Loading [MathJax]/extensions/TeX/boldsymbol.js

Liu T, Li H, He T, Fan CZ, Yan ZJ et al. Ultra-high resolution strain sensor network assisted with an LS-SVM based hysteresis model. Opto-Electron Adv 4, 200037 (2021). doi: 10.29026/oea.2021.200037
Citation: Liu T, Li H, He T, Fan CZ, Yan ZJ et al. Ultra-high resolution strain sensor network assisted with an LS-SVM based hysteresis model. Opto-Electron Adv 4, 200037 (2021). doi: 10.29026/oea.2021.200037

Original Article Open Access

Ultra-high resolution strain sensor network assisted with an LS-SVM based hysteresis model

More Information
  • 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.
  • Discovering the physics and dynamics of the solid earth is essential to meet the challenges of natural hazards, energy crisis, and climate changes. Solid earth geoscience is a data-driven filed which demands large datasets of geological events1. For geoscience data acquisition, it is required to sense the earth’s crustal deformation with a strain resolution less than 10-9 ε in a frequency region from static to 100 Hz2. Moreover, in order to refine the structure image of the errors induced by the Earth crustal damage, the strain sensing for geoscience research requires denser spatial coverage of individual sensors and more accurate recording instruments3. The broadband seismometer networks represent the state of arts technology and provide high quality Earth crustal deformation waveforms with broadband frequency content4. However, the dense seismometer networks deployed in areas where access and power supply are limited will consume a great effort and resources5.

    Recently, optical fiber strain sensor has attracted considerable research interests for geoscience applications, owing to their unique advantages of passive, multiplexing, and anti-electromagnetic interference6. For instance, optical fiber Bragg grating (FBG) based sensors have been widely exploited to monitor the earth tide, which possess a minimum static strain resolution of 270 pε2. However, the multiplexing capacity of the FBG strain sensors is limited by the bandwidth of the reflection spectrum. Moreover, the signal crosstalk between the sensors in the FBG sensor network will increase the noise floor of measurement7. Hence, the sensing range and spatial coverage density of the high-quality single point optical fiber sensor networks should be further promoted.

    As an alternative approach, optical fiber distributed acoustic sensor (DAS), which offers a long sensing distance without blind area8, 9, has demonstrated efficient seismic acquisition ability in seismology application such as natural hazard prediction and crust exploration10, 11. In general, DAS, which is realized based on phase-sensitive optical time domain reflectometry (φ-OTDR) technology, can interrogate the strain and temperature variations along the entire length of an optical fiber12, 13. With current technologies, DAS has achieved a dynamic strain resolution down to nano-strain level14. Moreover, the quasi-DAS assisted with ultra-weak FBG array has been proposed with pico-strain dynamic resolution above 10 Hz frequency range15, 16. Due to the high sensitivity, high spatial and temporal resolution, DAS has been developed and used for broadband seismic monitoring in oil/gas exploration17. Nevertheless, the frequency shift of the laser source, as well as the cross-sensitivity between temperature and strain, severely ruin the signal to noise ratio (SNR) of the DAS in low frequency band18, 19. The noise in ultra-low frequency band of the DAS system limits the availabilities for nature earthquake recording and earth tide monitoring. In order to improve the sensing performance in low-frequency domain, many efforts have been done to suppress the phase drift of the φ-OTDR. F. Zhu proposed an active compensation method to reduce the laser frequency shift influence by tracking and comparing the OTDR intensity traces with different frequencies19. But the response time of this method will be limited by the number of tuning frequencies. Furthermore, Q. Yuan has demonstrated the twice differential method to compensate the influence of laser frequency shift, and successfully detected the strain variation with amplitude of 5.9 nε at 0.1 Hz20. However, the strain resolution of the DAS in the mHz range is still much worse than the high-quality single point optical fiber sensor. Actually, the quasi-static measurement from mHz to Hz is essential to the solid earth geoscience research. To sense the mHz strain information with high sensitivity and dense spatial coverage, it is necessary for the ultra-low frequency noise of the DAS to be greatly suppressed.

    In this paper, we demonstrated a high-resolution strain sensor network with large sensing capacity based on φ-OTDR technology and scatter enhanced points (SEPs) array. In the prototype system, the optical fiber with SEPs array is divided into sensing fiber and reference fiber. The reference fiber packaged with strain isolation is used to compensate the ultra-low frequency noise induced by laser source frequency shift and environmental temperature change. The characteristics of the above phase noise are systematically analyzed. Then, a hysteresis model based on the hysteresis operator and LS-SVM is introduced to reduce the thermal hysteresis between the sensing fiber and reference fiber. Assisted with the LS-SVM based hysteresis compensation scheme, a strain sensor network with high resolution in the ultra-low frequency and large sensing capacity is successfully achieved.

    In order to achieve a large sensing capacity, the proposed high-resolution strain sensing network is interrogated by the φ-OTDR technology. The schematic diagram of the proposed sensing network for geoscience research is illustrated in Fig. 1. The sensing network consists of an interrogation office center and a special packaged sensing cable. In the interrogation system, an ultra-narrow linewidth laser (NKT x15) with linewidth of 100 Hz is used as a light source which is divided into a local oscillator laser and a probe laser by a 99:1 optical coupler. The probe laser is modulated into a series of pulses with frequency shift of 200 MHz by the acoustical optical modulator (AOM). After amplified by erbium doped fiber amplifier (EDFA), the pulses are injected into the sensing cable by a circulator. The backscattered light from the sensing cable is mixed with the local oscillator laser by a 50:50 coupler and then received by a balanced photodetector (BPD). Data acquisition card (DAQ) is used to acquire the heterodyne beat signals from the BPD.

    Figure 1.  Schematic diagram of the proposed high-resolution strain sensor network.

