℄ ℄ ℄
S
0
A
0
℄A
0
S
0
℄℄ ℄
<
>
<
>
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
℄
A
0
S
0
℄•
℄−−
◦
•
−−
•
A
A
0
b
c
l
c
t
C
C
c
C
p
C
s
d
d
31
δ
ǫ
ǫ
ii
ǫ
T
33
E
f
F(ω)
G
g
31
h
c
I,i
J
k
K
l
L
p
λ
onde
M
ν
n
N
Ω
φ
Q
c
r
R
p
R
s
σ
s
S
S
0
S
c
s(t)
s
′
(t)
∆s
degraded
∆s
damage
t
tanδ
θ
t
c
U(ω)
V
,U
pzt
,V
pzt
v
c
v
onde
v
ph
w
w
0
,w
1
ω
0
x
¯
x
ξ
y
Y
c
Y
11
c
Y
libre
ζ
℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄
℄ ℄ ℄
℄
[0
o
,45
o
,90
o
,−45
o
]
s
,s=1.
.
.N
℄
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
℄
ν
E
L
E
T
ν
T
ν
T
G
L
G
T
E
1
=E
L
ν
12
=ν
L
E
2
=E
3
=E
T
ν
23
=ν
T
G
12
=G
L
G
23
=G
T
S
ǫ
σ
ǫ
11
ǫ
22
ǫ
33
2ǫ
23
2ǫ
13
2ǫ
12
=
1
E
1
−ν
12
E
1
−ν
12
E
1
0 0 0
−ν
21
E
1
1
E
2
−ν
23
E
2
0 0 0
−ν
12
E
1
−ν
23
E
2
1
E
2
0 0 0
0
0 0
1
G
23
0 0
0
0 0 0
1
G
12
0
0 0
0 0 0
1
G
12
σ
11
σ
22
σ
33
σ
23
σ
13
σ
12
l
σ
l
=S
−1
ǫ
l
T
ǫ
T
σ
θ
T
ǫ
=
cos
2
(θ)
s
in
2
(θ)
0
0
0
s
in(θ)cos(θ)
s
in
2
(θ)
cos
2
(θ)
0
0
0
−s
in(θ)cos(θ)
0
0
1
0
0
0
0
0
0
cos(θ)
s
in(θ)
0
0
0
0 −s
in(θ) cos(θ)
0
−2s
in(θ)cos(θ) 2s
in(θ)cos(θ) 0
0
0
cos
2
(θ)−s
in
2
(θ)
T
σ
=
cos
2
(θ)
s
in
2
(θ) 0 0
0
2s
in(θ)cos(θ)
s
in
2
(θ)
cos
2
(θ) 0 0
0
−2s
in(θ)cos(θ)
0
0
1 0
0
0
0
0
0 cos(θ) −s
in(θ)
0
0
0
0 s
in(θ)
cos(θ)
0
−s
in(θ)cos(θ) s
in(θ)cos(θ) 0 0
0
cos
2
(θ)−s
in
2
(θ)
℄0
o
90
o
℄ ℄ ℄ ℄
℄ ℄
℄ ℄ ℄ ℄ ℄
℄ ℄
℄ ℄ ℄
℄ ℄ ℄ ℄
℄ ℄
≃
≃
≃
≃
℄ ℄ ℄ ℄ ℄ ℄℄
x y
d
z
x ξ z ζ
t
x
k
ω
ξ=A
x
f
x
(z)e
j(ωt−kx)
ζ=A
z
f
z
(z)e
j(ωt−kx)
x
x
z
y
y
℄℄ ℄ ℄ ℄ ℄ ℄
S
0
A
0
℄0
500
1000
1500
2000
2500
3000
0
2000
4000
6000
8000
Frequence
(kHz)
Vit
es
se
d
e
gr
ou
pe
(
m/
s)
0
500
1000
1500
2000
2500
3000
0
2000
4000
6000
8000
Frequence
(kHz)
Vit
es
se
d
e
ph
