Fuzzy Welding Flaw Detection

8/2/2019 Fuzzy Welding Flaw Detection

1/14

Fuzzy Sets and Systems 108 (1999) 145}158

Detection of welding #aws from radiographic images

with fuzzy clustering methods

T.W. Liao,* D.-M. Li, Y.-M. Li

Industrial and Manufacturing Systems Engineering Department, Louisiana State University, Baton Rouge, LA 70803, USA

Computer Science Department, Louisiana State University, Baton Rouge, LA 70803, USA

Received December 1996; received in revised form May 1997

Abstract

Manual interpretation of radiographic weld images is subjective, inconsistent, labor intensive, and sometimes biased.

This paper presents a welding #aw detection methodology based on fuzzy clustering methods. The methodology

processes each weld image line by line. For each line, 25 features are selected. The performance of two fuzzy clustering

methods, i.e. fuzzy k nearest neighbors (K-NN) and fuzzy c-means, are studied and compared. It is found that the fuzzy

K-NN classi"er outperforms the fuzzy c-means classi"er with the best results of 6.01% missing rate and 18.68% false

alarm rate. Issues related to the selection of features and training examples are also discussed. 1999 Elsevier Science

B.V. All rights reserved.

Keywords: Welding #aw; Radiographic NDT technique; Feature extraction; Fuzzy clustering

1. Introduction

Welding is one of the major joining processes.

Poor weld quality could be caused by inadequate

or careless application of established welding tech-

nologies or substandard operator training. Major

welding #aws include porosity, slag inclusions, lack

of fusion, lack of penetration, cracks, under"tting,

undercutting, residual stresses, etc. Most of these

#aws are subsurface and have to be tested nondes-

tructively. Nondestructive testing (NDT) tech-

niques for welded joints usually consist of visual,

* Corresponding author. Tel.: #1-504-388-5365; fax: #1-

504-388-5990; e-mail: [email protected].

radiographic, magnetic particle, liquid penetrant,

and ultrasonic testing methods [7]. NDT testing is

particularly important for critical applications

where weld failure can be catastrophic, such as in

pressure vessels, load-bearing structural members,

and power plants. Radiography and ultrasonic

testing are two most principal NDT methods to

examine welds for subsurface #aws. Radiography is

particularly e!ective in detecting volumetric defects

which contain either extra mass or missing mass.

This study focuses on the radiographic technique.

Conventionally, a radiographic weld image is

produced by permitting X-ray or gamma-ray

source to penetrate the welded component andexpose a photographic "lm, which is then inspected

by a certi"ed inspector using a view box. This

0165-0114/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 5 - 0 1 1 4 ( 9 7 ) 0 0 3 0 7 - 2


2/14

manual interpretation process is subjective, incon-

sistent, labor intensive, and sometimes biased.

Therefore, a few attempts have been made to devel-

op algorithms for identifying anomalies in welds.

Some of these works are reviewed below. Daumet al. [4] used a segmentation algorithm to detect

the defects, after subtracting a background imagefrom the original radiograph. The background

image was derived by a spline approximation.

A similar approach was adopted by Eckelt et al.

[6], except that they obtained the background

image by using various low-pass "lters. Gayer

et al. [8] developed a two-step method for the

automatic inspection of welding defects from real-

time radiography. The "rst step is a fast search for

defective regions achieved by two di!erent algo-

rithms based on the relative irregular behavior of

a defect. The second step is the "ne identi"cation

and location of defects achieved by a sequential

similarity detection algorithm or a thresholding

algorithm. The advanced Quality Technology

Group of Lockheed Martin Manned Space Sys-

tems has been interested in the computer-aided

interpretation of the Space Shuttle External Tank

welds. In one research project utilizing the Geomet-

ric Arithmetic Parallel Processor (GAPP), an over-all detection performance of 66.5% for #aws

ranging from 0.01 to '2.5 was reported. Thedetection method was a weak gradient detection

algorithm followed by a weld detector [3]. Liao

and Li [12] developed a welding #aw detection

methodology that processes each weld image line

by line. Each line pro"le is "tted before processed.