    The sensing cable is based on the specific packaged optical fiber with SEPs array21. The SEPs are inscribed by laser exposure on the single mode fiber (SMF) with a given interval. The scattering efficiency of the SEPs is improved by 10 dB compared to the Rayleigh scattering of the SMF22. A pair of SEPs along with the fiber between them compose one sensing section. The fiber with SEPs array is divided in to sensing fiber and reference fiber with the same SEPs number23. The sensing fiber is for the sensing of strain, and the reference fiber is for the compensation of the phase drift induced by the environmental temperature and laser frequency variation. The sensing sections in the sensing fiber and reference fiber are respectively defined as sensing channels and reference channels. The SEPs of the sensing channels and the corresponding reference channels are aligned, and fixed with the sensing cable by epoxy curing agents. The sensing fiber in the cable is applied with a pre-strain for sensing of the strain of the cable. While the reference fiber is loosened in the cable to isolate the strain of the cable. Generally, the different packaging method will induce the length difference between the sensing fiber part and reference fiber part, which will introduce the different sensitivity for temperature and laser frequency vibration as well. However, the sensitivity difference between the sensing fiber part and reference fiber part is linear, which can be eliminated by linear fitting. When the spatial width of the injected probe pulse is shorter than the interval between two SEPs of the sensing section, the detected interference signal behaves as a series of beat frequency pulse trains, which can be described as:

    I(t)=ANn=0[rect(tznn0/cτp)cos(2πfdt+ϕn)], (1)

    where A is the amplitude of the interference signal, N is the number of the SEPs in the fiber, n0 is the refractive index of the fiber core, c is the light speed in the vacuum, τp is the pulse width of the probe laser, zn is the location of the n-th SEPs in the fiber, and φn is the phase of the scattering light of the n-th SEP. φn can be demodulated from the interference signal by the digital orthogonal phase discrimination method, which is deduced as:

    ϕn=arctan(In(t)cos(2πfdt)In(t)sin(2πfdt)), (2)

    where In(t) is the interference signal scattering from the n-th SEP. Theoretically, the phase difference between two SEPs is only dependent on the change of optical path in the sensing section24, which can be obtained by subtracting the phase of two SPEs in the sensing section, as expressed blow:

    ϕ(k)=ϕk+1ϕk=4πn0νLεkc, (3)

    where k=1,2, ···, N−1 is the number of the sensing section in the fiber, ν is the optical frequency of the laser, and εk is the strain applied on the k-th sensing section. When ν and n0 are constant, the phase signal in the k-th sensing section will be only proportional to εk. However, it can be observed clearly that the phase signal of the sensing section φ(k) will be also influenced by variation of the laser frequency ν and refractive index n0. Generally, the laser frequency ν will shift along with the environmental temperature drift, and the refractive index n0 is also significantly influenced by the temperature variation of the fiber core. Thus, the laser frequency shift and fiber temperature fluctuation are the dominant noise sources in the ultra-low frequency domain.

    In the proposed strain sensor network, a reference fiber with strain isolated package is employed to compensate the phase noise in low frequency band induced by environmental temperature and laser frequency shift. The compensation efficiency is dependent on the phase relationship between the sensing channel and corresponding reference channel. In order to investigate the phase variation characteristics, the laser frequency variation and temperature change were applied on the sensing cable for test. When the laser frequency variation with amplitude of 600 MHz and frequency of 1 Hz was introduced by frequency demodulation, the phase change of the sensing part and reference part are respectively plotted in the Fig. 2(a). The phase waveforms of the sensing channel and reference channel are identical with the variation of the laser frequency. Moreover, the relationship of the phase change between the sensing channel and reference channel is linear, which is illustrated in Fig. 2(b). Therefore, the phase noise induced by laser frequency shift can be compensated by direct differentiation.

    Figure 2.  (a) Phase change induced by laser frequency shift. (b) Relationship between the reference channel and sensing channel for laser frequency shift.

    Furthermore, the temperature fluctuation and the corresponding phase change are plotted in the Fig. 3(a), where the trigonometric temperature fluctuation with the amplitude of 5 °C was applied by a TEC. From Figs. 3(b) and 3(c), the hysteresis phenomenon can be observed between the temperature and phase. Moreover, the relationship between the phase change of the sensing channel and reference channel also exhibits an obvious hysteresis characteristic, as shown in the Fig. 3(d). The hysteresis stems from different temperature features induced by the different package methods, which will bring about a significant compensation error by direct differentiation. Therefore, a precision hysteresis model between the sensing channel and reference channel should be built to reduce the temperature compensation error.

    Figure 3.  (a) Phase change induced by temperature fluctuation. (b, c) Enlarged images for phase change. (d) Relationship between the reference channel and sensing channel for temperature fluctuation.

    Research on the hysteresis has a long history about a century. The Preisach model, which has been widely used for the modeling of hysteresis, has been developed based on incorporates relay operators25, 26. Relay operator is the simplest example for a hysteresis nonlinearity, which is characterized by threshold a1<a2 and output values +1 and –1, as depicted in Fig. 4(a). For a given input x(t), the output of the Preisach model y(t) can be expressed as27:

    Figure 4.  Hysteresis operator. (a) Relay operator. (b) Play operator.
    y(t)=+0+d(r,s)Rsr,s+r[x](t)dsdr, (4)

    where d(r, s) is the density function, Rsr,s+r[∙] is the relay operator, r=(a2a1)/2 is the half-width value, and s=(a1+a2)/2 is the mean value of the relay operator. A dividing curve, ψ(r, t), is defined to divide the relay operator into two distinct regions. The output value of the relay operator is +1 in the region below the curve and -1 in the region above the curve, respectively. The dividing curve ψ(r, t) can be considered as the play between two mechanical elements of relay. Therefore, a play operator Pr[x] is determined, and the corresponding input-output behavior is illustrated in Fig. 4(b). Mathematically, the play operator can be obtained by linear superposition of relay elements as follows27:

    ψ(r,t)=Pr[x](t)=12+Rsr,s+r[x](t)ds. (5)

    Therefore, the Preisach operator can be expressed as:

    y(t)=0q(r,Pr[x](t))dr, (6)

    where

    q(r,s)=2s0w(r,σ)dσ. (7)

    According to the general form in Eq. (7), the Preisach model can be decomposed into a continuous set of play operators and a one-to-one mapping function. Generally, the input-output relationship of the Preisach model can be defined as:

    y(t)=F(Pr[x](t)), (8)

    where F(∙) is a function that maps the play operators set in the real-valued output y(t). Thus, the Preisach model can be implemented by approximating the mapping function based on the input and output value of real hysteresis materials through some identification methods, such as nonnegative least squares.

