1. Introduction

Fiber optic sensor technology is one of the most promising candidates among the numerous sensing technologies that are suitable for the structural health monitoring (SHM) [1]. This is due to the inherent fiber optic properties such as light weight, small size, non-corrosive, immunity to electromagnetic interference, distributed sensing capability, etc [2]. The vibration is important information for these types of applications because the intrinsic vibration frequencies can be used to evaluate the structural condition and to identify the internal damages at an early stage.

Many efforts have been made to fulfill the space-resolved vibration sensing systems [3–7]. Among them, the widely used approaches are based on either the optical time domain reflectometer (OTDR) [8] or the optical frequency domain reflectometer (OFDR) [9]. For the OTDR methods, a polarization sensitive OTDR method was reported to achieve the vibration measurement to have a response frequency up to 5 kHz with a measurement range of 1 km and a spatial resolution of 10 m [3]. A phase-OTDR method was also described to measure a vibration frequency response up to 1 kHz with a measurement range of 1.2 km and a spatial resolution of 5 m [4]. An improved performance of the phase-OTDR sensor was also realized to measure a vibration frequency response up to 8 kHz to have a spatial resolution as fine as 0.5 m for a measurement range of 1 km by use of the wavelet denoising data processing technique [5] and the polarization-maintaining (PM) configuration [6]. For the OFDR methods, M. Froggatt et al [8] firstly used the OFDR technique for the distributed temperature and strain sensing based on the analysis of the spectral shift of the local Rayleigh backscattering spectra in the wavelength domain. The OFDR for the distributed temperature and strain sensing application has advantages of a high spatial resolution and a simple configuration [10–14]. Based on this technique a dynamic vibration measurement with a high spatial resolution of 10 cm has been demonstrated [7]. As the method requires to measure a spectral shift of the local Rayleigh backscattering spectra continuously, disadvantageously a measurable vibration frequency is limited to 32 Hz. In this method, the measurement range is limited to 17 m due to a short laser coherent length [15]. All the previously reported methods have a significantly limitation for the measurement range, for example, the OTDR vibration sensing can achieve the longest measurement range about 1 km while the OFDR vibration sensor measurement length is only 17 m. Such short measurement range is limited to many practical applications in the field such as for the large structural health monitoring that typically requires a measurement distance of several kilometers to tens kilometers.

In this paper, we report a novel method to achieve a space-resolved long-range vibration detection system based on the correlation analysis of OFDR signals by using a standard single-mode optical fiber. By two separate measurements of the vibrated and non-vibrated states for the test fiber, the vibration frequency and position information can be extracted by the cross-correlation analysis of the beat signals between the vibrated state and non-vibrated state of the local Rayleigh backscattering (RB) in the spatial domain. In the previous reported methods [7], the vibration frequency information was obtained by analyzing the Rayleigh backscattering spectra in an optical frequency domain. However, in our method the vibration frequency information are extracted from the RB beat signal analysis in a spatial domain, thereby advantageously a maximal measurable vibration frequency can be increased up to 2 kHz or even higher with a spatial resolution of 5 m. By using of a highly coherent tunable laser source (TLS), i.e. with a narrow linewidth of ~1 kHz, our OFDR sensor measurable range can be up to 12 km. Moreover, we also studied two vibrations located at different positions of the test fiber and preliminarily experimental results show that it may be possible to further realize a distributed vibration sensor. To author’s best knowledge, this is the longest measurement range and the highest frequency response ever achieved by using the OFDR for a vibration sensor.

2. Operation principle and signal processing

2.1 Operation principle

An OFDR interferometer provides a beat signal that is produced by the optical interference between two light signals originating from the same linearly frequency chirped highly coherent light source. One signal $E_s(t)$is reflection light such as Rayleigh backscattering (RB) light from the fiber under test (FUT) along the test path, while another $E_r(t)$follows a reference path of the interferometer (see below Fig. 1 ). For a tunable laser source (TLS) having a linear optical frequency tuning speed $\gamma$, the optical field $E_r(t)$from the reference path can be written as

 

Fig. 1 Configuration of the OFDR system. The main interferometer is a modified fiber-based Mach-Zehnder interferometer. An auxiliary Michelson interferometer is used as a clock signal to trigger the DAQ. C1, C2 and C3 are 2 × 2 couplers, where C1 is a 1:99 coupler and C2 and C3 are 50:50 couplers. TLS is tunable laser source. PC is a polarization controller, BPD is a balanced photo-detector and DAQ is a data acquisition card. PZT 1 is at 10 km and PZT 2 is at 10.67 km.