The methodology consists of four parts: prepro-

cessing, curve "tting, pro"le-anomaly detection,

and postprocessing.

This paper presents a welding #aw detection

methodology based on fuzzy clustering methods.

The test results of fuzzy K-NN and fuzzy c-means

algorithms are compared. The weld images must be

in digital form to be processed by the computer.

This can be achieved either by using a real-time

radiography system directly or by digitizing "lms

using a high resolution digitizer. The later ap-

proach is taken in this study. But the same method

can be applied to data taken directly from a real-time radiography system. Rather than directly

processing the raw data, features with discrimina-

tion power are extracted upon which the classi"er

bases its determination of the class of the observed

object.

The remainder of this paper is organized as fol-

lows. In the next section, image acquisition proced-ure is detailed. Section 3 describes the methodology

including extraction of features, the fuzzy K-NNalgorithm, the fuzzy c-means algorithm, and the

post processing procedure. The test results are pre-

sented in Section 4, followed by discussion. The

conclusions are given in the last section.

2. Image acquisition

X-ray "lm strips of about 3.5 in wide by 17 in

long were digitized four at a time using the NDT

SCAN II digitizer [9]. Four strips were laid on the

digitizer with the scan direction orthogonal to the

long axis of the strips. The strips were digitized at

70 m resolutions (about 7 lp/mm) to produce a5000-pixel by 6000-line image, which is eventually

processed to "nd anomalies in the welds. Along

with each 5000-pixel by 6000-line image, a deci-

mated image of 20 times smaller (250-pixel by 300-

line) was also produced. Each pixel has 12 bits. Thedigitized images were all stored in the VICOM "le

format. Every image contains reference objects toidentify positions in the welds or to calibrate the

X-ray. These objects include rulers, penatrometers,

densitometers, identi"cation letters, space between

weld strips, etc. Only the items within the weld are

of interest.

Twenty-"ve probability-of-detection (POD)

tapes, originally prepared for the project conducted

by Lockheed Martin Electronics, Information

and Missile Group for Lockheed Martin Manned

Space Systems, are used in this study. Each POD

tape consists of a full-size image and a decimated

image. The POD test was designed to produce

the data from which a probability-of-detection

curve as a function of the object's size can be

produced. It is intended to give a measure of the

con"dence that objects of a particular size could

be found.

Prior to welding #aw detection, the 250-pixelby 300-line decimated image is "rst processed by

a weld extraction methodology [13] to "nd the

146 T.W. Liao et al. / Fuzzy Sets and Systems 108 (1999) 145}158


3/14

locations of welds. Processing the decimated image

reduces the amount of data needed to be processed,

thus shorten the processing time. Based on the

location information, the welds are then extracted

from the full size image and used for welding #awdetection.

3. Welding 6aw detection methodology

3.1. Feature extraction

Rather than directly using the raw data, some

measures or descriptors are often selected uponwhich the classi"er bases its determination of the

classes of the observed objects. These measures,

commonly called features, form the feature spacethat is generally of a much lower dimension

than the data space. The process of searching for

internal structure in data items, that is, for fea-

tures or properties of the data is called feature

extraction. Extraction of desirable features is an

extremely di$cult task and very much problem

dependent.

In this study, a trial-and-error procedure was

used to extract a total of 25 features from each

line image (or pro"le) of the weld image. Both

the original pro"le and its "tted pro"le, obtainedusing the cubic B-spline approach, are used to

extract these features. The e!ectiveness of these

features are illustrated by comparing a good pro"le

with a bad pro"le, as shown in Fig. 1. Fig. 2 plots

the normalized values of selected features for

both pro"les. Before describing the extracted fea-tures, the curve "tting procedure is "rst explained

below.

3.1.1. Curve xtting

The spline curve "tting algorithm introduced in

[5] serves as the noise reduction technique to

smooth the image. The smoothness of the "tted

curve can be controlled by changing the smoothing

factor. In this study, the smoothing factor is dy-

namically adjusted based on the &&roughness'' of the

test pro"le. Therefore, the implemented curve "t-ting algorithm can be deemed as an adaptive noise

reduction technique.

