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Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study

Haitao Li
Haitao Li
, 
Guoqing Zhang
Guoqing Zhang
, 
Nawaf Alhebaishi
Nawaf Alhebaishi
 y 
Hamdy Abdelhameed
Hamdy Abdelhameed
   | 13 dic 2021
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Publicado en línea: 13 dic 2021
Páginas: 249 - 264
Recibido: 17 jun 2021
Aceptado: 24 sept 2021
DOI: https://doi.org/10.2478/amns.2021.2.00071
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© 2021 Haitao Li et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Diagram of optical fibre receiving vibration signal.
Diagram of optical fibre receiving vibration signal.

Fig. 2

(a) The geometric meaning of DS. (b) DS value of points in (a). In (a), The curve is f(x) = d2x2. The solid points are the values of i2d2. The hollow points are the values of Δti2v¯2+2Δtiv¯l0¯ \Delta {\rm{t}}_{\rm{i}}^2{{\rm{\bar v}}^2} + 2\Delta {{\rm{t}}_{\rm{i}}}{\rm{\bar v}}\overline {{{\rm{l}}_0}} . The DS is the distance from the hollow point to the solid point with the same i. (b) shows the DS value in i. DS, deviation square.
(a) The geometric meaning of DS. (b) DS value of points in (a). In (a), The curve is f(x) = d2x2. The solid points are the values of i2d2. The hollow points are the values of Δti2v¯2+2Δtiv¯l0¯ \Delta {\rm{t}}_{\rm{i}}^2{{\rm{\bar v}}^2} + 2\Delta {{\rm{t}}_{\rm{i}}}{\rm{\bar v}}\overline {{{\rm{l}}_0}} . The DS is the distance from the hollow point to the solid point with the same i. (b) shows the DS value in i. DS, deviation square.

Fig. 3

The oscillogram of Ricker wavelet. fM = 50 Hz. (a) The time-domain figure; (b)The frequency domain figure.
The oscillogram of Ricker wavelet. fM = 50 Hz. (a) The time-domain figure; (b)The frequency domain figure.

Fig. 4

Simulation vibration signals made up of Ricker wavelet and noise. (a) All data is presented in a mesh. (b) Sampling points of No. 10 and No. 1 column of all data.
Simulation vibration signals made up of Ricker wavelet and noise. (a) All data is presented in a mesh. (b) Sampling points of No. 10 and No. 1 column of all data.

Fig. 5

The Scatter Diagram of No. 5 and 7 columns of Table 3.
The Scatter Diagram of No. 5 and 7 columns of Table 3.

Fig. 6

The time domain signal at 108 m.
The time domain signal at 108 m.

Complete process to simu fibre data.

No. True TDOA 1st 2nd
i DSi i DSi
1 8.055 7.9716 −9 248.021 0 0
2 7.062 7.4851 −8 28.806 0 0
3 6.071 8.02 −7 286.574 0 0
4 5.083 5.464 −6 1.424 −6 0
5 4.099 5.7098 −5 153.47 0 0
6 3.123 3.211 −4 0.612 −4 1.402
7 2.162 2.3093 −3 0.191 −3 0.03
8 1.236 2.1822 −2 22.245 0 0
9 0.414 0.8831 −1 2.88 −1 1.612
10 0 0 0 0 0 0
11 0.414 0.3109 1 0.032 1 1.28E−01
12 1.236 1.5947 2 2.861 2 1.199
13 2.162 2.7702 3 10.526 3 7.343
14 3.123 1.4064 4 124.818 0 0
15 4.099 4.1073 5 8.236 5 7.932
16 5.083 6.8807 6 221.649 0 0
17 6.071 6.5797 7 3.14 7 0.673
18 7.062 8.4726 8 70.983 0 0
19 8.055 7.1539 9 711.649 0 0
DSMSE 105.4509 2.2577
v¯ {\rm{\bar v}} 8508.390 9370.197
l0¯ \overline {{{\rm{l}}_0}} 1.419 0.958

Mean square error and success rate of five methods of Table 1.

