1. Introduction

A large part of the fiber optic networks comprises of aerial cables supported by utility poles due to practical and economic reasons [1]. As a downside, the aerial cables, unlike their underground counterparts, are highly exposed to environmental effects and disturbances such as extreme weather including icing, animal activities, pedestrian and vehicle traffic, pole failures and most frequently some additional weights hanging on the cables. These additional weights may be due to fallen tree branches, other fiber cables that are poorly installed on top of others or even parts of an old utility pole that is left connected to the cables after being replaced with a new utility pole, causing additional strain on the aerial cable. If not handled timely and properly, these weights may damage the fiber and cause network downtimes, in addition, they are a safety hazard for nearby pedestrians and vehicles as well. Hence, it is critical to monitor the additional weights hanging on the aerial cables for physical safety and security of the network.

Previously reported methods for detecting a weight on a fiber cable, have limited range and require a special fiber arrangement or setup such as a fiber Bragg grating [2,3]. Utilizing existing standard single-mode fibers, φ-DAS (phase-Distributed Acoustic Sensing) systems have shown enormous potential for smart-city / safe-city applications [4,5]. A φ-DAS system measures dynamic strain changes along the fiber by detecting the optical phase shifts of the backscattered light relative to the optical local oscillator. However, a stationary weight hanging on an aerial fiber cable does not result in a time-varying phase shift and therefore cannot be directly detected by a φ-DAS system. It is to be noted that at the moment that a weight, such as a tree branch, falls on an aerial fiber cable and generates instant vibrations, it can be detected and localized by the φ-DAS system; however, this instant event only indicates that a weight (or any other external agent) has touched the cable but not whether the weight stays hanging on the cable or falls off from the cable to the ground. Therefore, direct monitoring of the φ-DAS signal cannot be used to detect a stationary weight hanging on an aerial fiber optic cable. In our previous work, we have successfully detected a stationary weight hanging on an aerial cable in our testbed [6], but it required the knowledge of the utility pole locations along the fiber which limits its practical uses in the field.

In this work, we propose a novel method for detection and localization of these additional static weights on an aerial fiber network, using only ambient data recorded by a φ-DAS system without requiring the knowledge of the utility poles locations along the fiber route. The proposed method is based on operational modal analysis of the aerial fiber structure excited by only ambient effects, such as traffic and wind, and the experiments were performed using a dark fiber on an operational field fiber network for the first time.

2. Experimental setup

The static weight detection and localization experiments were conducted on an aerial field fiber route at Long Beach Island, NJ. The φ-DAS system was located inside a Verizon Central Office (CO) and connected to an outdoor grade telecom field fiber. The fiber route is consisted of ∼200-meter underground fiber cable, followed by aerial fiber cable on utility poles, intertwining with other aerial fiber cables. Two test locations along the fiber route to hang the additional weight were selected based on practical reasons such as accessibility and safety. The first test location was the middle point between the second and third utility poles (at around 242 m); and the second test location was the middle point between the fifth and the sixth utility poles (at around 335 m) as shown in Fig. 1(a). The locations of these poles along the fiber route were determined by hitting the corresponding poles with a hammer and analyzing the propagation of the vibrational wave using the φ-DAS system [7]. These poles are manually localized to estimate the weight locations along the fiber in order to confirm our final results and not required by the algorithm. The weight to be hung on the cable was chosen as 20 lbs., as the average weight of a tree branch that is within the safety limits.

 

Fig. 1. Overall experimental setup showing the fiber layout and selected locations for hanging the additional 20 lbs. weight.

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A φ-DAS system detects the minuscule vibrations and strain changes as a function of time along a fiber route at given spatial intervals defined by its sampling settings. Such a spatio-temporal data is usually visualized by a waterfall plot, where the x-axis denotes the location along the fiber and the y-axis denotes the time, and the signal strength is color-coded as seen in Fig. 2.

 

Fig. 2. Exemplary waterfall traces of the fiber route, a) no additional weight, b) 20 lbs. weight hanging at around 242 meters.

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As discussed before, a stationary weight hanging on an aerial fiber cable does not result in a time-varying phase shift and cannot be seen directly by a φ-DAS system. Fig. 2 shows the 15-minute-long exemplary ambient waterfall traces when there was no weight along the cable (Fig. 2(a)) and when there was a 20 lbs. stationary weight hanging at the first location (242 m), and as expected there was no visual difference between the waterfall graphs of those two cases. In other words, a static weight hanging on an aerial fiber cable is invisible to the spatio-temporal visualization of the φ-DAS signals.

