Damage Detection- Uniform Load Surface

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DOI: 10.1177/1475921706072062

2007 6: 99Structural Health MonitoringJialai Wang and Pizhong Qiao

Improved Damage Detection for Beam-type Structures using a Uniform Load Surface

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99

Improved Damage Detection for Beam-type

Structures using a Uniform Load Surface

Jialai Wang1 and Pizhong Qiao2,*

1Department of Civil, Construction, and Environmental Engineering

The University of Alabama, Tuscaloosa, AL 35487-0205, USA2Department of Civil and Environmental Engineering, Washington State

University, Pullman, WA99164-2910, USA

A combined analytical and experimental study is conducted to develop efficient and effective damage

detection techniques for beam-type structures. Unlike many other vibration-based damage detection

methods, in which the mode shapes are often chosen to retrieve damage information, the uniform load

surface (ULS) is employed in this study due to its less sensitivity to ambient noise. In combination with

the ULS, two new damage detection algorithms, i.e., the generalized fractal dimension (GFD) and

simplified gapped-smoothing (SGS) methods, are proposed. The GFD method is developed by

modifying the conventional definition of fractal dimension. By using a moving window, the GFD of ULS

can be obtained for each sampling point, and due to the irregularity of ULS introduced by the damage,

a peak exists on the GFD curve indicating the location of the damage. Not only does such a peak at the

GFD curve locate the damage, but also it reveals the relative size of the damage. The SGS method

is also proposed to take advantage of the simple deformation shape of ULS. Both methods are then

applied to the ULS of cracked and delaminated beams obtained analytically, from which the damage

location and size are determined successfully. Based on the experimentally measured curvature mode

shapes, both the GFD and SGS methods are further applied to detect three different types of damagein carbon/epoxy composite beams. The successful detection of damage in the composite beams

demonstrates that the new techniques developed in this study can be used efficiently and effectively in

damage identification and health monitoring of beam-type structures.

Keywords structural health monitoring damage detection algorithm generalized fractal

d i m e n s i o n s i m pl i f ie d g a pp e d s m oo t hi n g m e th o d v i b r a t i o n m o d e

shapes composites delamination crack

1 Introduction

Structural health monitoring (SHM) is one of

the most important keys in maintaining safety

and integrity of the structures and avoiding loss

of human life and/or monetary loss due to the

catastrophic failure of structures. Among manySHM techniques, the dynamic response-based

damage detection method [1,2] attracts most

attention due to its simplicity for implementation.

*Author to whom correspondence should be addressed.

E-mail: [email protected]

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Copyright 2007 SAGE Publications,

Vol 6(2): 009912

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This technique makes use of the dynamic

response of structures which offers unique

information on the defects contained with these

structures. Changes in the physical properties of

the structures due to damage can alter the

dynamic response, such as the natural frequency

and mode shape. These parameter changes can beextracted to predict damage detection informa-

tion, such as the presence, location, and severity

of damage in a structure. The natural frequency

provides the simplest damage detection method

since damage tends to reduce the stiffness of the

structure. Therefore, a reduction of natural

frequency may indicate the existence of damage

in the structure. However, the natural frequency

is a global feature of the structure, from which

the location of the damage is difficult to deter-

mine. The modal parameters (e.g., the mode

shape and flexibility), which can capture the local

perturbation due to damage, are used in order to

locate damage. However, the modal parameters

obtained experimentally are sensitive to ambient

noise. To reduce the effect of noise, a new modal

parameter, the uniform load surface (ULS) was

proposed [15]. It is easy to note that the ULS is

essentially a weighted average of mode shapes.

Consequently, it is less sensitive to noise

compared to the mode shapes. Although the

numerical analysis showed that the ULS was

effective in damage detection [14], there is noexperimental study or implementation of the

concept with experimental data reported yet. In

this study, a combined analytical and

experimental study is conducted to detect damage

in the beam-type structures using the ULS.

