustness of each ANN structure is analyzed and compared when this information is altered with noise. A good response is observed when the error level is up to the 10% of the bandwidth. All of this considering the number of neurons used and the time employed in the training. In the present research more than 800 simulations are presented to the ANN. Thus, it has been established the capabilities of each combination of the ANN structure and training algorithm for each requirement. Two kinds of ANN types have been studied in this paper: multilayer perceptron feedforward (MLP) and radial basis feedforward (RBF). These models have been chosen because their contrasted efficacy and their opposite characteristics. Two training algorithms have been used to train the MLP: the Levenberg-Marquardt (LM) algorithm and the Bayesian regularization (RB). The training algorithm used to train the RBF was the orthogonal least squares learning algorithm (OLS).

As a resume of the results obtained, the coupled MLP with BR training algorithm is well balanced with a high valuation in each capability. The main difference with the MLP and LM training algorithm is that MLP-LM needs less time to be trained that could be a critical parameter in the analysis of bigger structures. The coupled RBF-OLS is really good in reproducing in-out pattern of data at the expense of a great number of neurons and training time. However they present a low valuation in generalization and filter. In the full paper more conclusions and particularities are presented.

1

N. Bakhary, H. Hao, A.J. Deeks, "Damage detection using artificial neural network with consideration of Uncertainties", Engineering Structures 29, 2806-2815, 2007. doi:10.1016/j.engstruct.2007.01.013

2

Zhong-Xian Li, Xiao-Ming Yang, "Damage identification for beams using ANN based on statistical property of structural responses", Computer & Structures, 86, 64-71, 2008. doi:10.1016/j.compstruc.2007.05.034

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