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. 2019 Jan 14;19(2):310. doi: 10.3390/s19020310
d1, d2 distances between the leak and sensors 1 and 2
D distance between two sensors
B fluid bulk modulus
E Young’s modulus of the pipe wall
a, h pipe radius and wall thickness
β wave attenuation factor
k, kf fluid-borne wavenumber and free-field fluid wavenumber
T 0 estimate of the time delay
η loss factor of the pipe wall
c, cf propagation and fluid wavespeeds
x1(t), x2(t) leak signals measured
l(t) leak source signal
n1(t), n2(t) background noise
H(ω,d1), H(ω,d2) FRFs between l(t) and x1(t), x2(t)
h1(t), h2(t) IRFs between l(t) and x1(t), x2(t)
S12(ω) CSD between x1(t) and x2(t)
Φ12(ω), Φ21(ω) phase spectra of x1(t) and x2(t)
h21(n), h12(n), h(n) IRFs for measured signals
H(ω), H12(ω), H21(ω) FTs of h12(n), h21(n), h(n)
T ref reference time delay
λ max maximum order in the LMS algorithm