Algorithm Optimization for Rockfalls Alarm System Based on Fiber Polarization Sensing

The mountain scenario is often subject to catastrophic events such as rockfalls and avalanches, potentially dangerous for both people and civil infrastructures. Early-warning alarm systems that in case of such events can immediately turn on a traffic light on a mountain road and send remote alarms to control rooms, have already been developed in the geotechnical engineering sector, but all have some limitations and/or very high costs. In this work we propose an immediate-warning monitoring system based on fiber polarization sensing. Anomalies such as rockfalls and avalanches would change the instantaneous birefringence of the fiber installed in the area to be monitored, and can be sensed by looking at the state of polarization at the fiber output. The novelty of our paper is the development of an algorithm that is able to detect dangerous events, which we experimentally emulated on a reduced scale physical model of a mountain slope, in which fibers have been buried in different configurations. Our findings show that the system can correctly sense all the experimentally generated rockfall phenomena and for all the installed fiber configurations, and it is also robust to false alarms, provided that the monitoring algorithm main parameters are properly set.


I. INTRODUCTION
T HE use of optical fibers as sensing devices is not a recent idea [1]. Over the years it has been found that they are very suitable as sensors in many different scenarios, including chemical and mechanical applications, or even to sense temperature variations. This flexibility is beneficial to the geotechnical field, where modern monitoring techniques can be enhanced using fiber based systems [2]. Optical sensing techniques can be divided in two main classes: a) Distributed sensing [3]: this is the best solution in terms of performances. The whole fiber length can act as a sensor and anomalies can be detected and localized with high spatial resolution, ranging from cm to m. The drawbacks are typically the complexity of the systems and the high cost, due to the need of very sophisticated interrogators. Moreover, most of these systems are very slow, requiring up to several minutes for a full acquisition, thus they are not suitable for real-time fast alarm. b) Discrete sensing [4] [5]: this solution is based on the installation of a high number of sensors, tipically fiber Bragg gratings, along the fiber profile. Anomalies (external events inducing stresses on the fiber) can be localized, but discretely in space, with resolution depending on the number of sensors employed. Because of the high number of sensors needed to have an appropriate spatial resolution, this is usually again a high cost solution. Interferometric techniques can also be used to increase the event localization capability at a reduced cost [6], [7], [8]. In this work, we focus on the monitoring and immediate alarm generation in the mountain scenario, often subject to hazardous events that can damage roads or entire areas and harm lives [9], [10]. In particular, to monitor these events, we propose to sense the mechanical and vibrational stresses induced on the fiber by the surrounding terrain, that can be detected through a monitoring system based on underground fibers buried in situ. More specifically, since mechanical stresses (in our case mainly shear stresses, caused by falling rock masses [11]) induced on the fiber during our experiments will instantaneously change the birefringence, we measure the state of polarization at the fiber output. We point out that, focusing on the goal of fast alarm generation after a catastrophic event, distributed sensing with high spatial resolution is not strictly needed, but it is anyway required that vibrations are sensed in any position along the deployed fiber, as it actually happens when monitoring fiber polarization. The aim of this work is to characterize and study an optical fiber-based monitoring system, with the requirements of reliability, simplicity, improved performances with respect to current solutions and, above all, lower cost than a state of the art system.
Polarization sensing is obviously not a new idea, but in this work the novelty is in the following: 1) achievement of immediate alarm generation, with delay times in the order of one second. The typical application we have in mind is an alarm system in the mountain area that can for instance turn red a traffic light on a mountain road immediately after a rockfall or an avalanche. Clearly, speed of detection is a key element. 2) development of an algorithm for state of polarization detection. We optimize its parameter and validate it on an experimental small scale physical model. In the geotechnical and mountain engineering fields, a high number of (not optical) monitoring techniques have already been developed and installed [12], [13] concerning, for example, tracking of initiation mechanisms, the very first signs that some hazardous event could be about to manifest. Other methods are used to monitor the debris flow dynamics, that is to measure vibrations caused by the flowing mass, sense flow depth, basal stress or record surface flow velocity. The existing geotechnical solutions are typically affected by one or more of the following drawbacks: r Low reliability: the monitoring system should be located in positions where the acquired data are safe to be interpreted correctly. Unreliable data evaluations would increase false and missed alarms occurrences, when detecting dangerous events.