Fig. 1. Sample &&good'' and &&bad'' pro"les.

The spline curve "tting technique is brie#y de-

scribed below. Given a set of data points (xP, y

P),

r"1, 2,2 ,m, with a)xP(x

P>)b and a cor-

responding set of weights wP, the technique can be

applied to determine a spline s (x) o n [a, b], of

a speci"ed degree k with knots a"

,

,2 , E ,E>"b such that s (x) satis"es the following

constraints of the smoothness of "tting and the

T.W. Liao et al. / Fuzzy Sets and Systems 108 (1999) 145}158 147


4/14

Fig. 2. Plot of normalized feature values of the pro"les shown in

Fig. 1.

tightness of"tting :

"EG

(sI (G#)!sI(

G!)), (1)

"KP

(wP

(yP!s (x

P))))S, (2)

where g is the number of knots; sI (x) is the kth

derivative of the s(x); S is the smoothing factor

which determines the extent of smoothing.

The spline function s(x) constructed as linearly

independent B-splines of degree k has the following

expression:

s(x)"E

G\I

cGN

GI>(x), (3)

NGI>

(x)"(G>I>!

G)I>H

(G>H!x)I

>I>l"0, lOj (G>H!

G>J

),

(4)

(G>H!x)I

>"

(G>H!x)I,

0,

x)G>H

,

x'G>H

,(5)

where cG

is the B-spline coe$cient of s (x); k is the

degree of the spline function; and G

are the knots.

To impose that all B-splines vanish outside of the

interval [a, b], it is chosen that

\I"

\I>"2"

"

"a,

(6)

b"E>"E>"2"E>I"E>I> .

The constraints a!ects the spline s (x) in the fol-

lowing way. If S is large, the residuals, yP!s(x

P),

may be large. But s(x) can be expected to be

smooth. On the other hand, if S is small, the spline

will "t the data closely as required by small resid-uals at the cost of smoothness. An appropriately

chosen S allows a good compromise between the

closeness of "t and the smoothness. The values of

S depend on the weights wP. S is recommended to

be in the range ofm$'2m if the weights are takenas 1/y

Pwith y

Pan estimate of the standard devi-

ation ofyP

. If nothing is known about the statistical

error in yP, each w

Pcan be set equal to one and S is

determined by trial and error. In this research, the

later approach is taken.

It is a challenge to "nd a single smoothing factorS that works for all weld images, which are known

to have widely di!erent intensity levels and widths.

Therefore, it is desirable to have a smoothing factor

adaptive to each weld image to be tested. Accord-ingly, the concept of &&roughness'' is introduced

to indicate the noisiness of the original pro"le.

The &&roughness'' denoted by R is calculated as

follows:

R"N

G

(IG!I

G), (7)

where N

is the total number of#uctuation cycles

in the pro"le; IG

is the peak graylevel of the ith

#uctuation cycle; and IG

is the trough graylevel of

the ith #uctuation cycle. Each pair of peak and

trough constitutes a #uctuation cycle. One hundred

line pro"les were selected. For each pro"le, theR value was calculated and the appropriate S value

was found by trial and error. The speci"c smooth-

ing factor, de"ned as smoothing factor over width

=, is found to be a linear function of R. That is,S/="177#3.54R.

Note that the #uctuation cycles caused by

welding #aws should be excluded in calculating R.



5/14

Generally, the magnitude of the #uctuation cycle

(IG!I

G) caused by a #aw is considerably larger

than those caused by noises within a particular

pro"le. A recursive procedure is applied to detect

such outstanding values until the remaining valuesare closely clustered.

The FITPACK package, which is available [email protected], was used for curve "tting in this

study.

