• Opto-Electronic Advances
  • Vol. 4, Issue 5, 200037-1 (2021)
Tao Liu, Hao Li, Tao He, Cunzheng Fan, Zhijun Yan, Deming Liu, and Qizhen Sun*
Author Affiliations
  • School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, Wuhan 430074, China
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    DOI: 10.29026/oea.2021.200037 Cite this Article
    Tao Liu, Hao Li, Tao He, Cunzheng Fan, Zhijun Yan, Deming Liu, Qizhen Sun. Ultra-high resolution strain sensor network assisted with an LS-SVM based hysteresis model[J]. Opto-Electronic Advances, 2021, 4(5): 200037-1 Copy Citation Text show less

    Abstract

    Optical fiber sensor network has attracted considerable research interests for geoscience applications. However, the sensor capacity and ultra-low frequency noise limits the sensing performance for geoscience data acquisition. To achieve a high-resolution and lager sensing capacity, a strain sensor network is proposed based on phase-sensitive optical time domain reflectometer (φ-OTDR) technology and special packaged fiber with scatter enhanced points (SEPs) array. Specifically, an extra identical fiber with SEPs array which is free of strain is used as the reference fiber, for compensating the ultra-low frequency noise in the φ-OTDR system induced by laser source frequency shift and environment temperature change. Moreover, a hysteresis operator based least square support vector machine (LS-SVM) model is introduced to reduce the compensation residual error generated from the thermal hysteresis nonlinearity between the sensing fiber and reference fiber. In the experiment, the strain sensor network possesses a sensing capacity with 55 sensor elements. The phase bias drift with frequency below 0.1 Hz is effectively compensated by LS-SVM based hysteresis model, and the signal to noise ratio (SNR) of a strain vibration at 0.01 Hz greatly increases by 24 dB compared to that of the sensing fiber for direct compensation. The proposed strain sensor network proves a high dynamic resolution of 10.5 pε·Hz-1/2 above 10 Hz, and ultra-low frequency sensing resolution of 166 pε at 0.001 Hz. It is the first reported a large sensing capacity strain sensor network with sub-nε sensing resolution in mHz frequency range, to the best of our knowledge.
    $ I(t) = A\sum\limits_{n = 0}^N {[{\rm{rect}}\left(\frac{{t - {z_n} \cdot {n_0}/c}}{{{\tau _{\rm{p}}}}}\right) \cdot \cos (2{\rm{\pi}} {f_{\rm{d}}}t + }{\phi _n})]\;, $(1)

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    ${\phi _n} = {\rm{arctan}} (\frac{{{I_n}(t) \cdot \cos (2\pi {f_{\rm{d}}}t)}}{{{I_n}(t) \cdot \sin (2\pi {f_{\rm{d}}}t)}})\;,$(2)

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    $\phi (k) = {\phi _{k + 1}} - {\phi _k} = \frac{{4 \rm{π} {n_0}\nu L{ε _k}}}{c}\;,$(3)

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    $ y(t) = \int_0^{ + \infty } {\int_{ - \infty }^{ + \infty } {d(r,s){R_{s - r,s + r}}[x](t)\rm{d}s\rm{d}r} }\;, $(4)

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    $ \psi (r,t) = {P_r}[x](t) = \frac{1}{2}\int_{ - \infty }^{ + \infty } {{R_{s - r,s + r}}[x](t)\rm{d}s}\;. $(5)

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    $ y(t) = \int_0^\infty {q(r,{P_r}[x](t))\rm{d}r} \;, $(6)

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    $ q(r,s) = 2\int_0^s {w(r,\sigma )\rm{d}\sigma } \;. $(7)

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    $ y(t) = F({P_r}[x](t))\;, $(8)

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    $ y(u) = {{{w}}^{\rm{T}}} \cdot f(u) + b\;, $(9)

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    $ \begin{gathered} \min R({{w}},\xi ) = \frac{1}{2}{\left\| {{w}} \right\|^2} + C\sum\limits_i^n {\xi _i^2} \\ {\rm{s}}.{\rm{t}}.\;y_i = {{{w}}^{\rm{T}}} \cdot f({u_i}) + b + {\xi _i},i = 1,2,...,n\;, \\ \end{gathered} $(10)

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    $ L({{w}},b,\xi ,a) = R({{w}},\xi ) - \sum\limits_i^n {{a_i}({{{w}}^{\rm{T}}} \cdot f({u_i}) + b + {\xi _i} - {y_i})} \;, $(11)

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    $ \left[ {\begin{array}{*{20}{c}} 0&{{{{e}}^{\rm{T}}}} \\ {{e}}&{{{Ω}} + {{I}}/2C} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} b \\ {{a}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0 \\ {{y}} \end{array}} \right]\;, $(12)

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    $ {\Omega _{ij}} = K({u_i},{u_j}) = f({u_i}) \cdot f({u_j})\;(i = 1,\cdots,n;\;j = 1,\cdots,n)\;, $(13)

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    $ y(u) = \sum\limits_{k = 1}^n {{a_k}K(u,{u_k})} + b\;, $(14)

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    $ K(u,{u_k}) = {\rm{exp}} \left( - \frac{{\left\| {u - {u_k}} \right\|}}{\sigma }\right)\;, $(15)

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    $ {r_i} = \frac{i}{{m + 1}} \cdot {\left| x \right|_{\max }},\;i = 1,2,\cdots,m\;, $(16)

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    $ \begin{split} & \qquad z(0) = {p_r}(x(0),0), \\ & \qquad z(t) = {p_r}(x(t),z({t_i})), \\ & {\rm{ for }}\;{t_i} < t < {t_{i + 1}},0 \le i \le N - 1 \;, \end{split} $(17)

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    $ {p_r}(x,y) = \max \{ x - r,\min \{ x + r,y\} \}\;, $(18)

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    Tao Liu, Hao Li, Tao He, Cunzheng Fan, Zhijun Yan, Deming Liu, Qizhen Sun. Ultra-high resolution strain sensor network assisted with an LS-SVM based hysteresis model[J]. Opto-Electronic Advances, 2021, 4(5): 200037-1
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