System and method for monitoring traffic using a distributed acoustic sensing model trained with video input

Abstract

A computer-implemented method is disclosed for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input. The method includes receiving DAS training data representing strain or strain rate along a fiber optic cable and video training data captured from a segment of road covered by the same cable. A machine learning-based object detection model (e.g., YOLOv11) is applied to the video data to generate vehicle attribute data labels, which are aligned with the DAS training data. A neural network model (e.g., UNet) is trained using the aligned data to associate DAS signal patterns with vehicle classification outcomes. The trained DAS model is stored in memory and subsequently applied to operational DAS data to detect and classify vehicles in real time, producing model output such as synthetic strain maps or detection maps. Once trained, the model functions without requiring operational video data.

Description

FRAMO-P050-WO SYSTEM AND METHOD FOR MONITORING TRAFFIC USING A DISTRIBUTED ACOUSTIC SENSING MODEL TRAINED WITH VIDEO INPUT STATEMENT OF PRIORITY

[0001] This application claims priority to U.S. Provisional App. No.63 / 663,951 for a Method for Monitoring Traffic Using Convolutional Neural Networks with Video Signals Over Distributed Fiber-Optic Sensing. BACKGROUND

[0002] Fiber optic seismology is a technique that utilizes fiber optic cables to record a seismic wave field. Seismic waves can be categorized as surface waves, which travel along the Earth’s surface, or body waves, which travel within the Earth’s interior. Surface waves can be caused by various sources in urban areas. They are interface waves that travel along the free surface, but due to a skin-depth effect are influenced by the elastic properties of the subsurface. They are generally larger in amplitude and slower than body waves. They decay more slowly with distance compared to body waves, as they spread cylindrically rather than spherically. The two main types of surface waves are Rayleigh waves and Love waves.

[0003] As fiber-optic cables are commonly installed underground alongside traffic roads, the weight of passing vehicles causes the subsurface to deform. This deformation affects the fiber-optic cable, resulting in a tiny yet measurable strain. As the car moves away from a certain point on the road, the changes in the strain field are recorded as a strain. The seismic waves that propagate as a result of vehicular activity carry energy mainly in quasistatic frequencies which are approximately < 1 Hz, and therefore the strain changes mainly correspond to this spectral band.

[0004] Thus, this technique involves the measurement of minuscule phase changes in the backscattered light traveling through the cable and converting it to directional strain along the fiber. This innovative method offers numerous advantages, such as dense spatial-temporal measurements, utilizing existing fiber infrastructure, and the ability to cover large distances with a single cable.

[0005] According to the present disclosure, this technology can be applied to monitoring traffic in crowded areas through measuring and analyzing the signals from the fiber optic cablesFRAMO-P050-WO that are commonly deployed for communication purposes. One significant technology that enables the sensitive and accurate measurement of the fiber-optic cables is Distributed Acoustic Sensing (DAS). By generating pulses at one terminal of the fiber and analyzing the back- scattered light from various points along the fiber, DAS technology is capable of converting standard fiber-optic cables into arrays of thousands of individual sensors, which are sensitive to the seismic wave-field generated by anthropogenic and natural activity around them.

[0006] The DAS measurement procedure involves setting specific temporal and spatial resolutions for sampling the fiber. This configuration results in a 2-D array output, where one axis represents time and the other axis represents distance along the fiber. Each spatial sampling point along the fiber is referred to as a channel.

[0007] DAS transforms standard telecommunication fiber optic cables into dense seismic arrays. The underlying sensing mechanism relies on Rayleigh backscattering, occurring due to minuscule changes in density and refractive index along the fiber. Through an optical interrogator unit (IU), continuous laser light is pumped into the fiber, and the backscattered light is measured.

[0008] There are two main approaches to implementing DAS. The first is Optical Frequency Domain Reflectometry (OFDR), in which the backscattered pulse is analyzed in the frequency domain, and Optical Time Domain Reflectometry (OTDR), in which it is analyzed in the temporal domain. Among the OTDR methods, a phase OTDR (Φ − OT DR) estimates the phase of the backscattered signal by interferometry. This is a useful property as the phase change of the backscattered light is quasilinearly proportional to directional strain, or strain-rate, along the direction of fiber. The Φ − OT DR sensing method, used in the present disclosure, provides very high spatial (in the order of meters) and temporal (in order of KHz) resolution. A single IU can cover distances of tens of kilometers and more. In addition, the instrument response is very broadband, spanning about 17 octaves. Finally, DAS technology allows to re-purpose existing telecommunication infrastructure, significantly reducing efforts and costs of instrument deployment. For these reasons, DAS is well-suited for a variety of applications.

[0009] The ubiquity of existing fiber optic infrastructure in urban areas and its deployment mainly along roads makes it ideal for DAS-based traffic monitoring. Generally, the imprint of the vehicle weight, whose frequency content is <1 Hz, is used for traffic monitoring,FRAMO-P050-WO as opposed to other DAS applications that utilize wider frequency bands. Roadside DAS can, in general, provide valuable insights into traffic flow, vehicle classification, and road condition assessment. DAS has several advantages over existing monitoring approaches, which are typically vision-based, include pavement sensing, or rely on mobility (GPS) data. DAS data are intrinsically anonymous and preserve privacy, as opposed to cameras or mobility data. They are also complete as they do not depend on weather conditions or mobile phone access and data sharing permissions. The fiber infrastructure is entirely passive, maintained by telecommunications operators, and unlikely to be targeted by vandalism. With the increasing demand for smart city monitoring and efficient transportation management, the long-range sensing potential of DAS, given adequate fiber routing, makes it a cost-effective solution, as opposed to the linearly increasing cost of cameras or pavement sensors.

[0010] The majority of traffic monitoring studies using DAS focus on identifying and categorizing various vehicle types, including cars, trucks, and buses, leveraging standard optical fiber infrastructure for traffic monitoring. In addition to traditional signal and image processing approaches, recent progress in the field has seen the implementation of deep learning techniques, particularly convolutional neural networks (CNNs), to analyze DAS patterns and enhance vehicle classification accuracy. Methods such as U-Net architectures segment DAS waveform data into discernible vehicle paths, providing high-resolution, real-time monitoring across extensive distances. These methods can achieve vehicle identification accuracy rates exceeding 97% under controlled conditions, demonstrating significant potential for high-performance traffic monitoring applications.

[0011] Nonetheless, challenges persist particularly around data labeling, which is often time-consuming and subjective, complicating the application of fully supervised learning methods. This has led researchers to turn to synthetic dataset generation, simulating DAS signals to supplement labeled data and facilitate model training. However, synthetic datasets cannot fully encapsulate the complexity of real data which depends on variable fiber coupling, subsurface geology, imprecise fiber location, noise conditions, fiber geometry, vehicle type and model, and more. Consequently, unsupervised and self-supervised learning approaches have also been explored to address these limitations, though accuracy remains a challenge as these methodsFRAMO-P050-WO struggle with capturing complex noise and diverse vehicle trajectory patterns in dynamic settings.

[0012] The present disclosure improves the effectiveness of DAS technology in urban traffic monitoring, particularly in densely populated areas where vehicle density, lane complexity, and infrastructure constraints pose significant challenges to conventional monitoring systems. While existing DAS applications have demonstrated utility in detecting vehicular movement by capturing seismic strain patterns through roadside fiber-optic cables, their deployment is limited by the need for extensive calibration and the lack of labeled ground-truth data. The present solution addresses these limitations by introducing a novel training methodology that leverages video-based object detection systems, such as YOLO, to generate labeled data for training DAS-based neural networks. This approach allows DAS to inherit the labeling power of computer vision without requiring long-term reliance on video or violating privacy.