3.1.2. Features reyecting the symmetricity

ofxtted proxle

It is observed that the "tted pro"le generally is

symmetrical if there exists no defects in the line

image. The B-spline coe$cients cG

are used to com-pute the symmetricity. If we have n coe$cients c

Gin

one "tted pro"le which has no defects, the coe$c-ient c

will equal or almost equal to c

Land c

will

equal or almost equal to cL\

, and so on. Therefore,

the sum of di!erence between these corresponding

terms re#ects the degree of symmetricity (DOS) of

the "tted pro"le. In the case that n is an odd

number, the middle value cL>

is ignored. DOS

is selected as the "rst feature for welding #aw detec-

tion. A good pro"le tends to have a smaller DOS

value than a bad pro"le, as shown in Fig. 2 (0.41 vs.

0.72 shown as feature number 0).

Since a #aw usually covers more than one lines,

a pro"le defect is usually preceded and/or followed

by a similar pro"le anomaly. For each line image

to be tested, the preceding and subsequent two

lines are also considered to "nd the median DOS

as the second feature, designated as M}DOS. This

feature tells that if one line is &&bad'' but its sev-

eral neighbor lines are &&good'', then this line isprobably a noise. This feature is used to prevent

identifying a noise as a defect to decrease the false

alarm rate.

3.1.3. Goodness of proxle xtting

As shown in Fig. 1, a good pro"le is generally

&&smooth'' and its "tted pro"le tends to deviate from

the original pro"le uniformly. On the other hand,

a bad pro"le is always distorted in some form and

its "tted pro"le tends to have a large di!erence withthe original pro"le at the #aw boundary. Based on

this observation, the di!erence of the correspond-

ing point between the original pro"le and its "tted

pro"le is calculated. The range between the max-

imum di!erence and the minimum di!erence

divided by the average di!erence is used as the

feature to re#ect the goodness of "tting (GOF).GOF is selected as the third feature for welding

#aw detection.Based on the same argument used to derive the

second feature, the fourth feature is derived from

GOF and denoted as M}GOF.

3.1.4. Correlation between the template proxles and

the test proxle

Five representative good pro"les (original not

"tted) are selected as the template pro"les, as

shown in Fig. 3. Note that some of them look bad.

The following equation is used to calculate thecorrelation between the test pro"le and each of

these "ve template pro"les:

Corr(t, I)" tG*

IG/( t

G *I

G, (8)

where tG

and IG

are the intensity of the ith pixel for

the template pro"le and the test pro"le, respective-ly. The largest of these "ve values is selected as the

"fth feature. A high correlation is expected if the

test pro"le is a good one. For the good and bad

pro"les in Fig. 1, the values are 0.996 and 0.990,respectively. The di!erence between these two

values is negligible. This indicates that this feature

alone cannot tell a good pro"le from a bad one.

This feature is kept because it reduces the overall

false alarm rate, as shown in Table 1 (25-feature vs.

24-feature).

Note that the test pro"le must be registered with

the template pro"le before calculation. The peak

intensity location is used to achieve that. If the test

pro"le has a di!erent width with the template pro-"le, the smaller width is used.

3.1.5. Zoning features

Zoning features are extracted from "tted pro"les.

Each "tted pro"le to be tested is evenly divided into

four zones with each zone has one quarter of pro"le

width. Five primitives are de"ned as shown inFig. 4 with primitives a, b, c, d, and e covering

0$22.53, 45$22.53, [67.53, 903], [!67.53,



6/14

Fig. 3. Five template pro"les used to calculate correlation.

!903], and !45$22.53, respectively. Tracing

the pro"le from left to right pixel by pixel, thenumber of each primitive in each zone is sum-

marized. To account for varying width, the speci"c

number of each primitive is actually used, which is

computed as the total number of that primitivedivided by the zone width. If only primitive b exist

in zones 1 and 2, it is safe to say that no defects exist



7/14

Table 1

The results of feature selection

Number of features 4 20 21 24 25

False alarm rate % 32.90 27.49 49.00 23.11 22.99

Missing rate % 31.30 13.14 19.00 10.70 10.70

Total successful rate % 67.30 74.58 51.50 78.69 78.78

Fig. 4. Five primitives used to derive zoning features.

in these zones. In other words, it is highly possible

that there is defect of some sort in the line image if

primitives a, d, or e exist in zones 1 and 2. Similarly,

if only primitives d and e show up in zones 3

and 4, we can say that no defects exist in this

section. Otherwise, there is an indication of

defect.