r Coverage: monitoring is usually active over areas of limited extent, which could cause the system to miss dangerous events occurring in areas out of reach.
r Maintenance: the sensors installed need maintenance to be always fully operative. This represents a problem, since they are often difficult to reach. r For the specific target of our investigation, it is important for the in situ sensing devices to be inexpensive, since they might be damaged by catastrophic events. Existing fiber optics sensing techniques can solve or at least mitigate the majority of these problems, at the expense of increased cost and complexity. The best performing state of the art solutions are mainly distributed sensing techniques [14] based on Rayleigh, Raman and Brillouin scattering. Moreover, sensing is enabled on vibrations, strain and temperature, over distances up to few hundred km [15], and with spatial resolutions down to few centimeters (or even less) along the cable which, for geotechnical applications, represents an enormous advantage [16], [17], despite the high cost. On the contrary, our proposed monitoring system can be classified as "quasi distributed" since it can monitor events occurring in any position along the fiber (and not only in some positions as in discrete sensing solutions), but without the spatial resolution that distributed sensing can provide. This approach enables the monitoring of large geographical areas, but does not allow to locate events in space. It is anyway perfectly suitable for situations in which an alarm signal should be switched on, when strong and anomalous vibrations are detected in any position along the fiber length. Moreover, this solution does not need costly equipment or complex signal processing and, unlike current monitoring solutions in the geotechnical sector, can in principle have the interrogator placed 10-20 km away from the actual monitoring site, where a few hundred meters of fiber would be buried.
The system we propose in this manuscript is based on the monitoring of optical polarization [18]. The state of polarization (SOP) of light propagating inside an optical fiber can be uniquely described in a three dimensional space by the Stokes vector ( S), identified by the three Stokes parameters, S 1 , S 2 , S 3 . S 0 is not considered, since it represents the power at the fiber output, which is constant and does not carry any information. The three dimensional space over which S is identified, is the Poincaré sphere [19]. If external stresses are applied to the fiber, the birefringence [20], [21], [22] changes, resulting in the angular variation of the S vector in the Poincaré space. This variation can be detected by monitoring the SOP angular speed, the angular variation over time of the Stokes vector: we call this parameter state of polarization angular speed (SOPAS).
In the following Sections we will present a possible implementation and the related post-processing algorithms for a fiber based alarm system relying on detecting anomalous polarization variations, and then we will show our experimental demonstration based on a reduced scale model of the slope of a mountain ( Fig. 1), on which events emulating real rockfalls were generated. We have developed a post-processing and a real-time algorithm (implemented through Matlab) able to compute the SOPAS and, using a proper algorithm, detect if SOPAS anomalous variations take place over time.
The reminder of this manuscript is organized as follows: in Section II, the experimental setup used for the experiments is presented and explained in details, and in Section III the working principle of the detection algorithm is presented. Section IV reports the experimental demonstrator results including discussion on a true real-time implementation. A discussion is given in Section V, and conclusions in Section VI.

ALARM-GENERATING SYSTEM
Our proposal is based on the experimental setup shown in Fig. 2: the laser emits a linearly polarized continuous-wave (CW) optical signal with 0 dBm optical power to the in-situ fiber deployed underground, in the area to be monitored (e.g. a mountain gully), which in our case is the model in Fig. 1. The output end of the fiber is connected to a polarimeter, a commercial instrument that allows to measure the Stokes parameters with a sampling frequency f s . A PC then extracts the SOP samples from the polarimeter to process them according to the algorithm that will be described in the next Secttion III, and thus monitors the SOPAS time-evolution. The algorithm is developed to produce an alarm (e.g. a traffic light turning red or a remotely transmitted hazards alarm in a real-time scenario) if some anomaly is detected.
The optical source used in our experiments is a low cost (a few hundred euros) Fabry-Perot (FP) laser emitting light at 1550 nm. Light then propagates inside a single mode fiber (SMF), buried within the soil of the monitoring site model. The monitoring site recreated in our lab is a scale model of the slope of a mountain [23] (Fig. 1). Essentially, it is a ramp made of wood inclined by 30 • , 0.7 meters wide and about 3 meters long. It has been filled with a mixture of sand and soil for a total thickness of about 10 cm.
A total of three optical fibers have been deployed inside the soil at three different depths (1, 5 and 9 cm). The focus of this work is on the "transversal" (T) configuration, coloured in red in Fig. 2. The T fibers are installed in a serpentine layout, with six transversal crossings of the slope longitudinal section. We conducted several experiments also on other configurations installed longitudinally along the model, but we observed no significant differences and therefore we will not show them here. The soil and sand mixtures is enclosed within a layer of geotextile material (see Fig. 1(b)), to prevent it from being eroded by the repeated rockfalls. To distinguish fibers of the same kind buried at different depths, a convention has been adopted: number "1" indicates the deepest at 9 cm from the surface, number "2" refers to the middle one at 5 cm, and number "3" is for the most superficial, at 1 cm depth. For instance, T1 is used to name the fiber installed at the larger depth (9 cm) with a T configuration.
Three different types of mechanical stresses have been generated over the slope in order to emulate real, possibly dangerous, rockfall events: r Single rock (SR): rolling of a 270 grams single rock as in r Cylinder (C): rolling of a 890 grams test cylinder made of ceramic material, 15 cm long and with a diameter of 5 cm (see Fig. 3(a)).  weighting 280 grams on average, as shown in Fig. 3(b). A high number of SOPAS traces have been acquired, by generating many repetitions of the aforementioned events. Moreover, we performed several measurements of the "steady" condition, i.e. without any rockfall event: this "background noise" on SOP time evolution was important to study the occurrences of false alarms, as we will discuss in the following. At the bottom of the slope, we also built a scale reproduction of a rockfall metallic barrier [24], [25], over which different fibers layouts have been arranged, as shown in Fig. 4. These configurations have been selected in order to test which part of the barrier could be the most sensible to rockfalls, by placing the fiber on the perimeter of the grid (Fig. 4(c)), in the center ( Fig. 4(a) and (b)) or on a support ( Fig. 4(d)).
The polarimeter used to perform our tests is the Novoptel PM1000, equipped with a photodetector covering an extended C-band in the 1501-1565 nm range, analog bandwidth of 25 MHz and acceptable input optical power in the range from −36 dBm to +4 dBm. This device is connected by a USB cable to a computer where, through a Matlab script or the device GUI, hardware parameters such as the sampling frequency f s or the total acquisition time t tot can be set. The polarimeter registers can be queried to extract the Stokes parameters samples.

DETECTION
The block diagram of the algorithm developed to process the SOP samples and generate alarms when anomalous conditions are detected is shown in Fig. 5.
The polarimeter is the source of the Stokes parameters samples taken at discrete time instants Unless otherwise specified, all the results in this work have been obtained by first acquiring SOP samples for t tot seconds, and then elaborating the whole acquisition through Matlab, in post-processing. The results of some tests using the polarimeter as real-time source will also be shown: in this case SOP samples are extracted from the device registers at every instant. In our first experiments we chose f s = 48.83 kHz and a total acquisition time t tot = 21.5 seconds. The second block computes the SOPAS by applying (1) to each sample, where ω[k] is the discrete SOPAS, T s is the sampling period and ( S k , S k−1 ) is the dot product between the Stokes vectors at time k and at time k − 1.
The idea followed to compute the angular speed is similar to the calculation of the derivative of the angle in discrete time.