[0013] Specifically, the system employs camera-based object detection and classification to annotate vehicle passages during an initial DAS model training stage, aligning visual observations with DAS strain-rate signals. Once trained, the system can operate solely on DAS input, enabling large-scale, privacy-preserving monitoring without the need for ongoing visual data. This hybrid strategy effectively bridges the gap between rich but privacy-sensitive visual information and anonymous but unlabeled DAS signals. By combining these data sources during training, the present disclosure provides a scalable solution that reduces labeling costs, enhances classification accuracy, and improves the spatial interpretability of DAS signals across complex urban environments. Figure 1 illustrates the dual-stage approach, showing how the system transitions from a supervised visual+DAS training phase to a fully DAS-only inference phase. SUMMARY

[0014] Distributed Acoustic Sensing (DAS) has emerged as a powerful tool for real-time traffic monitoring in densely populated areas, offering high spatial and temporal resolution with minimal infrastructure requirements and ease of use. Growing demand for long-distance DAS measurements, in conjunction with the development of efficient algorithms for data processing,FRAMO-P050-WO has led to increased interest in the technology from both industry and academia. Machine- learning-based data processing, however, necessitates tedious calibration experiments that require significant effort and resources. Processing real DAS data generally requires both temporal and spatial calibration with respect to the objects moving above the surface near the fiber. When fiber location documentation is missing or outdated, spatial calibration becomes a significant challenge that has not yet been addressed with a fully automatic solution.

[0015] To solve this calibration challenge, the disclosers present a novel geophysics- driven approach enhanced by computer vision, signal processing, and gradient-based optimization. This approach offers a solution for the spatial calibration of a fiber with its surrounding environment, specifically aiming to determine the fiber’s sampling locations with an accuracy of no more than five meters from the actual fiber placement, while ensuring that the solution remains physically feasible. The present disclosure also introduces a method that integrates DAS data with co-located visual information. According to some embodiments, YOLO-derived vehicle location and classification data from camera inputs are used as labeled training data to train a neural network that can operate on DAS data alone. The resulting model achieves performance exceeding 94% for detection and classification, with a false alarm rate of approximately 1.2%. The system’s performance is demonstrated over a week-long traffic monitoring deployment, yielding statistical insights that may benefit future smart city developments. The present disclosure demonstrates the potential of combining fiber-optic sensing with visual information, with an emphasis on practicality, scalability, privacy protection, and minimized infrastructure costs to train a traffic monitoring DAS model.

[0016] Therefore, based on the foregoing and continuing description, the subject invention in its various embodiments may comprise one or more of the following features in any non-mutually-exclusive combination:

[0017] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising receiving, by a processor, DAS training data representing strain or strain rate along a fiber optic cable;

[0018] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising receiving, by theFRAMO-P050-WO processor, video training data from a training camera co-located with at least a portion of the fiber optic cable;

[0019] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising applying, by the processor, a machine learning-based object detection model to the video training data to generate vehicle attribute data labels;

[0020] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising aligning, by the processor, the vehicle attribute data labels with corresponding portions of the DAS training data in space and time;

[0021] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising training, by the processor, a neural network model using the aligned DAS training data and vehicle attribute data labels to associate DAS signal patterns with vehicle classification outcomes, thereby producing a trained DAS model;

[0022] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising storing the trained DAS model in a memory;

[0023] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising applying, by the processor, the trained DAS model to operational DAS data received from the fiber optic cable to detect and classify vehicles;

[0024] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising outputting, by the processor, model output comprising vehicle detection or classification results based on the operational DAS data;

[0025] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, wherein the trained DAS model can generate model output without input of operational video data;FRAMO-P050-WO

[0026] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the model output comprises a synthetic strain rate map generated using vehicle attribute data labels and a physical fiber layout model;

[0027] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the synthetic strain rate map is computed from a video tensor associating detected vehicles with their estimated mass and 3D location and a fiber object associating DAS sampling channels with 3D coordinates; and

[0028] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the synthetic strain rate map is generated from video training data recorded concurrently with the DAS training data and is used for fiber localization by comparison to the DAS training data.

[0029] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the model output comprises a synthetic image of the operational DAS data projected onto a synthetic strain rate map, the synthetic image depicting a classified vehicle as a time-varying strain pattern mapped to a spatial layout of the fiber optic cable; and

[0030] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the synthetic strain rate map is generated from video training data recorded concurrently with the DAS training data and is used for fiber localization by comparison to the DAS training data.

[0031] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the DAS training data comprises phase-shift measurements sampled at regular intervals along the fiber optic cable.

[0032] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the machine learning-based object detection model is a convolutional neural network trained to detect multiple vehicle classes.

[0033] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein applying the object detectionFRAMO-P050-WO model to the video training data further comprises detecting and tracking objects across video frames using a pre-trained object detection model;

[0034] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein applying the object detection model to the video training data further comprises interpolating missing object locations in frames where detections are absent using tracked object identifiers; and

[0035] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein applying the object detection model to the video training data further comprises assigning a consistent classification label to each tracked object based on the most frequently predicted class across frames.

[0036] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises determining a homography between ground-plane vehicle positions derived from the video training data and DAS signal locations within the DAS training data.

[0037] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the homography is refined by minimizing a calibration loss function comprising a Dice loss and a regularization term penalizing spatial discontinuity.

[0038] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the homography is further constrained using a physical fiber layout model representing the geometry of the fiber optic cable.

[0039] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the physical fiber layout model enforces continuity and curvature constraints on the homography alignment.

[0040] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises performing a spatio-FRAMO-P050-WO temporal calibration comprising striking the ground at a plurality of anchor locations along the fiber optic cable;

[0041] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises performing a spatio- temporal calibration comprising recording DAS responses at each strike; and

[0042] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises performing a spatio- temporal calibration comprising aligning DAS channels to world coordinates using a projection matrix and an assumed fiber burial depth.

[0043] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises applying a machine learning-based object detection model to the video training data to detect and classify moving objects;

[0044] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises discarding static objects that do not produce DAS signal patterns;

[0045] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises identifying, for each detected object, a location along the fiber optic cable that minimizes a distance metric relative to DAS signal channels;

[0046] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises generating a detection map representing a probability distribution over time and fiber location using a Gaussian envelope function; and

[0047] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attributeFRAMO-P050-WO data labels from the video training data comprises normalizing the detection map using a softmax activation function.

[0048] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises preprocessing the DAS training data using decimation and two- dimensional FK filtering to reduce noise and enhance signal quality;

[0049] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises generating vehicle attribute data labels from the video training data by:

[0050] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises generating vehicle attribute data labels from the video training data by applying a machine learning-based object detection model to track and classify moving vehicles;

[0051] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises generating vehicle attribute data labels from the video training data by removing static objects not expected to produce DAS signal patterns; and

[0052] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises generating vehicle attribute data labels from the video training data by interpolating missing detections based on tracking continuity;

[0053] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises computing a homography matrix to transform detected vehicle positions from image coordinates to a three-dimensional coordinate system aligned with the fiber optic cable;

[0054] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein generating the vehicle attribute data labels from the video training data comprises refining fiber alignment using a calibration optimization process implemented via stochastic gradient descent.FRAMO-P050-WO

[0055] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the DAS training data is preprocessed prior to training the neural network model.