as
e (
m/
s)
A
0
S
0
A
0
S
0
(a)
(b)
A
0
S
0
℄z ±
d
2
=0
c
l
c
t
tan(
βd
2
)
tan(
αd
2
)
=−
(k
4αβk
2
−β
2
2
)
2
tan(
βd
2
)
tan(
αd
2
)
=−(k
2
−β
2
)
2
4αβk
2
α
2
=ω
2
c
2
l
−k
2
,β
2
=ω
2
c
2
t
−k
2
f
λ
c
p
=f
λ
=ω
k
c
g
=
dk
A
0
S
0
℄ ℄ ℄ ℄ ℄ω
U(ω)
℄u(x
,t)=2Re
∞
0
U(ω)e
j(k(ω)x−ωt)
dω
k(ω)= ω
v
ph
(ω)
S
0
µs
µs
℄ ℄0
5
10
15
20
25
30
−1
0
1
Temps
(µs)
A
mp
lit
ud
e
0
5
10
15
20
25
30
−0
.05
0
0
.05
Temps
(µs)
A
mp
lit
ud
e
(a)
(b)
℄ ℄ ℄℄ ℄ ℄ ℄ ℄
Q
c
C
c
Y
11
c
h
c
g
31
S
c
v
c
ǫ
ii
℄V
0
=
Q
C
c
c
=
Y
11
c
h
c
g
31
S
c
(1−v
c
)
S
c
ǫ
ii
dS
s
θ
r=r
c
r=r
c
+2s
r
a
i
=0 a
0
=a
V
0
=
Q
C
c
c
=
Y
11
c
h
c
g
31
S
c
(1−v
c
)
S
c
(ǫ
rr
+ǫ
θθ
)rdrdθ=
Y
11
c
h
c
g
31
S
c
(1−v
c
)
S
c
(
du
dr
r
+
u
r
r
)rdrdθ
r
v
onde
f
λ
onde
n n=0,1,2,.
.
.
2r=
v
onde
f
(f)
n+
1
2
=λ
onde
(f) n+
1
2
℄n= 2rf
v
onde
(f)
−1
2
℄ ℄
0
10
20
30
40
50
60
70
80
90
100
−1
0
1
A
mp
lit
ud
e
no
r
ma
li
sé
e
temps
(µs)
0
10
20
30
40
50
60
70
80
90
100
−1
0
1
temps
(µs)
A
mp
lit
ud
e
no
r
ma
li
sé
e
0
10
20
30
40
50
60
70
80
90
100
−1
0
1
temps
(µs)
Dif
fé
re
nc
e
d’
a
mp
lit
ud
e
no
r
ma
li
sé
e
(b)
(a)
(c)
℄ ℄ ℄
5
10
15
20
−1
−0
.8
−0
.6
−0
.4
−0
.2
0
0
.2
0
.4
0
.6
0
.8
1
temps
(µs)
A
mp
lit
ud
e
S
igna
l
mesuré
Enve
loppe
Réf
lex
ions
,
autres
dommages
,
modes
.
.
.
Deux
ième
paquet
arr
ivé
Prem
ier
paquet
arr
ivé
℄ ℄
A
0
S
0
℄ ℄•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
Y
libre
I
V
ω
l
t
c
w
δ
C
ǫ
T
33
Ω
Y
libre
(ω)=I(ω)
V(ω)
=iωwl
t
c
(ǫ
T
33
(1−iδ))=iωC+Ω
Y
c
E
d
31
℄Y
c
(ω)=Y
libre
(ω)−iω
wl
t
c
(d
31
E)
℄ ℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄
℄
℄
y
x
b
w
y
y=b+wx
w b
b
w
0
y=w
0
+w
1
x
y
y
N
(x
1
,y
1
).
.
.
(x
n
,y
n
),n=1.
.
