Chen, Joseph C. "Neural Networks and Neural-Fuzzy Approaches in an In-Process Surface
Roughness Recognition System for End Milling Operations"
Computational Intelligence in Manufacturing Handbook
Edited by Jun Wang et al
Boca Raton: CRC Press LLC,2001

©2001 CRC Press LLC

16

Neural Networks and
Neural-Fuzzy
Approaches in an
In-Process Surface
Roughness Recognition
System for End

Milling Operations

16.1 Introduction

16.2 Methodologies

16.3 Experimental Setup and Design

16.4 The In-Process Surface Roughness Recognition
Systems

16.5 Testing Results and Conclusions
Numerous other studies have explored the topography of milled surfaces. Many of these focused on
predicting the two- or three-dimensional shape of a milled surface under ideal and non-ideal conditions.
Kline et. al. [1982] demonstrated the effects of cutter runout on surface errors, and surface errors or
dimensional inaccuracies were predicted using the cantilever beam theory for cutter runout. Another
study by Babin et al. [1985] applied the cantilever beam theory to predict the topography of wall surfaces
produced by end milling. Armarego and Deshpande [1989] presented one more milling process geometry
model that incorporates cutter runout to predict cutting forces.
Sutherland and Babin [1985] demonstrated a two-dimensional worst-case analysis of the slot floor
surface. However, the model for the slot floor surface significantly underpredicted surface roughness
values. Research by Kolarits and DeVries [1989] extended the previous model to account for varying cut
geometries and feed rates. This extended floor surface generation model improved prediction capabilities
considerably. However, the roughness parameter predictions for some of the tests were found to deviate
greatly from measured values.
You and Ehmann [1989] developed a comprehensive model to predict the three-dimensional surface
texture generated by ball end mills. They also presented an algorithm for three-dimensional representa-
tions of the machined surface; however, the effect of flexibility of the cutter-workpiece system was not
considered in this model. Montgomery and Altintas [1991] presented the effects of the cutter-workpiece
system flexibility in their force and surface prediction model in order to analyze the surface generation
mechanism in peripheral milling under dynamic cutting conditions.
All models previously discussed represent only deterministic cutting models, but most machined
surfaces exhibit interrelated characteristics of both random and deterministic components. Zhang and
Kapoor [1991] demonstrated the effect of random vibrations on surface roughness in the turning process.
These vibrations were shown to occur due to random variations in the microhardness of the workpiece
material. Ismail and others presented a surface generation model in milling that included both cutter
vibrations and the effects of tool wear [Ismail et al., 1993]. Melkote and Thangaraj [1994] presented
another enhanced end milling surface texture model including the effects of radial rake and primary
relief angles. These three models, limited to laboratory usage or based on theoretical analysis, could not
be implemented as an in-process monitoring system.
The findings of this literature review, in addition to communication with leading private industrial
research and development laboratories in the state of Iowa (including Winnebago Co. in Forest City;

is the most representative and commonly used algorithm, in addition to being relatively easy to apply;
additionally, it has been consistently successful when used in practical applications [Das et al., 1996;
Huang and Chiou, 1996].
The backpropagation algorithm can be divided into two main processes, the process of

learning

and
the process of

recalling

.

16.2.1.1 The Learning Process

Step 1. Given network parameters:
Set all the necessary parameters, such as the number of input neurons (

i

), the number of
hidden layers and the number of neurons included in each hidden layer (

h

), the number of
output neurons (

j

Equation (16.3)
Equation (16.4)
Step 5: Calculate the error term.
(a) The error term of the output layer:
Equation (16.5)
(b) The error term of the hidden layer:
Equation (16.6)
net W xh X h
hih
i
ih
=•
∑
_–_
θ
H f net
hh
net
h
=
()
=
+
1
1 exp
–
net W hy H y
jh hj h j
=〈−__
θ


©2001 CRC Press LLC

Step 6: Calculate the revised weight of the weight matrix and the revised bias of the bias vector.
(a) For the output layer:
Equation (16.7)
(b) For the hidden layer:
Equation (16.8)
Step 7: Adjust and renew the weight matrix and the bias vector.
(a) For the output layer:

W_hy

hj

= W_hy

hj
+

∆

W_hy

hj

,

(b) For the hidden layer:

W_xh

ih

= W_xh

ih
+

∆

W_xh

ih

,

θ

_h

h

=



, and the bias vector

θ_

h

and

θ_

y

.
Step 3: Load the input vector

X

of a testing example.
Step 4: Calculate and infer the actual output Y.
(a) Calculate the output vector

H

of hidden layers.
Equation (16.11)
Equation (16.12)
(b) Infer the actual output vector

Y


y

+

]. Each domain interval can be divided into 2

N

+ 1 regions. The value of

N

is dynamic for different variables, and the lengths of each region can be equal or unequal. Each
region is denoted by
∆∆
Why H y
hj j h j j
_,_–==
ηδ θ ηδ

∆∆
Wxh X h
ih h i h h
_,_–==
ηδ θ ηδ

net W xh X h
hih
i

=
+
1
1 exp
–
xx
ii
–
,
+
[]

©2001 CRC Press LLC

SN (Small N), S(N-1) (Small N-1), …, MD (Medium), … , LN (Large N),

Equation
(16.15)
and then assigned a fuzzy membership function. The divisions of the input and output spaces are shown
in Figure 16.1, where

N

is 2 for


V

). The output variable is the surface roughness average value,

R

a

. A triangular
membership function specified by three parameters {

a

,

b

,

c

} is employed as follows:
Equation (16.16)

FIGURE 16.1

The domain intervals of the input–output variables and triangular membership function.
MDS1S2S3 L1 L2 L3
0

x
1
+
0
triangle x a b c
xa
xa
ba
axb
cx
cb
bxc
cx
;,,
–
–
–
–
()
=
≤
≤≤
≤≤
≤







N

+ 1 fuzzy regions
quantifying the universe of discourse

X

i

.
The center points of each linguistic variable are
Equation (16.18)
Equations 16.17 and 16.18 are also used for the output variable

y.

16.2.2.2 Step 2. Generate Fuzzy Rules from Given Data Pairs through Experimentation

Three steps are used for generating fuzzy rules:
1. Determine the degree of input–output data obtained from the successful experiment.
2. Assign the input–output pairs to the region with the maximum degree.
3. Obtain one rule from one pair of designated input–output data.
In this study, the experimental input–output pairs were
Equation (16.19)
where

i

denotes the number of input–output pairs.
1. A human expert examined these rules to ensure their usefulness and correctness.

.
3. After all of the input and output elements were determined, each element was assigned to the
region with the maximum degree.
4. One rule from one pair of the desired input–output pair [

S

1

,

F

1

,

D

1

,

V

1

,

R

21
SFDVR
ii i i
a
i
,, ,, ,
[]
µ
x
xx
x
xxxx
xx
x
xxxx
i
ic
s
iccs
ci
s
icsc
()
=
∈+
[]
∈
[]