[0056] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the preprocessing comprises applying a median filter.

[0057] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the preprocessing comprises applying a low-pass filter.

[0058] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the preprocessing comprises applying a two-dimensional FK filter.

[0059] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the neural network model is trained using a cross-entropy loss.

[0060] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the neural network model comprises a convolutional neural network with a UNet architecture.

[0061] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises applying a manifold smoothness constraint on directional gradients of the model output.

[0062] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the trained DAS model is operable without access to operational video data.

[0063] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the model output is aggregated over time intervals and fiber segments to generate a map-based traffic report.FRAMO-P050-WO

[0064] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising augmenting the DAS training data by randomly dropping vehicle attribute data labels.

[0065] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising augmenting the DAS training data by injecting simulated Gaussian noise.

[0066] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the fiber optic cable location is automatically calibrated without manual annotation of a physical fiber layout model.

[0067] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the automatic calibration optimizes a predicted fiber path under physical constraints of curvature and continuity defined by the physical fiber layout model.

[0068] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising estimating vehicle speed based on the temporal progression of detected vehicle locations within the operational DAS data.

[0069] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the speed estimation is corrected using alignment parameters derived from calibration between the video training data and the DAS training data.

[0070] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the model output comprises a detection map including a class probability vector at each position and time window along the fiber.

[0071] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the class probability vector comprises a confidence score representing the likelihood of a vehicle classification outcome.

[0072] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the outputting step furtherFRAMO-P050-WO comprises filtering model output using a confidence threshold derived from the class probability vector.

[0073] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the trained DAS model is configured to detect the presence of a vehicle without determining a vehicle classification.

[0074] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein the vehicle attribute data labels comprise at least one of a vehicle location, a classification label, a bounding box, or a timestamp.

[0075] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising applying, by the processor, the trained DAS model to operational video data received from an operational video camera co- located with at least a portion of the fiber optic cable to detect and classify vehicles; and

[0076] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising outputting, by the processor, model output comprising vehicle detection or classification results based on the operational DAS data and the operational video data.

[0077] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising initializing fiber optic channel locations for alignment using a pre-optimization procedure that iteratively evaluates candidate fiber positions along a perpendicular axis relative to the road direction, wherein the initialization maximizes a normalized cross-correlation between simulated strain rate maps and processed DAS training data.

[0078] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising refining the initialized fiber optic channel locations using a gradient-based optimization process comprising generating simulated strain rate maps based on vehicle distances from candidate fiber positions; and

[0079] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input comprising refining the initialized fiber optic channel locations using a gradient-based optimization process comprising minimizing aFRAMO-P050-WO composite loss function comprising data fidelity and physical regularization terms, including constraints on channel spacing integrity and path continuity.

[0080] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises augmenting the DAS training data by performing horizontally flipping DAS training data windows;

[0081] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input wherein training the neural network model further comprises augmenting the DAS training data by performing vertically flipping DAS training data windows.

[0082] A traffic monitoring system comprising a non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform the method of any of claims 1–37.

[0083] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising receiving, by a processor, DAS training data representing strain or strain rate along a fiber optic cable;

[0084] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising receiving, by the processor, video training data from a training camera co-located with at least a portion of the fiber optic cable;

[0085] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising applying, by the processor, a machine learning-based object detection model to the video training data to generate vehicle attribute data labels;

[0086] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising aligning, by the processor, the vehicle attribute data labels with corresponding portions of the DAS training data in space and time;

[0087] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising training, by the processor, a neural network model using the aligned DAS training data and the vehicle attribute data labels toFRAMO-P050-WO associate DAS signal patterns with vehicle classification outcomes, thereby producing a trained DAS model;

[0088] A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising outputting the trained DAS model, wherein the trained DAS model is configured to generate model output based solely on operational DAS data, without requiring operational video data.

[0089] A traffic monitoring system trained according to the method of claim 47, the system comprising a fiber optic cable configured to generate DAS data representing strain or strain rate along a spatial path;

[0090] A traffic monitoring system trained according to the method of claim 47, the system comprising a processor operatively coupled to a memory storing a trained DAS model;

[0091] A traffic monitoring system trained according to the method of claim 47, the system wherein the trained DAS model is configured to receive, as input, operational DAS data sampled from the fiber optic cable;

[0092] A traffic monitoring system trained according to the method of claim 47, the system wherein the trained DAS model is configured to generate model output comprising vehicle detection or classification results based solely on the operational DAS data;

[0093] an output module configured to generate a time-resolved detection map indicating vehicle classification outcomes over the monitored area.

[0094] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, wherein the video training data is received from more than one training camera, each training camera co-located with at least a portion of the fiber optic cable.

[0095] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, wherein the training step further comprises training, by the processor, the neural network model using the aligned DAS training data, vehicle attribute data labels, and localization information from GPS, wherein a Kalman filter is applied to fuse the GPS data with the video training data and DAS training data to improve alignment, thereby producing a trained DAS model that associates DAS signal patterns with vehicle classification and location outcomes.FRAMO-P050-WO

[0096] A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, wherein the trained DAS model is configured to operate in real-time by processing incoming operational DAS data continuously to generate vehicle detection or classification results. DESCRIPTION OF THE FIGURES

[0097] Figure 1. Illustration of proposed approach. Right: the training stage, involving DAS and camera recording simultaneously. The camera and camera view lines represent the computer vision detection and classification algorithm for each of the objects. Left: the optimization-test stage or operational mode, involving only DAS, in which the disclosed algorithm learns to detect, classify, track, and estimate the location of each of the objects through use of the model and fiber optics data. Any moving object which is not part of the defined classes set is considered as noise and filtered out.

[0098] Figure 2. Strain rate in the Quasistatic approximation (constant time). (I) Each point along the fiber (light grey) aggregates phase-shift contributions from all objects (denoted as Xi), S(li) represent the point associated with this object along the fiber. (II) DAS recordings of the strain-rate (solid line) and Gaussian probability distributions to detect an object at different locations (dashed line).

[0099] Figure 3. Comparison between the camera and the DAS . (I) First frame of the scene, with 3 labels: 2 cars and a single bus. The dotted line represents the estimated location of the fiber (based on the calibration process). (II) Last frame of the scene, with 4 labels: 3 cars and a bus. (III) Recorded DAS data after pre-processing. (IV) Generated labels from camera. (V) The output of the model based on DAS only.

[0100] Figure 4. Use-case analysis of the model’s performance. (I) 5-frame sequence and its labeling with rectangular boxes. (II) The DAS recording in this time interval (model input). (III) Labeling from visual input (YOLO). (IV) DAS model output results. the disclosers consider vehicles 1-6 as success cases, and vehicle 7 as a failure case.

[0101] Figure 5. The detection map of a single class. A successful example of the smoothing post-processing stage. However, as seen, not all the lines were detected.FRAMO-P050-WO

[0102] Figure 6. Collecting statistics for smart city applications - vehicles counting throughout the week. (I), (II), (III), and (IV) represents Wednesday, Thursday, Friday and Saturday, respectively.

[0103] Figure 7.2 Minutes of DAS Data Before and After Processing.

[0104] Figure 8. Example of the smoothing post-processing stage.

[0105] Figure 9. Four statistical measurement over all the buses for an entire day, on Wednesday, March 22, 2023.

[0106] Figure 10. Four statistical measurement over all the cars for an entire day, Wednesday, March 22, 2023.