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By assuming that there is a vibration event occurring at a round-trip time delay $\tau$of the FUT, the vibration can cause phase change in $E_s(t)$ along the test fiber path that can be written as $\delta \sin (2\pi f_{m}t)$, where $f_m$is the vibration frequency and $\delta$ is the phase modulation amplitude. Assuming that a reflection reflectivity is $r(\tau )$ at $\tau$and $\alpha$is the fiber attenuation coefficient, a reflectivity with fiber attenuation can be written as $R(\tau )=r(\tau )\exp (-\alpha \tau c/n)$, where $c$ is the light speed in vacuum and n is the refractive index of fiber. Then $E_s(t)$ of reflection in a vibration state with the reflectivity and the fiber attenuation ($R(\tau )$) can be expressed as

According to the discussion in [16]

Assuming that the phase modulation amplitude $\delta$ is small (e.g., $\delta$<1), the first order of Bessel function is much bigger than the higher order terms, so the higher order terms in Eq. (4) could be neglected.

Substituting the Eq. (4) into Eq. (2), the beat signal $I_v(t)$ generated by the interference of the reference light $E_r(t)$ and backscattering light $E_s(t)$ can be expressed as

By comparing the Eq. (5) and Eq. (6), one can easily to see that the beat signal with the vibration has two additional frequency components $f_b-f_m$ and $f_b+f_m$. By a Fast Fourier transform (FFT) the measured time domain information as shown in Eq. (5) and Eq. (6) can be converted into the desired spatial domain. Thus the RB information in the spatial domain will have three frequencies $f_b$, $f_b-f_m$ and $f_b+f_m$. With an appropriate signal processing, the vibration frequency $f_m$can be retrieved from the measured RB light signals.

2.2 Signal processing

2.2.1 Identification of vibration location

The RB in an optical fiber is caused by random fluctuations in the index profile along an optical fiber. For a given fiber, the RB amplitude or reflectivity as a function of distance is a random but static property of the fiber and can act as a fiber “fingerprint” [12]. The spatially distributed “fingerprints” can be obtained from the beat signals in an OFDR measurement. The vibration on an optical fiber path results in a change in the “fingerprint” of the test fiber, which can be used to obtain the information of any vibration event along the fiber path. However, the RB or “fingerprint” of the fiber is very weak so that it could be easily swamped by the stochastic noises such as laser phase noise, polarization noise, coherence fading noise [17], etc. Moreover, the “fingerprint” is also impacted by any change in temperature and vibration in the environment [12]. However, a “fingerprint” for a fiber segment that contains several tens to hundreds points cannot be easily swamped by those stochastic noises.

For our proposed technique, the fiber “fingerprint” at the same location are separately measured twice. When there is no any vibration, two “fingerprints” from different measurements are very similar or identical, i.e. a “similarity” between the two “fingerprints” is very high, while, in contrast, when a vibration occurs, the two “fingerprints” from two separate measurements are different and a “similarity” is low. The cross-correlation analysis is used to estimate this “similarity” between two separate independent measurements. Based on the cross-correlation analysis, when the “similarity” is high, the cross-correlation signal mainly has one cross-correlation peak at the center, in contrast, when a “similarity” is low, the cross-correlation signal is chaotic, the main cross-correlation peak is low and contains many other cross-correlation peaks that are spread along main cross-correlation peak.

In order to quantitatively evaluate a “similarity” from the test fiber, we define a “non-similar level” to estimate a “similarity” from the cross-correlation analysis, which is the number of data points beyond the threshold value in the cross-correlation signals. The threshold is defined as a ratio of the highest cross-correlation peak, for example, a half of the maximum cross-correlation peak. A “non-similar level” is inversely proportional to a “similarity”. A lower “similarity” induces a higher “non-similar level”. Setting of a threshold level is very important. As mentioned above, the RB signal is usually very weak and carries lots of noise and this would impact an evaluation of the “similarity”. Consequently a “false alarm” for a vibration event may be caused. The selection of the threshold level need to balance between a “false alarm” of the vibration event and a detection sensitivity for the vibration. An increased threshold can reduce “false alarm” of the vibration event, but it also decreases the detection sensitivity for the vibration event measurement.

