Feasibility study of the automated detection and localization of

Feasibility study of the automated detection and localization of underground tunnel excavation using Brillouin optical time domain reflectometer Assaf Klar*a and Raphael Linkerb a

Dept. of Geotechnical Engineering, Faculty of Civil and Environmental Engineering, Technion, Haifa, Israel; b Dept. of Environmental, Water, and Agricultural Engineering, Faculty of Civil and Environmental Engineering, Technion - Israel Institute of Technology, Haifa, Israel ABSTRACT

Cross-borders smuggling tunnels enable unmonitored movement of people, drugs and weapons and pose a very serious threat to homeland security. Recent advances in strain measurements using optical fibers allow the development of smart underground security fences that could detect the excavation of smuggling tunnels. This paper presents the first stages in the development of such a fence using Brillouin Optical Time Domain Reflectometry (BOTDR). In the simulation study, two different ground displacement models are used in order to evaluate the robustness of the system against imperfect modeling. In both cases, soil-fiber interaction is considered. Measurement errors, and surface disturbances (obtained from a field test) are also included in the calibration and validation stages of the system. The proposed detection system is based on wavelet decomposition of the BOTDR signal, followed by a neural network that is trained to recognize the tunnel signature in the wavelet coefficients. The results indicate that the proposed system is capable of detecting even small tunnel (0.5m diameter) as deep as 20 meter. Keywords: BOTDR, Smuggling tunnels, Underground fence, Detection system, Fiber optics, Geomechanics

1. INTRODUCTION Cross-borders smuggling tunnels enable unmonitored movement of people, drugs and weapons and pose a very serious threat to homeland security. Depending on geo-political factors and intended tunnel use, these tunnels range from highly sophisticated infrastructures (for instance at the Mexico-US border, where tunnels are deep and wide and are equipped with communications devices and rail tracks) to shallow hand-dug crawling spaces. Small hand-dug tunnels are routinely excavated along the borders of Israel and the Palestinian-authority and are considered extremely problematic. In 2006 a Israeli soldier was abducted by such a tunnel near the border between Israel and Gaza-strip. More recently (December 2008), Israel lunched a military campaign in Gaza, codename Operation Cast Lead, with the aim of stopping the ongoing rocket attacks on southern Israel. Those rockets were smuggled into Gaza using underground tunnels which exist along the 14km border with Egypt. The military campaign attempted to destroy the vast underground smuggling infrastructure, using ground penetrating missiles† . The campaign ended after 3 weeks, after an agreement‡ regarding security measures was achieved between Israel and US. The agreement emphasizes the need for counter-smuggling tactics. This presumably includes technologies and approaches for detecting tunnels. Various approaches for tunnel detection have been investigated throughout the years. Electromagnetic induction sensors1, 2 can be used to detect tunnels that contain steel (reinforcement rod or rail tracks). Listening * Corresponding author: [email protected], Tel:

+972-4-8292647

†

Haaretz Service and News Agencies: http://www.haaretz.com/hasen/spages/1054466.html America.gov: http://www.america.gov/st/peacesec-english/2009/January/20090116141010dmslahrellek0.0438959.html ‡

Fiber Optic Sensors and Applications VI, edited by Eric Udd, Henry H. Du, Anbo Wang, Proc. of SPIE Vol. 7316, 731603 © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.810781