[0107] Figure 11. The speed of vehicles on Wednesday, March 22, 2023, throughout the day on the road.

[0108] Figure 12. Flattened System Design.

[0109] Figure 13. DAS output post decimation and pre-F-K filtering. Blue (black / dark grey) pixels represent lower values, as red (lighter grey) pixels represent higher values

[0110] Figure 14. DAS output post F-K filtering. Blue (black / dark grey) pixels represent lower values, as red (lighter grey) pixels represent higher values

[0111] Figure 15. DAS based strain map. Values are between [0,1]. Blue (black / dark grey) pixels represent lower values, as red (lighter grey) pixels represent higher values.

[0112] Figure 16. Estimated fiber optic channels projected locations.

[0113] Figure 17. Post initialization fiber optic channels projected locations.

[0114] Figure 18. Fiber optic channels projected locations before and after optimization process.

[0115] Figure 19. Fiber optic channels 3D locations after optimization process.

[0116] Figure 20. Video based generated strain map with guessed fiber channels locations.

[0117] Figure 21. Video based generated strain map with estimated fiber channels locations after optimization.

[0118] Figure 22. Convergence graph for the first 100 epochs, showing a rapid decrease in loss.FRAMO-P050-WO

[0119] Figure 23. Post-100 epoch convergence graph, showing stabilization of the convergence point despite the cosine with restarts annealing method.

[0120] Figure 24. Manual vs. automatic calibration. Manual calibration channel locations are in black, and automatic calibration channel locations are in white.

[0121] Figure 25. Fiber channel locations for the two runs. Results from the 9-minute scene (with buses only) are shown in dark gray, and results from the 1-minute scene are shown in white circles. As reference, manual calibration is depicted in white squares.

[0122] Figure 26. Schematic of an embodiment of a traffic monitoring system.

[0123] Figure 27. Schematic of an embodiment of a method of monitoring traffic.

[0124] Figure 28. Schematic of an embodiment of a method of training a DAS model using video input. DETAILED DESCRIPTION

[0125] DAS Measurements

[0126] Moving vehicles generate a seismic wavefield that comprises two major components. The first is the quasistatic (<1 Hz) signal, resulting from subsurface deformation due to loading by the weight of the vehicle. The second is the dynamic component which is due to seismic waves, mostly surface waves, generated by wheel-road interactions due to roughness of the road, especially bumps. These are generally observed in a frequency range of 2-20 Hz, but the exact values vary. Previous studies

[0015] ,

[0043] , [2] show that the Flamant-Boussinesq approximation adequately describes the instantaneous quasistatic deformation of the subsurface caused by an ideal point load at a given location. According to this approximation, the displacement along the x direction, ux, of a point x, y, z in the subsurface, as a response to a point load at the origin, is: (1).

[0127] The symbols in this equation are:FRAMO-P050-WO

[0128] x, y, z are spatial coordinates in 3-D space of the point at which the displacement is measured. The disclosers define the x axis to be along the direction the fiber-optic cable, the y axis complements it along the surface, and z is the perpendicular depth beneath the surface.

[0129] is the distance between the point load location and the location of the measurement.

[0130] F is the force applied by the point load on the ground.

[0131] G is the shear modulus of the ground, assumed to be homogeneous.

[0132] ν is Poisson’s ratio of the medium, assumed to be homogeneous.

[0133] DAS Measurements: In Φ−OT DR, the measured phase changes are quasilinearly related to strain or strain-rate along the direction of the fiber. The interferometric nature of the measurement is such that the phase difference, and thus strain, is computed over a subset of the array called a gauge length, and whose size is typically several to tens of meters. Given a gauge length L, the quasistatic field induced by a vehicle and recorded by DAS will thus be the spatial derivative of the average displacement along the direction of the fiber (Eq.1), computed over the gauge length L. In practical terms, the DAS system measures the strain (or strain-rate) along the fiber rather than directly measuring the displacement ux. Additionally, the measurements are not taken at individual points along the cable, but represent an average over a certain distance known as the gauge length

[0013] , denoted as L. Consequently, the recorded response captured by the DAS system should be modeled as a spatial derivative of the average displacement along the gauge length of Eq. (1): .was optically configured to measures the strain rate, the response of the medium should actually be differentiated with respect to time as well. The response of the fiber strain rate to a point load at the origin is thus: (3).FRAMO-P050-WO

[0135] The DAS measurement procedure involves setting specific temporal and spatial resolutions for sampling the fiber. This configuration results in a 2-D array output, where one axis represents time and the other axis represents distance along the fiber. Each spatial sampling point along the fiber is referred to as a channel.

[0136] The disclosers emphasize that vehicles are accurately described by a multi-point loading, applied at the points of contact of the wheels with the surface. The total recorded signal is thus a linear combination of several point loads, and multipole expansions of this equation are necessitated

[0051] .

[0137] In practice, setting up the IU involves setting specific temporal and spatial resolutions for sampling the fiber. According to some embodiments, DAS systems allow the control of the gauge length, but it is fixed in the IU of the present disclosure; however other embodiments are envisioned. Acquired data are thus 2-D, with [time, distance along the fiber] dimensions. The disclosers refer to each spatial sampling point along the fiber as a channel. It is important to note that the channel spacing differs from the gauge length, and refers to the distance between successive measurement points. In this study, the disclosers use a channel spacing of 1m, and a gauge length of 10m.

[0138] Camera model

[0139] The present disclosure defines a general world coordinate system and an object i, such that the object’s (vehicle) location is then represented by a three-dimensional vector Xi related to the origin of the axis. Adopting the common pinhole camera model, the disclosers then can define the projection matrix P, which represents the mapping between the object three three- dimensional world location to its two-dimensional image location in pixels xi

[0045] . Namely, for any object i: xi = PXi. Mathematically, it is convenient to represent the fiber location as a 3D curved line S and to parameterize it by the length parameter l, such that S(l) is a 3D point along the fiber, with distance l from its beginning. Similarly, the 2D camera projection of the fiber is s(l) = PS(l).

[0140] The distance function between the fiber and object is given by: d (Xi, F(s)) = | | Xi− S(l) | |2= | | P−1(xi− s(l)) | |2(4).FRAMO-P050-WO

[0141] In general, the projection matrix is not invertible because it projects from 3D to 2D (any point xi, s(l) can be back-projected to a line instead of a point). However, the disclosers assume that the surface of the road can be represented as a 2D plane. In this case, the mapping between pixels and true location can be represented by an homography transformation

[0046] .

[0142] Strain-rate map model: the disclosers introduce the concept of the strain-rate map as an extension of equation 3 as function of time t and distance along the fiber l: ,Namely, ρ is the local contribution of each possible loading point, in space and time, to the phase shift measured at a certain distance along the fiber, dV = dx * dy * dz, and all other values are as previously defined. It is noteworthy that by approximating the scene as occurring on a 2D plane, the disclosers can redefine the volume integral as a surface integral. If the subsurface properties are approximately constant along the fiber, the disclosers can also neglect the spatial dependence of the density function on G and ν. In addition, the disclosers also assume that the fiber installation depth is constant and that the fiber is deployed in parallel to the road, simplifying that x ≈ l. Whereas the last assumption is not necessarily correct for every point along the fiber trajectory, it is crucial because the disclosed study utilizes a spatially invariant model. Nevertheless, the disclosers later discuss a method to relax this assumption wherein other embodiments are envisioned. Under these assumptions, the density function becomes: (6),

[0144] with d = d(⃗r, S(l)) the distance between the loading and measurement points. the disclosers further assume a discrete number of loading points: ,ci, from the fiber, class type, time, and the location along the fiber, respectively. By transitioning from the variable force F to the classFRAMO-P050-WO number ci, the disclosers effectively categorize the objects into distinct equivalence classes, each identified by a class label. It should be noted that this approach is an approximation, as it treats different forces and thus vehicle weights within the same class as indistinguishable.