.N
w
1
¯
x ¯
y
w
1
=
N
i=1
(x
i
−¯
x)(y
i
−¯
y)
N
i=1
(x
i
−¯
x)
2
w
0
=¯
y−w
1
x
¯
y
m
φ
i
(x)
y=w
0
+
m
i=1
φ
i
(x)x
i
∼w
0
+
m
i=1
w
i
x
i
℄
φ
w
℄f(x
,w)=
M
i=1
w
i
φ
i
(x)+w
0
|
x|
ǫ
ǫ
E(w)=
N
1
N
i=1
|
y
i
−f(x
i
,w
)|
ǫ
+|
w|
|
2
|
x|
ǫ
=
0
|
x|<ǫ
|
x|−ǫ
℄α
∗
i
α
i
f(x
,α
∗
,α
)=
N
i=1
(α
∗
i
−α
i
)K(x
i
,x
)+λ
0
α
∗
i
≥0,α
i
∀
i
α
∗
i
α
i
=0,∀
i
K(x
i
,x
)
f(x
,w)
K(x
a
,y
b
)=
M
i=1
φ
i
(x
a
)φ
i
(x
b
)
℄α
∗
α
C
E(α
∗
,α
)=ǫ
N
i=1
(α
∗
i
+α
i
)−
N
i=1
y
i
(α
∗
i
−α
i
)+1
2
N
i=1
N
j=1
(α
∗
i
−α
i
)(α
∗
j
−α
j
)K(x
i
,x
j
)
N
i=1
(α
∗
i
−α
i
)=0,0≤α
∗
i
,α
i
≥C
,∀
i
℄
g
i
(x
i
,x
)
℄f(x
,α
∗
,α
)=
N
i=1
(α
∗
i
−α
i
)g
i
(x
i
,x
)+λ
0
℄℄
℄ ℄ ℄ ℄ ℄ ℄
1,
2
1
1
1
2
1
2
A
0
S
0
0
0
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
0
0
℄ ℄ ℄ ℄ ℄℄
ω
Generated
PZT
ω
s
s
p
p
p
s
p
℄ ℄
δ
3
−
5
−
2
Generated
℄ ℄<
℄ ℄℄ ℄
>
ω
1
Y
1
(ω)
=
1
jωC
s
+R
s
℄1
Y
2
(ω)
= 1
Y
1
(ω)
+
jωL
p
1+jω
L
p
R
p
+ω
2
C
p
L
p
= 1
Y
1
(ω)
+
jωL
p
1+2j
ω
ω
o
ξ−
ω
ω
o
2
ω
o
ξ
ω
o
=
1
L
p
C
p
ξ= 1
2R
p
L
p
C
p
℄ω
o
ξ
s
p
L
p
p
s
s
p
s
p
p
p
3
℄
s
ω
o
ξ
℄ ℄ ℄ ℄
=
℄s
s
<
p
p
p
s
s
p
p
p
s
s
℄℄
℄
<
>
<
>
℄ ℄
o
o
℄ ℄<
>
o
o
o
℄ ℄∆s
damage
(t)
∆s
degraded
(t)
s
′
(t)
s(t)
s
′
(t)=s(t)+∆s
degraded
(t)+∆s
damage
(t)
s
′
(t)
φ
s(t)+∆s
damage
(t)=s
′
(t)−∆s
degraded
(t)=IFFT[
ke
jφ
FFT(s
′
(t))
]
0
0
0
0
0
0
µ
℄0
0
0
0
℄ ℄
0
0
0
0
℄
0
0
0
0
0
0
0
0
0
0
1,
2
1
1
1
2
1
2
A
0
S
0
℄ ℄ ℄ ℄ ℄ ℄ ℄
0
0
℄ ℄ ℄ ℄℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄ ℄
Y
(
ω)pzt
℄Generated
℄ ℄ ℄℄ ℄
s
s
p
p
p
s
p
℄s
s
p
p
p
ω
i
ξ
i
Y(ω)
pzt
=
jωC
1
s
+R
s
+
n
i=1
jωL
i
1+2j(
ω
ω
i
)ξ
i
−(
ω
ω
i
)
2
−1
ξ
i
= 1
2R
pi
L
pi
C
pi
, ω
i
=
1
L
pi
C
pi
Rre
f
=
100
Ugenera
ted
Igenera
ted
a)
b)
PZT
Cs
Rs
Cp1
Rp1
Lp1
i
=
1
:n
Rpn
Cpn
Lpn
n
th
resonance
1s
t
resonance
Ω
℄3
0
0
℄A
0
=
U
T
+
U
b
S
0
=
U
T
-
U
b
U
T
U
b
℄ ℄V
pzt
(ω)
ǫ
ii
0
100
200
300
400
500
600
700
800
900
1000
−2
0
2
4
6
8
10
Frequency
(kHz)
Re
(
Y
PZ
T)
0
100
200
300
400
500
600
700
800
900
1000
−4
−2
0
2
4
6
Frequency
(kHz)
I
m (
Y
PZ
T)
0
200
400
600
800
1000
0
20
40
60
80
100
0
2
4
6
8
10
12
x
10
−3
Frequency
(kHz)
Adhes
ive
Coverage
Degradat
ion
(%)
Re
(
Y
PZ
T)
0
200
400
600
800
1000
0
50
100
−2
0
2
4
6
8
x
10
−3
Frequency
(kHz)
Adhes
ive
Coverage
Area
(%)
I
m (
Y
PZ
T)
a)
c)
d)
b)
V
pzt
(ω)
ǫ
ii
V
pzt
(ω)=
jωQ
Y
pzt
(ω)
pzt
(ω)
∝
1
Y
pzt
(ω)
S
pzt
ǫ
ii
dS
0
100
200
300
400
500
600
700
800
900
1000
−5
0
5
10
x
10
−3
Frequency
(kHz)
Re
(Y
P
ZT
)
0
100
200
300
400
500
600
700
800
900
1000
−2
−1
0
1
2
3
4
5
6
x
10
−3
Frequency
(kHz)
I
m(
Y
PZ
T)
0
200
400
600
800
1000
0
20
40
60
80
100
−5
0
5
10
x
10
−3
Frequency
(kHz)
Young
’s
Modu
lus
Degradat
ion
(%)
Re
(Y
P
ZT
)
0
200
400
600
800
1000
0
20
40
60
80
100
−2
0
2
4
6
x
10
−3
Frequency
(kHz)
Young
’s
Modu
lus
Degradat
ion
(%)
I
m(
Y
PZ
T)
d)
c)
b)
a)
80
%
60
% 50
% 40
% 20
%
100
%
100
%
80
%
60
% 50
% 40
% 20
%
℄ ℄ ℄ ℄
Generated
0
100
200
300
400
500
600
700
800
900
1000
−5
0
5
10
15
x 10
−3
Frequency (kHz)
Re
(Y
P
ZT
)
0
100
200
300
400
500
600
700
800
900
1000
−6
−4
−2
0
2
4
6
8
x 10
−3
Frequency (kHz)
I
m(
Y
PZ
T)
100%
75% 50
% 25%
75% 50
% 25
% 0%
100%
0
%
a)
b)
ξ
i
ω
0
0
℄∆
∆
s
′
(t)=s(t)+∆s
degraded
(t)+∆s
damaged
(t)
S
′
(ω)=S(ω)+∆S
degraded
(ω)+∆S
damaged
(ω)
ω
ω
φ
ω
F(ω)=
S(ω)+∆S
S(ω)
degraded
(ω)
FEM
=A(ω)e
jφ(ω)
A(ω)=
A
reference
(ω)
A
degraded
(ω)
, φ
(ω)=φ
reference
(ω)−φ
degraded
(ω)
ω
φ
A
degraded
(ω)
φ
degraded
(ω)
A
reference
(ω)
φ
reference
(ω)
S(ω)
S
damaged
(ω)
∆S
damaged
(ω)=S
′
(ω)−
S(ω)
F(ω)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≃
0
0
℄
ω
φ(ω)
℄0
0
0
0
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
Actua
l
damage
Phantom
damage
Phantom
damage
d)
b)
c)
a)
0
0
0
0
0
0
0
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
D
istance
(m)
Di
st
an
ce
(
m)
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Phantom
damage
Actua
l
damage
a)
d)
c)
b)
0
0
0
0
0
0
0
0
∼
0
0
1,
2
2
1
1
1
2
℄ ℄ ℄
℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄
≃
℄
8
±
±
±
3
℄ ℄
℄ ℄ ℄
0
20
40
60
80
100
✁1
✁0.5
0
0.5
1
T
ime
(µs)
No
r