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devices3 can be used to detect acoustic (mechanical) waves that originate from inside the tunnels. Finally, the propagation of radar-type waves between two parallel boreholes (transmitting and receiving antennas) can be used to detect tunnels.4, 5 Although this method has yielded the most promising results, it requires the constant presence of personnel to move the antennas from one borehole to another. Even though the results of some of these methods are satisfying for large tunnels, detection of small (< 1m diameter) tunnels remains a major challenge. Underground excavation in soil (unlike in rock) causes substantial deformations and strains in the medium, which are not limited to the immediate vicinity of the excavation. A sensing device, sufficiently sensitive, could detect these strains and hence the excavation process, at least in principle. Fiber-based Brillouin optical timedomain reflectometry (BODTR) is the natural candidate for performing such a measurement. The ability of BODTR sensors to provide distributed measurements of temperature and strain over tens of kilometers has been demonstrated in several studies.6–8 Although the sensitivity and/or spatial resolution of the early systems were rather limited, systems with sensitivity of less than 5με and spatial resolution of 1m are currently commercially available. This improvemed performance has led to the use of BOTDR devices in a number of applications that require distributed strain measurements.9, 10 In particular, BOTDR devices are being used in geotechnical engineering to monitor the effect of excavations on pipelines and foundation piles.11–13 Although these studies deal with the effects of excavations of larger tunnels, for underground transportation and water systems, they clearly demonstrate the ability of the fiber-based BODTR sensors to detect soil strains. The objective of the present study is to determine the feasibility of using a similar approach for detecting the excavation of small (diameter < 1m) tunnels in clayey soils. Fig. 1 presents one possible configuration for the suggested smart underground fence† . This option consists of a horizontal fiber buried at shallow depth. The tunnel excavation is associated with stress relief within the soil. This stress change leads to the development of static (permanent) displacements within the domain, although with decreasing magnitude with increasing distance from the tunnel. The buried fiber will be strained due to those displacements, and hence the tunnel may be identified by investigating the affected BOTDR signal. Note that the cable itself may affect the developed displacement, and these aspects of soil-cable interaction are considered in the current work.

Shallow depth

Optical fiber

0

Smuggling Tunnel

Smuggling Tunnel

Figure 1. Geometerical configuration of the underground fence: an optical fiber is buried horizontally few feet below ground surface.

The pertinent question is what are the detection limits in terms of false alarms and localization of small deep tunnels. This paper attempts to answer this question by a combined analytical-experimental approach, in which analytical solutions of tunnel excavations are combined with experimental measurements of surface activities to create simulated signals. These signals are used to calibrate and validate a system that detects, and to some extent localizes, tunneling activities automatically. †

A different layout which entails optical fibers within mini-pile was also considered, but due to space limitation is not presented in the current paper.

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The paper is composed of four main sections. The first section presents the general principle behind BOTDR strain measurements. The second section presents the analytical framework used for evaluating the tunnelinginduced strains in the fibers. The third section presents the simulation of BOTDR readings, including measurement error and noise, the post-processing of the signals using wavelet decomposition and neural network modeling. The fourth section presents the results of the feasibility study.

2. BRILLOUIN OPTICAL TIME DOMAIN REFLECTOMETRY - BOTDR Brillouin scattering results from the interaction of light photons with acoustic waves (phonons). When a pulse of light travels along the optical fiber, a small fraction of the light is scattered back toward the launch. In the case of Brillouin scattering, the frequency of the backscattered light is shifted by an amount proportional to the acoustic velocity at the scattering location:14 2nVa (1) νB = λ where νB is the Brillouin shift, Va is the acoustic velocity within the fiber, n is the refractive index of the fiber, and λ is the wavelength of the incident light-wave. Temperature changes and fiber elongation (straining) change the acoustic velocity within the fiber. By resolving the back scattered signal in time and frequency, a complete strain profile along the full length of the fiber can be obtained. This is illustrated in Fig. 2: the traveling pulse of light is scattered back from every point along the fiber. Using the velocity of light in the fiber, this time domain information is converted into location (distance along the fiber). By resolving the frequency content of the back scattered light, the 3D graph illustrated in Fig. 2 is obtained. The shift of the peaks correspond to the changes Brillouin shift, and hence can be translated back to strain or temperature reading. Note that the power of the backscattered light may decrease both due to straining and distance from the fiber. However, since the shift in frequency is of interest (and not the power) this does not affect the results, and the analysis can be conducted over a significant length of fiber, up to 30km. This ability to monitor tens of kilometers, together with the fact that cheap conventional optical fibers may be used as the sensors, makes this technology a perfect candidate for detection systems along borders. (2) While the light pulse travels along the fiber, a fraction of/f is scattered back. The passing time from the launch of the pulse and the arrival of the backscattered light infers on the location of measurement (distance).

(3) The backscattered light wiil change its frequency if the fiber is strained.

(4) By resolving the frequency content of the backscattered light, a 3D graph can be generated. The peaks correspond to the Brillouin shift There fore changes in strains can be resolved from such a graph.

(1) A laser generates a pulse of light with a specific light frequency.