[0146] Substituting into 5: ,. However, the disclosers assume Figure 2 (I) illustrates the above model, in which the phase shift at time t and distance along the fiber l is the sum of the contributions from every loading point along the road. The contribution to the phase shift is determined by the location of each object and its weight, approximately represented by the object class, and can be expressed using the analytical expression introduced herein. However, the disclosers are interested in the probability distribution to detect an object at a specific location and time. Therefore, instead of the analytical solution, the disclosers associate a Gaussian probability distribution to the point along the fiber that is nearest to the object S(li). Figure 2 (II) shows the Gaussian probability distribution (dashed) associated with each point along the fiber S(li), and its comparison with the real DAS recording data (solid).

[0148] The disclosers choose not to use the analytical model directly as it contains many assumptions that may not be realistic in a real-life scenario - homogeneity of subsurface parameters, no influence of the precise car position along the road / lane, fiber installed parallel to the road, and accurate representation of a vehicle by a single point load. Whereas a full inversion approach may be theoretically possible, the disclosers opt for a simpler, more robust approach that does not depend on many unknown parameters.

[0149] Method

[0150] 1) Detection map: Similarly to 5, the disclosers define another function D(t, l) for any set of object classes C = {c1, c2, ..., cN } (e.g. cars or trucks). This function specifies, at time t and distance along the fiber l , the probability that DAS sensed each of the objects in the class, including the zero object of noise only. The disclosers can formulate it as:FRAMO-P050-WO .use a deep learning model T to learn the map between the phase-shift function and the detection map: (10).

[0152] Whereas this mapping can be conducted in various ways, the disclosers choose a UNET architecture [39, 21] to leverage the high spatio-temporal coherency offered by DAS. The training process follows a self-supervised regime in which the processing of visual data from the camera yields the ground truth detection map. the disclosers use the following loss function: .of the network training, the disclosers apply standard preprocessing to the DAS data to highlight physically meaningful signals. First, the disclosers apply a sample-by-sample and channel-by-channel median filter, which mitigates instrument noise and optical response variations along the fiber. Then, the disclosers apply low-pass filtering and down sampling to 30 Hz to match the visual sampling frequency and minimize computation time. Finally, the disclosers apply 2-D FK-filtering to maintain signals with phase velocities between 2 − 90 km / h and frequencies below 1 Hz, as this is the range of quasistatic signals excited by moving vehicles.

[0154] Experiment

[0155] Data Collection

[0156] The experiment was conducted for about a week at Klausner Street near the Tel- Aviv University in Israel. There is ample traffic to and from the university and a nearby science museum, including multiple regularly operating bus lines. Whereas DAS recording took place for a week, the disclosers recorded 9 hours (8AM - 5PM) of a weekday with a smartphoneFRAMO-P050-WO camera (Samsung Galaxy 23 Ultra) mounted on a tripod on top of a nearby university building, yielding a diagonal point-of-view (See Figure 3). The portion of the fiber along the road is approximately 350 meters long, with the camera covering approximately 80 meters of the road. The disclosers trained the model and assessed its performance using the section observed by the camera as the disclosers have ground truth labels, but apply the trained DAS network to the entire fiber. The dataset is accessible in

[0038] .

[0157] Spatio-temporal Calibration

[0158] While the disclosers had rough maps outlining the installed fiber’s path, the disclosers conducted a manual calibration process to accurately align the video recordings with the DAS measurements. This step is crucial as the disclosers assume perfect spatio-temporal synchronization between the fiber and the camera. For the calibration, the disclosers selected 80 reference anchors along the anticipated fiber path covered by the camera. Then, the disclosers struck the ground at these anchors with a hammer, recording the exact times and channels along the fiber where the impacts were most pronounced. To locate the fiber in the 3D world coordinate system, the disclosers used the projection matrix (as explained in II-B) and assumed, based on infrastructure maps, that the fiber is buried at 90 cm depth. The disclosed findings suggest that the fiber runs primarily parallel to the road and deviates by at most 1 m in the perpendicular direction. Throughout the experiment, the disclosers assume that the projection matrix remains constant thanks to the stability of the camera. Figure 3 schematically marks the fiber’s position along the street.

[0159] Data Annotation

[0160] To generate ground truth labels (vehicle attribute data labels) from the visual data, the disclosers use the YOLOv11 Ultralytics

[0024] algorithm on the recorded video. This algorithm can detect, track, and classify objects in the scene such as cars, trucks, buses, pedestrians, motorcycles, and more.

[0161] As used herein, a machine learning-based object detection model refers to a computer-implemented model trained using supervised or semi-supervised learning techniques to detect and classify objects in video frames. In certain embodiments, the object detection model can be a convolutional neural network (CNN) such as YOLO including YOLOv8 or YOLOv11,FRAMO-P050-WO configured to output object bounding boxes, class labels, and tracking identifiers for vehicles in a scene, although other models are contemplated.

[0162] In this study, the disclosers focus on three classes: cars (small vehicles), buses or trucks (large vehicles), and noise. the disclosers have also attempted to expand the disclosed model classes to trucks only and motorcycles. However, the results were unsatisfactory, mainly due to the uneven class distribution in the data (many more buses than trucks) and the poor DAS signal-to-noise ratio of motorcycles. After the detection, the disclosers filter out static objects, such as parked cars, as they do not generate any strain-rate signal.

[0163] Then, to annotate any object in the detection map, the disclosers use the Gaussian envelope of the phase-shift function, as depicted in Figure 2 (II). Practically, for each moving detected object Xi, the disclosers find the location among the fiber l∗ which minimizes the distance (see equation 4): (12).

[0164] This defines the detection lineDAS image. Then, the disclosers used a Gaussian filter to smear the probability of detection along time and space, represented by DAS channels. The Gaussian’s standard deviation was chosen to be around 1 / 12 seconds on the temporal axis and approximately 2.5 meters on the spatial axis, with both equating to 2-3 pixels. These parameters were chosen empirically and were highly correlated with the functional strain- rate shape, as can be seen in Figure 2 (II). Visually, it can be seen that they generally encapsulate the high-energy portion of the signal, but the disclosers again emphasize the approximate nature of this formulation.

[0165] Thus, the disclosers obtain a detection map D(t, l), as shown in Figure 3, which expresses the probability of detecting each of the objects. The probability is normalized between 0 to 1 and sums up to 1 among the channels, namely ||Dc(t, s)||1 = 1. The normalization is provided by the softmax activation function utilized in the UNet architecture’s output.

