In the neural network strategy of this report, a numerical analysis based on two-dimensional finite element method was performed to create the training data set for network [1]. The synthetic data were calculated for a total of six crack angles ranging from 0 to 75 (Grad), with equal increment of 15 (Grad) angle and for a total of five crack depths ranging from 5 mm to 15 mm, with equal increment of 2.5 mm. The pre-processing of the simulated signals before they are entered into the trained network included transformating its into frequency domain, and then using only second, third, fourth and fifth Fourier coefficients as inputs. Thus, the network had four sensory units, three associated units, and two response units. The feed- forward algorithm to adjust the connection weights and the threshold values had been used with only difference that there were the analog outputs from the response units, instead of the binary outputs.

The training set consisted of 72 model signals including three signals from each angle and four depths for different lift-off distances and openings. The threshold for sigmoidal transformation function was chosen to be 0.5 and the learning rate used for updating the weights was 0.2.The algorithm converged after 550 iterations.

It was of course of primary interest of verify the performance of the network for synthetic data different from the data used for training. For the inputs of 'measured' signals for crack angles of 10, 40, 60 (Grad), the network estimates the crack angle as 13.1, 47.8, 64.2 (Grad), respectively. For the inputs of 'measured' signals for crack depths of 7.5 mm, 10 mm, 15 mm (with other lift-off distances and openings), the network estimates the crack depths with maximum error of 2.5 mm (for signal with biggest lift-off distance). For all these cases the accuracy of the estimation is quite good. REFERENCE

1. V. P. Lunin, S. V. Kirsanov, "A Finite Element Code MAGNUM for Analysis of Electromagnetic Field on Personal Computers", 37^thInternational Scientific Colloquium", Illmenau, 1992, pp. 107-111.