However, our proposed approach based on operational modal analysis of the ambient data recorded by a φ-DAS system can detect and localize such a static weight by calculating the changes in the natural frequency of the aerial fiber structure.

The φ-DAS system, used in the experiment is a commercially available NEC brand SpectralWave LS model DAS interrogator, and was operated at a sampling rate of 2 kHz and was set at a gauge length of 2.45 meters, which was also the measurement step-size of the system. 8 ns optical pulses are generated by a combination of electro-optic and acousto-optic modulation. Five sets of ambient data were recorded covering the range of 200 m – 500 m along the fiber route. Those data sets were: 1- for the case when there was no weight on the fiber, 2- for the case when the additional weight was hung only at the first test location, 3- for the case when the additional weight was hung only at the second test location, 4- for the case after the weight was removed from the fiber (i.e., same as the first case, but ∼1 hour later), and 5- again for the case when there was no weight but taken 116 days later, to test the long term repeatability of the method. Each data set was recorded for 10 minutes with only ambient excitations (i.e., there were no controlled acoustic nor vibration sources in the field). Another point to note is that for the data sets with the weight hanging on the cable, the data recording started after both the weight and the cable recovered to stationary state.

3. Theory and method

Based on their physical properties, such as geometry, mass and temperature, the aerial cables (like any other structure) have their own natural frequencies and vibrational modes which can be excited by either ambient effects such as wind and traffic, or controlled effects such as hammer hits or shakers [8]. In our approach, we consider each aerial fiber segment between two utility poles as a unique mechanical structure with its own response function and natural frequencies. When there is a structural change on the aerial fiber cable, such as due to an additional weight, its frequency characteristics will change as well, similar to a change in a guitar string’s note due to a changing tension. So, our method divides the fiber route under investigation into overlapping fiber segments, measures the frequency characteristics of these individual fiber segments as a baseline and looks for stationary and local changes that are associated with an additional static weight hanging on the fiber. Hence our proposed method can determine on which fiber segment the static weight is located.

For practical reasons, we focus on an operational modal analysis (OMA) approach, also known as “output-only modal analysis” since it only needs ambient excitations rather than a controlled force in the field [9]. Thus, there is no need for fieldworks, and the whole additional weight monitoring/detection can be done remotely from one end of the fiber cable. OMA as a response-only technique is widely used in civil engineering applications to identify the modal parameters such as natural frequencies, damping and mode shapes of a structure under ambient excitation. The vibrations of the structures under investigation are measured by carefully placed vibration sensors on the structure. In our case however, the fiber structure that is under investigation is also the sensor itself, which makes this analysis very practical. In OMA, the input forces are not measured but assumed to be approximately white noise. Another assumption is that the input forces are not confined to a specific point along the structure and randomly distributed around the structure spatially. The vibrations due to the wind and the vehicular traffic satisfy both conditions, since they are non-local and generate broadband vibrations without a significant modulation in the frequency range of interest (0 Hz - 40 Hz). As we will discuss further, even if the spectrum of input ambient excitation is colored noise, the calculated physical modes of the structure will not be affected [9].

There are several techniques of OMA to extract the modal parameters of a structure, such as stochastic subspace identification (SSI) method [10], peak-picking (PP) method [11] and frequency domain decomposition (FDD) method. We used FDD approach for our application since it has higher accuracy to resolve closely spaced modes, and also performs better with noisy data [12].

In FDD analysis, the system response is calculated via the power spectral density (PSD) matrix of the output where m is the number of discrete sensing points along the structure. The ambient data in time domain are recorded by individual sensors, and then the PSD matrix elements (ij) are constructed as multiplication of discrete Fourier transforms of i^th sensor data and complex conjugate of discrete Fourier transform of the j^th sensor data. So all the diagonal elements of the PSD matrix are the corresponding power spectral densities, and off diagonal elements are the cross spectral densities of different sensor data. The PSD matrix is conventionally denoted as ${\hat{G}_{yy}}({j{\omega_i}} )$, where ${\omega _i}$ are the discrete frequency values, and the subscript “yy” denotes that this is the response PSD matrix. In the next step of our algorithm, singular value decomposition (SVD) is applied to the PSD matrix as shown in Eq. (1) [13].

