7 An Acoustic Emission Source Localization Method Based Ant Colony …
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the unknown source P 0 , set its position coordinate to (x 0 , y 0 ), and the initial time of
excitation to t 0 .
7.2.3 Search for the Fastest Waveform Path
Every grid node P xy in the set G N is used as the potential source excitation position. Then the theoretical shortest path L
k
xy can be obtained by tracing the shortest
path from the node P xy to the kth sensor. If the grid node P xy is in the empty region,
the L
k
xy is considered to ∞. ACLM uses the ant colony algorithm to trace the shortest
path L
k
xy .
7.2.3.1 Ant Colony Algorithm [10]
An ant colony has the ability to select the shortest pathway from a set of alternative
pathways between their nest and the food source. Ants find the shortest path based
on the simple communication mechanism, which is guided by a pheromone trail
that is left from ants on the ground. The level of pheromone will dissipate over time.
Therefore, the shorter path will end up with a higher level of pheromone as it required
less travel time. The role of this trail is to guide the other ants towards the target point.
7.2.4 Calculate the Theoretical Travel Time
Interpolation can be used to increase the density of the grid in complex areas. The
shortest path between the sensor and the point that is not in the grid can be interpolated
from the nodes in the surrounding region. It is a useful way to reduce the calculation
of the algorithm, though this may introduce small errors into the location results
because of the distance error between interpolation and the shortest path.
For the source generated by the point P xy , the theoretical travel time t
k
i j corresponds
to the shortest propagation path L
k
xy between the source and the kth sensor divided by
the velocity C. The time difference between two different sensors l and m corresponds
to the difference of travel time t
lm
xy .
7.2.5 Collect Data of Arrivals
m sensors are installed at different positions of the structure to capture the arrivals of
the AE event. Each sensor is located on the grid node so the position of the sensor is
known. For the two-dimensional model, there are four unknowns (P -wave velocity,
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the unknown source P 0 , set its position coordinate to (x 0 , y 0 ), and the initial time of
excitation to t 0 .
7.2.3 Search for the Fastest Waveform Path
Every grid node P xy in the set G N is used as the potential source excitation position. Then the theoretical shortest path L
k
xy can be obtained by tracing the shortest
path from the node P xy to the kth sensor. If the grid node P xy is in the empty region,
the L
k
xy is considered to ∞. ACLM uses the ant colony algorithm to trace the shortest
path L
k
xy .
7.2.3.1 Ant Colony Algorithm [10]
An ant colony has the ability to select the shortest pathway from a set of alternative
pathways between their nest and the food source. Ants find the shortest path based
on the simple communication mechanism, which is guided by a pheromone trail
that is left from ants on the ground. The level of pheromone will dissipate over time.
Therefore, the shorter path will end up with a higher level of pheromone as it required
less travel time. The role of this trail is to guide the other ants towards the target point.
7.2.4 Calculate the Theoretical Travel Time
Interpolation can be used to increase the density of the grid in complex areas. The
shortest path between the sensor and the point that is not in the grid can be interpolated
from the nodes in the surrounding region. It is a useful way to reduce the calculation
of the algorithm, though this may introduce small errors into the location results
because of the distance error between interpolation and the shortest path.
For the source generated by the point P xy , the theoretical travel time t
k
i j corresponds
to the shortest propagation path L
k
xy between the source and the kth sensor divided by
the velocity C. The time difference between two different sensors l and m corresponds
to the difference of travel time t
lm
xy .
7.2.5 Collect Data of Arrivals
m sensors are installed at different positions of the structure to capture the arrivals of
the AE event. Each sensor is located on the grid node so the position of the sensor is
known. For the two-dimensional model, there are four unknowns (P -wave velocity,