    Least square support vector machine (LS-SVM) has been successfully introduced in modeling application for the global optimization property28. Compared to the standard SVM, LS-SVM uses the least squared loss function instead of the ε-insensitive loss function. Hence, the analytical solutions of LS-SVM can be obtained by solving linear equations instead of quadratic programming problem. For a given training data set {(ui, yi), uiRn, yiR}, the LS-SVM model is expressed as:

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

    where f(u) is the nonlinear mapping from the input space to higher feature space, w is the weight vector, and b is the bias. The optimization problem in the LS-SVM is obtained through the equation:

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

    where C is the regularization parameters, and ξi is the error between the actual output and predictive output. The problem can be solved by defining the Lagrangian equation as follow:

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

    where ai is the Lagrangian multiplier. The conditions for optimality are the saddle point of L, which can be found by solving the partial derivatives. After eliminating the w and ξi, the solution is given by the following linear equations:

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

    where e=[1, ···, 1]T, y=[y1, ···, yn]T, a=[a1, ···, an]T are the support vectors, I is the identity matrix, and the Gram matrix Ω is defined as follows:

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

    where K(ui, uj) is the kernel function, which can be used to avoid the computation of the mapping function f(u). Thus, the LS-SVM model for function regression can be formulated as:

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

    where ak and b are the solutions of the Eq. (13). The kernel function must satisfy the Mercer condition29. The radial base function (RBF) kernel is widely used in nonlinear function regression, which is expressed as:

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

    where σ is the width parameter of the KBF kernel. Therefore, for preassigned hyperparameter σ and C, the mapping function can be determined through Eq. (13). Moreover, the hyperparameters σ and C determine the generalization ability and complexity of the LS-SVM model, which should be optimized to ensure a high modeling accuracy along with high testing accuracy.

    To establish a Preisach model, the density function d(r, s) of the model should be approximated from real hysteresis loops. In the classical Preisach model, the model parameters can be tuned by two approaches. One approach is predefined mathematical forms with a few free parameters30, and another approach is using the numerical density function whose values are identified by the method of nonnegative least squares31. However, both of the two methods are complex and time-consuming. As an alternative approach, the LS-SVM is an adaptive approximation strategy, which can be used as a general function estimator to approximate the Preisach model mapping function F(∙). The LS-SVM based hysteresis model consists of two parts: a discrete play operator, and a memoryless mapping function, which are exhibited in Fig. 5. The discrete play operator memory is used to convert the Preisach model in Eq. (7) into a discrete form, which comprises m play operators with threshold values r1, r2, ···, rm. The threshold values are determined by the following equation:

    Figure 5.  Block diagram of the LS-SVM based hysteresis model.
    {r_i} = \frac{i}{{m + 1}} \cdot {\left| x \right|_{\max }},\;i = 1,2,\cdots,m\;, (16)

    where |x|max is the maximum absolute value of the input x(t). The number of the hysteresis play operator m determines the modeling accuracy and complexity of the hysteresis model. Additionally, due to that the classical Preisach model is a rate-independent hysteresis model, the rate of the input signal \dot{x}\left(t\right) is included in the model so that the model can be used to estimate the rate-dependent hysteresis behavior. Therefore, the input vector of the LS-SVM u consists of m play operators, input signal x(t), and the rate of input \dot{x}\left(t\right) . Formally, the output function of play operator z(t)=Pr[x](t) on each subinterval [ti, ti+1], where x(t) is piecewise monotonic on 0=t0<t1<t2<…<tN=tE, is inductively defined by27:

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

    where

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

    where r is the threshold value of the play operator. After converting the model input x(t) into the discrete paly operators, the operator vectors set are used to obtain the memoryless function F(∙) through the memoryless mapping function, which is established by a LS-SVM. The LS-SVM is trained though the Eq. (13) with the given training data. The hyperparameters σ and C of the LS-SVM are tuned by the k-fold cross-validation to ensure the high generalization ability of the hysteresis model.

    In the experiment, an optical fiber with 112 SEPs array is enclosed in the sensing cable with the packaging method as shown in Fig. 1. The SEPs array possess -45 dB reflectivity with an interval of 5 m. When a probe laser pulse is injected into the sensing cable, the coherent beat signals backscattering from the sensing cable are recorded in Fig. 6(a). It is obvious the backscattering signal has 112 stable beat frequency pulses with high SNR, corresponding to 112 SEPs. The former 56 beats frequency pulses scattering from the SEPs belong to the sensing fiber and the latter part come from the reference fiber. As the sensing principle describes above, the 56 beat frequency pulses from the sensing fiber or reference fiber can compose into 55 sensing channels Si (1≤i≤55) and 55 reference channels Ri (1≤i≤55), respectively. The sensing channel Si and the corresponding reference channel Rj (j=56-i) are combined into a sensor element. Therefore, the proposed strain sensor network can interrogate a sensing cable with 55 sensing elements. To calibrate the strain sensitivity of the sensor elements, the static strain from 2 με to 20 με with a step of 2 με is applied to the sensor element 28 at the end of the sensing cable by a precision displacement stage. The relationship between the phase change and the applied strain amplitude is illustrated in Fig. 7, which presents a high sensitivity of -47.04 rad/με and high precision with R-square over 0.999.

    Figure 6.  (a) Received beat frequency signal. (b) Beat frequency signal of sensor element 55 and 54.
    Figure 7.  The relationship between phase change and strain.

    To train the hysteresis model between the sensing channel and reference channel, a triangular-wave temperature with the same period and variable rate was applied to the sensor element 28, which is shown as the red line in Fig. 8(a). The triangular-wave temperature fluctuation used to train the LS-SVM model can provide a temperature change with different input rate, which can construct a complete set of training data. The corresponding phase of the sensing channel and reference channel are also plotted in the Fig. 8(a), respectively. The relationship between the sensing channel and reference channel is illustrated as the color scatter distribution in Fig. 8(b). The hysteresis loops curve reveals that the thermal hysteresis characters of the strain sensor is dependent on the change rate of the applied temperature. The larger change rate of the temperature will introduce the wider hysteresis loop. Therefore, the thermal hysteresis of the proposed strain sensor is a rate-dependent hysteresis model. The phase signal of the reference channel is set as the input of the proposed LS-SVM based hysteresis model, while the phase signal of the sensing channel is the output. The regression result of the LS-SVM based hysteresis model is plotted as the black line in Fig. 8(b). The results prove the highly regression accurate for the thermal hysteresis modeling. The modeling error of the LS-SVM based hysteresis model is also exhibited in the Fig. 8(c). Compared to the large compensation error of the direct differential method, the root mean squared error (RMSE) between the LS-SVM model output and phase signal of the sensing channel is less than 0.095 rad.

    Figure 8.  (a) Temperature change waveform and corresponding phase change for model train. (b) Hysteresis loops for temperature change and the regression result. (c) Compensation error.