Our proposed method measures the vibrational characteristics of aerial fiber structures by a φ-DAS system. The φ-DAS system collects ambient data along the fiber cable at a step size $\varDelta x$ of 2.45 meters, as illustrated in Fig. 3, and since those sensing points are on the same physical structure that is the fiber optic cable, their inherent structural vibrations are correlated and contain information regarding the structural properties of the aerial fiber cable while their individual random noise is uncorrelated.

 

Fig. 3. Segments of the aerial fiber cable

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If the pole locations along the fiber route (i.e. the borders of aerial fiber segments) are known, which requires a fieldwork for each individual pole, then one can apply the FDD algorithm only to these segments. In this improved version however, this manual labor is avoided by scanning the whole fiber route which only increases the computation time. To analyze the whole route, the aerial fiber is divided into 14.7-meter-long segments, consisting of $m = 6$ adjacent sensing points (φ_i – φ_i+5) and overlapping 50% with the neighboring segments as pictured in the figure below. By inspecting all these segments, the whole route was scanned and analyzed. One should also note that, this arbitrary segmentation of the fiber route does not affect our results, since the weight detection is based on the relative local changes in the SVD map and not on the absolute SVD values.

Firstly, the $6 \times 6$ PSD matrix was calculated for each segment using the 10-minute-long ambient data and then the SVD was applied to obtain the singular values for each discrete frequency values. As a result, a singular value map was obtained for the aerial fiber route as shown in Fig. 4. In this map, the x-axis corresponds to the center locations of the segments along the aerial fiber, and the y-axis corresponds to the frequency values, the magnitudes of the singular values for each frequency and location are color-coded.

 

Fig. 4. SVD maps in the range of 0–40 Hz in frequency domain and 200–500 m in the spatial domain for the cases a) no weight, b) 20 lbs. at 242 m, and c) 20 lbs. at 335 m.

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4. Results and discussion

The aerial fiber range under investigation was from 200 meters to 500 meters, covering a total of 123 sensing points, which generated 40 segments that were analyzed with our method. The resulting SVD versus location graph (i.e., the SVD map) for the baseline case with no additional weight on the cable is shown in Fig. 4(a). Fig. 4(b) and 4(c) illustrate the SVD maps for the cases when the additional 20 lbs. weight was hung at around 242 meters and 335 meters, respectively. The center points of each segment are spaced by 7.3 meters (i.e. 3 sensing points), which is the spatial resolution of the SVD map. All those figures are calculated from 10-minute long ambient data taken after the weight and aerial cable became stationary.

As seen in Fig. 4(b) and 4(c), the SVD shapes have changed compared to the baseline Fig. 4(a), at the segments where the weight was hung. However, due to the logarithmic scale used in the z-axis and the limited contrast of the color map, visual observation of the SVD maps to detect and localize the weight on the fiber route may be misleading.

For quantitative analysis and automation, we have developed a similarity function to quantitatively measure how much the SVD shape of a segment has changed relative to baseline. Each column in Fig. 4 is the SVD result of a specific segment, and can be considered as a multi-dimensional vector, where each frequency corresponds to a different dimension. The “distance” of such a multi-dimensional vector to the baseline can be measured to quantify the change in SVD shape. Since the main motivation was to detect and locate the change in the overall shape of the SVD maps instead of total energy, the inverse cosine similarity is chosen as the distance metric [14]. The resulting distance values are plotted as functions of locations in Fig. 5. A distance value of “1” means the SVD shape is identical to the baseline, while larger distance indicates larger variation in the SVD shape from the baseline.

Figure 5(a)/5(b)) depicts the cosine similarity between the baseline (Fig.4a) and the case where 20 lbs. was at 242/335 meters (Fig. 4(b)/4(c)). It can be easily observed in these figures that the weight is detected and localized at the segment location where the frequency characteristics of the aerial cable changed most. According to the peaks of the similarity indices, the weight location for the first and second cases are calculated to be the segments centered at 240 meters and 335 meters, respectively.

 

Fig. 5. The SVD distances between a) the baseline and the case of weight at 242 meters, b) the baseline and the case of weight at 335 meters, c) the baseline before and after weight experiments, and d) the baseline before the experiment and the baseline taken after almost 3 months. A threshold distance of 1.3 was shown on all figures.