C

Figure 2. Time and frequency analysis of fiber

Currently there are two Brillouin scattering configurations commercially available: [a] Brillouin backscattering in which a single source of light is used as the probe, and [b] stimulated Brillouin in which a pump laser light-wave enters one end of the fiber and a counterwave probe enters the other end. The interaction between the pump

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and the probe signals maximizes the information available from the scattering, and hence increases significantly the accuracy of the strain estimate. There are two types of errors involved in the BOTDR readings. One is a random error, whereas the other is associated with the spatial resolution induced by the length of the light pulse inside the fiber. The random error of a typical BOTDR analyzer corresponds to a normal distribution with a standard deviation of σ = 15με (i.e. accuracy of 30με) for backscattering Brillouin configuration, and σ = 2με (i.e. accuracy of about 4με) for stimulated Brilluoin configuration. As√this error is random, it may be reduced by averaging multiple readings, in which case a reduction factor of 1/ N (N is the number of readings) is achieved. The other departure from the exact strain profile comes from the limit on spatial resolution. The BOTDR measures a weighted average of the strain over ∼ 1m, at points spaced by ∼ 10cm. This limit comes from the physical length of the pulse of light in the optical fiber, with the result that the BOTDR profile is roughly the convolution of the true strain profile with the shape of the light pulse. As a result, for example, a very localized disturbance will appear as a distributed profile, with a shape similar to the Gaussian bell curve. Temperature changes influence the BOTDR strain reading and therefore temperature compensation is necessary. This can be achieved easily by obtaining a reading of an unstrained fiber. The Brillouin scattering is such that temperature changes lead to a linear change in the Brillouin frequency shift, and, therefore, the arithmetic involved in the compensation is straightforward. Most telecommunication cables are made such that the inner glass core is protected from the outer shell by a lubricant or gel. Although this type of fiber is not suitable for strain measurements, they are ideal for temperature compensation because the inner fiber is not strained even when the outer coating is strained. Calculation wise, since changes in Brillouin shift are linear with strain and temperature changes (i.e. ΔνB = cε Δεf + cT ΔT , where εf is the longitudinal strain in the fiber and T is the temperature), a set of equations can be written to relate the behavior of two closely placed cables, which experience the same temperature and strain changes. A solution for the strain and temperature can be obtained as:  β     1 SF − cSF cLF 1 cLF ΔνB Δεf cSF ε ε (2) = ; α = εSF ; β = TSF α 1 LF ΔT ΔνB β − α − cSF cε cT cSF T

T

LF ΔνB

SF where is the change of Brillouin shift recorded in the lubricated cable and ΔνB is the change of Brillouin SF SF shift recorded in the ”strain sensor” fiber. cε , cT are the strain and temperature coefficients of the ”strain LF sensor” and cLF are the coefficients of the lubricated cable. These coefficients can be easily determined by ε , cT and a calibration setup where fibers are heated and strained. For the cables used in the current research cSF ε −5 −7 were found to be equal to 5 · 10 GHz/με and 5 · 10 GHz/με, respectively. The low value of α indicates cLF ε that the lubricated cable can be used for independent measurements of temperature, without the need to solve the above set of equations. The temperature coefficients of the two fibers were practically identical and equal SF is used to to 1 · 10−3 GHz/◦ C. Note, that if the temperature changes are ignored altogether (and only ΔνB SF SF evaluate the strain by Δεf = ΔνB /cB ), an error of 20με for each degree Celsius will be introduced into the evaluation of strain. The above compensation method was used in the experiments presented in later sections.

3. TUNNELING-INDUCED DISPLACEMENTS AND DEVELOPED STRAINS IN THE FIBERS As the tunnel is being excavated, deformations, although small, develop in the soil. If the fiber is infinitely flexible, it will ”follow” the soil deformation as it would develop in a green field (a field where no fibers exist). In this case the longitudinal strains in the fiber will be equal to that of the soil along the axis of the fiber. However, in order to avoid assuming a priori that the fiber-soil interaction is negligible, modeling of the soil-fiber interaction has been included in the present study. The analysis of the developed strains in the fiber is based on the following assumptions: [1] The fiber is always in contact with the soil, [2] the soil (in the vicinity of the fibers) is homogenous linear elastic continuum, [3] the tunnel is unaffected by the existence of the fiber (i.e. unaware of soil-fiber interaction). Generally, assumption 2 is violated in soil mechanic problems. However, in this specific problem of small hand-dug tunnel it is more than reasonable, since the strains induced near the surface by the tunnels are very small so that the soil remains in its elastic range. Assumption 3 is also very reasonable as long as the tunnel is not very close to the fiber.

