Application of Kalman learning algorithm multilayer neural network to estimates of ore grades

Abstract

We have estimated lead (Pb) and zinc (Zn) grades along boreholes in an ore body based on geophysical logging data by using a Kalman learning algorithm, which is a variety of a back propagation neural network. The data set is from a Swedish mine, the Zinkgruvan Mine. It includes data from seven boreholes. Data on three geophysical logging parameters, gamma-ray, density and susceptibility, and the corresponding Pb and Zn grades obtained from chemical analysis of core samples were available from each borehole. Five of the boreholes were used for training the network and two boreholes were used for testing the successfulness in employing the network results for predictions of Pb and Zn grades. The principal idea of the Kalman learning algorithm is discussed. The minimum error rates of the Pb and Zn grades in the test set are 0.060 and 0.095, respectively. Their corresponding average prediction errors between predicted values from the network and the observed values obtained from the chemical analysis of core samples (expressed as a percentage) are 21.2 and 27.1 %, respectively. The optimum configuration of the neural network is a 4-layer neural network with 3 neurons in the input layer, 7 neurons in the first hidden layer, 3 neurons in the second hidden layer, and 1 neuron in the output layer. The optimum numbers of training epochs for Pb and Zn grades are 600 and 1400, respectively. The results obtained from applications of the Kalman learning algorithm to estimates of Pb and Zn grades in the test set are highly promising. A comparison with results from a conventional back propagation neural network shows that the results obtained from the Kalman learning algorithm are much better. Hence, the Kalman learning algorithm is demonstrated to be more effective than the conventional back propagation algorithm in predicting the ore grades.