40 Localization of Acoustic Emission Sources …
455
The parts of the rib protruding from the shell plate may cause the change of the
acoustic propagation paths, and the acoustic velocity may also vary greatly after
transmitting through the weld or rib. In particular, the location accuracy of the AE
source will be lower in the small triangular area composed of the apexes of the
crescent rib and the intersecting curves of the main cone and the branch cones (that
is the intersection area of A1 and A2), and in the area of the combined welds of the
crescent rib and branch pipes which is near the waist line.
40.3.2 Dispersion Curves of AE Signals
Dispersion is a physical phenomenon while the sound velocity varies in function of
frequency. Since the actual AE signal includes components of various frequencies,
and the sound velocity depends on frequency, hence the components of different
frequencies in the AE signal will propagate at different speeds in the medium. The
velocity of longitudinal, shear, surface waves is independent of wave frequency,
while the velocity of plate wave is related to the frequency of the wave, dispersion
occurs, and the sound velocity in the plate is approximately distributed between the
longitudinal velocity and the shear velocity.
The dispersion curves(the steel plate with a thickness of 50 mm, longitudinal wave
velocity of 5900 m/s, shear wave velocity of 3230 m/s) are obtained from Wavelet
software[5, 6] of Vallen Systeme GmbH, in which A0, A1, A2 and A3 represent zeroorder, first-order, second-order and third-order asymmetric lamb waves, respectively,
while S0, S1, S2 and S3 represent zero-order, first-order, second-order and third-order
symmetric lamb waves respectively (Fig. 40.4).
40.3.3 Principle of AE Location for Two Sensors and Sound
Velocity Measurement
When the AE source lies in the line between the two sensors, the location of TDOA
for two sensors is the usual linear location, but most of the time, the AE source is not
aligned between the two sensors. As shown in Fig. 40.6, the trajectories of all points
with the same time difference is a hyperbola. For the calculated coordinate axis x,
only when the AE source aligned between the two sensors, the calculated results of
the AE location is true (ignoring the velocity changes). For AE sources deviating
from the connection between the two sensors, the linear location result tends to the
center of the connection between the two probes. The larger the deviation value (y 0 )
is, the greater the location error will be [7]. Formula (40.1) shows the calculation of
location of TDOA for two sensors (Fig. 40.5).
455
The parts of the rib protruding from the shell plate may cause the change of the
acoustic propagation paths, and the acoustic velocity may also vary greatly after
transmitting through the weld or rib. In particular, the location accuracy of the AE
source will be lower in the small triangular area composed of the apexes of the
crescent rib and the intersecting curves of the main cone and the branch cones (that
is the intersection area of A1 and A2), and in the area of the combined welds of the
crescent rib and branch pipes which is near the waist line.
40.3.2 Dispersion Curves of AE Signals
Dispersion is a physical phenomenon while the sound velocity varies in function of
frequency. Since the actual AE signal includes components of various frequencies,
and the sound velocity depends on frequency, hence the components of different
frequencies in the AE signal will propagate at different speeds in the medium. The
velocity of longitudinal, shear, surface waves is independent of wave frequency,
while the velocity of plate wave is related to the frequency of the wave, dispersion
occurs, and the sound velocity in the plate is approximately distributed between the
longitudinal velocity and the shear velocity.
The dispersion curves(the steel plate with a thickness of 50 mm, longitudinal wave
velocity of 5900 m/s, shear wave velocity of 3230 m/s) are obtained from Wavelet
software[5, 6] of Vallen Systeme GmbH, in which A0, A1, A2 and A3 represent zeroorder, first-order, second-order and third-order asymmetric lamb waves, respectively,
while S0, S1, S2 and S3 represent zero-order, first-order, second-order and third-order
symmetric lamb waves respectively (Fig. 40.4).
40.3.3 Principle of AE Location for Two Sensors and Sound
Velocity Measurement
When the AE source lies in the line between the two sensors, the location of TDOA
for two sensors is the usual linear location, but most of the time, the AE source is not
aligned between the two sensors. As shown in Fig. 40.6, the trajectories of all points
with the same time difference is a hyperbola. For the calculated coordinate axis x,
only when the AE source aligned between the two sensors, the calculated results of
the AE location is true (ignoring the velocity changes). For AE sources deviating
from the connection between the two sensors, the linear location result tends to the
center of the connection between the two probes. The larger the deviation value (y 0 )
is, the greater the location error will be [7]. Formula (40.1) shows the calculation of
location of TDOA for two sensors (Fig. 40.5).