[0166] Training the Neural Network

[0167] The data were shuffled and divided into batches consisting 48 samples each, such that any sample covers approximately about 30 seconds. Next, the disclosers partitioned 70% of the data for training purposes, 15% for validation, and 15% to serve as a test set for which theFRAMO-P050-WO disclosers report final results. the disclosers perform augmentation on the training dataset by applying both horizontal and vertical flips. Horizontal flipping acts as a time reversal, whereas vertical flipping represents a spatial reversal, similar to flipping from north to south. This augmentation was done in order to minimize inherent biases in the data due to uneven lane usage and stronger signals for southbound traffic due to proximity to the fiber. The training process lasted 100 epochs, employing a learning rate of 0.001 and a weights decay coefficient of 0.001, incorporated inside the AdamW optimizing algorithm

[0033] . This algorithm combines the advantages of adaptive weight updates with regularization techniques to encourage better generalization and prevents over-fitting. Using AdamW, the disclosed aim is to strike a balance between efficiently updating the network weights based on the gradients and regularizing the model to improve its overall performance. To optimize the network, the disclosers employ the Cross Entropy Loss function, which allows one to effectively measure the dissimilarity between the predicted probabilities and the ground truth labels. The disclosers also tried to optimize the model using Dice loss, L1, L2, and Huber loss, but all yielded subpar results.

[0168] Score Metrics

[0169] To give an objective and independent metric to score the disclosed performance, the disclosers separate evaluation metrics for detection and classification, as derived in Appendix B. For any pair of detection maps D (labeled), and Dˆ (model output), the disclosers define: (13); and ,set. Additionally, the disclosers evaluated the Dice loss and the False alarm

[0022] . The Dice loss was proven effective for alignment tasks because it emphasizes the overlap between predicted regions and actual regions of interest. Table I shows a summary of the disclosed results, indicating the validity of the approach. Detection ↑ Classification ↑ Dice Loss ↓ False Alarm ↓FRAMO-P050-WO 94.2% 94.0% 0.581 1.28% TABLE I: Results summary of the model. The arrows indicate the direction of the better results.

[0171] Case-studies and Noisy Labeling

[0172] Utilizing visual-based algorithms such as YOLO for data labeling often introduces some noise. For example, some vehicles may be missed or improperly segmented during detection. Here, the disclosers analyze both the successes and failures of the model, which the disclosers find to be strongly correlated with the noisy labeling.

[0173] Figure 4 provides a detailed example showcasing results with 7 vehicles observed in a short time span of approximately 30 seconds. Most vehicles were correctly detected and classified by the model, but vehicle number 7, moving in the father lane from north to south, was entirely overlooked. An interesting event occurs with vehicle number 4, where the visual-based algorithm (YOLO) altered its classification across frames, but the model classified it as a constant class, indicating some ability of the disclosed network to deal with errors in the labeling. Another notable success is observed in point 3, where the DAS model effectively identified the bus over a greater distance than the vision-based algorithm (YOLO). It is also apparent that there is an additional green patch located between 1 and 4 in the model’s output, likely due to noise in the signal. Although this counts as an error in the loss calculation, it will not be regarded as an object since its area is too insignificant.

[0174] Empirical evidence shows that the model primarily underperforms when the SNR is very low, typically at the further lane from the fiber. Additionally, the training labels are often quite noisy, yet interestingly, the neural network occasionally manages to mitigate their negative effects and accurately detect and classify vehicles.

[0175] Manifold smoothness - Dealing with noisy labeling

[0176] To overcome noisy labeling consequences, the disclosers suggest adding a prior to the model’s output. The disclosers use a masked version of the total variation loss, working only along the 1-dimensional trajectory (1D manifold). The underlying idea is to reduce the gradients across each detection line, thereby motivating the model to favor ”smooth” configurations.: (15),FRAMO-P050-WO

[0177] while ∇M ≡ M(x, y) * ∇. Namely, for a given mask M, where M = 1 inside an arbitrary domain (1D trajectories in the disclosed case), and M = 0 anywhere else, ∇M calculates the directional gradient in that domain and ∇M = 0 anywhere else. To calculate M the disclosers used the well known Hough transform algorithm

[0018] . This loss function can be used as a regularizer during the training, or as a post-processing fine-tuning stage. In the disclosed tests, the disclosers limit ourselves to the case of post-processing stage: after the training process, the disclosers performed another fine-tuning training to minimize the LSmooth term. Qualitatively, the disclosers found that this approach leads to more reasonable results (e.g. it transforms any dashed or segmented line into a solid one), as can be seen in Figure 5, but that is also requires intensive manual calibration in tuning the Hough transform parameters. the disclosers leave room for improvement in this method to future studies.

[0178] Pre-Processing

[0179] In the preprocessing stage, raw data obtained from fiber optic sensors undergo several essential transformations to enhance its quality and extract meaningful information:

[0180] Multi-channel Median Filter - To reduce background noise, the disclosers use a median filter for each channel separately, namely, for each location along the fiber. This step increases the SNR of the DAS signal.

[0181] Temporal Low-pass Filtering and Downsampling - The raw data is recorded in very high temporal frequency (1Khz), while for the disclosed purposes the disclosers don’t need such high temporal resolution. Therefore, and to further attenuate high-frequency noise components, the data undergoes temporal low-pass filtering. Then, the disclosers downsample the data to match the same temporal resolution of the camera (in the disclosed case, 30Hz). This matching is not a must but the disclosers found it helpful in the calibration process and the algorithm.

[0182] FK Filter - The FK-filter is a spatio-temporal frequency filter which is necessary to filter-out the non-relevant spectral contents. This filtering technique enables the extraction the data which is not in the interval between velocity interval, typically for traffic is in the range of 2 km / h to 90 km / h. A visual example is shown in figure 7.

[0183] Metrics derivationFRAMO-P050-WO

[0184] For each pair D (label) and D̂ (model’s output) the disclosers define the following metrics:

[0185] Detection: - the disclosers considered a detection of an object as the probability to distinguish it well from noise. Therefore, the disclosers define the score as follows: (16); and (17).set. Note that this score is calculated pixel-wise, therefore, the disclosers also calculate the average over all the pixels. Explicitly: .It is important to note that guessing a consant value, namely P(Dp̂ = n) = α leads to a guessing score of: (19).than non- noise: P (Dp = n) > P (Dp = n)̄ and the disclosers get a maximum detection score by guessing α = 1, which leads to CDetection = Num of noisy pixels / Total number of pixels. Practically, this number varies between 0.5 to 0.8.

[0189] Classification: - the disclosers consider a classification score similar to the detection score, with a non-noise normalization factor: (20).FRAMO-P050-WO

[0190] Similarly, this score is done for any pixel in the image.

[0191] 3) Dice Loss: - The Dice loss is defined as follows: (21), wherefor D and Dˆ, respectively and for each class (except from noise). The sets are defined by the pixels that have higher probability distribution for this channel, indicating a class was detected. The threshold was tuned manually to be 0.5.

[0192] Manifold Smoothness (22).Namely, for a given mask M, where M = 1 inside an arbitrary domain (1D trajectories in the disclosed case), and M = 0 anywhere else, ∇M calculates the gradient in that domain and ∇M = 0 anywhere else. To calculate M the disclosers used the well known Hough transform algorithm. The process goes as follows:

[0194] For any detection map, the disclosers can create a threshold image of it (convert it to a binary image of 0 or 1, according to the detection probability for each channel). Then, on the thresholded image, the disclosers apply Hough Transform over the image to get a set of detected lines: wherein n is the number of detected lines in the image.line, the disclosers run from its starting point (x1,y1) to its final point (x2,y2) with a loop parametrized by a t parameter, and the directional gradient of the detection map D(x,y) is then calculated on each point along the line: ,wherein represents the unity vector along the line.