To take the information of neighboring pro"les

into account, three pro"les (one to be tested, one

preceding it, and one following it) are processed at

one time and the average values is used as the

features for the test pro"le. Each test pro"le has

four zones and the number of each "ve primitives is

calculated for each zone. Therefore, we have 20

features with the "rst "ve corresponding to the "ve

primitives in zone 1, the next "ve corresponding tothe "ve primitives in zone 2, and so on. Fig. 2 shows

that primitives d and e exist in the second zone (the

14th and 15th features) of the bad pro"le shown in

Fig. 1, indicating the #aw.

3.2. Fuzzy k-NN algorithm

Bezdek suggested that interesting and useful al-

gorithms could result from the allocation of fuzzyclass membership to the input vector thus a!ording

fuzzy decisions based on fuzzy labels [16]. The

fuzzy K-NN algorithm [10] is one such algorithms

been developed utilizing fuzzy class memberships of

the sample sets and thus producing a fuzzy classi-

"cation rule.

Under the condition that the value di!erence

among the feature data is not too big, the fuzzy

K-NN algorithm requires no preprocessing of the

labeled sample set prior to use. The algorithm as-

signs class membership to a sample vector rather

than assigning the vector to a particular class. The

advantage is that no arbitrary assignments are

made by the algorithm. But, if the value di!erence

among the features is large enough, we should

normalize the data prior to use to get a much better

result.

Given a set of sample vectors, +x1 , x2 ,2 ,xn,a fuzzy c partition of these vectors speci"es thedegree of membership of each vector in each of

c classes. It is denoted by the c by n matrix U, whereuGH"u

G(x

H) is the degree of membership ofxj in class

i, for i"1, 2,2 , c, and j"1, 2,2 , n. The follow-

ing properties must be true for U to be a fuzzyc partition.

AG

uGH"1, (9)

0(LH

uGH(n, (10)

uGH3[0, 1]. (11)

The basis of the algorithm is to assign member-

ship as a function of the vector's distance from itsK nearest neighbors and those neighbors' member-

ships in the possible classes. Let ="+x1 ,x2 ,2 ,xn, be the set of n labeled samples, also letuGH

, or uG(xj), be the membership in the ith class of

the jth vector of the labeled sample set. The algo-

rithm is as follows [11]:



8/14

BEGIN

Input x, of unknown classi"cation.

Set K, 1)K)n.

Initialize i"1.

DO UNTIL (K nearest neighbors to x found)Compute distance from x to xi .

IF (i)K) THENInclude xi in the set of K nearest neighbors

ELSE IF (xi closer to x than any previous nearest neighbor)

THEN Delete the farthest of the K nearest neighbors,

Include xi in the set of K nearest neighbors.

END IF

END DO UNTIL

Initialize i"1.

DO UNTIL (xassigned memberships in all classes)

Compute uG(x) using Eq. (12).

Increment i.

END DO UNTIL

END

Here, the assigned memberships are given as fol-

lows:

uG(x)"

)H

uGH

(1/#x!xH#K\)

)H

(1/#x!xH#K\)

. (12)

According to Eq. (12), the assigned memberships

of x are in#uenced by the inverse of the distances

from the nearest neighbors and their class member-ships uGH

. The variable m determines how heavily

the distance is weighted when calculating each

neighbor's contribution to the membership value. Ifm"2, then the contribution of each neighboring

point is weighted by the reciprocal of its distance

from the point being classi"ed. As m increases, the

neighbors are more evenly weighted, and their rela-

tive distance from the point being classi"ed have

less e!ect. As m approaches one, the closer neigh-

bors are weighted far more heavily than those

farther away. The commonly used m is 2. #*#denotes the Euclidean distance.