To locate and size the damage, a lot of

damage detection algorithms [1,2] have been

developed. Most of them require the baseline data

of the healthy structures which is difficult to

obtain and sometime unavailable. The spatial

wavelet transform has become very popular

recently [13], and it could detect small perturba-

tion due to damage without the knowledge of the

healthy structure. The complexity of calculation

and the edge effect are two major drawbacks of

this method. Numerical simulation [10] also

showed that it is difficult to determine the size of

a vertical crack in beams by examining the

wavelet coefficients. The gapped-smoothing

method proposed by Ratcliffe and Bagaria [9] is

another efficient damage detection algorithm

without knowing the data of an undamaged

structure. Compared to the wavelet transform,

this method has a simpler calculation scheme, but

exhibiting lower accuracy in determining the

location of damage. In a recent study byHadjileontiadis et al. [3], a novel fractal dimension

(FD) damage detection algorithm was presented.

This method calculated the FD of a mode shape

by using a moving window. The resulting FD

curve was then used to detect damage. Damage

location and size were determined by a peak on

the FD curve which is attributed to the local

irregularity of mode shape introduced by damage.

This method successfully detected the location

and size of the crack in a cantilever beam when

the first mode shape was used. When the higher

mode shapes were considered, this method might

give misleading information as demonstrated in

their study. To overcome this shortcoming, a

modification on the definition of conventional

FD is proposed in this study. The resulting

modified FD bears no physical meaning of FD,

and therefore, it is referred to as the generalized

fractal dimension (GFD) in this study. The GFD

seems to have the same potential as the wavelet

transform in damage detection, but much easier in

calculation.

2 Simulation of Damaged Beams

2.1 Free Vibration of Cracked

Cantilever Beams

The free vibration of a cantilever beam of

length L with a transverse edge crack at x0 as

shown in Figure 1(a) is first considered. The edge

crack introduces the local flexibility at the crack

location, and it is conventionally modeled as a

rotational spring with infinitesimal thickness atthe crack location (see Figure 1(b)) [8].

The bending stiffness of the spring is determined

by the fracture mechanics principle and

given by [8]:

KT1

c 5:346

h

EIf

a

h

1

100 StructuralHealthMonitoring 6(2)



4/13

where h and a are the thickness of the beam and

the depth of the crack, respectively; E and I are

the modulus of elasticity and the moment inertia

of the beam, respectively; and f(a/h) is a

nondimensional parameter determined by the

crack geometry.

The equation of motion of the cracked beamis obtained as [12]:

w0000 x, t A

EI w x, t w0 x0, t

00 x x0 2

where wx, t w2x, t w1x, t. Equation (2)

can be solved by the variable separation method

using

w x, t Wxej!t: 3

Substituting Equation (3) into Equation (2) yields

the characteristic equation as

W0000x A!2

EI Wx W0x0

00 x x0 : 4

By considering the boundary conditions at the

cantilever end and using Laplace transformation,

the solution of Equation (4) is obtained as

Wx W000

2 S2 x

W0000

3

S3x W0x0

S1 x x0 H x x0 5

where ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiA!2=EI4

p , S1x sinhx sinx,

S2x coshx cosx, and S3x

sinhx sinx.

The boundary conditions at the free end are

given as

W00L 0, W000L 0 6

and the continuity conditions at the crack are

given as

W0 x0

W0 x0

EI

KTW00x0: 7

Substituting Equations (5) and (7) into the

boundary conditions in Equation (6) yields an

eigenvalue equation of , which can only be

solved numerically.

2.2 Free Vibration of Delaminated

Beams

The free vibration of a delaminated cantilever

beam shown in Figure 2 can be modeled as an

assembly of four sub-beams. The equations of

motion for each sub-beam are given by

EIw0000i x, t Awi x, t 0: 8

The displacement shape functions are thenobtained by the variable separation method as:

Wix Ci1cos ix Ci2sin ix Ci3cosh ix

Ci4sinh ix 9

where iffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiAi!2=EIi

4p

, i 1,2,3, and 4; 16 co-

efficients Cij (i, j 1, 2, 3, and 4) in Equation (9)

x0

L

ha

x0

x

1

A cantilever beam with an edge crack

2

Rotational spring model

(a)

(b)

Figure 1 Cracked cantilever beam model.

z

z

xH1

H2H3x

x

L1 a L2

L

1 423

x

Figure 2 Delaminated cantilever beam model.

Wang &Qiao Damage Detection for Beam-type Structures 101



5/13

can be determined by the following sixteen

boundary and continuity conditions.