A procedure to identify a vibration location is shown in Fig. 2 . The measurement and signal processing are as follows: 1) the OFDR system runs two measurements to acquire two sets of the optical frequency domain information: one is without any vibration on the FUT and another one has the vibration, then 2) the measured beat signal information in a time domain is converted to a spatial domain information by using the FFT, 3) a sliding window is applied to scan crossing over the total spatial domain signals by dividing them into several segments namely localized RBs, 4) to perform cross-correlation computation at each localized RB regions between the vibrated state and non-vibrated state successively along the sensing fiber and thereby to obtain the “non-similar level” for each fiber segments. When the analyzed segments are not at the position of the vibration event, the “non-similar level” is low, in contrast, when at a position of the vibration event, the “non-similar level” is high, and finally 5) to locate a position of a striking change of the “non-similar level” and this is a vibrated position. A detail analysis will be presented in the following experiment section.

 

Fig. 2 Illustration of the vibration position and frequency measurement by the OFDR

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Assuming that N is the number of data points for a local RB segment, $\Delta x$ is a spatial resolution of the vibration event and equals a width of the sliding window, which can be expressed as

2.2.2 Measurement of vibration frequency

After locating the vibration event, we can use the local spatial domain RB information at the vibration position to retrieve the vibration frequency $f_m$ . According to Eq. (5) and Eq. (6), the local RB beat frequency of the non-vibrated state will only have $f_b$ in the frequency domain or at the position z (corresponding to a round-trip delay$\tau$) in the spatial domain. However, for a vibrated state the local fiber RB beat frequencies will have three frequency components of $f_b$, $f_b-f_m$ and $f_b+f_m$,thereby the local fiber RB appears at three different frequency components $f_b$, $f_b-f_m$ and $f_b+f_m$. Comparison of the “similarities” for the local RB or “fingerprint” of a test fiber between the non-vibrated and vibrated states should be not only at $f_b$ but also at$f_b-f_m$ and $f_b+f_m$. The cross-correlation analysis is implemented to measure any “similarity” and cross-correlation peak that would be appeared at both center main lobe (i.e. $f_b$) and two side lobes (i.e. $f_m$ and $-f_m$). The$f_m$ can be estimated as:

3.Experiment and results

3.1 Experimental setup

The experimental setup of the OFDR is shown in Fig. 1. The main interferometer is a modified fiber-based Mach-Zehnder interferometer. The TLS has a narrow line-width of ~1 kHz and a center wavelength along 1550 nm. The laser frequency tuning speed is 2 GHz/s. Although our OFDR setup is polarization-dependent, the local RB lights from particular section of a standard single-mode fiber does not contain only single data point but there are several hundred data points that are involved in the cross-correlation analysis. Thus, the characteristics of the RB from any local segment could not be easily completely swamped by polarization noise and an impaction on the cross-correction by the polarization variation is existed but small. Nevertheless, in order to achieve an improved performance, a polarization diversity detection or polarization scrambling technique may be used to reduce any polarization noise [17,18]. To minimize any degradation of a tuning nonlinearity from the TLS on the measurement, the auxiliary Michelson interferometer is used as a clock signal to trigger (rise slope) the DAQ in the OFDR system to sample the interference signal from the main measurement interferometer at the equidistant optical frequency points [18,19]. By this method, a maximum measurement length of the OFDR is limited by the fiber path length difference of the auxiliary interferometer in order to satisfy the Nyquist Law. Specifically, the path difference of the auxiliary Michelson interferometer should have more than twice longer than a maximum measurement fiber length. In our OFDR system, the path difference of the auxiliary Michelson interferometer is about 30 km, thereby a maximum measurement length is about 15 km. The sample clock generated from the auxiliary interferometer is about 600 kS/s. Two Piezoelectric transducers (PZT) fiber stretchers with a 12 m wounded fiber are added to the FUT at positions of 10 km and 10.67 km, respectively, to serve as two independent vibration sources. A total length of the FUT used in our experiment is about 12 km.