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When the tunnel is very close to the fiber, the tunnel can easily be detected regardless of the interaction model. Therefore the above assumptions do not constitute any limitation on the feasibility study. It can be shown, following similar derivations as in works of pipelines deformation due to tunneling,15, 16 that under these assumptions the fiber deformation can be solved using the following equation: (GSf + I)uf = ugf

(3)

where G is the is the flexibility matrix of the soil, Sf is the global stiffness matrix of the fiber, uf is a vector representing the displacements of the fiber, and ugf is a vector representing the green field displacement values along the position of the fiber. The element Gij gives the displacement at point i due to unit loading at point j, and can be constructed analytically using Mindlin solution.17 Once a solution for uf is obtained, the strains in the fiber can be obtained directly by differentiating the fiber deformation. It is interesting to see that if the fiber is infinitely flexible (i.e. Sf =0) then the displacements of the fiber are those of the green field. In any other condition the fiber itself modifies the domain displacements. Currently there is no experimental data in the literature regarding the green field displacement generated by very small and deep hand-dug tunnels (e.g. tunnels with a diameter of 0.5m and depth greater than 10m). Therefore the analysis must be based on some analytical or empirical relations for the green field displacements. Two different relations for tunneling induced green field displacements are used in the present feasibility study. One is empirical, based on correlation from a number of different tunneling cases,18 and the other is based on elastic continuum solution.19 Clearly, hand-dug tunnels might induce different displacements than those based on these relations, but this is a general unknown which is yet to be solved. The difference between these relationships is significant, so that it is reasonable to assume that they cover the range of behavior associated with small deep hand-dug tunnels, and hence dot not limit the conclusion of the feasibility study. Moreover, the significant difference between the models allows evaluation of the sensitivity of the proposed system against imperfect modeling, by calibrating the detection system using one model and testing it with the other model. Note that the empirical relation18 supplies only the vertical displacements in the soil, but it may be completed if a relaxing assumption that the displacement vectors are directed towards the tunnel centerline is made.20 One of the important parameters used in tunneling engineering is the volume loss, VL , which defines the ratio of settlement volume to tunnel volume: ∞ uz dx (4) VL = −∞ 2 πDt /4 where Dt is the diameter of the tunnel and uz is the vertical displacement. The volume loss parameter reflects the quality of the tunneling process. In underground construction, volume losses will typically be in the range of 1% (for very good tunneling process) to 5% (for poor tunneling process). The volume loss is one of the controlling parameters in the current feasibility study, and is a basic input parameter to both the empirical relation18 and the elastic continuum solution.19 Fig. 3 illustrates a solution for a specific case of a 0.5m diameter tunnel at depth of 10m and a volume loss of 2%. As can be seen a significant difference exists between the solution based on the empirical relation18 and that based on elastic continuum.19 It should be noted that the presented elastic solution is based on uniform contraction of the tunnel, and it is likely that the addition of an ovalization to its deformation will bring the two solutions closer. In typical civil engineering projects, where tunneling induced displacements may inflict damage to existing structure, a difference between prediction models is unfavorable, as it makes deterministic analysis problematic. However, in the current application of evaluating an automated detection system, we wish the models to be as broad as possible, as this allows evaluation of system robustness against imperfect modeling. As can be seen from Fig. 3, the results that take into account the interaction between the fiber and the soil (Eq. 3) are practically identical to the solution which forces the fiber to “follow” the soil. This indicates that the fiber is indeed very flexible compared with the soil (for which the Young’s modulus, Es , was assumed to be 20000kPa in the vicinity of the fiber). A difference of about 10% in the developed strain appears when the fiber stiffness (EA) is increased 100 fold. The reinforced Fujikura fiber (for which the calculation was conducted) is already a very stiff fiber,

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Solution based on soil fiber interaction Solution based on “following” the green field displacements

)