The boundary conditions at both ends are

given as

W10 0, W010 0, W

004L2 0, W

0004 L2 0

10

and the displacement continuity conditions at the

crack are given by

W1L1 W20, W01L1 W

020,

W20 W30, W020 W

030,

W2a W3a, W02a W

03a,

W2a W40, W02a W

04a: 11

The force continuity is expressed as

P2 P3 P1 0, Q2 Q3 Q1,

M2 M3 H1

2 P3 M1

P2 P3 P4 0, Q2 Q3 Q4,

M2 M3 H1

2 P3 M4: 12

The displacement compatibility in the

x-direction requires

P2a

EA2

H3

2 W040

H3

2 W01L1

P3a

EA3

H2

2 W040

H2

2 W01L1

:

13

Therefore,

P3 EA2A3

A2 A3

H1

2a W01L1 W

040

: 14

Substituting Equation (9) into Equations (10)

(14) yields a set of 16 homogeneous linear

equations of coefficients Cij. To avoid a trivial

solution, the determinant of a coefficients matrix

of the linear equations must be zero, which

presents an eigenvalue equation ofi. The natural

frequency and mode shape of the delaminated

cantilever beam can be obtained by solving the

eigenvalue equation.

3 Uniform Load Surface (ULS)

The uniform load surface (ULS) was first

studied by Zhang and Aktan [15], and it was

found that the ULS is least sensitive to the

experimental errors. In a recent study of Wu and

Law [14], the ULS was shown to be very sensitiveto local damage and could be used to effectively

detect damage in the structure.

Considering a structure system with n degrees

of freedom, its modal flexibility is defined as

fk, l

Xnr1

rkTr l

!2r15

where r is the rth mass normalized mode shape

and !r is the rth nature frequency; fk, l is the

modal flexibility which references to the deforma-

tion at point k of the structure under the load atpoint l. Therefore, the deformation at point k

under the uniform load all over the structure

becomes:

k Xnl1

fk, lXnl1

Xnr1

rkrl

!2r

Xnr1

rkPn

l1 rl

!2r

Xnr1

wrrk

!2r: 16

Equation (16) indicates that the ULS is a

weighted average of mode shapes, and therefore,it is less sensitive to experimental error than the

mode shapes. Noting that every term in the

summation of Equation (16) has a factor of 1=!2r ,

the ULS converges very fast as the number of

contributing lower modes (n) increases.

Therefore, the ULS can be approximated by the

first few mode shapes.

4 Damage Detection Algorithms

Most of the existing model-based damage

detection methods require the baseline data of

healthy structures. The damage index is usually

calculated using the difference between the

damaged and intact structural model data. To

avoid the extra and difficult task of obtaining the

data of healthy structures, two new damage

detection algorithms capable of detecting the




6/13

damage without the knowledge of the intact

structures are proposed.

4.1 Generalized Fractal Dimension

(GFD) Method

The concept of fractal and its correspondingmathematical properties were established by

French mathematician Mandelbrot [7]. In mea-

suring a fractal curve, if the ruler length is

reduced by 1/r, its length would correspondingly

increase to L rD multiplying the original one.

D is called the fractal dimension (FD) of a fractal

curve. A regular smooth curve has a dimension

of 1; while a fractal curve has a fraction dimen-

sion which is >1. In general, the larger the value

ofD, the more irregular the curve. Therefore, the

fractal dimension has a potential to serve as a

damage index to reveal the irregularity intro-

duced by local damage in the structure as demon-

strated in a recent study by Hadjileontiadis et al.

[3]. In the FD method, a moving window with a

fixed size is used, and the FD is then calculated

for a small segment of mode shape falling into

the moving window. By sliding the moving

window along the beam, an FD curve along the

beam length can be plotted for a given mode

shape. Then, the damage can be detected by a

sharp peak displaying in the FD curve. The

Katzs FD expression [6] was used in their study:

FDMx logn

logn log d xi, M =L xi, M 17a

L xi, M

XMj1

ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiy xij

y xij1 2

xij xij1 2q

17b

d xi, M

max1jM

ffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffi ffiffiffiffiy xij

y xi 2

xij xi 2q

17c

where M is the number of points on the mode

shape falling into the moving window,

x 1=2xi xiM, n L= and is the average

distance between successive points.

