A First Course in FUZZY and NEURAL CONTROL

5.7. EXAMPLE 2: TRAINING A NEURAL NETWORK 185

Computeallthenineweightupdates:

1.∆w 10 =−η(δh 1 )(x 0 )=−(0.1)(− 5. 098 ◊ 10 −^6 )(1) = 5. 098 ◊ 10 −^7

2.∆w 11 =−η(δh 1 )(x 1 )=−(0.1)(− 5. 098 ◊ 10 −^6 )(1) = 5. 098 ◊ 10 −^7

3.∆w 12 =−η(δh 1 )(x 2 )=−(0.1)(− 5. 098 ◊ 10 −^6 )(3) = 1. 5294 ◊ 10 −^6

4.∆w 20 =−η(δh 2 )(x 0 )=−(0.1)(8. 056 ◊ 10 −^4 )(1) =− 8. 056 ◊ 10 −^5

5.∆w 21 =−η(δh 2 )(x 1 )=−(0.1)(8. 056 ◊ 10 −^4 )(1) =− 8. 056 ◊ 10 −^5

6.∆w 22 =−η(δh 2 )(x 2 )=−(0.1)(8. 056 ◊ 10 −^4 )(3) =− 2. 417 ◊ 10 −^4

7.∆u 10 =−η(δy 1 )(h 0 )=−(0.1)(− 0 .0170)(1) = 0. 0017

8.∆u 11 =−η(δy 1 )(h 1 )=−(0.1)(− 0 .0170)(0.9997) = 0. 0017

9.∆u 12 =−η(δy 1 )(h 2 )=−(0.1)(− 0 .0170)(0.9526) = 0. 0016

Using the delta rule, the new weights are updated as

W =

∑

w 10 +∆w 10 w 11 +∆w 11 w 12 +∆w 12

w 20 +∆w 20 w 21 +∆w 21 w 22 +∆w 22

∏

u =





u 10 +∆u 10

u 11 +∆u 11

u 12 +∆u 12





In this example, we see that since the weight updates are very small, the network
is very nearly trained to obtain the desired outputd=0. 9. Repeated compu-
tations will make the outputy 1 tend toward any desired near-zero tolerance.

5.7 Example2:traininganeuralnetwork ...............

In this example, we discuss a practical application of significance to the cot-
ton ginning industry. Typically, when cotton undergoes ginning, trash particles
from the harvesting process have to be removed. Trash is comprised of bark from
the cotton plants, pieces of stems (sticks), leaves, crushed leaves (pepper), and
other extraneous matter from the cotton farms. The ginning process comprises
machines that can remove most or all of the trash particles. Thefinal grade
of ginned cotton is determined by the amount of remaining trash that cannot
be removed from the cotton without seriously affecting the material properties.
Identifying trash, therefore, constitutes a significant step in optimizing the num-
ber of trash-removing machines that can be placed on line during the ginning
process.
Identifying trash particles requires that we identify the features of each type
of trash, and determine which features can be used to distinguish between
ìbark,î ìstick,î ìleaf,î and ìpepper.î Once we have the features, we can choose
the appropriate neural network architecture, and train the neural network to