[0196] Lsmooth is given by accumulating the absolute value of all the directional gradients for each of the nnn lines, and averaging over all the lines in the image.FRAMO-P050-WO

[0197] Minimizing Lsmoothover the pixels domain, leads the detection map to be more smooth (in the directional gradient sense). the disclosers trained the detection map in an unsupervised way for 50 epochs with Adam optimizer and learning rate of 0.1. An example of the results can be shown in Figures 5 and 8.

[0198] Phase Pattern Statistics

[0199] Figures 9 and 10 present statistical information about cars and buses, respectively, for an entire day. Each statistical measure is derived from the phase shift recorded by the DAS: 1) The mean value represents the average phase shift. 2) The standard deviation quantifies the variation in the phase shift distribution. 3) The area denotes the count of pixels identified as an object. 4) The top 5 percent indicates the value at the 5% upper end of the distribution for each object.

[0200] Speed Statistics

[0201] Figure 11 shows an example of the speed distribution along a single day.

[0202] Building on the prior understanding that contours identified as vehicular objects often resemble tilted ellipses, the disclosers heuristically estimate the tilt angle by analyzing the standard deviations of pixel coordinates along both axes, σx and σy. The angle θ is calculated as: .

[0203] It isthe direction of travel, as the disclosed primary goal is to compute the speed. If distinguishing the driving direction is required, the tilt orientation can be determined from the pixel coordinates, with an angular adjustment of 90◦. The computed angle is then converted to velocity by applying units conversions that depend on the sampling rates in both the temporal and spatial axes, as well as reversing any resizing operations performed during the learning pipeline.

[0204] Automatic Calibration of DAS and Camera (FOS Calibration)

[0205] In the disclosed system and method, the disclosers leverage a DAS interrogator unit to capture seismic signals within its sensitivity range. The output of the interrogator unit consists of seismic signals recorded over a specific time period, presented as 2-D arrays. TheseFRAMO-P050-WO arrays exhibit spatial and temporal correlations between neighboring samples, allowing them to be interpreted as gray-scale images - depicting the real form of seismic interference in the fiber. Thus these arrays will serve as the ground truth labels of the disclosed project. On the other hand, utilization of computer vision techniques of depth estimation and object detection, combined with prior research and formulation of the strain caused by moving vehicles nearby the fiber - enables one to generate synthetic image of the DAS data. Obtaining similarity between the two images is essentially equal to unveiling the fiber’s trajectory as the strain formulas presented above embody the location of the fiber relatively to objects nearby the disclosed data consists of street scene video recordings that were conducted concurrently with DAS recording of a fiber that is located nearby the road. According to certain embodiments, the presently disclosed system can be described by the diagram in Figure 12 and can includes the following steps:

[0206] 1) Optic-Fiber Signal Filtering: The raw data obtained from the optic-fiber contains noise and irrelevant information. To prepare the input samples for the optimization process, decimation and F-K filtering are applied to enhance data quality and remove unnecessary information underlies in the recorded signal.

[0207] 2) Vehicle Tracking and Classification: A video camera is utilized alongside the DAS interrogator to record the scene simultaneously. To extract all objects from the recorded video frames, the widely recognized YOLOv8 model is applied for tracking and classification. However, in order to generate strain rate maps that align with the optic-fiber space required additional actions to be taken: a. Removal of still objects: YOLO detects all objects in the frame, while the DAS is sensitive to moving objects exclusively. Thus, standing objects must be removed to ensure consistency between the two datasets. b. Spatial Interpolation of missing detections: YOLO often missdetects objects. Since the disclosed method is highly dependent on the differentiability of information, the disclosers utilize the tracking mechanism of YOLO to interpolate detections in frames that they are missing. c. Class Interpolation: YOLO may classify the same object differently in different frames. For that cause the disclosers will take the most frequent classification that YOLO provides.FRAMO-P050-WO

[0208] 3) 2D to 3D projections - By setting a point in the scene as the origin, and gathering real distances along the scene, the disclosers calculate a homography matrix that can help transform each pixel in the frame into a point in Euclidean space. The DAS sampling points, that assemble the fiber trajectory, are also coupled with 3D locations that are relative to the origin.

[0209] 4) Strain Rate Map Generation: By posing the fiber sampling points, along with the detected vehicles in 3D space, the disclosers can use formulas (1), (2) and (3) help to calculate the approximated strain rate amplitude.

[0210] 5) Calibration Optimization - Using PyTorch platform for establishing computational graphs - it is possible to use variations of SGD to optimize the initial location estimated for the fiber. According to certain embodiments, the alignment between the video- derived vehicle positions and the DAS signal locations is further refined using a calibration optimization process. This process is implemented using a computational graph platform, such as PyTorch, and applies variations of stochastic gradient descent (SGD) to iteratively minimize a calibration loss. The optimization adjusts the estimated physical fiber layout to better align with observed DAS responses and video-derived object trajectories, improving the spatial correspondence between modalities.

[0211] DAS Signals Pre-Processing

[0212] The recorded fiber was situated adjacent to a dual carriageway accommodating various modes of transportation, including cars, buses, motorcycles, and pedestrians. Furthermore, within the recorded road segment, there exists a designated bus stop. To the best of the disclosed knowledge, the fiber’s alignment closely matches the direction of the road. These descriptions, together with additional factorssuch as fiber medium coupling, have a notable impact on the data. Since the disclosed primary objective was to detect and classify vehicular movements, the pre-processing steps employed were specifically tailored to facilitate this task. As mentioned before, the data the was captured by the disclosed DAS system is shaped as a matrix with one axis corresponds with time and the other with distance. The two axes are affected by the spatial sampling rate, that was determined to be 1m−1, and the temporal sampling rate, that was set to 1KHz. This temporal sampling rate is not necessary for the disclosedFRAMO-P050-WO research, as the relevant frequency band that carry vehicular movement signature are quasistatic. Thus, the data was down-sampled to 30Hz, containing frequencies up to 10Hz.

[0213] To eliminate signals that exhibit velocities inconsistent with vehicles and exclude waves with frequencies higher than 3Hz (2Hz for quasistatic waves with a safety margin), it is necessary to employ a two-dimensional filter. A one-dimensional filter alone cannot effectively address the underlying two-dimensional problem and fails to consider the signal speed along the x-axis. Thus, the disclosers utilized an F-K filter. F-K filtering involves the conversion of seismic data, typically represented in the time and displacement domain, into the frequency and wave number (F-K) domain. The seismic data is then subjected to filtering to eliminate undesired frequencies outside the desired seismic signal range. Subsequently, the data is converted back to the time-displacement domain. In simple terms, this filter consists of a two-dimensional Fourier transform, followed by a two-dimensional band-pass filter, and finally a reverse two-dimensional Fourier transform. The disclosed use of the F-K filter was tailored to capture the characteristics of the road monitored in the data acquisition experiment. Hence, the disclosers eliminated any signals with a wave number (K) greater than 0.045, and any velocity outside the range of [2.5, 25] m / s (corresponding to 9 − 90 km / hr). See figure 13 and figure 14 for a visualization of the FK filter’s impact on the disclosed DAS data, depicting 60 seconds of sampling over 90 channels.