For a cantilever beam with a crack (the depth

of crack a 0.1h) at x0 0.3L (Figure 1(a)), the

normalized first three mode shapes can be

obtained analytically by the solution presented

before. By using Equation (17), the FD curves of

the first three mode shapes are obtained and

presented in Figure 3. In this figure, the resolutionof the mode shape is 301, and the size of the

moving window M is 4. It can be seen that the

peak values really exist in Figure 3; however, they

are not at locations where the damage is in the

first two mode shapes (see Figure 3(a) and (b)). As

expected, there is a peak existing at the location of

crack in the FD curve of the third mode shape;

however, another peak appears at x0 0.79L

where there is no damage (Figure 3(c)). The results

in Figure 3 indicate that the existing FD fails to

detect damage in this case, leading to a need for

modification of the method.

As shown in Equation (17a), the FD is

mainly determined by the ratio of Ls/ds which

can be written as

LSxi, M

ds xi, M

PMj1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

yxij yxij1=xij xij1

2r

max1jM

xij xi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

yxij yxi=xij xi2r :

17d

Noting that yxij yxij1=xij xij1

y0xij1, Equation (17d) implies that a peak will

appear on the FD curve at the same location

wherey0 (the first derivative) reaches a peak value.

Such a peak value is induced by the waviness of

the mode shape and can be mistakenly interpreted

as an indicator of damage as demonstrated in

Figure 3. It is also shown in Equations (17) that

damage can cause irregularity in mode shape

which leads to a peak value at the location of the

crack on the FD curve. However, if this irregular-

ity is too small compared with the peak value of

y0, the FD peak value caused by damage will be

too small and overshadowed by the ones caused

by the waviness of the mode shape itself. Such a

phenomenon is illustrated in Figure 3(d). In this

figure, the close-up of the FD curve at the vicinity

of the crack of the first mode shape (Figure 3(a))

is presented. A peak is clearly shown at the




7/13

location of the crack since the much larger value

of FD at the clamped end is not presented in the

same figure. To avoid this difficulty caused by the

overshadowing ofy0, the FD algorithm is modified

so that the peak value induced by y0

can bereduced. This can be simply accomplished by

introducing a scale parameter S in the FD

algorithm, leading to a modified or generalized

FD method as,

GFDM, sx

logn

log n log dSxi, M =LSxi, M 18a

dSxi, M

max1


8/13

on the GFD curve indicates the existence and

location of the damage. It should be pointed out

that the GFD bears no conventional physical

meaning as compared to the FD, and it only

serves as an indicator of damage.

In Equation (18d), S must be chosen suffi-

ciently large in order to detect damage success-fully. Theoretically, S can be chosen as large as

you wish. However, a significantly large value of

S can cause a calculation problem as shown in

Figure 4(d). In this figure, although the peak

value still exists at the location of crack, the

oscillation also takes place on the GFD curve

due to the limitation of precision in the compu-

ter. Therefore, a proper value of S should be

chosen not only large enough, but also not too

large to cause calculation oscillation due to the

limitation of computer precision.

The GFD is then applied to the ULS of

cracked and delaminated cantilever beams

obtained in the previous section to see whether

the damage can be effectively detected by this

method. Two different crack sizes (a/h 0.1 and

a/h 0.2) are considered in obtaining the ULS of

the cracked cantilever beam (Figure 1(a)). The

GFD curves of these two ULS are presented in

Figure 5. The location of the crack is clearly

detected by a sharp peak on the GFD curves.

The larger size crack (i.e., a/h 0.2) causing a

higher peak at the location of crack than the

smaller one (i.e., a/h 0.1) (see Figure 5(a))

suggests that the size of the damage can also be

relatively quantified by the GFD approach. Itshould be pointed out that the same value of S

(S 100) is used in Figure 5(a). As shown in

Equation (18d), the GFD is smaller if a larger

S-value is used. Therefore, the consistent S-value

should be used when the GFD is implemented to

determine the size of the crack. The application

of the GFD to detection of delamination is

shown in Figure 5(b). Unlike the cracked beam

in which the crack causes a sharp peak on the

GFD curve, the delaminated beam introduces a

sub-curve in the delamination area on the GFD

curve which may indicate not only the location,

but also the size (length) of the delamination.

