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which was computed in two phases, during the training process and the testing process.
The deviations were calculated as the difference between the actual speed and the es-
timated speed, both for the training and testing sets. The second performance indicator
that was used to evaluate the generalization capacity of the tested configurations is the
Generalization Factor (GF), defined by Eq. (1).
GF =
k
n
∗ 100 (1)
Where n is the number of patterns that compose the validation set and k is the
number of such patterns estimated with an error less than 2 % (this value having been
fixed as a threshold level). Table 2 summarizes the results obtained from an alternative
configuration of neural networks for estimating feed speed (network number two). It is
quite evident that the configuration number 1 (with three hidden layers) showed better
generalization performance since GF is 100%. However, the MAD seemed to be a little
high from the operational point of view. If one considers an error of 31 mm/min in the
estimated feed speed, this may lead to undesirable or inappropriate time estimations
and tool life expectations significantly overestimated. Thus the selected configuration
was number 3, in Table 2 (with two hidden layers), which MAD is 1,3 mm/min, con-
sidered as acceptable from the operational point of view. Moreover, the generalization
factor of near 85% seems to be adequate, if one consider that the training set takes into
account a wide variety of types of milling tools and workpiece materials. The same type
of analysis was conducted to obtain the architecture of the first ANN that performs the
estimation of the cutting speed. Table 3 shows the selected configuration parameters for
both networks. Figure 3 (left) shows the net output and expected cutting speed values
obtained after the network was entirely trained and a comparison between the original
testing data and the parameters estimated by the neural network (Fig.3 right). For the
selection of feed speed a single layer network with one hidden layer was trained using
the same training data set used for training the network that selects the cutting speed.
Figure 4 (left) shows the convergence of the output mean error for the network that
was trained for selecting the cutting speed, where it can be noticed the low number of
epochs needed for attain the minimum required error. Figure 4 (right) shows the con-
vergence of the output mean error for the network during the training process of the
network for selecting the cutting speed. Again, the low number of epochs needed for
attain the minimum required error can be noticed. Figure 5 (left) shows the net out-
put and expected feed speed values obtained after the network was entirely trained and
on the right side of the Figure 5 a comparison between the original testing data and
the parameters estimated by the neural network is shown. To evaluate the performance
of the two developed networks, an additional test set was prepared for simulation and
comparisons ends. The results of the simulation tests were classified according differ-
ent criteria. Table 4 shows the performance in terms of percent error of the two both
networks according to the operation type (refer Figure 1). Table 5 presents the results
of the test grouped according to the material workpiece. Finally, table 6 presents the re-
sults obtained by the two networks according the hardness of the workpiece. As can be
appreciated, from table 5 and 6, network 1 presented the best results with errors within
the 3%. As it can be observed in the tables shown above, the approach presents different
performance between network 1 and network 2, i.e. network 1 performs better estima-
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