    After training the hysteresis model by the hysteresis operator LS-SVM, the phase signal of the sensing channel is compensated by the trained hysteresis model. To estimate the compensation accuracy of the hysteresis model, the sensor element 28 is applied with a temperature fluctuation with amplitude of 5 °C, and strain signal with frequency of 0.01 Hz and amplitude of 20 nε. The original signals of the sensing channel and reference channel are plotted in the Fig. 9(a). The compensation result of the directly differential method and hysteresis model are illustrated in Fig. 9(b), respectively. It can be seen that the measured strain signal by the direct differentiation method is almost buried in the phase noise induced by the temperature fluctuation. However, the strain signal can be observed clearly in the phase of the sensing channel compensated by the hysteresis model. Moreover, the power spectrum density (PSD) of the original signal, compensated signals by direct differential method and hysteresis model is exhibited in the Fig. 9(c). In the PSD of the original signal and signal compensated by direct differentiation, the signal peak of strain vibration at 0.01 Hz is almost buried in the noise peaks induced by the temperature fluctuation. However, after compensating by LS-SVM based hysteresis model, the signal of the strain vibration can be obtained more clearly, 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. Moreover, the bias drift induced by the laser frequency shift is also suppressed compared with the uncompensated original signal.

    Figure 9.  (a) Original phase signal for temperature change and strain signal. (b) Compensation results for two methods. (c) PSD of the original result and compensation results.

    Additionally, to evaluate the strain resolution of the proposed strain sensor network, the sensing cable is placed in a quiet environment and isolated with vibration and strain. The original phase signals of the sensing channel and reference channel from sensor element 28 are plotted in Fig. 10(a), where a severe phase drift induced by the environment temperature change and laser frequency variation is observed. The compensated phase in time domain and frequency domain are illustrated in Figs. 10(b) and 10(c) respectively. The sine wave phase noise in the sensing channel and reference channel with frequency nearly 0.001 Hz is introduced by the air conditioner system in the lab, which will control the room temperature with fixed period. The bias drift of the sensing channel in time domain is eliminated by compensating with the LS-SVM based hysteresis model. In the frequency domain, the noise PSD below 0.1 Hz is suppressed clearly by compensation. Compared to the compensation method by direct differentiation, the noise of the compensated sensor by LS-SVM hysteresis model is further suppressed by 20 dB below 0.01 Hz. For compensation by hysteresis model, the phase power spectral density of the compensated sensor element is better than Sp(f)=5.01×10-4 rad·Hz-1/2 in the frequency range above 10 Hz, corresponding to a minimum dynamic strain resolution of 10.5 pε·Hz-1/2. Moreover, the phase noise power spectral density below 0.01 Hz even at 0.001 Hz is superior to 0.251 rad·Hz-1/2, which suggests the ultra-low frequency strain resolution of 166 pε @ 0.001 Hz. Remarkably, the quasi-static sensing resolution in mHz range of the strain sensor network can compete with the high-quality single point fiber sensor. Moreover, the sensor network proves a 55 sensor elements access capacity in the experiment and possesses a potential sensing capacity up to thousands of sensing channels which can match with the DAS system. It is the first reported strain sensor network to have sub-nε resolution in mHz frequency range along with ultra-large sensing capacity to the best of our knowledge. The large sensing capacity along with ultra-high quasi-static sensing resolution makes the proposed strain sensor network has potential applications in geoscience research.

    Figure 10.  (a) Original phase signal in a quiet environment. (b) Compensation results for two methods. (c) Noise floor PSD of the original result and compensation results.

    We have demonstrated an ultra-high resolution strain sensor network based on φ-OTDR technology and SEPs array fiber. To reduce the ultra-low frequency noise induced by the laser frequency shift and temperature field change, the phase of the sensing fiber is compensated by the reference fiber with strain isolated package. The hysteresis operator based LS-SVM hysteresis model is introduced to reduce the thermal hysteresis nonlinearity between the sensing fiber and reference fiber. After compensated by the hysteresis model, the SNR of a sinusoidal strain vibration with a frequency of 0.01 Hz increase by 24 dB compared with direct compensation, which proves the compensation accuracy of the LS-SVM hysteresis model. Moreover, the phase noise level in the quilt environment presents a high dynamic resolution of 10.5 pε·Hz-1/2 in the frequency range above 10 Hz, and ultra-low frequency sensing resolution of 166 pε at 0.001 Hz. The high resolution in the ultra-low frequency and the large sensing capacity make the strain sensor network play an irreplaceable role in the geoscience research.

  • We are grateful for financial supports from the National Natural Science Foundation of China (NSFC) (No. 61922033 & 61775072); Major Technology Innovation of Hubei Province (2019AAA053); Foundation for Innovative Research Groups of Hubei Province of China (2018CFA004); and Innovation Fund of WNLO.

  • T. Liu, H. Li and Q. Z. Sun proposed the original idea of the project. Q. Z. Sun supervised the project. Z. J. Yan and D. M. Liu participated the discussion of the research. T. Liu, T. He and C. Z. Fan carried out the experiments and collected the data. T. Liu analysed all the data. T. Liu and Q. Z. Sun wrote the paper. All authors discussed the results and commented on the manuscript.

  • The authors declare no competing financial interests.

  • [1] Bergen KJ, Johnson PA, de Hoop MV, Beroza GC. Machine learning for data-driven discovery in solid Earth geoscience. Science 363, eaau0323 (2019). doi: 10.1126/science.aau0323

    CrossRef Google Scholar

    [2] Liu QW, Tokunaga T, He ZY. Ultra-high-resolution large-dynamic-range optical fiber static strain sensor using Pound–Drever–Hall technique. Opt Lett 36, 4044–4046 (2011). doi: 10.1364/OL.36.004044

    CrossRef Google Scholar

    [3] Asheden CL, Lindsay JM, Sherburn S, Smith IEM, Miller CA et al. Some challenges of monitoring a potentially active volcanic field in a large urban area: Auckland volcanic field, New Zealand. Nat Hazards 59, 507–528 (2011). doi: 10.1007/s11069-011-9773-0

    CrossRef Google Scholar

    [4] Davis EE, Heesemann M, Lambert A, He JH. Seafloor tilt induced by ocean tidal loading inferred from broadband seismometer data from the Cascadia subduction zone and Juan de Fuca Ridge. Earth Planet Sci Lett 463, 243–252 (2017). doi: 10.1016/j.jpgl.2017.01.042

    CrossRef Google Scholar

    [5] Kimura T, Murakami H, Matsumoto T. Systematic monitoring of instrumentation health in high-density broadband seismic networks. Earth Planets Space 67, 55 (2015). doi: 10.1186/s40623-015-0226-y

    CrossRef Google Scholar

    [6] Huang WZ, Zhang WT, Luo YB, Li L, Liu WY et al. Broadband FBG resonator seismometer: principle, key technique, self-noise, and seismic response analysis. Opt Express 26, 10705–10715 (2018). doi: 10.1364/OE.26.010705

    CrossRef Google Scholar

    [7] Jiang P, Ma LN, Hu ZL, Hu YM. Low-crosstalk and polarization-independent inline interferometric fiber sensor array based on fiber Bragg gratings. J Lightw Technol 34, 4232–4239 (2016). doi: 10.1109/JLT.2016.2597301

    CrossRef Google Scholar

    [8] Zhao ZY, Tang M, Lu C. Distributed multicore fiber sensors. Opto-Electron Adv 3, 190024 (2020).