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( r 10 e ib f

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FUJIKURA SM 4 Reinforced fiber was considered. EA=35kN 5.2mm

e h t

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Figure 3. Example of analytical solution for strain in a horizontal laid fiber, based on ground displacement input from the empirical relation of Mair et al.18 and the elastic continuum solution of Verruijt and Booker.19

and fibers 100 times stiffer do not exist. Consequently, it may be concluded that a horizontally laid fiber will follow the soil deformation closely, regardless of its type. The formulation assumes that the fiber is attached to the ground, and there is no relative slippage, due to local failure, between the fiber and the soil. This assumption can be validated by evaluating the contact stress τc : EA ∂ 2 uf EA ∂εf (5) = τc = S ∂x2 S ∂x where S is the perimeter of the fiber cross section. The values of τc for the presented cases are very small (< 0.03kP a), so that slippage is very unlikely. Only when the tunnel is very close to the fiber will slippage be an issue. If a failure criterion of τf = σv tanδ is adopted (where σv is the vertical stress at the fiber level, and δ is taken as 10◦ ) slippage would occur (for the specific tunnel considered in the example) only if the tunnel is at depth smaller than about 3m. In this case however, the strain would be significant (> 400με) and detection would not be an issue regardless of fiber slippage. The solutions presented in this section are ”clean” from any noise or measurement errors. Those, however, must be included in the evaluation of an automated detection system. Details on the incorporation of the noise and errors are given in the next section.

4. SIMULATED BOTDR SIGNALS, SURFACE DISTURBANCES, AND POST PROCESSING 4.1 Simulated BOTDR signals Due to the high cost required to perform underground excavations, this feasibility study is performed mostly using simulated BOTDR signals derived from the relationships mentioned in the previous section.18, 19 Due to the BOTDR’s limited spatial resolution, a signal corresponding to a localized strain will be smeared. Loosely speaking, the BOTDR measures a weighted average of the strain over ∼ 1m, at points spaced by ∼ 10cm. This limited spatial resolution comes from the physical length of the pulse of light in the optical fiber. As a result, for example, a localized disturbance will appear as a distributed profile, similar to a normal distribution. Mathematically, the weighted averaged strain is:  εA (x) =

∞

−∞

εf (τ )g(x − τ )dτ

(6)

where εA (x) is the averaged strain obtained at point x along the fiber, εf (x) is the actual strain in the fiber, g(x) is the weighing function. Note that if εf (x) = δ(x) (delta function) then εA (x) = g(x). In other words, the weighing function g(x) can be determined experimentally by introducing a local disturbance in the fiber and recording the BOTDR signal. Results of such experiments12 showed that g(x) corresponds well to a Gaussian

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√ curve, = exp(−0.5x2 /ω 2 )/ 2πω 2 , with an ω value of 0.28m. In the current application the spatial resolution has little effect on the results, as the strain profile is very wide with a low gradient. Nonetheless, this feature is considered in the simulations. In addition to the spatial resolution, a random error is involved in the measurement. The simulated signal is therefore: εs (x) = εA (x) + R[σ]

(7)

where εs (x) is the simulated signal, and R[σ] is a generator of pseudo-random numbers with a zero-mean normal distribution and a standard deviation σ. In the current study, a σ of 2με was used (i.e. accuracy of 4με), which corresponds to the typical error of the stimulated Brillouin configuration. The models mentioned in the previous section were used to generate εf (x) along the fiber, while Eqs. 6 and 7 were used to transform the expected strains into simulated BOTDR readings.

4.2 Surface disturbances In order for the proposed system to be of practical interest, it should not only detect tunneling activities efficiently, but should also yield few false alarms (false positive detections). Since the depth of the horizontally-placed fiber is relatively shallow, the most probable causes for such false alarms are above-ground activities. The BOTDR signals of two such above-ground disturbances were recorded experimentally, in the 60m long soil trench at the Technion using the optical equipment of Omnisens. The disturbances included surface loading of 100 to 400kg, and wetting a 5 meter section of the soil. Fig. 4a shows the strain profile recorded with the loadings, while Fig. 4b shows the strain recorded as a result of the wetting. Those results are after temperature compensation using Eq. 2. Note that the strain profile in Fig. 4a is not fully symmetric, even though the fiber is strained symmetrically. This is an outcome of slight imbalance in the Mach-Zehnder electro-optic modulator, which is involved in the stimulated BOTDR.21 In other words, the weighing function g(x) of this specific analyzer is not fully symmetric. This has an apparent effect only when there is an abrupt change in the Brillouin frequency (i.e. only when there is an abrupt change in strain or temperature along the fiber, as in the localized loading case). The influence of this asymmetry on the performance of the proposed system was investigated and found to be marginal, since the tunneling induced strains are not localized. The experimental signals shown in Fig. 4 were added at random locations along the simulated BOTDR signals. 400

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Figure 4. Results from surface disturbance experiments, (a) Strain reading from loading test, (b) strain reading from wetting test.

4.3 Post processing As mentioned above, it is imperative for the system to identify tunneling activities while filtering out the signals due measurement noise and disturbances efficiently. In the present study, automated signal interpretation is achieved using wavelet decomposition of the BOTDR signal followed by a neural network. The main feature of wavelet decomposition is that the resulting coefficients contain information about both the location and shape

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(sharpness and amplitude) of the signal components.22, 23 This is a key advantage of the distributed BOTDR measurement over other localized devices, as the shape of the signal plays a major role in distinguishing excavation activities from other surface activities. While wavelet decomposition by itself does not produce a compressed representation of the original signal, most of the information of interest is typically contained in a few of the resulting wavelet coefficients. Several approaches for identifying these coefficients have been described in the literature, such as eliminating all ”small” coefficients using either simple thresholding,24, 25 mutual information26 or genetic algorithms.27 In this study, the approach recommended by Trygg and Wold,28 which consists of retaining the coefficients with the highest variance, is used: during the calibration phase, after applying the wavelet transformation to all the signals, the resulting coefficients are concatenated (row-wise), and the variance of the resulting matrix is calculated (column-wise) (Fig. 5). The positions of columns with the largest variances are recorded and the corresponding coefficients are extracted and used as inputs to a neural network.29 During the testing phase, after applying the wavelet decomposition to the signal, the same coefficients are extracted and inputted into the neural network. Distance lep m aS Wavelet decomposition Wavelet coefficients

Coefficient variance

Compact representation of the signals

Neural Network

Tunnel detection and localization

Figure 5. Flow chart of detection algorithm.

The neural network was trained to predict the ratio ξh = VL Dt2 /zt , which is a measure of the impact of the tunnel on the fiber (zt is the depth of the tunnel). Other choices, such as training the neural network to predict a binary number (i.e. tunnel or no tunnel) or the ratio ξh = VL Dt2 /zt2 (to which the maximum horizontal strain at the surface is proportional in the two considered ground displacement models) were also considered, but resulted in poorer detection performances when imperfect modeling was considered (i.e. when the system was trained with one model and tested with the other). As can be seen from Fig. 3, the effect of a tunnel is restricted up to approximately 20m on either side of the tunnel. Based on this observation, it was decided to split the continuous BOTDR signal into segments of 25m, and the process illustrated in Fig. 5 was applied separately to each and every segment. The wavelet decomposition was performed up to level 10 and the 15 coefficients and the highest variance were retained. The system was trained with 40,000 cases, and tested with 60,000 cases. The training and validation was conducted for tunnels at depth ranging from 10 to 40m and volume loss from 0.1% to 2%.

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5. RESULTS Fig. 6 shows the rate of detection and false alarms, as function of a decision threshold, for a system calibrated and tested with signals based on the empirical soil displacement model.18 The classification whether a detection was correct or false, for a given threshold value, was made according to the logic presented in Table 1. S 0 represents the segment beneath which a tunnel exists, S ±1 represents segments adjacent to S 0 , and S >±1> represents any segments farther away from S 0 . For each segment, the process of Fig. 5 was applied to the BOTDR signal, resulting with a neural network prediction for ξh . According to the decision chart, if the neural network prediction, ξh , for S 0 is above the threshold value, ξhth , a correct detection is declared, since the tunnel is positioned at that segment. If the neural network prediction is above ξhth in segment S >±1> the detection is classified as false alarm, as the tunnel is located far away, and cannot be responsible for the high predicted ξh . If, however, the neural network prediction is above the threshold value in a segment adjacent to a segment that contains a tunnel (i.e. S ±1 ) it is not classified as a false alarm. This is because the tunnel can be located just beneath the edges of segment S 0 , and may affect segment S ±1 as well. In other words, if a simple threshold was to be applied to the neural network prediction in a straightforward manner, some tunnels would likely be detected twice (in the correct and adjacent segment) and the rate of tunnel detected would be overestimated. Table 1. Classification of results; X denotes that the value does not influence the classification.