Using the angular speed to detect anomalies occurring on the fiber allows to reduce a three dimensional problem into one dimension, much easier to manage. In particular, the mechanical stresses occurring on the fiber can be easily observed through the SOPAS, since birefringence variations along the fiber induce abrupt changes of the SOP. In the proposed algorithm there are two key parameters:   is set to one second, when no event is generated (in black) and for 10 RF events occurrences, measured through fiber T3. The inset in Fig. 6 shows how the SOP change rate evolves during events with different mechanical intensity, related to the size and weight of the items used to generate them. The relationship between vibrations and SOP variation is first of all non linear, but also it depends on how the vibrations generated by the falling rocks impinge on the underground fibers. This is thus hard to be properly defined, even though it is evident that a higher angular speed is produced by stronger events. In our specific experimental setup, RF is the most intense as it is composed of several rocks, SR is the weakest as it is generated only by a small rock, C is in between as it is generated by a cylinder bigger than the single rock. At the output of the FIR filter we obtain the smoothed SOPAS samples ω s [k].
r ω th : is the SOPAS threshold value, in rad/s. If the algorithm detects ω s [k] > ω th an alarm signal is generated. As an example, Fig. 7 shows one SOPAS trace for a single RF event measured on fiber T3, compared to a threshold ω th =0.045 rad/s. The two-state alarm signal is also represented in red. In a real world scenario, it could trigger a traffic light turning red and/or send a message to a remote emergency control room. As any "binary" alarm system, its performance depends on the probability of the following three situations: r Correct detection (CD): events are accurately detected in the SOPAS time evolution, with no FAs or MDs. Ideally, our system should always be in the CD condition. The probability for the other two conditions to occur is minimized by appropriately choosing T mov and ω th . In Fig. 8, the same SOPAS evolution of a RF event is reported for three different T mov values. For increasing values of the averaging window, the oscillations in the original SOPAS evolution reduce, making the algorithm more robust. Nevertheless, peaks are also lower, requiring a lower threshold to be selected. If the threshold value is set too high without accounting for this effect, MD cases are likely to happen. On the other hand, a very low value of T mov could enhance the noise oscillations and, if the threshold is set too low, trigger the alarm generating FAs. The choice of T mov is also paramount since it is the parameter that determines the speed of reaction of our system. In fact, to a first approximation, the system latency is directly proportional to T mov (plus the polarimenter and DSP internal delay in data transfer). These considerations show that the setting of the pair of parameters T mov and ω th is key for the correct operation of our setup.

A. SOP Post-Processing Approach for Parameter Setting
In this Subsection we focus on selecting, for each fiber in our setup, the optimal parameters of the detection algorithm. To perform this analysis, for each fiber we have generated 10 RF, 10 C, 10 SR events, and also acquired 3 steady state traces. These traces show a "noisy" random SOPAS evolution, and are essential in assessing the probability of false alarms. In total, 33 events per fiber have been generated, that is 99 for the whole set of T fibers. The sampling frequency is set to 48.83 kHz and the acquisition time is 21.5 seconds.
The output of the post-processing analysis is a twodimensional color map showing, for each parameter pair [T mov , ω th ], whether or not the algorithm works in CD mode. We call these "detection maps" (see for instance Fig. 9). To generate these maps we acquired the 13 SOPAS traces per fiber (10 traces for the event and 3 traces for the steady state) and averaged them using several T mov values, from 0.1 seconds to 3 seconds, in order to obtain the smoothing effect reported in Fig. 8. The resulting averaged SOPAS traces are then compared against different thresholds ω th , and the results obtained as follows: r if the averaged SOPAS for all 10 events has at least one sample above threshold and all the samples of the averaged steady-state event below threshold we are in a CD condition.
r if at least one sample of the averaged steady-state event is above threshold, we are in a FA condition. r if all the samples of the averaged SOPAS evolution for at least one of the 10 events are below threshold we are in MD condition. In Fig. 9 an example of detection map for the single rock events over fiber T3 is reported using the following color convention: green color if all 10 events have generated CD, red color if there was at least one FA (ω th too low) or MD (ω th too high). Thus, all parameter pairs falling in the green area yield a correct working condition for the 10 events on the specific fiber.