    Google Scholar

    [9] Wang BZ, Ba DX, Chu Q, Qiu LQ, Zhou DW et al. High-sensitivity distributed dynamic strain sensing by combining Rayleigh and Brillouin scattering. Opto-Electron Adv 3, 200013 (2020). doi: 10.29026/oea.2020.200013

    CrossRef Google Scholar

    [10] Jousset P, Reinsch T, Ryberg T, Blanck H, Clarke A et al. Dynamic strain determination using fibre-optic cables allows imaging of seismological and structural features. Nat Commun 9, 2509 (2018). doi: 10.1038/s41467-018-04860-y

    CrossRef Google Scholar

    [11] Ajo-Franklin JB, Dou S, Lindsey NJ, Monga I, Tracy C et al. Distributed acoustic sensing using dark fiber for near-surface characterization and broadband seismic event detection. Sci Rep 9, 1328 (2019). doi: 10.1038/s41598-018-36675-8

    CrossRef Google Scholar

    [12] Masoudi A, Newson TP. Contributed review: distributed optical fibre dynamic strain sensing. Rev Sci Instrum 87, 011501 (2016). doi: 10.1063/1.4939482

    CrossRef Google Scholar

    [13] Wang ZN, Zhang L, Wang S, Xue NT, Peng F et al. Coherent Φ-OTDR based on I/Q demodulation and homodyne detection. Opt Express 24, 853–858 (2016). doi: 10.1364/OE.24.000853

    CrossRef Google Scholar

    [14] Chen D, Liu QW, He ZY. High-fidelity distributed fiber-optic acoustic sensor with fading noise suppressed and sub-meter spatial resolution. Opt Express 26, 16138–16146 (2018). doi: 10.1364/OE.26.016138

    CrossRef Google Scholar

    [15] Wu MS, Fan XY, Liu QW, He HY. Highly sensitive quasi-distributed fiber-optic acoustic sensing system by interrogating a weak reflector array. Opt Lett 43, 3594–3597 (2018). doi: 10.1364/OL.43.003594

    CrossRef Google Scholar

    [16] Liang GH, Jiang JF, Liu K, Wang S, Xu TH et al. Phase demodulation method based on a dual-identical-chirped-pulse and weak fiber Bragg gratings for quasi-distributed acoustic sensing. Photonics Res 8, 1093–1099 (2020). doi: 10.1364/PRJ.389400

    CrossRef Google Scholar

    [17] Mateeva A, Lopez J, Chalenski D, Tatanova M, Zwartjes P et al. 4D DAS VSP as a tool for frequent seismic monitoring in deep water. Leading Edge 36, 995–1000 (2017). doi: 10.1190/tle36120995.1

    CrossRef Google Scholar

    [18] Zhong X, Zhang CX, Li LJ, Liang S, Li Q et al. Influences of laser source on phase-sensitivity optical time-domain reflectometer-based distributed intrusion sensor. Appl Opt 53, 4645–4650 (2014). doi: 10.1364/AO.53.004645

    CrossRef Google Scholar

    [19] Zhu F, Zhang XP, Xia L, Guo Z, Zhang YX. Active compensation method for light source frequency drifting in Φ-OTDR sensing system. IEEE Photonic Technol Lett 27, 2523–2526 (2015). doi: 10.1109/LPT.2015.2468075

    CrossRef Google Scholar

    [20] Yuan Q, Wang F, Liu T, Liu Y, Zhang YX et al. Compensating for influence of laser-frequency-drift in phase-sensitive OTDR with twice differential method. Opt. Express 27, 3664–3671 (2019). doi: 10.1364/OE.27.003664

    CrossRef Google Scholar

    [21] Sun QZ, Yan ZJ, Liu DM, Zhang L. Optical fiber sensor network and industrial applications. In: Peng GD. Handbook of Optical Fibers 1–46 (Springer, 2019); https://doi.org/10.1007/978-981-10-1477-2_20-1.

    Google Scholar

    [22] Li H, Sun QZ, Liu T, Fan CZ, He T et al. Ultra-high sensitive quasi-distributed acoustic sensor based on coherent OTDR and cylindrical transducer. J Lightw Technol 38, 929–938 (2020). doi: 10.1109/JLT.2019.2951624

    CrossRef Google Scholar

    [23] Liu T, Li H, Ai F, Wang J, Fan CZ et al. Ultra-high resolution distributed strain sensing based on phase-OTDR. In Proc. Optical Fiber Communications Conference (IEEE, 2019). https://doi.org/10.1364/OFC.2019.Th2A.16.

    Google Scholar

    [24] Ai F, Sun QZ, Zhang W, Liu T, Yan ZJ et al. Wideband fully-distributed vibration sensing by using UWFBG based coherent OTDR. In Proc. Optical Fiber Communications Conference (OSA, 2017). https://doi.org/10.1364/OFC.2017.W2A.19.

    Google Scholar

    [25] Bobbio S, Milano G, Serpico C, Visone C. Models of magnetic hysteresis based on play and stop hysterons. IEEE Trans Magn 33, 4417–4426 (1997). doi: 10.1109/20.649875

    CrossRef Google Scholar

    [26] Ge P, Jouaneh M. Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators. Precis Eng 20, 99–111 (1997). doi: 10.1016/S0141-6359(97)00014-7

    CrossRef Google Scholar

    [27] Brokate M, Sprekels J. Hysteresis and Phase Transitions (Springer, New York, 1996).

    Google Scholar

    [28] Suykens JAK, Vandewalle J, De Moor B. Optimal control by least squares support vector machines. Neural Netw 14, 23–35 (2001). doi: 10.1016/S0893-6080(00)00077-0

    CrossRef Google Scholar

    [29] Vapnik V. Statistical Learning Theory (Johan Wiley & Sons, New York, 1998).

