FUZZY CLUSTERING, GENETIC ALGORITHMS AND NEURO ... - ITM

622 P.F. VAN LITH et al.
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FIGURE 12 Input space and rule locations for fuzzy model obtained with ANFIS.
Contour plot indicates degree of fire, dots indicate input data.
formance of the different technique is possible. The most important
criteria for comparison in this work are:
. Modeling errors.
. Transparency and interpretability of the identified models.
. Sensitivity to initialization.
With respect to modeling errors, it can be seen in Figs. 6–8 that all of
the constructed hybrid models perform comparably. All techniques are
capable of producing a fuzzy submodel with acceptable performance.
The differences between the hybrid models are caused by the various
submodels for , since the physical model structure is the same for
all of the hybrid models. This discrepancy with the measurements is
caused by a series of errors. First of all, the fuzzy submodels are
identified using estimates of . Furthermore, the submodels are fit to
these estimates, introducing fitting errors. Finally, as mentioned
before, the runs in Figs. 6–8 are free runs, which means that model
errors are propagated through the simulation run by integration and
will increase in magnitude. Modeling errors can be reduced by optimizing
the parameters of the fuzzy submodel once the hybrid model is
constructed, by using hybrid model output and state measurements
(Table VI). This is a topic for future research. Since every identification
technique yielded a suitable fuzzy submodel, it is interesting to make a