3.2 Identification of vibration event location

Spatial domain (or frequency domain) information (see Fig. 3 ) can be obtained from time domain information by the FFT. A sliding window with a width of Δx is used to sample local RB from the FUT.

 

Fig. 3 Rayleigh backscattering in a spatial domain. The reflectivity of Rayleigh backscattering is about −80 dB. The first Fresnel reflection at 10 km is caused by an APC connection and its reflectivity is −66 dB. The second Fresnel reflection at 11.95 km is from an open APC connector and its reflectivity is −59 dB. The red box is the sliding window with a length of Δx to select local RB.

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Here we firstly discuss experimental test which has only one vibration event in the FUT from PZT 2 located at 10.67 km. The phase modulation deep of the PZT 2 ($\delta$) is 0.83 rad under a condition of the PZT driving voltage of 1 v at a wavelength along 1550 nm. As discussed earlier, $J_1(\delta )$ in Eq. (4) is much bigger than other high order terms of the Bessel function. Indeed for a practical application, a phase modulation “deep” caused by an external vibration is small so that this selection (setting) of the phase modulation deep for our experiment should be reasonable regarding its application.

A pre-defined “non-similar level” threshold can be chosen based on many experimental tests that is a half of the maximum peak by solving the global optimizing problem among several factors as mentioned before. With this set threshold we can achieve a vibration event corresponding to an intensity equaling to a phase modulation deep $\delta$ = 0.83 rad, a spatial resolution up to 5 m and a false alarm <5%. The spatial resolution comes from the number of data points N that is selected to be 100. A spatial resolution $\Delta z$ of our OFDR instrument is 0.05 m ($\Delta F$ = 2 GHz). Thus based on Eq. (7) a spatial resolution $\Delta x$for our OFDR is 5 m.

Analyzed cross-correlation results are shown in Fig. (4) . As mentioned above, the vibration position is obtained by the cross-correlation analysis between the vibrated state and non-vibrated state of local RB signals. When the local RB light is not sampled from the vibration position, a clear single peak is observed from the cross-correlation analysis as shown in Fig. 4(a), but when the local RB signal comes from one vibration position of the FUT, the analyzed cross-correlation shows chaotic and multiple peaks as shown in Fig. 4(b).

 

Fig. 4 Analyzed cross-correlation between local RBs in the non-vibrated state and vibrated state: (a) not at the vibration position, (b) at the vibration position. A “non-similar level” is number of points beyond a set threshold.

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A change in the “non-similar level” is used as a criterion to determine an occurrence of a vibration event at the current location. The “non-similar level” distribution along the FUT is shown in Fig. 5(a) . In addition, a “non-similar level” also reflects a vibration intensity as shown in Figs. 5(a) and 5(b). A “non-similar level” for a PZT voltage 1.5 v (i.e. $\delta$ = 1.245 rad) is higher than that for a PZT voltage 1 v (i.e. $\delta$ = 0.83 rad), thereby this indicates a “non-similar level” is in proportional to a vibration intensity.

 

Fig. 5 Measured distributed “non-similar level” as a function of fiber length. A voltage of the PZT is (a) 1 v, (b) 1.5 v. A striking change (for the “non-similar level” beyond 20 points) can be used to locate a position of the vibration and any small change on other locations can be shielded. The length of local RB Δx is 5 m, which determines a spatial resolution of the located vibration. A “non-similar level” at a PZT’s voltage 1.5 v is higher than a PZT’s voltage 1 v. A “non-similar level” is in proportional to a vibration intensity.

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3.3 Measurement of vibration frequency

After locating a position of the vibration event, the local RB signal at this position is known. This local RB is processed by the cross-correlation analysis between the vibrated and non-vibrated states. In our experiment shown in Fig. 6 , a vibration frequency of the PZT fiber stretcher can be adjusted to simulate for different vibration frequencies. The sinusoidal voltage signal with a frequency of 2 Hz, 50 Hz, 200 Hz, 1000 Hz or 2000 Hz was applied on the PZT 2 for our experimental testing and an applied voltage on the PZT 2 is 1 v. The test results from our experiment are shown in Figs. 6(a)- 6(f), in which the vibration frequencies can be accurately measured by our new proposed method.