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To verify the repeatability and consistency of the baseline SVD map for different levels and types of ambient excitations, we repeated the baseline SVD measurements three times. The baseline was measured firstly just before the weight was applied, and secondly after the weight was removed. The weather conditions for these two ambient data sets were as follows: 75° F average temperature, 54% humidity, and 2.486 mph average winds from southwest direction while the fiber route is along north-south direction. Finally, a third baseline measurement was taken 116 days after the weight experiments had been completed. The weather conditions for this, much later data set, was as follows: 43° F average temperature, 39% humidity, and 15.535 mph average winds from northwest direction. The distance indexes between the baselines recorded just before and just after the weight experiments are illustrated in Fig. 5(c). The distance indexes between the baselines recorded just before the weight experiments and 116 days after the experiments are shown in Fig. 5(d). All these baselines show a similarity distance fluctuations less than 1.25 over a time duration of 116 days, and hence our threshold distance value was set at 1.3 for weight detection alert.

The observed fluctuations of similarity distance across different times may stem from several factors. The frequency characteristics of the aerial cable depend on its mechanical properties, which are mostly affected by its temperature which may vary significantly over the year. Also, the utility poles are part of the mechanical fiber structures and some changes on the poles, such as the installation of a new transformer or new cable along the route may affect the frequency characteristics of the fiber structure as well. Another factor is the associated noise in the measurement system and non-uniform and slow-varying Rayleigh backscattering intensities from the fiber optic cable. All of these reasons may be accounted for the minor changes and fluctuations in the baseline SVD results. Nevertheless, as shown in Fig. 5(d), these fluctuations are bounded and smaller compared to the changes in the SVD shape caused by additional weights on the fiber.

Furthermore, the strength of the ambient excitation (heavy traffic vs. low traffic or strong wind vs. weak wind), will only change the total energy transferred to the aerial structure hence it only shifts the overall value of the SVD map without changing its profile shape, and consequently not results in a peak in the SVD distance nor a false detection. Another benefit of comparing the target SVD map to a baseline is that our method does not require a white spectrum of the ambient excitation sources. As long as the spectrum profiles of the excitation sources are statistically similar across all the measurements including baseline, and the excitation is both broad and strong enough to cover and excite the fiber cable’s signature vibrational modes, it is valid to compare the SVD maps across the measurement. Finally, if the ambient excitation due to the wind or traffic includes a certain strong modulation in the frequency range of 0–40 Hz for some unknown reason and somehow leaks into the SVD map, this will show up at every location along the fiber route, since the wind and traffic are non-local events. Thus, by only keeping the local changes and eliminating the global changes in the SVD map, real static weights can be distinguished from modulated wind or traffic excitations. In practical operation, when a global peak is present, that data set may simply be omitted and the measurements can be repeated at a later time. To further mitigate the influence by the uncertainty from ambient excitation sources, longer time intervals, e.g., hours or even days, of data can be used for SVD map calculation, or the algorithm can be adapted to average the results from multiple spans of 10-minute-long ambient data.

In a real-life application scenario, it is expected that the baseline should be updated regularly, and also more adaptive alert threshold mechanisms can be developed such as a machine-learning based or majority voting-based approach.

One other important question that one might ask is, how the proposed method will act for different values of weight, and whether the relation between the amount of weight and the SVD change can be exploited to determine the mass of the weight hanging on the aerial cable. As expected, as the tension on the cable increases due to a heavier weight, the resonant frequency of the cable shifts to higher values as well. However, this relation depends on other structural factors such as the cable type, the way cable is mounted on the poles, whether it is supported by other cables or not, etc. Since these conditions are not uniform along a fiber route, a direct conversion of frequency shift to the mass of the weight is not practical nor possible without a prior calibration along the fiber route. Hence, we focused this initial work on detection and localization of the weight rather than weighing the weight.

5. Conclusion

In conclusion, a novel method based on OMA was proposed to detect and localize stationary weights hanging on aerial telecommunication fibers using only ambient data from a φ-DAS system without additional devices or activities in the field. The method does not need prior knowledge of utility pole locations along the fiber route. The approach was tested and verified on an actual carrier network and successfully located a 20 lbs. weight at two separate locations within a distance error of 2 meters which is well within the spatial resolution of the generated SVD map. The results are promising for using φ-DAS technology on existing telecommunication fibers not only for environmental sensing but also for physical network health monitoring and structural inspection.