456
W. Wu et al.
⎧
⎪ ⎨
⎪ ⎩
l = l A − l B =
(x + c) 2 + y 2 −
(x − c) 2 + y 2 = v · t
x
2
l 2 /4
−
y
2
c 2 − l 2 /4
= 1
⇒
⎧
⎨
⎩
if l = 0, then x = 0
if y = 0, then x = ±
l
2
and l 1 =
l + v · t
2
, l x =
v · t
2
(40.1)
The method of sound velocity measurement proposed in this paper is based on
the fact that the distance between the AE source and the sensor directly affects the
measured sound velocity, this method takes into account the difference of the sound
velocity calculated by the signal received by the sensor near or far from the AE source.
A ring of sensors array is arranged around the circumference of the steel bifurcated
pipe, pencil lead breaks (PLBs) are implemented at a certain position where is in the
connection line of the two sensors selected. The time when the PLBs signal arrive
at the two sensors respectively is recorded and TDOA (t) is calculated, l is the
distances difference of respective source distances from the two sensors. The mean
value of the TDOA of the three PLBs signals at the same position is t, and a data
point (t, l) is obtained.
The equation of linear regression of a series of data points (t i , l i ) is y = ax +b,
where a is the slope and b is the intercept.
In the experiment, 18 data points of (t i , l i ) and 6 data points of (t i , l i )
were obtained, as shown in Table 40.2 (The maximum sensors space involved in the
calculation of sound velocity is 2700 mm). The time error bars and linear regression
line of the data are shown in Fig. 40.6.
The analysis shows that when l is small, the variance of the time difference(the
time error bar) is short relatively, when l increases, the time error bar is longer and
the time difference is larger.
The regression equation is: y = 4622x − 28, so the value of 4600 m/s can be
taken as the sound velocity.
Table 40.2 Velocity Measurement
l (mm)
t 1 (ms)
t 2 (ms)
t 3 (ms)
t (ms)
Velocity (m/s)
350
0.0825
0.0820
0.0701
0.0782
4488
650
0.1502
0.1510
0.1502
0.1505
4313
750
0.1753
0.1757
0.1757
0.1756
4278
1150
0.2597
0.2598
0.2596
0.2597
4432
1350
0.2662
0.2930
0.2929
0.2840
4756
2700
0.5994
0.5786
0.5992
0.5924
4509
W. Wu et al.
⎧
⎪ ⎨
⎪ ⎩
l = l A − l B =
(x + c) 2 + y 2 −
(x − c) 2 + y 2 = v · t
x
2
l 2 /4
−
y
2
c 2 − l 2 /4
= 1
⇒
⎧
⎨
⎩
if l = 0, then x = 0
if y = 0, then x = ±
l
2
and l 1 =
l + v · t
2
, l x =
v · t
2
(40.1)
The method of sound velocity measurement proposed in this paper is based on
the fact that the distance between the AE source and the sensor directly affects the
measured sound velocity, this method takes into account the difference of the sound
velocity calculated by the signal received by the sensor near or far from the AE source.
A ring of sensors array is arranged around the circumference of the steel bifurcated
pipe, pencil lead breaks (PLBs) are implemented at a certain position where is in the
connection line of the two sensors selected. The time when the PLBs signal arrive
at the two sensors respectively is recorded and TDOA (t) is calculated, l is the
distances difference of respective source distances from the two sensors. The mean
value of the TDOA of the three PLBs signals at the same position is t, and a data
point (t, l) is obtained.
The equation of linear regression of a series of data points (t i , l i ) is y = ax +b,
where a is the slope and b is the intercept.
In the experiment, 18 data points of (t i , l i ) and 6 data points of (t i , l i )
were obtained, as shown in Table 40.2 (The maximum sensors space involved in the
calculation of sound velocity is 2700 mm). The time error bars and linear regression
line of the data are shown in Fig. 40.6.
The analysis shows that when l is small, the variance of the time difference(the
time error bar) is short relatively, when l increases, the time error bar is longer and
the time difference is larger.
The regression equation is: y = 4622x − 28, so the value of 4600 m/s can be
taken as the sound velocity.
Table 40.2 Velocity Measurement
l (mm)
t 1 (ms)
t 2 (ms)
t 3 (ms)
t (ms)
Velocity (m/s)
350
0.0825
0.0820
0.0701
0.0782
4488
650
0.1502
0.1510
0.1502
0.1505
4313
750
0.1753
0.1757
0.1757
0.1756
4278
1150
0.2597
0.2598
0.2596
0.2597
4432
1350
0.2662
0.2930
0.2929
0.2840
4756
2700
0.5994
0.5786
0.5992
0.5924
4509