After this preliminary investigation on the T mov and ω th parameters, we focus on trying to reduce the sampling frequency of the SOPAS evolution. We started by observing the typical frequency content of a SOPAS trace during an anomalous event: an example is given in Fig. 10 as time-frequency spectrogram. It is evident that most of the spectral content is below 10 Hz, as it is typical for these kinds of mechanical vibration events on the terrain [26], [27]. Although in our case we work on a reduced scale experimental model, this frequency range is in line with those reported in other paper dealing with similar topics, such as [28] and [29]. The inset of Fig. 10 shows how a short (about 1 m) span of fiber reacts to mechanical vibrations in a controlled laboratory environment. We induced 2 Hz sinusoidal oscillation on the fiber, for 30 seconds, once every two minutes by means of a vibration generator. The result is shown again as spectrogram: the 2 Hz frequency component and also its higher and lower harmonics are perfectly visible in the spectrum of the SOPAS, indicating that the frequency components of the mechanical stress are transferred to the SOP variation. However, the way this transfer occurs is not trivial, and depends on factors such as length of the fiber, distance of the event from it, and intensity of the stress. Thanks to this observation, we reduced  the sampling frequency down to f s = 95.4 Hz, which happens to be the lowest one enabled by the polarimeter: this is in itself an interesting result, since it goes in the direction of reducing the computational effort. For instance, f s = 95.4 Hz would allow the use of extremely low cost analog-to-digital converters (ADC) and DSP processing boards. Regarding the polarimeter, in our setup we use a quite expensive (about 12000 euros) "high end" device which potentially allows extremely high sampling frequency, but there are lower cost instruments (around 5000 euros) on the market with sampling rates in the 100 sample/s range. Besides this techno-economic consideration, when reducing f s we also observed in all cases an enhanced operational space in the aforementioned color map, due to the fact that the used polarimeter has a decreasing noise level for decreasing f s , as demonstrated in the following.
The map shown in Fig. 9 refers to a single fiber but we extended the study further to have a global picture of the situation on all the three T fibers and three events repeated ten times (thus 90 cases in total). Fig. 11(a) and 11(b) summarize the experimental results showing the intersection between the detection maps, respectively with f s = 48.83 kHz and with f s = 95.4 Hz. The dark green area is the region where the algorithm is able to correctly detect all of the 90 events per fiber (ten repetitions of the C, SR and RF events for each of the T fiber at three different depths). One unit on the colorbar corresponds to one set of ten SR, RF or C events that, for a single fiber, has been correctly detected. A set is not correctly detected if at least one of the ten events in the set is not correctly detected. In this case the set does not add to the colorbar count. A clear advantage can be observed when using the lowest sampling frequency (f s = 95.4 Hz), as the dark green area is much larger in Fig. 11(b) (it represents the 12% of the whole parameter space in Fig. 11(a), whereas it represents about the 40% of the total in Fig. 11(b), a threefold increase).
The same analysis has been performed also for the other application, i.e. for the rockfall barriers, keeping f s to the optimal value of 95.4 Hz. In this case 20 SR events were generated by launching one small stone 20 times. The detection maps are shown in Fig. 12. Maps 12(a), 12(b), 12(c) and 12(d) refer to RB1, RB2, RB3 and RB4 configurations, respectively. The ability of the system to detect single rocks when applied to the barrier is even greater: the green area covers more than 70% of the entire parameters space in all cases, except for configuration RB1 (Fig. 12(a)), where it is just the 46%. The best performing configuration is the RB2, with a green area covering the 94% of the map, because, as shown in Fig. 4, in order to create the loops, two portions of fibers are almost overlapping at the center of the barrier, where the stone is more likely to hit, enhancing the effect on the SOPAS.

B. Long Term Measurement
In this Subsection, we apply the algorithm in Fig. 5 to continuously monitor over long time windows (up to tens of minutes) and for many anomalous events. This approach was used to test the post-processing algorithm introduced in the previous sections in a more realistic scenario, where the events occur sequentially at time instants unknown a priori. The parameters set for the acquisitions are f s = 95.4 Hz and t tot = 22.9 minutes. The events generated are: three RF, one SR and one C, and are shown in Fig. 13. Specifically, they were generated in the following order during the acquisition: RF, SR, RF, C, and lastly RF again. Fig. 13 shows the three detection scenarios: false alarm in Fig. 13(a) (T mov = 0.3 seconds, ω th = 0.015 rad/s); correct detection in Fig. 13(b) (T mov = 1 second, ω th = 0.06 rad/s) and Fig. 13(c) (T mov = 2 seconds, ω th = 0.06 rad/s); missed detection in Fig. 13(d) (T mov = 3 seconds, ω th = 0.06 rad/s). The blue line represents the smoothed SOPAS, the black dashed line represents the threshold value, while the red dots highlight the time instants in which the alarm signal would be triggered. These graphs confirm that, by appropriately choosing the parameters pair ω th and T mov the algorithm can be made to work according to the detection map of Fig. 11(b). For example, Fig. 13(a) shows that by picking T mov = 0.3 seconds and ω th = 0.015 rad/s, we get FA, which is predicted by the detection map. This is confirmed also for the other three cases. For instance, when we pick a parameters pair inside the green area of Fig. 11(b) the algorithm correctly detects all the different events (see Fig. 13(b) and 13(c)). In a real field installation, we envision that a higher layer algorithm can adaptively set these two parameters, and in particular the threshold ω th .

C. Real-Time Processing Approach
In this Subsection, we focus on a true real-time application of the algorithm on the same experimental setup (see Fig. 2). The Stokes parameters are now extracted from the polarimeter internal memory and the algorithm was modified to operate in real-time, generating alarms immediately after the detection of anomalous events. Thanks to a sampling frequency smaller than 100 Hz, it was possible to use a simple Matlab script on a standard laptop: to extract the Stokes vector from the device and compute one sample of SOPAS, in the current version, the algorithm introduces a latency of the order of 1 ms.
In our real-time implementation, the SOPAS time evolution is displayed at every sampling instant: each time ω th is exceeded the point on the curve is plot in red and a sound is emitted. We performed several test and show three of them in Fig. 14. The sampling frequency was set to 95.4 Hz, and the parameter pair values were chosen from the map in Fig. 11(b), in order to generate CD, FA and MD, and test the consistency of the post-processing results with the real-time approach. The three subfigures in Fig. 14 show: a) Correct detection ( Fig. 14(a)): parameters were set to T mov = 0.3 s and ω th = 0.07 rad/s. A SR, a C and a RF event were correctly detected. b) False alarm (Fig. 14(b)): parameters were set to T mov = 0.3 s and ω th = 0.015 rad/s. No events were generated in this case, but the threshold was too low and the noise alone triggered the alarm. c) Missed detection (Fig. 14(c)): parameters were set to T mov = 1 s and ω th = 0.09 rad/s. A SR, a C and a RF event were generated, but only the RF was detected. Fig. 14 shows that also in a real-time application, if the parameters pair is set appropriately, the algorithm works correctly, and the performance is consistent with that estimated in post-processing through the detection maps.

V. DISCUSSIONS
Compared to a real installation (e.g. on a mountain gully), the SOPAS traces obtained on the small-scale model are less noisy in the steady state condition since the fiber is shorter, but the anomalous events that we were able to generate are weaker than in a real mountain environment. We envision that f s around 100 Hz and T mov of a few seconds, could approximately remain the same also in a real environment. In fact, the chosen f s allows to detect anomalies whose spectral content is limited to a few tens of Hz, as for the events of interest in our case. Moreover, we experimentally verified that the tested averaging window values work for a whole range of weak and intense events. The setting of ω th is the most crucial, since this SOPAS threshold at  [31], [32], [33], [34], [35], [36], [37]. which real anomalous events should trigger an alarm, depends on many factors, such as: 1) depth at which the fiber are deployed underground; 2) position of the fibers (for instance, in the center of a gully or slighlty on its side); 3) strength of the anomalous events; 4) characteristics of the SOPAS noise in the steady state; 5) composition of the debris material; 6) the flow dynamicssmooth or surge type flows. Moreover, landslides and debris flows are often erosive phenomena. Erosion, entrainment and deposition processes result in crucial change of local material compositions, properties and flow dynamics, including the flow depth, speed and mobility [30]. For these complex, but realistic situations, the performances of the proposed system should also be checked.In a real installation, the probability of false alarms can be high since spurious events (animals or people crossing the fibers, for example) would commonly occur and a threshold based algorithm, although adaptive, would likely sense them. This can be mitigated by monitoring in parallel more than one fiber by means, for example, of an optical switch, and activate the alarm only if ω th is exceeded on the SOP variation on all of them. In fact, anomalous extreme events are usually spatially diffused, and would surely be detected by more than one fiber, whereas spurious events are usually localized and would be sensed by only one of them. Machine learning algorithms [38], [39], [40] can also be used to distinguish between steady state and hazardous conditions, and can also enable event type classification. Regarding viability and cost of a real installation, we have recently installed a monitoring system like the proposed one in the Valle d'Aosta region, Italy. Here, an optical fiber bundle, containing 24 fibers, runs for a few hundred meters along a mountain road, and is then buried inside a corrugated hose for extra 100 m, along the gully. Access to the fibers is possible through manholes placed every 100 m. The cost associated to the installation can be high, but can be mitigated. Firstly, optical fibers are rather inexpensive: one cable containing around 50 fibers can cost around 1 EUR/m. Moreover, many roads nowadays have already been outfitted with data-carrying optical fiber cables and thus the cost associated with the excavation can, in some cases, be reduced or disregarded. Furthermore, we are working on a system configuration which allows to exploit different fibers contained in the same cable, to monitor different sites by using the same interrogator, equipped with a low cost optical switch. Another cost element is related to the need to replace the damaged fiber in the event of a particularly strong catastrophic rockfall phenomenon. In a practical installation, we envision the interrogator to be placed in a convenient location several km far from the mountain slope. Potential damages would occur only on the portion of the fiber installed in the "dangerous" area, which would be only a few hundred meters long. The breaking point could be determined by exploiting an optical time domain reflectometer (OTDR), which can pinpoint any loss on the cable with cm accuracy. Moreover, such a catastrophic event causing a cable break, would for sure be sensed by our system, that would generate the alarm and fulfill its duty before fiber replacement can take place. A system with these characteristics could really represent a valid alternative to current early warning and detection systems available on the market. A comparison of pros and cons is summarized in Table I with respect to most common sensors. The proposed system combines the high accuracy with the robustness and durability required in a mountain environment, at a comparable cost with the cheapest alternatives. It also avoids the need of installation of sustaining systems on site, as well as of electric supply along gullies where cable electricity is usually not available and photovoltaic cells may be harmed by bad exposure. The system may also allow to monitoring different slopes at the same time, as well as large areas, with a single acquisition system. Another suitable alternative in this case would be the remote radar doppler which, however, would require full and clear visibility of the scenario from the installation point and would be much more expensive in the end.

VI. CONCLUSION
In this work we proposed and demonstrated a fiber-based mountain anomalous event alarm system, completely relying on polarization variation sensing. Dangerous events have been emulated over a scale model of a mountain slope, where different fiber configurations have been installed. The alarm algorithm is low on complexity and based on SOPAS computation, smoothing operation and threshold comparison. Its performances strongly depend on T mov , ω th and f s : detection maps have been generated to appropriately set the first two parameters and avoid FA and MD, while we proved that the optimal choice of sampling frequency is the lowest available one, 95.4 Hz. By setting f s = 95.4 Hz, the detection map shows a clear increase of the operational space, compared to higher sampling frequencies.
It has been successfully tested that if the parameters pair is chosen appropriately from the map, correct detection of the dangerous events can always be obtained, even in a real-time scenario. Moreover, one of the main results of this work is having optimized performances setting a low f s , which opens to the possibility of using less costly devices. The proposed system is then reliable, simple and requires a low cost interrogator.