Apparatus and method of detecting leakage of pipe by using distance difference-frequency analysis
An apparatus for detecting leakage of a pipe by using a distance difference-frequency analysis includes: vibration detecting sensors, which are mounted at a predetermined distance in a longitudinal direction of a pipe and are configured to measure vibration signals of the pipe; and a control unit, which is configured to calculate a cross-correlation function by using the vibration signals, to reveal time delay information in the frequency domain by calculating time-delay frequency analysis diagram for the cross-correlation function, to calculate a distance difference-frequency analysis diagram by applying compensation conversion using frequency-dependent propagation speed information to the time-delay frequency analysis diagram, and to detect a leakage component of the pipe in the distance difference-frequency analysis diagram.
1. An apparatus for detecting leakage of a pipe by using a distance difference-frequency analysis, the apparatus comprising:
vibration detecting sensors, which are mounted at a predetermined distance in a longitudinal direction of a pipe and are configured to measure vibration signals (x 1 (t) and x 2 (t)) of the pipe; and
a control unit, which is configured to calculate a cross-correlation function (C 12 (τ,f)) by using the vibration signals, to reveal time delay information in the frequency domain by calculating time-delay frequency analysis diagram for the cross-correlation function, to calculate a distance difference-frequency analysis diagram (D 12 (δ,f)) by applying compensation conversion using frequency-dependent propagation speed information (c(f)) to the time-delay frequency analysis diagram, and to detect a leakage component of the pipe in the distance difference-frequency analysis diagram (D 12 (δ,f)),
wherein the cross-correlation function C 12 (τ)) is calculated by an Equation below:
C 12 (τ)= E [ x 1 ( t ) x 2 ( t +τ)]
Herein, E[ ] represents an expected value and τ represents a time delay.
2. The apparatus of claim 1 , wherein:
the control unit is configured to detect the leakage component of the pipe and to generate a leakage position display signal.
3. The apparatus of claim 2 , further comprising:
a display unit, which is configured to display the leakage position of the pipe based on the leakage position display signal.
4. A method of detecting leakage of a pipe by using a distance difference-frequency analysis, the method comprising:
measuring vibration signals (x 1 (t) and x 2 (t)) from one pair of vibration detecting sensors, which are mounted at both sides in a longitudinal direction of a pipe, respectively;
calculating a cross-correlation function (C 12 (τ,f)) by using the vibration signals;
revealing time delay information in the frequency domain by calculating time-delay frequency analysis diagram for the cross-correlation function;
calculating a distance difference-frequency analysis diagram (D 12 (δ,f)) by applying compensation conversion using frequency-dependent propagation speed information (c(f)) to the time-delay frequency analysis diagram; and
detecting a leakage component of the pipe in the distance difference-frequency analysis diagram (D 12 (δ,f)).
5. The method of claim 4 , wherein:
the cross-correlation function (C 12 (τ)) is calculated by an Equation below:
C 12 (τ)= E [ x 1 ( t ) x 2 ( t +τ)]
Herein, E[ ] represents an expected value and τ represents a time delay.
6. The method of claim 4 , wherein:
The frequency-dependent propagation speed information (c(f)) is calculated by an Equation below:
c
(
f
)
=
c
f
(
1
+
(
2
B
f
)
/
r
E
h
/
r
2
-
ph
(
2
π
f
)
2
)
-
1
2
Herein, c f represents a sound speed of a fluid, B f represents bulk modulus of elasticity, r represents a radius of the pipe, h represents a thickness of the pipe, E represents Young's modulus of a material of the pipe, ρ represents density of the pipe, and f represents frequency.
7. The method of claim 4 , wherein:
the time delay-frequency analysis uses a method of Wigner Ville distribution or short time Fourier transform (STFT) for the cross-correlation function.
8. The method of claim 4 , further comprising:
displaying a leakage position of the pipe using a vertical edge detection method.