    Google Scholar

    [30] Shirley ME, Venkataraman R. On the identification of Preisach measures. Proc SPIE 5049, 326–336 (2003). doi: 10.1117/12.499462

    CrossRef Google Scholar

    [31] Stakvik JÅ, Ragazzon MRP, Eielsen A A, Gravdahl JT. On implementation of the Preisach model: identification and inversion for hysteresis compensation. Model, Ident Control 36, 133–142 (2015). doi: 10.4173/mic.2015.3.1

    CrossRef Google Scholar

  • Related articles

    Jie Hu, Weihao Lin, Liyang Shao, Chenlong Xue, Fang Zhao, Dongrui Xiao, Yang Ran, Yue Meng, Panpan He, Zhiguang Yu, Jinna Chen, Perry Ping Shum
    Opto-Electronic Advances    2024, 7(12)   doi: 10.29026/oea.2024.240105
    Kexuan Liu, Jiachen Wu, Zehao He, Liangcai Cao
    Opto-Electronic Advances    2023, 6(5)   doi: 10.29026/oea.2023.220135
    Jingbo Yin, Yulong Zhao, Minghui Hong
    Opto-Electronic Advances    2024, 7(12)   doi: 10.29026/oea.2024.240222
    Zhuo Wang, Bo Zhang, Dezhi Tan, Jianrong Qiu
    Opto-Electronic Advances    2023, 6(1)   doi: 10.29026/oea.2023.220008
    Yuncheng Liu, Ke Xu, Xuhao Fan, Xinger Wang, Xuan Yu, Wei Xiong, Hui Gao
    Opto-Electronic Advances    2024, 7(1)   doi: 10.29026/oea.2024.230108
    Laiyang Dang, Ligang Huang, Leilei Shi, Fuhui Li, Guolu Yin, Lei Gao, Tianyi Lan, Yujia Li, Lidan Jiang, Tao Zhu
    Opto-Electronic Advances    2023, 6(2)   doi: 10.29026/oea.2023.210149
    Zhi Jiang, Cizhe Fang, Xu Ran, Yu Gao, Ruiqing Wang, Jianguo Wang, Danyang Yao, Xuetao Gan, Yan Liu, Yue Hao, Genquan Han
    Opto-Electronic Advances    2025, 8(1)   doi: 10.29026/oea.2025.240114
    Zeev Zalevsky
    Opto-Electronic Advances    2025, 8(3)   doi: 10.29026/oea.2025.250026
  • 1.  Yan, Q., Wei, Z., Lin, Z. et al. Apart and A Part: Overlapped vibration recognition for distributed optical fiber sensing based on deep learning separation. Optics and Laser Technology, 2025.
    2.  Lu, X., Krebber, K. Suppression of Rayleigh fading induced errors in φOTDR by different pulse widths for improving the reliability of civil infrastructure monitoring. Optics and Laser Technology, 2025.
    3.  Chen, J., Li, H., Ai, K. et al. Near-field Multi-source Localization and Signal Enhancement with ASP-assisted DAS. IEEE Transactions on Instrumentation and Measurement, 2025.
    4.  Chen, J., Li, H., Xiao, X. et al. Fully distributed fiber-optic streamer with small channel spacing for marine seismic acquisition. Ocean Engineering, 2024.
    5.  Lv, Y., Xiao, X., Li, H. et al. Strain measurement with adaptive local feature extraction method based on special fiber OFDR system. Optics Express, 2024, 32(4): 5043-5055.
    6.  Ai, K., Fan, C., Chen, J. et al. Low-Frequency Drift Compensation Method for Interferometry Fiber-Optic Vibration Sensing Using Sampling Matched Integral Fitting Difference. 2024.
    7.  Nagarajan, P., Sathiya, D., Pulugu, D. et al. Self-powered wearable implantable smart sensor and medical electronics based on nanogenerator. Self-powered Sensors: a Path to Wearable Electronics, 2024.
    8.  Zhang, Y., Xu, Z., Wu, J. et al. Nanometer-Resolution and Large-Dynamic-Range Optical Fiber Displacement Sensor Based on Single Pound-Drever-Hall Feedback Loop. Journal of Lightwave Technology, 2024.
    9.  Chen, J., Li, H., Ai, K. et al. Low-altitude UAV Surveillance System via Highly Sensitive Distributed Acoustic Sensing. IEEE Sensors Journal, 2024.
    10.  Li, J.-T., Chang, B., Du, J.-T. et al. Coherently parallel fiber-optic distributed acoustic sensing using dual Kerr soliton microcombs. Science Advances, 2024, 10(3)
    11.  Zhang, X., Zhang, Y., Wang, L. et al. Current Status and Future of Research and Applications for Distributed Fiber Optic Sensing Technology | [分 布 式 光 纤 传 感 技 术 研 究 和 应 用 的 现 状 及 未 来]. Guangxue Xuebao/Acta Optica Sinica, 2024, 44(1): 0106001.
    12.  Li, H., Fan, C., Xiao, X. et al. Research Progress in Scattering Enhanced Microstructured Fiber and Its Distributed Sensing Technology | [散 射 增 强 微 结 构 光 纤 及 其 分 布 式 传 感 技 术 研 究进 展]. Guangxue Xuebao/Acta Optica Sinica, 2024, 44(1): 0106008.
    13.  Yan, B., Zhang, K., Zeng, Z. et al. Sand Particle Content Monitoring in Sand-Water Two-Phase Flow Based on Distributed Acoustic Sensing. Journal of Lightwave Technology, 2023, 41(24): 7448-7454.
    14.  Kalim, U., Ren, J.-T., Ke, S.-S. et al. Bound states of Dirac fermions in the presence of a Fermi velocity modulation. EPL, 2023, 144(5): 50001.
    15.  Liang, Y., Sun, J., Zhang, J. et al. Prediction of fiber Rayleigh scattering responses based on deep learning. Science China Information Sciences, 2023, 66(12): 222301.
    16.  He, T., Zhang, S., Li, H. et al. An Efficient Separation and Identification Algorithm for Mixed Threatening Events Applied in Fiber-Optic Distributed Acoustic Sensor. IEEE Sensors Journal, 2023, 23(20): 24763-24771.
    17.  Chen, M., Geng, S., Zheng, F. et al. Nonlinear error compensation for microfiber knot current sensors based on artificial neural network. Optical Fiber Technology, 2023.
    18.  Chen, J., Li, H., Xiao, X. et al. Fully distributed hydroacoustic sensing based on ultra-highly sensitive and lightweight fiber-optic hydrophone cable. Optics and Lasers in Engineering, 2023.
