40 Localization of Acoustic Emission Sources …
457
40.4 Analysis of Location Accuracy of AE Sources
Location Uncertainty (LUCY for short) and Location Error (LE for short) are
considered as criteria to evaluate the location accuracy of AE sources in the paper.
40.4.1 Definition of Location Uncertainty and Location Error
Location uncertainty (LUCY) describes how well a calculated source position fits
with the measured arrival time differences. LUCY is basically the standard deviation
from a set of measured values to a set of calculated values.
LUCY can only be calculated if the system of equations considered by the location
algorithm is overdetermined, E.g. if for linear location an event consists of 3 hits,
LUCY can be calculated.
Assuming that the calculated coordinate of AE source is (x s , y s ), the sound velocity
entered in the location calculation software is v u , that is, the sound velocity of the
first hit is v f = v u , and the coordinate of the sensor receiving the hit first is (x f , y f ).
The time of flight (TOF) of the first hit is t f :
t f =
(x f − x s ) 2 + (y f − y s ) 2
v u
(40.2)
The coordinate of the No. i-th sensor in the channel group is (x i ,y i ), and the time
difference of i-th hit and the first hit is dT i , then the time of flight (TOF) of the i-th
hit t i is:
t i = t f + dT i
=
(x f − x s ) 2 + (y f − y s ) 2
v u
+ dT i
(40.3)
The measured value of distance D i represents the distance between the sensor (x i ,
y i ) and the calculated location of the AE source:
D i =
(x i − x s ) 2 + (y i − y s ) 2
(40.4)
The calculated value of distance between the sensors (x i ,y i ) and the calculated
location of the AE source is:
457
40.4 Analysis of Location Accuracy of AE Sources
Location Uncertainty (LUCY for short) and Location Error (LE for short) are
considered as criteria to evaluate the location accuracy of AE sources in the paper.
40.4.1 Definition of Location Uncertainty and Location Error
Location uncertainty (LUCY) describes how well a calculated source position fits
with the measured arrival time differences. LUCY is basically the standard deviation
from a set of measured values to a set of calculated values.
LUCY can only be calculated if the system of equations considered by the location
algorithm is overdetermined, E.g. if for linear location an event consists of 3 hits,
LUCY can be calculated.
Assuming that the calculated coordinate of AE source is (x s , y s ), the sound velocity
entered in the location calculation software is v u , that is, the sound velocity of the
first hit is v f = v u , and the coordinate of the sensor receiving the hit first is (x f , y f ).
The time of flight (TOF) of the first hit is t f :
t f =
(x f − x s ) 2 + (y f − y s ) 2
v u
(40.2)
The coordinate of the No. i-th sensor in the channel group is (x i ,y i ), and the time
difference of i-th hit and the first hit is dT i , then the time of flight (TOF) of the i-th
hit t i is:
t i = t f + dT i
=
(x f − x s ) 2 + (y f − y s ) 2
v u
+ dT i
(40.3)
The measured value of distance D i represents the distance between the sensor (x i ,
y i ) and the calculated location of the AE source:
D i =
(x i − x s ) 2 + (y i − y s ) 2
(40.4)
The calculated value of distance between the sensors (x i ,y i ) and the calculated
location of the AE source is: