6 Correlation Analysis of Acoustic Emission Signals …
65
6.2 Principle of Cross-Correlation
The dependence of instantaneous value at different time points is described by
the correlation function. Presumption that x(t) is a sample of stationary stochastic
process. In practical application, x(t) is the signal which the sensors received from
signal source. In this article, x(t1) and x(t 1 + τ) represent the signals at different
propagation distances to the same damage source.
Cross-correlation of x(t) at t = t 1 and t = t 1 + τ is computed by the average value
of multiplication for different x(t) in the range of T. Correlation function R x (τ) of
x(t) can be obtained by the limitation algorithm.
R x (τ ) = lim
T→∞
1
T
T
0
x(t)x(t + τ )dt
(6.1)
In order to simplify the dependence between x(t) at t = t 1 and t = t 1 + τ and
to avoid the signal amplitude effects, with the correlation function normalized by
introducing the dimensionless groups, correlation coefficients are obtained. Where
μ x is the mean of x(t) and σ
2
x is the variance of x(t). From Formula (6.2), there
exists a linear relation between ρ x (τ) and R x (τ), and so ρ x (τ) is used to describe the
AEsignal correlation.
ρ x (τ) =
lim
T→∞
∫
T
0 [x(t) − μ x ][x(t + τ) − μ x ]dt
σ 2
x
=
R x (τ) − μ
2
x
σ 2
x
(6.2)
6.3 Acoustic Emission Signals
To overcome the complexity of practical signals, hypervelocity impact simulation is
utilized to give the effective and simplified AE signals which have the broad frequency
components with less noise and evident amplitude features at different propagation
distances. AE signals were obtained at the gauges placed at different distances to the
impact damage source, as shown in Fig. 6.2. Ref. [9] gives the details of the model
and algorithm for the hypervelocity impact simulation.
Stress wave emission is produced in the impact failure point when the hypervelocity projectiles impact the Aluminum plate. AE signals can be sampled with the
normal velocity at 44 different gauges. Table 6.1 lists the representations of different
gauges from the impact damage source.
65
6.2 Principle of Cross-Correlation
The dependence of instantaneous value at different time points is described by
the correlation function. Presumption that x(t) is a sample of stationary stochastic
process. In practical application, x(t) is the signal which the sensors received from
signal source. In this article, x(t1) and x(t 1 + τ) represent the signals at different
propagation distances to the same damage source.
Cross-correlation of x(t) at t = t 1 and t = t 1 + τ is computed by the average value
of multiplication for different x(t) in the range of T. Correlation function R x (τ) of
x(t) can be obtained by the limitation algorithm.
R x (τ ) = lim
T→∞
1
T
T
0
x(t)x(t + τ )dt
(6.1)
In order to simplify the dependence between x(t) at t = t 1 and t = t 1 + τ and
to avoid the signal amplitude effects, with the correlation function normalized by
introducing the dimensionless groups, correlation coefficients are obtained. Where
μ x is the mean of x(t) and σ
2
x is the variance of x(t). From Formula (6.2), there
exists a linear relation between ρ x (τ) and R x (τ), and so ρ x (τ) is used to describe the
AEsignal correlation.
ρ x (τ) =
lim
T→∞
∫
T
0 [x(t) − μ x ][x(t + τ) − μ x ]dt
σ 2
x
=
R x (τ) − μ
2
x
σ 2
x
(6.2)
6.3 Acoustic Emission Signals
To overcome the complexity of practical signals, hypervelocity impact simulation is
utilized to give the effective and simplified AE signals which have the broad frequency
components with less noise and evident amplitude features at different propagation
distances. AE signals were obtained at the gauges placed at different distances to the
impact damage source, as shown in Fig. 6.2. Ref. [9] gives the details of the model
and algorithm for the hypervelocity impact simulation.
Stress wave emission is produced in the impact failure point when the hypervelocity projectiles impact the Aluminum plate. AE signals can be sampled with the
normal velocity at 44 different gauges. Table 6.1 lists the representations of different
gauges from the impact damage source.