    19.  Chen, M., Han, J., Liu, J. et al. Output Prediction of Helical Microfiber Temperature Sensors in Cycling Measurement by Deep Learning. Photonic Sensors, 2023, 13(3): 230308.
    20.  Yan, B., Li, H., Zhang, K. et al. Quantitative Identification and Localization for Pipeline Microleakage by Fiber Distributed Acoustic Sensor. Journal of Lightwave Technology, 2023, 41(16): 5460-5467.
    21.  Zhu, Y., Zhou, R., Su, S. et al. Flexible three-axis tactile sensor based on double-layer electrospun polyimide nanofiber membrane. Sensors and Actuators A: Physical, 2023.
    22.  Lan, T., Zhang, C., Huang, L. et al. Dynamic intrinsic spectrum reconstruction of narrow-linewidth laser based on band-extended frequency noise. Optics and Laser Technology, 2023.
    23.  Lee, T., Beresna, M., Masoudi, A. et al. Enhanced-Backscattering and Enhanced-Backreflection Fibers for Distributed Optical Fiber Sensors. Journal of Lightwave Technology, 2023, 41(13): 4051-4064.
    24.  Yan, B., Zhang, K., Li, H. et al. Acoustic Field Imaging of Pipeline Turbulence for Noninvasive and Distributed Gas Flow Measurement. IEEE Sensors Journal, 2023, 23(12): 12868-12875.
    25.  Fan, C., Li, H., Zhang, K. et al. 300 km ultralong fiber optic DAS system based on optimally designed bidirectional EDFA relays. Photonics Research, 2023, 11(6): 968-977.
    26.  Cao, K., Xu, T., Ma, L. et al. Distributed optical fiber sensing in coherent Φ-OTDR with a broadband chirped-pulse conversion algorithm. Optics Express, 2023, 31(4): 6649-6658.
    27.  Liu, H., Hu, D.J.J., Sun, Q. et al. Specialty optical fibers for advanced sensing applications. Opto-Electronic Science, 2023, 2(2): 220025.
    28.  Yang, Q., Xie, W., Yang, J. et al. Frequency drift noise suppression in φ-OFDR based on optical phase-locked loop. 2023.
    29.  Yan, B., Zhang, K., Xiao, X. et al. Pipeline Two-phase Flow Sand Concentration Monitoring based on Distributed Acoustic Sensing. 2023.
    30.  Yan, B., Fan, C., Xiao, X. et al. High-accuracy Localization of Pipeline Microleakage by using Distributed Acoustic Sensor. 2023.
    31.  Ai, K., Fan, C., Chen, J. et al. High Resolution Millihertz Fibre-Optic Strain Sensor Based on Time Delay Interferometry. 2023.
    32.  Rao, Y.. The cornerstone of fiber-optic distributed vibration/acoustic sensing: Ф-OTDR. Opto-Electronic Advances, 2023, 6(7): 230063.
    33.  Fan, C., Xiao, X., Li, H. et al. Full Link SNR Equalization das System over 80km Based on Gradient Discrete Scattering Enhanced Fiber. 2023.
    34.  Zhang, B., Liu, K., Liu, K. et al. Research on dynamic variance threshold algorithm based on distributed fiber vibration sensor system | [基于分布式光纤振动检测系统的动态方差阈值算法研究]. Guangdian Gongcheng/Opto-Electronic Engineering, 2023, 50(2): 220205.
    35.  Zhang, C., Zou, N., Song, J. et al. Digital signal processing and application of Φ-OTDR system | [Φ-OTDR 系统的数字信号处理及应用]. Guangdian Gongcheng/Opto-Electronic Engineering, 2023, 50(2): 220088.
    36.  Jing, J., Liu, K., Jiang, J. et al. Highly sensitive and stable probe refractometer based on configurable plasmonic resonance with nano-modified fiber core. Opto-Electronic Advances, 2023, 6(6): 220072.
    37.  Huang, Y., Zhao, H., Zhao, X. et al. Pattern recognition using self-reference feature extraction for φ-OTDR. Applied Optics, 2022, 61(35): 10507-10518.
    38.  Zhang, G., Xiong, Z., Guo, M. et al. Low-Frequency Optical Fiber Fabry-Perot Acoustic Sensor Based on All-Phase Cross-Correlation Demodulation. Journal of Lightwave Technology, 2022, 40(22): 7431-7438.
    39.  Fan, C., Li, H., Yan, B. et al. High-precision distributed detection of rail defects by tracking the acoustic propagation waves. Optics Express, 2022, 30(22): 39283-39293.
    40.  Jiang, L., Lan, T., Dang, L. et al. Ultra-narrow linewidth vertical-cavity surface-emitting laser based on external-cavity weak distributed feedback. Optics Express, 2022, 30(21): 37519-37525.
    41.  Yan, Q., Zhou, C., Feng, X. et al. Galloping Vibration Monitoring of Overhead Transmission Lines by Chirped FBG Array. Photonic Sensors, 2022, 12(3): 220310.
    42.  Li, H., Fan, C., Shi, Z. et al. Spatio-temporal joint oversampling-downsampling technique for ultra-high resolution fiber optic distributed acoustic sensing. Optics Express, 2022, 30(16): 29639-29654.
    43.  Zhou, X., Wang, F., Liu, Z. et al. Hybrid B-OTDR/Φ-OTDR for multi-parameter measurement from a single end of fiber. Optics Express, 2022, 30(16): 29117-29127.
    44.  Zhang, J., Zhao, X., Zhao, Y. et al. Unsupervised learning method for events identification in φ-OTDR. Optical and Quantum Electronics, 2022, 54(7): 457.
    45.  Li, H., Liu, T., Fan, C. et al. Fading Suppression for Distributed Acoustic Sensing Assisted With Dual-Laser System and Differential-Vector-Sum Algorithm. IEEE Sensors Journal, 2022, 22(10): 9417-9425.
    46.  Lin, S., Wang, Z., Qi, Y. et al. Wideband Remote-Sensing Based on Random Fiber Laser. Journal of Lightwave Technology, 2022, 40(9): 3104-3110.
    47.  Wu, H., Liu, Y., Tu, Y. et al. Multi-Source Separation Under Two 'Blind' Conditions for Fiber-Optic Distributed Acoustic Sensor. Journal of Lightwave Technology, 2022, 40(8): 2601-2611.
    48.  Miao, Z., Li, Y., Xiao, X. et al. Direct optical fiber monitor on stress evolution of the sulfur-based cathodes for lithium–sulfur batteries. Energy and Environmental Science, 2022, 15(5): 2029-2038.