The membership assignment to the ith class for

the labeled data xj (say in class j ) is computed

according to the following equation:

uGH"

0.51#(nG/K) ) 0.49

(nG/K) ) 0.49

if i"j,

if iOj .(13)

The value nG

is the number of the neighbors

found which belong to the ith class. This method

attempts to fuzzify the memberships of the labeled

samples, which are in the intersecting class regions

of the sample space, and leaves the samples that are

well away from this area with complete member-

ship in the known class. As a result, an unknown

sample lying in this intersecting region will be in-

#uenced to a less extent by the labeled samples that

are in the fuzzy area of the class boundary. Obvi-

ously, the memberships calculated by Eq. (13)

satisfy Eqs. (9)}(11).

3.3. Fuzzy c-means algorithm

Fuzzy c-means algorithm, also called fuzzy

ISODATA, was "rst presented by Bezdek [2]. It is

considered that all samples in the universe belong

to a certain class but all with a di!erent member-

ship.

The purpose of clustering is to determine the

cluster centers which are the representative values

of features corresponding to the classi"ed catego-

ries. Let X"+x1 , x2 ,2 ,xp,3RQ , x"(x

, x

,

2 , xQ) be a feature vector, and x

GHis the jth feature

of individual xi . For each integer c, 2)c(n, letVAL

be the vector space of real (c;n) matrices and letuGH

denote the ijth element of any U3VAL

. The res-ultant function u

G: XP[0, 1] becomes a member-

ship function, and uG

is called a fuzzy subset or fuzzy



9/14

cluster in X. Here uGH"u

G(xj ) is called the grade of

membership ofxj in the fuzzy set uG. In the space of

samples, assuming that there are n samples which

can be divided into c classes. Consider the following

subset ofVcn :

Mfc"+U3Vcn "uGH3[0, 1] i , j,. (14)

Each U3MDA

is called a fuzzy c-partition of X;M

DAis the fuzzy c-partition space associated with X.

For any real number m3 (1,R), de"ne the real

value function JK

:Mfc;LcPR by

JK

(;,


10/14

Fig. 5. Histograms of the distance values between (a) positive and (b) negative examples and their means.



11/14

frequency is selected. Accordingly, 75 pairs of

examples with 75 each in the &&good'' and &&bad''

classes are selected initially as the training data.

The e!ectiveness of"ve di!erent sets of features

are studied. The "rst set consists of four features:DOS, M}DOS, GOF, M}GOF. The second fea-

ture set uses only the 20 zoning features. The thirdset comprises 21 features: zoning features plus cor-

relation. The fourth set consists of 24 features:

DOS, M}DOS, GOF, M}GOF and zoning fea-

tures. The "fth set includes all 25 features: DOS,

M}DOS, GOF, M}GOF, correlation, and zoning

features. The test results are provided in Table 1.

The missing rate indicates the percentage of bad

lines misclassi"ed as good. The false alarm rate is

the percentage of good lines misclassi"ed as bad.

The total successful rate is computed as the number

of correct classi"cations over total lines tested. The

best feature set is the set with all 25 features with

10.70% missing rate, 22.99% false alarm rate, and

78.78% total successful detection rate. Therefore,

all 25 features are applied in identifying welding

#aws.

To further reduce the missing rate and false

alarm rate, the training data are expanded by in-

cluding some examples which were misclassi"edpreviously. The performance of three expanded sets

of examples with 91, 108, and 141 pairs, respective-ly, are studied. The results are shown in Table 2.

From this table it can be seen that the best case is

the training data set containing 108 pairs of exam-

ples with false alarm rate of 18.67%, missing rate of

6.01%, and total successful rate of 83.15%. This

results is, though not perfect, considered to be very

good when compared with past studies. The results

also imply that more examples do not always pro-

duce better performance. More examples are good

if they reinforce the classi"cation capability. Other-

Table 2

The results of di!erent training data sets

The number of training data 78 91 108 141

(pairs of good and bad examples)

False alarm rate % 22.99 2 2.18 18.68 26.51

Missing rate % 10.90 8.52 6.01 34.48

Total successful rate % 78.78 79.79 83.15 72.34

wise, the classi"er will get confused and yield

a worse result, as in the case of the training data set

of 141 pairs of examples. In this particular case,

both the false alarm and missing rates increase.