CC SCOT ML GCCSC based on SCOT GCCSC based on ML
MSE 5.943 17.0042 5.2276 5.6606 0.9272
Success Rate 100% 42.1053% 89.4737% 94.7368% 100%

The overall process of excavation data treatment.

No. TDOA 1st 2nd 3rd 4th 5th
i DSi i DSi i DSi i DSi i DSi
11 0.30 1 76.82 1 22.90 1 5.46 1 1.83 1 0.02
12 0.40 2 73.13 2 11.87 2 0.09 2 0.92 2 6.18
13 0.45 3 20.16 3 1.15 3 20.17 3 34.44 0 0
14 0.61 4 1.15 4 34.72 4 103.16 0 0 0 0
15 0.71 5 40.03 5 195.43 0 0 0 0 0 0
16 0.82 6 246.77 6 577.32 0 0 0 0 0 0
17 0.81 7 889.91 0 0 0 0 0 0 0 0
18 0.93 8 1902.98 0 0 0 0 0 0 0 0
20 0.95 −8 1878.44 0 0 0 0 0 0 0 0
21 1.94 −7 504.32 0 0 0 0 0 0 0 0
22 1.61 −6 63.24 −6 268.29 0 0 0 0 0 0
23 1.56 −5 13.22 −5 24.83 −5 101.21 0 0 0 0
24 1.05 −4 81.91 −4 0.01 −4 31.30 −4 62.44 0 0
25 0.28 −3 0.08 −3 16.31 −3 40.42 −3 53.09 0 0
26 0.32 −2 37.20 −2 3.69 −2 0.42 −2 2.83 −2 8.66
27 0.25 −1 52.07 −1 14.75 −1 3.11 −1 0.87 −1 0.01
47 0.53 1 228.79 1 77.38 1 24.15 1 11.17 1 2.14
48 0.81 2 322.49 2 94.42 2 22.01 2 6.90 2 0.06
49 1.36 3 388.30 3 110.21 3 24.98 3 6.87 3 0.04
50 1.81 4 172.13 4 34.59 4 3.03 4 0.06 4 3.18
51 2.55 5 20.72 5 9.16 5 2.03 5 2.11 5 0.13
65 0.63 1 303.47 1 106.37 1 35.55 1 17.58 1 4.40
66 1.13 2 520.48 0 0 0 0 0 0 0 0
67 1.45 3 407.44 3 124.57 3 33.62 3 11.92 3 1.26
68 1.94 4 157.81 4 40.46 4 8.47 4 1.33 4 0.00
DSMSE 336.12 88.42 27.01 14.29 2.17
v¯ {\rm{\bar v}} 32894.05i 21501.91i 8321.26i 8756.23 16942.8
l0¯ \overline {{{\rm{l}}_0}} −5.50i −4.884i −6.976i 4.498 0.951
ɛ 100 40 10 10
MinPts 5 5 5 5

Comparison of TDOA estimation for simu fibre data.

No. CC SCOT ML GCCSC based on SCOT GCCSC based on ML Real
−9 7 −2 7.3147 7.3945 7.9716 8.055
−8 8 8 8.2805 8.8228 7.4851 7.062
−7 5 5 4.9436 4.3144 8.02 6.071
−6 7 −7 6.9048 6.3663 5.464 5.083
−5 9 −6 6.0667 8.9716 5.7098 4.099
−4 3 −3 2.7389 2.8608 3.211 3.123
−3 5 −1 −1.1754 −1.2043 2.3093 2.162
−2 5 −10 5.2752 5.0414 2.1822 1.236
−1 1 1 0.7914 0.9828 0.8831 0.414
0 0 0 0 0 0 0
1 0 13 −0.016 0.1585 0.3109 0.414
2 2 3 2.8405 2.7737 1.5947 1.236
3 3 −14 3.6201 3.1296 2.7702 2.162
4 1 9 0.9783 1.2096 1.4064 3.123
5 4 −8 3.9291 4.1022 4.1073 4.099
6 8 14 7.8445 7.9643 6.8807 5.083
7 11 −13 11.2104 11.013 6.5797 6.071
8 3 3 11.0275 3.4893 8.4726 7.062
9 6 −10 6.4191 6.4771 7.1539 8.055
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