Neural network pattern recognition of electromagnetic ellipticity images.

Abstract

A backpropagation neural network was trained to estimate the spatial location (offset and depth) of a target given an image of the electromagnetic ellipticity. A length of galvanized pipe buried 2m deep was used as a target. Three components of the magnetic field were measured from which the ellipticity was calculated. Finite element models of the target at different offsets and depths were used to calculate the theoretical ellipticity. The theoretical results were used for training the neural network. The network was tested on additional theoretical models and the field data. The input data representation is important in obtaining good results from the neural network; generally, the smaller the input vectors, the better the results. Five different representations were examined: the whole image, the subsampled image, trough-peak-trough, peak amplitude and frequency-domain. The frequency-domain representation estimated the target locations with the least error. The network was examined for its ability to generalize, to extrapolate beyond the spatial limits of the training set, and to ignore noise. The ability to generalize from theoretical training data to theoretical test data was good for all data representations. Extrapolation errors were satisfactory up to 1.5 model spacings away from the limits of the training set. The ability to ignore noise was generally best for smaller representations with the least amount of training. A third parameter, conductivity-area product was added to the network to more closely simulate the results from standard inversion routines and to test the ability of the network to scale to larger problems. The addition of multiple training examples for each model location improved the results. The increase in training set size dominated the scaling results. The time required for convergence increased exponentially with training set size. Data representation did not have as great an effect on training time.