The classi"cation results serve as the inputs tothe postprocessing operation which draws a rectan-

gular box around the image area where the classi-"er classi"ed as defect. Fig. 6 shows sample weld

images in which inclusions are detected. One clear

Fig. 6. Sample detection results of &&inclusion'' type welding

#aws.



12/14

Fig. 7. Sample detection results of &&crack'' type welding #aws.

miss is noted. Fig. 7 shows sample weld images in

which cracks are successfully detected. Fig. 8 shows

the detection of a lack of penetration defect. Theimages were processed for contrast enhancement

by using the tools provided in the Khoros software

package [11] before presented.

4.2. Based on fuzzy c-means

The fuzzy c-means classi"er is a unsupervised

one. It does not require training data. Using all 25features, the fuzzy c-means classi"er is also applied

to the same test data set to determine its perfor-

Fig. 8. Sample detection results of &&lack of penetration'' type

welding #aws.

mance in welding #aw detection. The missing rate is8.50% while the false alarm rate is 33.19%. Com-

pared with those results obtained by the fuzzy

K-NN classi"er, the missing rate is 3.45% higher

and the false alarm rate is 15.52% higher.

5. Discussion

The success of an automated pattern classi"ca-

tion system depends both on the classi"er and the



13/14

features the classi"er operates on. Automated iden-

ti"cation of welding #aws from radiographic im-

ages is no exception. This study demonstrates that

a higher successful rate can be achieved by using

the fuzzy K-NN classi"er versus the fuzzy c-meansclassi"er. A higher successful rate is also achieved if

all 25 features are used compared with other sub-sets of features tested.

It is well known that a solution to a pattern

recognition task is highly problem dependent.

A good solution to one task might not be

good for another. For any pattern recognition

task, there might exist an optimal solution. But

the optimal solution is usually unknown. To "nd

the optimal feature set, two streams of feature

selection methods can be generally distinguished.

The "rst relies on searching an optimal trans-

formation T to reduce the dimension of the orig-

inal feature space [14]. Suppose that the original

features are z

through zK

and the selected fea-

tures are f

through fL

, n(m. Hence, in matrix

notation, f"Tz. The second approach to feature

selection is concentrated on searching an optimal

subset of the feature set using a search procedure

based on an appropriate measure of e!ectiveness

[15].In selecting features for the subject application,

a trial and error procedure was followed. A featureis "rst generated based on our knowledge of the

problem domain and then tested to determine its

e!ectiveness. The feature is selected if it is proved

e!ective. Otherwise, it is discarded. The 25 features

selected might not form the best feature set. There

might be a better feature which actually exists but

not generated. But if there is a better feature, we do

not know what it is. This is one area where im-

provement could be made. Although unlikely, there

might also exist a better feature subset because we

did not test all possible subsets of 25 selected fea-

tures, either.

As far as the classi"er is concerned, many classi-

"ers other than the two fuzzy clustering methods

utilized in this study could also be used. Bayes

classi"er and multilayer perceptron neural network

are just two established examples. Not to mention

other newly developed algorithms such as thevalidity-guided (re)clustering algorithm [1]. The

open question is &&Is there a better classi"er than

the fuzzy K-NN classi"er for the subject applica-

tion?'' This is another area needed to be further

investigated in the future.

The unknown is how much room is left for

improvement. Trying not to be too pessimistic,but our experience tells us that it is impossible

to achieve 0% missing and false alarm rates. Due tothe nature of the radiographic image data, an

attempt to decrease the missing rate will most

likely incur higher false alarm rate also. Therefore,

in our opinion, a more reasonable goal is to

achieve 0% missing rate at minimum false alarm

rate. Such a system can then be trusted to perform

NDT inspections for a critical application. Of

course, it will still require a human expert to verify

the detection results to "lter out the false alarms.

Nevertheless, with such a system available the ef-

fort required from the human expert will be greatly

reduced.