The different features of the GFD caused by

these two types of damage may also serve as

a tool to identify damage types in the structures.

It can be noted that the GFD shows a

similar fashion in damage detection as the spatial

wavelet transformation [13]. Compared to wavelet

1

1.00001

1.00002

1.00003

Mode 3 S = 10000

0.99999999

1.00000001

1.00000003

1.00000005

1.00000007

Mode 1

0.999999

1.000001

1.000003

1.000005

0 0.2 0.4 0.6

x

0 0.2 0.4 0.6

x

0 0.2 0.4 0.6

x

0 0.2 0.4 0.6

x

GFD

GFD

Mode 2

0.999998

1.000001

1.000004

1.000007

1.00001

GFD

GFD

(a) (b)

(c) (d)

Figure 4 Damage detection using the generalized fractal dimension (GFD): (a) crack is located by the GFD with a

proper S-value (S 100) using the first mode shape; (b) crack is located by the GFD with a proper S-value (S 100)

using the second mode shape; (c) crack is located by the GFD with a proper S-value (S 100) using the third mode

shape; and (d) oscillation caused by using a large S-value (S 1000) in the GFD method.




9/13

transform, the proposed GFD method enjoys the

following advantages: (a) simpler in calculation;

(b) less storage space needed for data; and

(c) easier to determine the crack size. Another

important feature of the GFD is that it onlyrequires a small segment of the measured signal

which makes it ideal for online data processing.

Figure 5(b) also shows that GFD may have the

potential to identify damage type.

4.2 Simplified Gapped-smoothing

(SGS) Method

The gapped-smoothing method was proposed

by Ratcliff and Bagaria [9] to locate delamination

in a composite beam without utilizing the data of

a healthy beam. This technique assumes that the

same shape of the healthy structure is smooth

and continuous and can be approximated by a

third order polynomial, and the damage will

introduce irregularity to the smooth mode shape.

To capture this irregularity, the mode shape of a

damage structure is compared with a locally

smooth third order polynomial, rather than the

healthy mode shape, and their difference is used

as a damage index. Since the ULS of a healthy

beam is a fourth order polynomial, one can

assume the ULS of healthy beam has the follow-

ing form of

yx c0 c1x c2x2 c3x3 c4x4: 19

In this study, unlike in the gapped-smoothing

method, where the polynomial needs to be

determined for every point, Equation (19) is for

the whole ULS due to the simple shape of the

ULS, and the coefficients c0, c1, c2, c3, c4 can be

determined by conducting a regression analysis

on the ULS obtained numerically or experimen-

tally. The damage index (DI) based on the

proposed simplified gapped-smoothing (SGS)

method is simply defined as the square of devia-tion (regression error) of the measured data from

the smoothed value given by Equation (19)

SGSx

ymeasuredx c0 c1x c2x2 c3x

3 c4x4

2: 20

The same set of damaged cases studied by the

damage detection algorithm using the GFD

method is examined by this method, and the

results are presented in Figure 6. For the cracked

beam shown in Figure 6(a), the crack is detectedby a sharp peak value of SGS and the value of

SGS in terms of DI gives the relative size of the

crack. In the case of the delaminated beam, the

starting and ending of the delamination are

indicated by two peak values of SGS as demon-

strated in Figure 6(b). These two successful cases

of different types of damage demonstrate that the

SGS method based on the ULS may serve as an

improved damage detection algorithm for the

beam-type structures.

5 Damage Detection of Carbon/Epoxy Composite Beams

Carbon/epoxy composites are commonly used

in structures undergoing higher stresses, such as

the aircraft and aerospace structures, due to their

high specific stiffness and strength. However,

0.99999999

1

1.00000001

1.00000002

1.00000003

1.00000004

0 0.5 1

x

GFD

a=0.2

a=0.3

(a)

(b)

0.99999

1.00001

1.00003

1.00005

0 0.2 0.4 0.6

x

GFD

a/h=0.1

a/h=0.2

Figure 5 GFD damage detection based on ULS:

(a) cracked cantilever beam and (b) delaminated canti-

lever beam.




