18.6 Results

Evaluating the effectiveness of a process control system is not a trivial endeavor; there are various criteria for efficient control that can be established, and there are numerous conditions for which the controller must be able to perform. In evaluating the performance of the fuzzy classifier system it is important to keep in mind the control objective, which is to neutralize the solution as fast as possible while not violating the constraints placed on the flow rates. Additionally, it is important to realize that if the controller can accomplish the control goal from extreme portions of the control space (when the solution is initially extremely acidic or extremely basic), it should perform well in the more moderate portions of the control space. The performance of the fuzzy classifier system is compared to the performance of a fuzzy controller that was developed by the authors for the pH titration system.

Figure 18.2 summarizes the performance of the fuzzy classifier system. In the particular case depicted, the fuzzy classifier system is posed with the problem of neutralizing a basic solution by acid addition. As can be seen in the figure, the fuzzy classifier system rapidly locates rules for driving the pH to values that range roughly between 5.2 and 8.5, which is the region in which a titration curve is most nonlinear. Then, after a brief period of exploration, the controller is able to evolve into a form that forces the pH to the desired value of 7. Figure 18.3 shows the performance of a fuzzy controller that was designed by the authors to solve the pH problem. Note that this controller drives the pH to a value that is between 6.5 and 7.5. It is important to note that the performance of the author-developed fuzzy controller can be improved by altering the membership functions (Karr and Gentry, 1993), but this is a time-consuming task to accomplish without the assistance of some computational algorithm such as a genetic algorithm. Nonetheless, the two figures demonstrate the fact that the fuzzy classifier system contains a mechanism for improving its performance through the discovery aspects of a genetic algorithm.

Figure 18.2  The fuzzy classifier system neutralizes a basic solution.

Figure 18.3  A fuzzy controller neutralizes a basic solution.

Figures 18.2 and 18.3 demonstrate the effectiveness of the fuzzy classifier system in the pH problem environment. Although the results presented do not alleviate concerns as to the ability of the fuzzy classifier system to perform effectively in process control problems, they do point to the potential of these fuzzy rule discovery systems. These results demonstrate the ability of the system to discover both rules and fuzzy membership functions for effectively manipulating a highly nonlinear physical environment.

18.7 Review and Future Work

The previous section provided results that indicate a fuzzy classifier system is capable of efficiently controlling a pH titration system. However, there are still a number of research issues left open. The following topics are currently under investigation:

•  The pH titration system is being extended to include external perturbations such as additions of a buffering solution. This extension will make the pH titration system more like chemical systems currently used in industry, and will force the fuzzy classifier system to discover rules in real time more often than it has to with the current physical system.

•  A general purpose credit assignment system is being developed. Currently, the credit assignment system is specialized for the pH titration system. For the fuzzy classifier system to be easily applied to alternative process control problems, a general purpose credit assignment algorithm must be developed.

•  The fuzzy control aspect of the fuzzy classifier system is being improved. The center of area algorithm for selecting a single crisp action is but one of a number of potential solution algorithms that have been proven effective in fuzzy controllers. Current efforts are centered on including fuzzy singletons into the fuzzy classifier system. Successful implementation of this algorithm should improve the effectiveness of the fuzzy actions prescribed by the rule sets.

•  Alternative schemes for encoding the classifiers are being considered. The effectiveness of the genetic algorithm’s search is highly dependant on the coding scheme used. Although the current coding seems to be effective, recent research efforts (Karr, 1991) indicate that there may be more efficient ways to encode the information concerning the rules and the fuzzy membership functions.

•  A micro genetic algorithm is being incorporated into the fuzzy classifier system. The micro genetic algorithm is a small-population genetic algorithm that has been reported to perform well across a spectrum of search problems, and in the problem of locating fuzzy membership functions in particular (Karr and Gentry, 1993). If this effort is successful, the fuzzy classifier system should be able to locate effective rules in less time than it currently takes.

The material in this book has provided the reader with an overview of a project conducted at the U.S. Bureau of Mines in which many facets of artificial intelligence were woven together to solve industrial problems. Much of the synergy realized to accomplish the research effort is applicable to numerous other scientific problems. However, there is still much to be done. In the next chapter we provide a very brief overview and address some of aspects of this work that we believe are fertile research areas.

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Karr, C. L., and Gentry, E. J. (1993). Fuzzy control of pH using genetic algorithms. IEEE Proceedings on Fuzzy Systems, 1(1), 46–53.

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Valenzuela-Rendón, M. (1991). The fuzzy classifier system: A classifier system for continuously varying variables. In K. Belew and L. Booker (Eds.), Proceedings of the Fourth International Conference on Genetic Algorithms, 346–353.