6. Conclusions

We have presented a fuzzy clustering based

methodology for detecting welding #aws from

radiographic images. The methodology processeseach image line by line. For each line, 25 features

are selected. The fuzzy K-NN classi"er is found togive lower missing rate and lower false alarm rate

than the fuzzy c-means classi"er. Detailed dis-

cussions were also given related to the selection of

training data and feature set. Five di!erent sets of

features were tested. It was found that the set with

all 25 features is the best.

Currently, the system at best can achieve 6.01%

missing rate and 18.68% false alarm rate. To im-

prove the system performance, future research will

devote to "nding better features and classi"ers.

Ideally, a 0% missing rate at minimum false alarm

rate should be attained.

Acknowledgement

This work is supported jointly by Lockheed

Martin Manned Space Systems, New Orleans andthe Board of Regents, Louisiana through the

LEQSF(1994-96) RD-B-06 grant.



14/14

References

[1] A.M. Bensaid, L.O. Hall, J.C. Bezdek, L.P. Clarke, M.L.

Silbiger, J.A. Arrington, R.F. Murtagh, Validity-guided

(re)clustering with applications to image segmentation,

IEEE rans. Fuzzy Systems 4 (2) (1996) 112}123.

[2] J. Bezdek, Pattern Recognition with Fuzzy Objective Func-

tion Algorithms, Plenum Press, New York, 1981.[3] E. Cloud, K. Fraser, S. Krywick, Automated examination

of X-ray welds, Final Report to ockheed Martin MSS,

Lockheed Martin Electronics, Information and Missiles

Group, Orlando, Florida, 1992.

[4] W. Daum, P. Rose, H. Heidt, J. H. Builtjes, Automatic

recognition of weld defects in X-ray inspection, Brit. J.

ND 29(2) (1987) 79}82.

[5] P. Dierckx, Curve and Surface Fitting with Splines, Claren-

don Press, Oxford, 1993.

[6] B. Eckelt, N. Meyendorf, W. Morgner, U. Richter, Use of

automatic image processing for monitoring of welding

process and weld inspection, Proc. 12th =orld Conf. on

ND, 1989, pp. 37}41.[7] G.R. Edward, Inspection of welded joints, in: ASM Hand-

book, vol. 6,=elding, Brazing and Soldering, ASM Interna-

tional, Materials Park, Ohio, 1993, pp. 1081}1088.

[8] A. Gayer, A. Saya, A. Shiloh, Automatic recognition of

welding defects in real-time radiography, ND Interna-

tional 23 (3) (1990) 131}136.

[9] W.A. Graeme, Jr., A.C. Eizember, J. Douglass, Digital

image analysis of nondestructive testing radiographs, Ma-

terials Evaluation (Feb. 1990) 117}120.

[10] J.M. Keller, M.R. Gray, J.A. Gigens Jr., A fuzzy k-nearest

neighbor algorithm, IEEE rans. System Man Cybernet.SMC-15 (1985) 580}585.

[11] K. Konstantinides, J.R. Rasure, The Khoros software de-

velopment environment for image and signal processing,

IEEE rans. Image Processing 3 (3) (1994) 243}252.

[12] T.W. Liao, Y.-M. Li, An automated radiographic NDT

system for weld inspection: Part II, Flaw detection, ND

& E International 31 (3) (1998) 183}192.

[13] T.W. Liao, J.-W. Ni, An automated radiographic NDT

system for weld inspection: Part I, Weld extraction, ND

& E Int. 29 (3) (1996) 157}162.

[14] W.S. Meisel, Computer-Oriented Approaches to Pattern

Recognition, Academic Press, New York, 1972.

[15] W. Siedlecki, J. Sklansky, On automatic feature selec-tion, Int. J. Pattern Recognition Artif. Intell. 2 (1988)

197}220.

[16] L. Zadeh, Fuzzy sets, Inform. and Control 8 (1965) 338}353.


Fuzzy Welding Flaw Detection

Documents

Transcript of Fuzzy Welding Flaw Detection