ma
li
ze
d
a
mp
lit
ud
e (
V)
0
200
400
600
800
1000
0
0.5
1
Frequency (kHz)
No
r
ma
li
ze
d
a
mp
lit
ud
e (
V)
0
20
40
60
80
100
✁1
✁0.5
0
0.5
1
T
ime
(µs)
No
r
ma
li
ze
d
a
mp
lit
ud
e (
V)
0
200
400
600
800
1000
0
0.5
1
Frequency (kHz)
No
r
ma
li
ze
d
a
mp
lit
ud
e (
V)
0
20
40
60
80
100
✁1
✁0.5
0
0.5
1
T
ime
(µs)
A
mp
lit
ud
e
dif
fe
re
nc
e (
V)
0
200
400
600
800
1000
0
0.5
1
Frequency (kHz)
A
mp
lit
ud
e
dif
fe
re
nc
e (
V)
(b)
(
f)
(d)
(a
)
(c)
(e
)
℄ ℄ ℄ ℄
℄ ℄
0
5
10
15
20
25
30
35
40
45
50
4
3
2
1
0
1
2
3
4
T
ime
(µs)
A
mp
lit
ud
e (
m
V)
F
ind max
imum amp
l
itude
F
ind peaks 20
dB down
Extract
t
ime
d
ifference
℄
℄ ℄
℄ ℄ ℄
<
>
℄
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
℄ ℄ ℄
max
℄0
5
10
15
20
25
0
1
2
3
4
5
6
7
Impact number
Da
ma
e
di
a
me
te
r
m
m
Fa
i
lure
reso
ld
0
5
10
15
20
5
10
15
20
25
Actua
l
RN
I
Es
ti
ma
te
d
R
NI
Test plate 1
Test plate 2
Test plate 3
Test plate 4
Linear fit
≃
0
1
2
3
4
5
6
7
0
5
10
15
20
25
Dama e
d
iame
ter mm
I
mp
ac
ts
❈r
it
ica
l
D
iame
ter
℄±
±
≃
℄ ℄ ℄ ℄ ℄ ℄℄ ℄
℄
1,
2
2
1
1
1
2
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄
℄ ℄
≃
℄8
±
±
±
3
℄ ℄ ℄
o
℄ ℄ ℄ ℄℄
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
LF
c
or
re
la
ti
on
v
ari
an
ce
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
PS
D
va
ri
an
ce
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
HF
ma
xi
mu
m
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
RF
s
ta
nd
ar
d
de
vi
ati
on
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
LF
me
di
an
0
5
10
15
20
25
30
0
0
.5
1
Impact
number
(N)
Ti
me
s
ig
na
l
me
an
a
mp
lit
ud
e
(c)
(a)
(e)
(b)
(d)
(f)
℄℄ ℄
generated
℄Rre
f
=
100
Ugenera
ted
Igenera
ted
a)
b)
PZT
Cs
Rs
Cp1
Rp1
Lp1
i
=
1
:n
Rpn
Cpn
Lpn
n
th
resonance
1s
t
resonance
Ω
ω
i
ξ
i
Y(ω)= 1
jωC
s
+R
s
+
n
i=1
jωL
pi
1+2j(
ω
ω
i
)ξ
i
−(
ω
ω
i
)
2
−1
ξ
i
= 1
2R
pi
L
pi
C
pi
, ω
i
=
1
L
pi
C
pi
i
n
th
Generated
℄
A
0
S
0
℄ ℄0
0
ω
∆
ω
∆
ω
ω
0
10
20
30
0
200
400
600
800
1000
0
20
40
Impact
number
(N)
Frequency
(kHz)
A