 

Fig. 6 Analysis of the cross-correlation between the local RB non-vibrated state and vibrated state. (a)-(f) is for a PZT driven voltage of 1 v with a sine waveform, (g) and (h) have the same PZT driven voltage (i.e. 1 v) but using a square waveform and triangular waveform, respectively. (a) $f_m$ = 50 Hz, $\Delta f$ = 1 Hz and $m_{\max }$ = 200, (b) $f_m$ = 200 Hz, $\Delta f$ = 1 Hz and $m_{\max }$ = 400, (c) $f_m$ = 1000 Hz, $\Delta f$ = 2 Hz and $m_{\max }$ = 800, (d) $f_m$ = 1000Hz, $\Delta f$ = 4 Hz and $m_{\max }$ = 800, (e) $f_m$ = 2Hz, $\Delta f$ = 0.5Hz and$m_{\max }$ = 400, (f) is the local zoom of (e), (g) $f_m$ = 50 Hz, $\Delta f$ = 1 Hz and$m_{\max }$ = 200, (h) $f_m$ = 50 Hz, $\Delta f$ = 1 Hz and $m_{\max }$ = 200.

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The parameters $\Delta f$ and $m_{\max }$ can be varied according to the requirement for the measurable vibration frequency. For measuring the frequencies of 2 Hz, 50 Hz, 200 Hz, 1000 Hz or 2000 Hz, different $\Delta f$ and $m_{\max }$ are used. Noting that, due to a frequency tuning speed limitation of the TLS that was used in our experiment, i.e. the laser frequency tuning speed $\gamma$cannot be increased beyond 2 GHz/s, we can only adjust the $\Delta F$ to obtain the different $\Delta f$ values. For a minimal measurable vibration frequency $f_{\min }$, its theoretical value is a frequency resolution of the OFDR $\Delta f$. In practical, $f_{\min }$ needs to be more than $\Delta f$ because of noises in the system. In our experiment, the $f_{\min }$ can be up to 2 Hz under the condition of $\Delta f$ = 0.5 Hz ($\gamma$ = 2 GHz/s,$\Delta F$ = 4 GHz) as shown in Figs. 6(e) and 6(f). Decreasing $\Delta f$ can achieve much smaller $f_{\min }$, which is limited to the maximal$\Delta F$of TLS. For a maximal measurable vibration frequency $f_{\max }$, we can increase $\Delta f$ and $m_{\max }$ for measuring the higher $f_{\max }$based on Eq. (9). However, if both $\Delta f$and $m_{\max }$are increased, the length of the local RB ($\Delta x_{\max }$) should be increased because $\Delta x_{\max }=m_{\max }c/2n\Delta F$. For example, under the condition of $\Delta f$ = 4 Hz ($\gamma$ = 2 GHz/s,$\Delta F$ = 0.5 GHz) and $m_{\max }$ = 800, $\Delta x_{\max }$is 160 m. Although a longer $\Delta x_{\max }$does not impact a spatial resolution of the vibration event, it could decrease a maximum measurable range. Again for example, by assuming that a FUT length is $L_{\max }$, a maximum measurement range is decreased to $L_{\max }-\Delta x_{\max }$. To solve this problem, a TLS with a higher $\gamma$is necessary to increase a maximum measurable vibration frequency $f_{\max }$.

Moreover, for locating a vibration event a local RB's segment size $m_{\max }$is set 100. Under this setting there is no obviously visible side lobes as shown in Fig. 4(b), which brings a difficult to identify the vibration frequencies. However, for the frequency measurement, $m_{\max }$ is chosen to be 200~800 and then the side lobes are much clear with an increased $m_{\max }$as shown in the Figs. 6(a)-6(d). The reason for this phenomenon above is that an impact on the local RB’s characteristics caused by a vibration is inversely proportional to a local RB’s segment size, therefore, in the cross-correction analysis, the bigger segment size is, the clearer cross-correction peaks and the higher SNR [10]. For locating a vibration event, a SNR of the cross-correction doesn’t need to be very high and $m_{\max }$ could be selected relatively short to ensure an enough spatial resolution and a high detection sensitivity. For measuring a frequency of a vibration event, a SNR of the cross-correction needs to be high, thus it is necessary to select a longer $m_{\max }$.