10/13

the carbon/epoxy composite laminates, like other

composite materials and structures, are susceptible

to defects, which can significantly reduce thestrength of the structures and eventually grow to

catastrophic failure. The key to avoid the devas-

tating effect of the failure of carbon/epoxy compo-

site is to develop reliable SHM techniques which

can detect and identify the damage in the struc-

ture. To this aim, an experimental study was

recently carried out [4,5] to detect the damage in

carbon/epoxy beams with various damage cases,

and the experimental data (i.e., the curvature

mode shapes and natural frequencies) are pro-

cessed with the two aforementioned damage detec-

tion algorithms (i.e., GFD and SGS) developed in

this study.

The tested composite beam specimens were

made of carbon fiber and epoxy resins with a

total [0/90]4T lay-up of eight layers. The size of

the beam is 241.3 25.4 1.75 mm3. After

being clamped in the cantilever configuration,

the free span of the specimens was 228.6 mm.

An 8 12mm2 ceramic (lead-zirconate-titanate,

PZT) patch was attached to each specimen near

the clamped end as actuator, and the polymer

(polyvinylidenefluoride, PVDF) films were used as

sensors. The location of PVDF sensors used in the

test is shown in Figure 7. Three types of damage

were considered in the experiments, i.e., delamina-tion, impact, and saw-cut. The delamination was

created by inserting a piece of Teflon tape between

the second and third layers of the composites

during fabrication. The impact damage was cre-

ated by dropping an 8.0 kg mass from a height of

304.8 mm onto an undamaged carbon composite

beam, and then the actuators and sensors were

installed for measurement. The saw-cut with a saw

width of 1.6mm was used to cut the beam to

about 60% of the beam thickness through the

width of the beam. During the testing, a sweep

sine with a magnitude of 140V was run through

the PZT actuator to excite the beams. The

responses at each sensor point were measured by

the PVDF sensors and recorded by a dSPACE

data acquisition system. The recorded data were

then used in the modal analysis to generate the

mode shapes. It should be pointed out that the

resulting mode shape based on the PVDF sensors

is referred to as the curvature shape in this study,

which is not the actual curvature shape of the

beam, rather than the mode shape of the differ-

ence of slopes at the two ends of the PVDF sensor[11]. In order to construct the ULS, the first three

mode shapes and frequencies were obtained for

each specimen tested. The measured natural fre-

quencies are presented in Table 1. Three delamina-

tion cases (A, B, and C) were studied in Hamey [4]

and Hamey et al. [5]; for the sake of brevity, only

the results of delamination case C are presented in

this study to demonstrate the validity of the GFD

and SGS methods. The measured curvature mode

shapes are discussed in detail for each damage

case.

5.1 Delaminated Beam C

Delaminated beam C has a 25.4 mm delamina-

tion beginning at the location of Sensor 5 and

ending at the location of Sensor 7 (see Figure 7).

The SGS curve of measured curvature ULS is

calculated and presented in Figure 8(a). The

0.00E+00

3.00E05

6.00E05

9.00E05

1.20E04

0 0.5 1

x

DI

a=0.2

a=0.3

0.00E+00

2.00E08

4.00E08

6.00E08

0 0.2 0.4 0.6

x

DI

a/h=0.1

a/h=0.2

(a)

(b)

Figure 6 SGS damage detection based on ULS:

(a) cracked cantilever beam and (b) delaminated canti-

lever beam.




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delamination beginning location is picked up by a

distinct peak value appearing at the location ofSensor 4 on the SGS curve. Owing to the low

resolution of measurement, the ending location of

the delamination is not clearly detected by the

SGS method. Figure 8(b) shows the result of

damage detection of delaminated beam C using

the GFD method. Similarly, a distinct peak value

at the location of Sensor 4 indicates the beginning

location of the delamination. Note that the actual

beginning location of the delamination is at the

location of Sensor 5, while the detected location is

at the location of Sensor 4. This difference oflocating the delamination is caused by the

finite size of the PVDF sensor. The PVDF sensor

used in the experiment has a length of 38.1 mm;

while the space between the two sensor locations

is only 12.7mm. This means that part of the

sensor at Location 4 already falls in the delami-

nated region. Therefore, the curvature measured

at the location of Sensor 4 actually includes the

effect of delamination and reflects as a peak

in damage detection using either the SGS or

GFD curve. To increase the accuracy of damage

locating, smaller sensors and more measurements

are needed.

