An artificial neural network (ANN) is a processing unit with a design inspired by the neural structure of human brain (Huang and Wanstedt, 1998). Neural networks have been applied in a wide range of geoscience applications (e.g. Baan and Jutten, 2000). The major reason for the popularity of neural networks is their good performance in non- linear multivariate problems. A complete description of neural networks algorithms has
already been prepared by many researchers (e.g. Hassoun, 1995). A summary is given here.
A neural network is comprised of three different layers, namely input, output and the middle (hidden) layer (Figure 4.3). Each layer consists of neurons (nodes) and the neurons are connected by weighted links which pass signals from one neuron to another. The weights in the network structure are determined by back-propagating the errors between the inputs and the outputs. Neural networks trained with the back propagation method have been applied successfully as prediction tools in a wide range of engineering fields (Garrett, 1994; Baudu, 1995; Annandale et al., 1996; Huang and Wanstedt, 1998; Sonmez et al, 2006).
An artificial neural network can be used for both supervised and unsupervised learning. In the supervised learning approach, the network learns from existing examples. This requires the existence of sufficient number of examples for optimum performance (Hassoun, 1995). These examples form a set of known “input-output pairs”, usually called a training set, and the task is to learn the input-output rules from these examples. Once the network has learned the relationship between the input and output for the training dataset, then this relationship can be applied to predict output values for other data sets.
In an unsupervised learning approach, only the inputs are known and there is no information of corresponding outputs. In this case the network seeks for specific features of the data, such as clusters. The unsupervised neural network approach has not been investigated in this research.
Figure 4.3. Structure of an artificial neural network showing three layers. Note that there is no connection between nodes of a given layer.
In a typical neural network training procedure, the data set is divided into three separate portions called training, validation and test sets. The training set is used to develop the desired network while the validation set is allocated for the purpose of controlling the network training. The validation set sometimes referred as testing set, is not included in the training set during training of the network. The validation set only enables the user to adjust the network training process for the best outcome. The test dataset which is not involved in network design and training is then used to test the performance of the trained network.
A number of factors such as training time, training error and network structure should be considered during design and training of neural networks. The training time for the network is an important factor. Basheer and Hajmeer (2000) proposed the optimum time to stop training a network would be the time that the prediction error for the testing dataset (here validation set) starts to increase (Figure 4.4). The training error (root mean square error) typically decreases with increase in training time at first, but over-training usually degrades the network performance. In other words the network has memorized the examples and patterns rather than learning. A network that has memorized the examples could only be able to respond to the same examples and will not be able to perform well with examples outside those used in the training stage.
The complexity of the multi layered neural network structure increases by the addition of either extra hidden layers or an increase in the number of nodes in the hidden layer. The hidden layers are normally likened to a “black box” within the network system. However the invisibility of a hidden layer does not mean that the function of this layer can not be evaluated (Mohaghegh et al., 1995). In fact based on mathematical functions within each node in every layer the performance of network can be evaluated (Yang and Zhang, 1997).
Figure 4.4. Criteria for selection of optimum network and training cycle (Basheer and Hajmeer, 2000). As the training cycles increases the prediction error reduces, however the prediction error for validation data (Testing) will start to increase after a certain training cycle known as optimum training point. This point that defines the optimum number of training cycles is regarded as the sufficient number of cycles for best performance of the network.
It is possible to assess the relative importance of each input variable in a neural net using the Yang and Zhang (1997) method. This approach enables the user to identify the most significant input variables that have an impact on output based on calculation of the derivative of output with respect to each input parameter. However, assessment becomes very complex when the number of nodes in a hidden layer (and number of hidden layers) increases. An alternative approach is to use the sum of the weights that can provide a quick way to evaluate the importance of each input parameter in a neural net. The sum of the weights is the sum of the absolute weights of the connections from the input node to all the nodes in the hidden layer.
A supervised learning approach has been used and implemented for prediction of comminution classes of Ernest Henry (Chapter 5) and Cadia East (Chapter 6) data. Comparison of neural network approach with minimum distance algorithm (LogTrans) for prediction of comminution classes has also presented in Chapters 5 and 6.
4.5.
Geometallurgical Modeling Applications
The geometallurgical models developed based on classification schemes (Section 4.2) can be applied during process planning or process optimization stage. These two process stages are briefly explained in the following subsections. However the choice of
classification scheme for geometallurgical modeling purposes (i.e. planning or optimization) depends primarily on ore processing variability. This can be identified by statistical analysis of comminution data and using statistical techniques (e.g. Histogram charts). Judgment on comminution variability is valid when a representative number of small-scale comminution tests are available.
A large processing variability explained by comminution attributes, suggests potential ore variability and hence a need for effective geometallurgical characterisation of orebody. In this case, the GC or PC method could be more appropriate than the CC or CPC for geometallurgical class definition and comminution modeling. This is because normally more geological and petrophysical data are available than comminution information that could provide a means for effective characterisation of ore variability. The GC approach should be exercised with great caution due to issues discussed in Section 4.2.1.
If there is only limited comminution variability defined based on statistical analysis it may suggest that it is highly unlikely that ore geological variability in a deposit can have a significant impact on comminution response. Thus it is highly likely that created classes based on GC or PC approach will reflect similar comminution behavior. Hence definition of geometallurgical classes based on the CC or CPC approach could better characterize ore comminution behavior and are more appropriate in this case.