0
a
mp
lit
ud
e
co
ns
ta
nt
0
10
20
30
0
200
400
600
800
1000
−200
−150
−100
−50
0
50
Impact
number
(N)
Frequency
(kHz)
A
0
un
wr
ap
pe
d
ph
as
e
ch
an
ge
(
o
)
0
10
20
30
0
200
400
600
800
1000
0
50
100
Impact
number
(N)
Frequency
(kHz)
S
0
a
mp
lit
ud
e
co
ns
ta
nt
0
10
20
30
0
200
400
600
800
1000
−200
−150
−100
−50
0
50
Impact
number
(N)
Frequency
(kHz)
S
0
un
wr
ap
pe
d
ph
as
e
ch
an
ge
(
o
)
(b)
(d)
(c)
(a)
A
0
S
0
ω
ω
ω
φ
ω
F(ω)=
S(ω)+∆S
S(ω)
degraded
(ω)
FEM
=A(ω)e
jφ(ω)
A(ω)=A
reference
(ω)
A
degraded
(ω)
, φ
(ω)=φ
reference
(ω)−φ
degraded
(ω)
ω
φ
A
degraded
(ω)
φ
degraded
(ω)
A
reference
(ω)
φ
reference
(ω)
∆S
damaged
(ω)=S
′
(ω)− S(ω)
F(ω)
A
0
S
0
S(ω)
0
✶0
20
✸0
✹0
50
60
✼0
80
90
0
5
10
Adhes
ive
cove
rage
deg
rada
t
ion
(%
)
Si
mu
la
te
d
mo
da
l
da
mp
in
g
(
%)
0
5
10
15
20
25
4
6
8
Impac
t
numbe
r
(N
)
Me
as
ur
ed
mo
dal
da
mpi
ng
(
%)
0
5
10
15
20
25
20
30
40
Impac
t
numbe
r
(n
)
Ad
he
siv
e
co
ve
ra
ge
de
gr
ad
ati
on
(
%)
(c
)
(b
)
(a
)
em
i
t
ter
rece
iver
℄A
0
S
0
A
SCF
(ω)=A
PZT1
(ω)∗A
PZT2
(ω), φ
SCF
(ω)=φ
PZT1
(ω)+φ
PZT2
(ω)
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
LF
c
or
re
la
ti
on
v
ari
an
ce
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
PS
D
va
ri
an
ce
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
HF
ma
xi
mu
m
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
RF
s
ta
nd
ar
d
de
vi
ati
on
0
5
10
15
20
25
0
0
.5
1
Impact
number
(N)
LF
me
di
an
0
5
10
15
20
25
30
0
0
.5
1
Impact
number
(N)
Ti
me
s
ig
na
l
me
an
a
mp
lit
ud
e
wo
SCF
w
ith
SCF
(c)
(a)
(e)
(b)
(d)
(f)
℄℄ ℄
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
℄=
0
5
10
15
20
25
1
0
1
2
3
4
5
6
7
8
Da
ma
ge
di
a
ma
te
r
(
m
m)
Fa
i
lurethresho
ld
(NDT)
•
℄−−
≃
℄ ℄0
5
10
15
20
25
0
5
10
15
20
25
30
35
Ac
tu
❛lRN
I
Est
i
m
✂t
❡ ❞R
NI
◦
•
−−
℄±
±
0
1
2
3
✄5
✻ ☎0
5
10
15
20
25
D
✆m
✆❣e
✝i
✆me
te (mm
)
R
UL
(
R
NI
)
0
1
2
3
✄5
✻ ☎5
0
5
10
15
20
25
R
UL
(
R
NI
)
Be
f
♦e
❙✞❋Af
te
❙✞❋ ✞it
ic
✆l
✝i
✆me
te
•
≃
≃
℄ ℄℄ ℄
A
0
S
0
8.
4±6.
7
5.
1±4.
3
±
±