5.2 Impact Damaged Beam

The impact damaged beam has an 25.4 mm

long damage beginning at the location of Sensor

4 and ending at the location of Sensor 6. Both

the SGS and GFD methods are used to detect

damage based on the measured curvature-based

ULS. As shown in the SGS (Figure 9(a)) and

GFD (Figure 9(b)) curves, the location of impactdamage area was clearly indicated by the two

peaks at the locations of Sensors 4 and 7,

respectively.

5.3 Saw-cut Damaged Beam

The saw-cut was created on the tested beam to

simulate crack type of damage. The location of

the saw-cut is at the location of Sensor 6. The

SGS curve is obtained and given in Figure 10(a),

and it is observed that there is a sharp peak

appearing on the SGS curve at the location of the

saw-cut, which is very similar to the numerical

simulation of the cracked beam (Figure 6(a))

presented in Section 4.2. In Figure 10(b), the GFD

method is applied to the ULS, and once again a

distinct peak on the GFD curve at the location of

Sensor 6 clearly indicates the location of

the crack.

Table 1 Nature frequencies of healthy and damaged

composite beams.

ModeHealthy

(Hz)Saw-cut

(Hz)Impact(Hz)

Delam. C(Hz)

1 32.8 27.99 33.82 29.232 180.8 169.23 181.78 179.06

3 500.5 481.99 505.06 489.01

Figure 7 Sensor layout for the composite beam.

0.00E+00

1.00E07

2.00E07

3.00E07

0 5 10 15 20

Sensor location

Sensor location

SGS

1

1.02

1.04

1.06

1.08

0 10 20

GFD

(a)

(b)

Figure 8 Damage detection of delaminated beam C:

(a) SGS of delaminated beam based on ULS and (b) GFD

of delaminated beam based on ULS.




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6 Conclusions

In this article, a combined analytical and

experimental study is conducted to develop effi-

cient and effective damage detection techniques

for the beam-type structures. A relatively new

concept, the uniform load surface (ULS), is

chosen to extract damage information with two

newly developed damage detection algorithms,

i.e., the general fractal dimension (GFD) and

simplified gapped-smoothing (SGS) methods.

Both the GFD and SGS can be easily calculated

and used as the damage index to detect damage

in structures without the knowledge of the

healthy one. Numerical simulations show

the effectiveness and accuracy of both the

damage detection algorithms in assessing

the damage in the cracked and delaminated

beams. Experimental data of the measured curva-

ture mode shapes and natural frequencies are

used to construct the ULS of the beams with

various types of damage, which are then imple-mented with the two damage detection algo-

rithms. The SGS and GFD parameters

demonstrate that they could detect three types of

damage in carbon/epoxy composite beams. For

the delamination far away from the clamped

boundary, cracked (i.e., by saw-cut), and impact

types of damage, both methods provide clear

indication of the locations of the damage. The

two proposed damage detection algorithms (i.e.,

GFD and SGS methods combined with the ULS)

can be used in assessing damage of the beam-typestructures.

Acknowledgment

This study is based upon the work supported by the Air

Force Office of Scientific Research (AFOSR) under

Contract No. FA9650-04-C-0078.

0.00E+00

1.00E08

2.00E08

3.00E08

0 5 10 15 20

DI

1

1.004

1.008

1.012

1.016

GFD

(a)

(b)

Sensor location

0 5 10 15 20

Sensor location

Figure 9 Damage detection of impact damaged beam:

(a) SGS of impact beam based on ULS and (b) GFD of

impact beam based on ULS.

0.00E+00

2.00E08

4.00E08

6.00E08

0 5 10 15 20

Sensor location

Sensor location

DI

1

1.005

1.01

1.015

1.02

1.025

0 10 20

GFD

(a)

(b)

Figure 10 Damage detection of saw-cut beam: (a) SGS

of saw-cut beam based on ULS and (b) GFD of saw-cut

beam based on ULS.




13/13

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