Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 263

Table 6.4(a). Summary of monitoring indices selected as network inputs

Input
terminal of
network

Input
representation

RMS value of the signal
in the frequency band

1 x 1 [0, 300] Hz.

2 x 2 [300, 600] Hz

3 x 3 [600, 1000] Hz

4 x 4 [1000, 1500] Hz

5 x 5 [1500, 2500] Hz

Table 6.4(b). Summary of the conditions for various flank wear

Output terminal
of the network

Fuzzy
MF

Tool condition Flank wear

y 1 1 Initial wear 0 < wear < 0.1 mm

y 2 2 Normal wear 0.05 < wear < 0.3 mm

y 3 3 Acceptable wear 0.25 < wear <0.5 mm

y 4 4 Severe wear 0.45< wear <0.6 mm

y 5 5 Failure wear > 0.6 mm

w 11

x 1

y 1

Initial Normal Acceptable Severe Failure

x 2

1.0

y 2

x n

y n

w n m

Flank Wear
(mm)

Inputs ( x 1 , x 2 , …, x n ) ,
outputs (y 1 , y 2 , …, y n )
y j = max (min ( x i ,w ij ) )

0.05, 0.1, 0.25, 0.3, 0.45, 0.5, 0.55, 0.6

Figure 6.11. Fuzzy neural net topology (left), fuzzy membership functions of drilling
conditions (right)

The fuzzy membership functions of drilling conditions based on experimental
data and the observed system behaviour are set for output indices of the hybrid
network, and are shown in the Figure 6.11. The reason for choosing a trapezoidal
membership function is that it is difficult to quantify what exact percentage of tool
wear corresponds to a certain linguistic variable. In order to improve the training
speed of the hybrid network, the tool wear conditions are coded as follows: initial
(1,0,0,0,0); normal (0,1,0,0,0); acceptable (0,0,1,0,0); severe (0,0,0,1,0); and failure