Segment S 0 (contains tunnel)

Prediction of the neural network in a given section Above threshold X X

Segment S ±1 (no tunnel) Segment S

>±1>

(no tunnel)

Classification

X

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X

X Correct detection: Tunnel is in segment S 0

X No detection; No false alarm

Above threshold False alarm in segment S >±1>

As seen from Fig. 6, a threshold value of ξhth = 5 · 10−5 m (dashed line) appears to provide an optimal trade-off between the false alarm rate and the number of missed detections: approximately 25% of the tunnels are not detected and the false alarm rate is less than 1%. Threshold for optimal trade-off

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Figure 6. Rates of correct detections and false alarms as a function of the decision threshold. The neural network was trained using data generated with the empirical soil displacement model.18 The data presented corresponds to a testing stage with the same model.

Very similar results were obtained when the system was both trained and calibrated using the elastic continuum ground displacement model.19 In order to study the sensitivity of the proposed system to imperfect modeling, two additional analyses were performed in which different models were used for calibration and testing stages: calibration using the empirical ground displacement model18 and testing using the elastic continuum model,19 and vice versa. The results of all combinations are shown in Fig. 7, where it appears that the optimal

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Figure 7. Rates of correct detections and false alarms as function of the decision threshold for all combinations of training and testing models (i.e. Mair et al.18 and Verruijt and Booker19 ). Only the results of the testing stages are shown.

threshold value remains ξhth = 5 · 10−5 m. It can be seen that the mismatch between the models used at the calibration and validation stages has limited impact on the detection performances, with an increase of missed tunnels from 25% to 35% (for ξhth = 5 · 10−5 m) when the system is trained with the empirical model18 and tested with the continuum one.19 These results are extremely important and very encouraging since any ”real” detection system would have to be calibrated using signals generated with a model that would of course be imperfect. The present results show that model imperfection should not diminish the performance of the system drastically. Fig. 8 details the performance of the system, as function of tunnel depth and volume loss, for a very small tunnel of Dt = 0.5m, when the optimal threshold value, ξhth = 5 · 10−5 m, is used. A random population of

Trained Validated MM Mair et al. Mair et al. VV Verruijt & Booker Verruijt & Booker MV Mair et al. Verruijt & Booker VM Verruijt & Booker Mair et al.

Figure 8. Detection rate as function of volume loss and depth for tunnel diameter Dt = 0.5m.

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2100 tunnels was used for each of the histograms shown in Fig. 8. As can be seen, the detection rate may decrease significantly with depth if the volume loss is small (less than 1%). However, for tunnels of depth smaller than 20m, detection rate remains high even when volume loss is only 0.5%. Note that larger tunnels would be identified more easily even under smaller volume losses (this may be identified from the parameters involved in the thershold ratio).

6. SUMMARY AND CONCLUSIONS Recent advances in strain measurements using optical fibers allow the development of smart underground fences that could identify and prevent the excavation of smuggling tunnels accross borders. The first stages in the development of such a system based on the Brillouin Optical Time Domain Reflectometry (BOTDR) were presented. The proposed automated detection system is based on wavelet decomposition of the BOTDR signal, followed by a neural network. Soil-structure interaction, which may alter the green field displacement, and other issues such as measurement spatial resolution, random errors, and surface disturbances (which were derived from a field test), were addressed in the study. To investigate the robustness of the system against imperfect modeling, two different ground displacement models were used for calibration and evaluation of the proposed system. Results indicated high performance even when the tunnel being excavated is extremely small (0.5m in diameter) and volume loss is greater than 1%. For smaller volume losses, the detection rate depended on the depth of the tunnel. Half a meter is roughly the lower practical limit of tunnel diameter, as people cannot crawl through much smaller spaces. In case of larger tunnels, with similar volume losses, detection rate would increase significantly. The ability of the system to detect tunneling activities, while remaining mostly insensitive to measurement noise and above-ground disturbances, can be attributed to the wavelet decomposition ability to capture the wide patterns of strain profile associated with tunnels and distinguish between these patterns and those from localized random errors and other disturbances. Clearly, the present feasibility study did not encompass all possible phenomena and inaccuracies that would exist in the field (as most of them are unknown). However it indicated that the potential of such a system is high. Following research stages, and in particular field validation-tests, are still required before such a system could become fully operational.

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