For a practical application, any vibration on the fiber may not be necessarily to be an ideal sine (waveform) vibration, in fact it could be any vibration waveforms or their combinations. In order to simulate this situation, 50 Hz square waveform and triangular waveform vibration are applied on the PZT 2, respectively, and experimental results are shown in the Figs. 6(g) and 6(h), where the noise of the cross-correlation is higher than the sine waveform because the square and triangular waveform vibrations have multiple frequency components. Nevertheless, the side lobes that reflect frequency information can still be detected accurately.

3.3 Multiple vibration events measurement

Our above proposed method is not limited to detect a single vibration event but it could even measure multiple vibration events. This means any vibration at the location after the previous vibration event contain vibration information not only coming from those interested vibration events at the late positions of the test fiber but also from the previous vibration that is located on their round-trip optical paths. Although the RB signals at the far vibration locations are contaminated by their previous vibration, their both “non-similar levels” and cross-correlation peaks are different if comparing with that of the previous vibration event. To verify an ability to detect these multiple vibration events, two PZTs (i.e. PZT 1 and PZT 2) are applied on our test fiber and the measurement result is shown in Fig. 7(a) where there are two “step” changes for the non-similar level, one along 10 km and another one along 10.67 km, which are exactly corresponding two PZTs locations. The second “step” change is higher than that of the first one due to a superposition of two vibration events, i.e. a cumulative vibration intensity from both vibrations. Figure 7(b) shows a first vibration event's frequency, but in Fig. 7(c) there are also many cross-correlation peaks although a SNR of the cross-correlation signals is poor. Interestingly in Fig. 7(c) the highest cross-correlation peak with a frequency along 40 Hz corresponds to a frequency difference between two applied vibration frequencies on two PZTs while the second highest peak frequency at 154 Hz is a sum frequency of two vibration event frequencies. Since a frequency of the first vibration event is known (i.e. 97 Hz), the second vibration event’s frequency can be estimated as 57 Hz. Although the preliminary investigation results for two vibration events are still not perfect, they do indicate a possibility to realize a distributed vibration sensor where a more intelligent signal processing might be required. A further improvement may be possible to use a wavelet analysis and other time-frequency analysis method to detect the multiple vibration events, especially it is interesting in detecting a large number of vibration events along an optical fiber.

 

Fig. 7 (a) Measured distributed “non-similar level” as a function of a fiber length with two vibration events. The PZT 1 and PZT 2 are located at 10 km and 10.67 km and are applied by a 1 v sine waveform vibration with a frequency 97 Hz and 57 Hz, respectively. Two striking changes can be used to locate two positions of the vibration events. (b) (c) Analysis of the cross-correlations between the local RB non-vibrated and vibrated states: (b) a location of the fiber segment is between the position of PZT 1 and PZT 2 and (c) the location of the fiber segment is after the PZT 2. In (b), there is only one frequency component of 97 Hz, but in (c), there are many frequency components that contain a sum frequency of 154 Hz and a difference frequency of 40 Hz from two vibration frequencies applied on two PZTs (i.e. PTZ 1 and 2). A vibration frequency 57 Hz for the second event can be estimated.

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4. Conclusion

A space-resolved long-range vibration detection system based on the correlation analysis in the spatial domain between the RB vibrated state and non-vibrated state has been demonstrated, where the RB vibrated and non-vibrated states from a standard single mode optical fiber were acquired by an OFDR. Particularly the cross-correlation between the vibrated state and non-vibrated state of the local RB was processed and analyzed to extract both the vibration frequency and position information. The system was tested to have a frequency response up to 2 kHz, a spatial resolution for the vibration event of 5 m and a measurement range of 12 km. It is also possible to further improve its maximum frequency response and to increase a spatial resolution by using a TLS with broader tuning range and faster tuning speed. In addition, some preliminarily experimental investigations of two vibration events are described that could probably further lead to a distributed vibration sensor.