Industrial Applications of Genetic Algorithms:Hydrocyclone Model Using Genetic Programming

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Conclusions

Following the six steps above proves to be quite useful in implementing genetic programming for solving a particular problem. Although each of these steps results in facets of the run that can dramatically affect the results obtained, the most important ones appear to be the selection of the terminals and functions, and their relationship to the ideas of sufficiency and closure.

RESULTS

A genetic programming simulation was run according to the guidelines and parameters set forth in the preceding sections of this chapter. Since the objective was to consider the effectiveness and robustness of genetic programming as a system identification tool, the hydrocyclone problem was considered in stages.

The split size (d50) of a hydrocyclone is generally considered to be a function of eight variables; D50= f(Dc, Di, Do, Du, h, Q, φ, ρ). However, a system identification problem with eight variables is terribly challenging. Additionally, many mineral separation plants are not interested in the functional relationship between all eight of the independent parameters because they have no control over some of them. Furthermore, some of these independent variables are constant in a particular situation. Thus, in the initial phase of this work, the split size was considered to be a function of but three variables: d50= f(Dc, Di, Do). Figures 15.3 and 15.4 provide an indication of the effectiveness of using genetic programming for this problem.

Figure 15.3 is a 45° plot in which the model predicted value of d50 is plotted against the actual data value. If the model exactly matched the data, all of the points would fall on a 45° line. It can be seen from the figure that for the majority of the split size values, the model does an adequate job of predicting. However, for the larger split sizes, the model performance degrades. Interestingly enough, this phenomenon is observed in many hydrocyclone models.

Figure 15.3 The 45° plot above shows that for most split sizes, the model discovered using genetic programming was quite effective.

Figure 15.4 shows basically the same information as is depicted in Figure 15.3, only in a different form. Figure 15.4 is a bar graph indicating the number of model predicted values that were accurate to a given accuracy. Here, it can be seen that most of the values are reasonably accurate. Be advised that some of the large percent errors are due to the fact that the d50 values are quite small.

Figure 15.4 The above bar graph demonstrates the fact that the majority of the d50 values predicted by the model are easily within the accepted engineering accuracy of 10%.

Phase two of this research effort considered additional independent variables. At this point, the hydrocyclone split size was considered to be a function of four variables: d50= f(Dc, Di, Do, φ). Figures 15.5 and 15.6 provide an indication of the effectiveness of using genetic programming for this problem. Figure 15.5 is a 45° lot while Figure 15.6 is the corresponding bar chart. Notice that although the hydrocyclone model discovered using genetic programming is not as accurate in the previous example, it still performs acceptably. A further increase in parameters would have associated with it a further degradation in performance. Efforts are ongoing to improve the performance of genetic programming in this problem domain.

Figure 15.5 The 45° plot above shows that the model discovered using genetic programming was effective.

Figure 15.6 The above bar graph demonstrates the fact that although most of the d50 values predicted by the model are within the accepted engineering accuracy of 10%, many are not. This is due in part to the fact that so many of the d50 sizes are quite small, and therefore, small differences correspond to large percent errors.

CONCLUSIONS

In this chapter, genetic programming was used to solve a rather difficult system identification problem from the separation industry. A modeling equation was discovered that allowed for the accurate prediction of split size as a function of up to four variables. Efforts are ongoing to extend the work so that the relationship between the split size and all eight variables generally considered important in this problem can be determined.

The results presented here are quite promising. System is a very difficult yet very important problem in a wide range of industries. If genetic programming can effectively improve or simplify the process of developing modeling equations, then the economic impact can be substantial.

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