    49.  Zhao, X., Sun, H., Lin, B. et al. Markov Transition Fields and Deep Learning-Based Event-Classification and Vibration-Frequency Measurement for ϕ-OTDR. IEEE Sensors Journal, 2022, 22(4): 3348-3357.
    50.  Ma, L., Xu, T., Cao, K. et al. Signal Activity Detection for Fiber Optic Distributed Acoustic Sensing with Adaptive-Calculated Threshold. Sensors, 2022, 22(4): 1670.
    51.  Yan, B., Zhang, K., Li, H. et al. Pipeline Micro Leakage Detection via Fiber Optic Acoustic Sensing System. 2022.
    52.  Cunzheng, F., Hao, L., Baoqiang, Y. et al. Modulation Instability Suppression for Fiber Optic DAS Assisted with Dual Wavelength Lasers. 2022.
    53.  Shi, Z., Yang, J., Li, H. et al. Crust Deformation Detection System based on Coherent Optical Fiber Sensing Technology. 2022.
    54.  Li, T., Ba, D., Zhou, D. et al. Recent progress in optical fiber sensing based on forward stimulated Brillouin scattering | [前向受激布里渊散射光纤传感研究进展]. Guangdian Gongcheng/Opto-Electronic Engineering, 2022, 49(9): 220021.
    55.  Geng, F., Huo, X. A Self-Powered Sport Sensor Based on Triboelectric Nanogenerator for Fosbury Flop Training. Journal of Sensors, 2022.
    56.  Cunzheng, F., Hao, L., Baoqiang, Y. et al. 246km Long Distance fiber optic DAS System Based on Multi-Span Bidirectional EDFAs and Cascaded AOMs. 2022.
    57.  Shi, Z., Yang, J., Li, H. et al. Crust Deformation Detection System based on Coherent Optical Fiber Sensing Technology. 2022.
    58.  Cunzheng, F., Hao, L., Baoqiang, Y. et al. Modulation Instability Suppression for Fiber Optic DAS Assisted with Dual Wavelength Lasers. 2022.
    59.  Cunzheng, F., Hao, L., Baoqiang, Y. et al. 246km Long Distance fiber optic DAS System Based on Multi-Span Bidirectional EDFAs and Cascaded AOMs. 2022.
    60.  Liu, S., Yu, F., Hong, R. et al. Advances in phase-sensitive optical time-domain reflectometry. Opto-Electronic Advances, 2022, 5(3): 200078.
    61.  Deng, M., Zhang, T., Nan, X. et al. Enhanced sensitivity of optical fiber vibration sensor based on radio-frequency Michelson interferometer. Optics Letters, 2021, 46(24): 6079-6082.
    62.  Cunzheng, F., Hao, L., Tao, H. et al. Large dynamic range optical fiber distributed acoustic sensing (das) with differential-unwrapping-integral algorithm. Journal of Lightwave Technology, 2021, 39(22): 7274-7280.
    63.  Xu, N., Wang, P., Wang, Y. et al. Crosstalk noise suppressed for multi-frequency φ-otdr using compressed sensing. Journal of Lightwave Technology, 2021, 39(22): 7343-7350.
    64.  Liu, K., Fan, J., Luo, B. et al. Highly sensitive vibration sensor based on the dispersion turning point microfiber Mach-Zehnder interferometer. Optics Express, 2021, 29(21): 32983-32995.
    65.  Shi, Z., Yan, B., Fan, C. et al. Nano-Strain Optical Fiber Sensing System Based on Coherent Phase Detection Technology. 2021.
    66.  Cunzheng, F., Hao, L., Baoqiang, Y. et al. 246km Long Distance fiber optic DAS System Based on Multi-Span Bidirectional EDFAs and Cascaded AOMs. 2016.
  • Created with Highcharts 5.0.7Amount of accessChart context menuAbstract Views, PDF Downloads StatisticsAbstract ViewsPDF Downloads2024-042024-052024-062024-072024-082024-092024-102024-112024-122025-012025-022025-030204060Highcharts.com
    Created with Highcharts 5.0.7Chart context menuAccess Class DistributionFULLTEXT: 85.4 %FULLTEXT: 85.4 %PDF: 14.6 %PDF: 14.6 %FULLTEXTPDFHighcharts.com
    Created with Highcharts 5.0.7Chart context menuAccess Area DistributionOthers: 64.2 %Others: 64.2 %United States: 21.1 %United States: 21.1 %Russia: 5.6 %Russia: 5.6 %France: 3.5 %France: 3.5 %Germany: 1.3 %Germany: 1.3 %India: 1.0 %India: 1.0 %Singapore: 0.4 %Singapore: 0.4 %Italy: 0.4 %Italy: 0.4 %Japan: 0.3 %Japan: 0.3 %United Kingdom: 0.3 %United Kingdom: 0.3 %Canada: 0.2 %Canada: 0.2 %Australia: 0.2 %Australia: 0.2 %Egypt: 0.1 %Egypt: 0.1 %Saudi Arabia: 0.1 %Saudi Arabia: 0.1 %Belgium: 0.1 %Belgium: 0.1 %Norway: 0.1 %Norway: 0.1 %Mexico: 0.1 %Mexico: 0.1 %Malaysia: 0.1 %Malaysia: 0.1 %Netherlands: 0.1 %Netherlands: 0.1 %Poland: 0.1 %Poland: 0.1 %Ukraine: 0.1 %Ukraine: 0.1 %Spain: 0.1 %Spain: 0.1 %Thailand: 0.0 %Thailand: 0.0 %Austria: 0.0 %Austria: 0.0 %Vietnam: 0.0 %Vietnam: 0.0 %Brazil: 0.0 %Brazil: 0.0 %Lithuania: 0.0 %Lithuania: 0.0 %Republic of Korea: 0.0 %Republic of Korea: 0.0 %Republic of Ireland: 0.0 %Republic of Ireland: 0.0 %Switzerland: 0.0 %Switzerland: 0.0 %Venezuela: 0.0 %Venezuela: 0.0 %Turkey: 0.0 %Turkey: 0.0 %Denmark: 0.0 %Denmark: 0.0 %Estonia: 0.0 %Estonia: 0.0 %Indonesia: 0.0 %Indonesia: 0.0 %Cambodia: 0.0 %Cambodia: 0.0 %Philippines: 0.0 %Philippines: 0.0 %Bangladesh: 0.0 %Bangladesh: 0.0 %Israel: 0.0 %Israel: 0.0 %OthersUnited StatesRussiaFranceGermanyIndiaSingaporeItalyJapanUnited KingdomCanadaAustraliaEgyptSaudi ArabiaBelgiumNorwayMexicoMalaysiaNetherlandsPolandUkraineSpainThailandAustriaVietnamBrazilLithuaniaRepublic of KoreaRepublic of IrelandSwitzerlandVenezuelaTurkeyDenmarkEstoniaIndonesiaCambodiaPhilippinesBangladeshIsraelHighcharts.com
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Figures(10)

Article Metrics

Article views(10586) PDF downloads(1787) Cited by(66)

Access History

Catalog

/

DownLoad:  Full-Size Img  PowerPoint