11.3 Neural Network Model of Grinding

The grinding process is common in the mineral processing industry, and is characterized by several performance measures, all of which are important in various circumstances. Generally, there are four measures that are especially important indicators of the efficiency of a particular grinding process: (1)fineness of the ground product, (2) energy costs associated with the process, (3) a parameter associated with the viscosity of the slurry, and (4) a second parameter associated with the viscosity of the slurry containing the ground product. These performance measures all are functions of four basic input parameters: (1) the percent solids by weight of the feed to the grinding circuit, x_S, (2) the maximum ball size, x_B, (3) the mill speed, x_M, and (4) the dispersant addition, x_D. Four individual neural networks have been trained to predict each of the performance measures (output variables) given the values of the four input parameters. The neural networks used to model grinding were classic three layer, backpropagation neural networks with four input nodes, eleven hidden nodes, and a single output node. In the training of each network, a learning rate of 0.2 was used while the momentum term was set at 0.05. Figure 11.4 demonstrates the effectiveness of the neural network model used to predict fineness. In this figure, the model predicted fineness is plotted against a measured value. Realize that if the model were exact, all of the points in this plot would lie on a 45° line. Also, it is important to note that Figure 11.4 consists of data the neural network model had not seen before; it is not the training data.

Figure 11.4  The neural network model predicts fineness quite accurately, as is borne out by a correlation coefficient of 0.963.

The NN is a valuable tool for modeling grinding because the physical phenomena occurring in grinding are not easily modeled with first principle models. The neural network model was trained over a two-week period using 400 training data sets and a 486 personal computer. The two-week development period included the time needed to consider various NN architectures and system parameters (α and φ).

11.4 Neural Network Model of Hydrocyclone

Hydrocyclones are a standard method of classifying slurries in the mineral processing industry. Hydrocyclones are continuously operating separation devices that utilize centrifugal forces to accelerate the separation of particles. They have achieved such popularity because of their simplicity, their durability, and their relatively low cost. Hydrocyclones are now used increasingly in closed-circuit grinding, de-sliming circuits, de-gritting procedures, and thickening operations (Willis 1979).

A typical hydrocyclone is shown in Figure 11.5. The mechanics of this device were originally described in Chapter 10; they are repeated here for convenience. The lower portion of a hydrocyclone is a conical vessel with an opening at the apex or bottom to allow for the removal of the coarse or heavier particles. The conical section is joined to a cylindrical section, the top of which is closed with the exception of an overflow pipe known as a vortex finder. The vortex finder prevents the tangentially fed mineral from going directly into the overflow, while allowing the fine particles a means of exiting the hydrocyclone. In this cylindrical section the actual separation occurs, due to the existence of a complex velocity distribution that carries the coarse particles to the apex and the fine particles out the top.

Figure 11.5  Hydrocyclones are extremely popular separators because of their simplicity, their durability, and their relatively low cost.

Hydrocyclones have traditionally been modeled using empirical relationships. Plitt (1976) developed a model to predict the d₅₀ or split size that is still used extensively today. The split size is that size particle (given by diameter of the particle) that has an equal chance of exiting the hydrocyclone either through the underflow or the overflow, and is often used to quantify the size separation. Unfortunately, this particular model does not perform well across a spectrum of hydrocyclone sizes. In Chapter 10, we saw how a genetic algorithm could be used to tune such a computer model, but that exercise was dependent on the basic modeling equation, which may or may not be valid across a spectrum of hydrocyclone cyclones. Therefore, a neural network model of a hydrocyclone has been developed and tested. As with the grinding circuit model, the hydrocyclone model is a three-layer, backpropagation neural network. The neural network has eight input nodes, eleven hidden nodes, and one output node. The inputs to the neural network model are: the diameter of the hydrocyclone, D_c, the diameter of the slurry input, D_i, the diameter of the overflow, D_o, the diameter of the underflow, D_u, the height of the hydrocyclone, h, the volumetric flow rate into the hydrocyclone, Q, the percent solids, φ, and the density of the solids, ρ. The output of the neural network model is the d₅₀ size. Again, the learning rate and the momentum term were set to 0.2 and 0.05, respectively. Figure 11.6 shows the performance of the neural network model. The model predicted d₅₀ is plotted against a measured value. The correlation coefficient for the curve is 0.984.

Figure 11.6  A neural network model of a hydrocyclone predicts the d₅₀ size without the necessity of a modeling equation. The correlation coefficient for the curve is 0.984.