11.5 Neural Network Model of Flotation

Froth flotation is a common method of separating minerals. In froth flotation, minerals are separated when selected particles are rendered hydrophobic (water repellent) with chemical agents (called collectors) and attach to air bubbled through a slurry containing the minerals. These bubble-particle groups then rise to the top of the flotation cell, where they are removed as a froth. Hydrophilic (water attracted) particles are not attracted to the air and settle out separately. In the iron industry, the objective of the flotation process is to remove silica from iron deposits because most commercial uses often require the product to contain less than 6 pct silica. A computer model of flotation could assist in achieving this goal of 6 pct silica through improved system design and process control.

Although several computer models of the flotation process have been developed and tested (Schuhmann, 1942; Tomlinson and Fleming, 1965; Flint and Howarth, 1971), most of the models are effective for only a narrow range of flotation applications. To be effective in the investigation of alternative process control strategies and in the development of improved flotation circuit designs, a computer model must be robust. The robust modeling capabilities of neural networks quite possibly will be adequate to produce a computer model of froth flotation. Such a model could then be used in control systems.

There are a number of system variables that play a role in determining the amount of silica that will appear in the product for iron flotation. However, the purity of the product is particularly sensitive to two parameters: (1) the amount of amine (a collector) used and (2) the feed mass flow rate into the flotation cell. Thus, the fuzzy linguistic model presented in this paper is a two-input (amine flow rate and feed mass flow rate), one-output (percent silica in the product) model of a conventional flotation cell used in the iron industry. The neural network had five hidden nodes, used a learning rate of 0.02, and a momentum value of 0.05. The data used to produce the computer model was acquired from an industrial cooperator; the data was real-world data obtained from an operating plant.

Figure 11.7 shows the performance of the NN model of flotation. The correlation coefficient for this curve is 0.941. Although this model does not match the data as well as the grinding and hydrocyclone models, it still performs adequately for use in the control systems being developed in this book.

Figure 11.7  A neural network model of a flotation circuit provides a correlation coefficient of 0.941.

11.6 Review/Preview

Neural networks are computational paradigms based on an analogy with the mammalian brain. They consist of layers of computational nodes connected by weighted synaptic connections. Each computational node receives input signals, sums these signals, passes the signal through a squashing function (a sigmoidal function), and passes its activation function value on to other nodes. Neural networks employ supervised learning in which it is supplied with a set of data cases that contain values of input and output values. These data cases are used to train the neural networks. This approach is different from most modeling techniques that are programmed rather than trained. Backpropagation networks are able to propagate errors calculated using the training cases back through the network and make adjustments to the weights in the network so that the network matches the supplied training cases.

Neural networks are inviting modeling tools because they do not require the user to have any understanding of the system being modeled (although in the authors’ experience, it is almost always useful to spend some time becoming informed about the system being modeled so that the process of developing the NN model can be expedited). They simply use data collected from the system, and a bit of user patience in adjusting the neural network parameters, to become effective models. However, there are some aspects of neural networks that are troubling to potential users. The question we hear most is “how do I really know what it is doing?” The answer, we are afraid, is “you don’t.” This black-box nature of neural networks is simply too much for some users to overcome. Therefore, in the next chapter we will address a modeling technique that is similar to a neural network in that it can be trained, but very different in that the relationships between the input and output parameters is spelled out in terms of a set of rules. In the next chapter we introduce the idea of using fuzzy rule bases to model physical systems.

References

Flint, L. R., & Howarth, W. J. (1971). The collision efficiency of small particles with spherical air bubbles. Chemical Engineering Science, 26, 1155–1168.

McClelland, J. L., and Rumelhart, D. E. (1988). Parallel distributed processing. Cambridge, MA: The MIT Press.

Pao, Y. (1989). Adaptive pattern recognition and neural networks. Reading, MA: Addison-Wesley Publishing Company, Inc.

Schuhmann, R. (1942). Flotation kinetics. I. Methods for steady state study of flotation problems. Journal of Physical Chemistry, 46, 891–902.

Tomlinson, H. S., & Fleming, M. G. (1965). Flotation rate studies. International Mineral Processing Congress, 6, 563–579.

Wasserman, P. D. (1989). Neural computing: Theory and practice. New York, NY: Van Nostrand Reinhold.

Willis, B. A. (1979). Mineral Processing Technology. Toronto: Pergamon Press.