Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 264

(0,0,0,0,1). If the tool condition is acceptable, then the output values of the hybrid
network are (0,0,1,0,0).
Once the hybrid neuro-fuzzy network has learnt the above nonlinear mapping
from a given set of training examples consisting of ( x , y ) values, thereafter, for a
new set of monitoring indices ( i.e . related to the frequency band of the vibration),
obtained from the drilling process through accelerometer, charge amplifier, and the
signal processing unit, the network will generate or predict a set of y values. The
maximum of y i , namely J , is converted to 1, and the others are converted to 0. For
instance, if J = max{ y i _ i =1, 2, 3, …, 5) = y 2 = 0.8, the predicted output of the
hybrid network is (0,1,0,0,0). This prediction indicates that the tool wear condition
belongs to the normal category. Exploiting the prediction capability of the hybrid
network and adopting similar methodologies one can monitor the tool wear in an
automated manufacturing system.
6.9 Concluding Remarks
In this chapter a hybrid neuro-fuzzy modelling frame work is proposed. An
accelerated training algorithm, based on either the backpropagation or Levenberg-
Marquardt algorithm and in combination with a modified error index extension,
has also been developed for training Takagi-Sugeno-type multi-input multi-output
or multi-input single-output neuro-fuzzy networks. The increased speed of training
convergence was experimentally confirmed on some examples of modelling and
forecasting of time series. It was observed that the addition of a small modified
error index term to the original performance function improves the convergence
speed of both standard backpropagation and the Levenberg-Marquardt algorithm
significantly.
The trained neuro-fuzzy network itself is found to be powerful for modelling
and prediction of dynamics of various nonlinear phenomena. However, the fuzzy
rules generated through neuro-fuzzy training are occasionally found to be not
transparent enough, in the sense that a clear interpretation of all the tuned fuzzy
sets is not possible. This is due to the fact that the membership functions, finally
tuned through neuro-fuzzy network training, are frequently very similar to each
other or they greatly overlap each other, giving rise to a difficult situation to
interpret. To solve this problem and to improve the interpretability of fuzzy rules,
set-theoretical similarity measures should be computed for each pair of fuzzy sets
and highly similar fuzzy sets should be merged together into a single set (Setnes,
Babuška, Kaymark, 1998) as discussed in detail in Chapter 7. Furthermore, the
tuned membership functions building a universal fuzzy set within the universe of
discourse should be removed because they do not contribute anything to the rule
base. Also, because the parameters of the Gaussian membership functions are
unconstrained, it is probable that the fuzzy partition occasionally may not look like
the usual fuzzy partition. In such cases, the interpretation of a trained neuro-fuzzy
system may also not be possible.
An additional issue is the determination of the optimum number of fuzzy rules
and hence, also the determination of optimum number of membership functions.
This is essential, because an unnecessarily larger rule base may overfit the noisy