[0214] Object Detection

[0215] One object of the disclosure revolves around the generation of synthetic strain rate maps that best resemble the DAS output data. Following the filter that was introduced previously, the disclosers aim to detect, track, and classify the vehicles in the scene in each frame. For that purpose, the disclosers utilized YOLOv8, a state-of-the-art computer vision pre- trained model that can perform all of the above tasks. When the disclosers apply the model, the disclosers document its results in a DB that includes the objects track ID, class and data regarding their location (in terms of pixels in the frame). Nevertheless, YOLOv8 has some drawbacks that can impair the strain rate map generations that were overcame as follows:

[0216] 1) Handling Still Objects - YOLO detects all of the objects in a frame, but since the DAS interrogator measures strain rate - still objects do not affect it and should be excluded from further calculations. Hence, an algorithm was developed that documents the data of movingFRAMO-P050-WO objects only by keeping an associative array that couples every tracked object with its previous locations. Only if the displacement between the current detected location and the previous one goes over some preset threshold - the data of the object will be documented.

[0217] 2) Missing detections - YOLOv8 often misses the detection of objects in some frames, resolving in discontinuity of the presence of vehicles in the processed data. This fault has fatal implications over the accuracy of the strain rate generation algorithm that the disclosers will later present, as continuity of the strain function is a necessary condition for its differentiability. To deal with this fault the disclosers utilize the YOLOv8 tracking mechanism; however, other suitable tools employing similar mechanisms are envisioned. For each tracked object (that has distinct track ID) the disclosers look for its first and last frame of appearance, and linearly interpolate its location in missing frames.

[0218] 3) Miss-classification - Despite its ability to track objects and even give them a distinct identifier, YOLOv8 may classify each object differently in each frame. Different classes (for example a private car versus a bus) have different mass that is later reflected in the disclosed calculations. To handle this fault the disclosers iterate over each of the tracked objects, identify the most frequent class that it was classified with, and then assign it to all of its instances in the detection DB.

[0219] Depth Estimation – Pixel to Euclidean Space Projections

[0220] Formulas (1), (2) and (3) depict the link between the spatial coordinates x, y, z and the strain rate. Hence the ability to pose both fiber and vehicles in relation to the same origin is crucial. The disclosed first task in that manner would be to pose the vehicles along the scene. Since the experiment was conducted with monocular filming, the homography matrix

[0052] was utilized to perform transformations from the pixel space to the Euclidean space.

[0221] The homography matrix is a 3x3 invertible matrix with 8 DoF and it is used to perform plane to plane transformations. In order to calculate it the disclosers had to provide real distance estimations of objects in the scene in relation to the origin. Moreover, it is worthy to note that the homography matrix construction is subjected to the assumption that the scene is approximately plane (i.e. all vehicles travel at z = 0).

[0222] Once the disclosers have the homography matrix, the disclosers apply it over each vehicle detection to project its location in the frame to a 3D location in the real scene.FRAMO-P050-WO

[0223] Strain Map Generation

[0224] A cardinal focus of the disclosed research was to generate the synthetic strain rate map out of a street scene video. Now that the disclosers have extracted all of the required information from the video the disclosers can formulate the following algorithm to calculate the strain rate map.

[0225] For that cause, the disclosers transform the information stored in the DB the disclosers have created into a tensor V T (video tensor) such that it couple each frame to the moving vehicles detected in it, and each vehicle is coupled to its approximated mass and location in the scene 3D space. In addition to that, the disclosers create a fiber-optic abstract object FO (fiber object) that couples each sampling channel with a 3D coordinate in the scene space.

[0226] The presently disclosed algorithm relies on the following formulation, and uses the tensor and fiber-optic object above to calculate the strain rate map: ,wherein T = .

[0227] Algorithm 1 Strain Rate Calculation Using Fiber Optic Locations and Vehicle Detections:

[0228] 1: Input: VT, FO

[0229] 2: Output: SR ∈ R|frames|×|channels|

[0230] 3: Initialize a strain map S ∈ R|frames|×|channels|and set its elements to 0.

[0231] 4: Assume each vehicle has a 3D location and mass coupled to it

[0232] 5: Begin:

[0233] 6: for each frame in VT do

[0234] 7: for each vehicle in the frame doFRAMO-P050-WO

[0235] 8: Transform vehicle 3D coordinates to fiber space coordinates (See Eq.1)

[0236] 9: for each channel in FO do

[0237] 10: s ← calcStrain(vehicle, channel) (Eq.2)

[0238] 11: S[frame, channel] ← S[frame, channel] + s

[0239] 12: end for

[0240] 13: end for

[0241] 14: end for

[0242] 15: SR ← (Eq.4)

[0243] 16: Return SR

[0244] Optimization

[0245] According to some embodiments, the disclosed system and methods optimize the coordinates x, y, z that are coupled to each channel. The optimizer is a compound unit, with two phases of optimization: initialization stage, responsible for choosing the best initial fiber optic channel locations; fine alignment optimization stage, responsible for optimizing channels locations and revealing the fiber’s trajectory and curvature.

[0246] Fiber Optic Locations Initialization

[0247] The presently disclosed empirical experience showed that not any guessed location of the fiber optic will converge to a reasonable location. The initialization has a great impact over the loss convergence and the integrity of the result. Hence, the disclosers developed a pre-optimization phase that is solely designated for choosing the best initial fiber optic channel locations. In this phase the disclosers use normalized cross-correlation to be the metric the disclosers want to maximize. Equivalently, the disclosers opt to minimize the term: (25).

[0248] In this phase the disclosers iterate over possible points that define the borders of initialization of the fiber optic. Since the road in the disclosed filming goes across the x axis of the frame, the disclosers iterate over the y dimension - initializing each time the fiber opticFRAMO-P050-WO locations and generate the strain map as if it was there. At the end of the iterative process the disclosers take the set of points that yielded the highest cross correlation with the DAS processed data.

[0249] Strain Rate Map Fine Alignment Optimization

[0250] The second stage of the disclosed optimizer focuses on the segmentation optimization of video-based generated strain maps, which are compared to DAS-based strain maps, treated as the ground truth. the disclosers use gradient based optimizer with annealing. Its forward step requires calculating the distances of each vehicle from the fiber and generation of a new video-based strain map. The disclosers define a set of regularizers and loss functions to guide the evaluation phase of the optimization process. A detailed explanation of these regularizers and loss functions is provided herein along with the optimizer configurations used.

[0251] Regularization: To impose a physical solution on the optimizer, the disclosers have designed two regularizers that are added to the loss function and should be minimized.

[0252] a) Integrity: The sampling channels along in the fiber space are 1 meter distant away from each other. This implies that the Euclidean distance between each two consecutive channels can be at most 1 meter. Hence if the disclosers denote (#channels − 1) and d .an upper bound for the regularizer. the disclosers denote the upper bound as ’UB’ and the lower bound as ’LB’. Therefore, in practice, the disclosers use the following formula: (27).

[0254] b) Smoothness: To get reasonable fiber trajectory in terms of curves, the disclosers define another regularizer denoted as Rsmoothness. To calculate Rsmoothness the disclosers use Frenet–Serret formulas which can be used to describe the behavior of a spaceFRAMO-P050-WO curve. One of Frenet-Serret formulas’ parameters is κ which represents the curvature (measures how sharply the curve bends). κ depends on the tangent unit vector T. If the disclosers denote the arc length as s the disclosers get that κ is given by: (28); and (29).disclosed purposes, the disclosers can simply set κ to be the Laplacian of the fiber’s channels locations: (30).radius of curvature denoted as ρ and given by: . the disclosers want to limit ρ by preset threshold. This limitation implies component of Rsmoothness regularizer which the disclosers formulate as follows: (31).the disclosers can now formulate the regularizer: .use coefficients for each component to control the regularizers influence. To simplify the formulation the disclosers exclude them from the formulas.FRAMO-P050-WO

[0259] 2) Loss: In the strain map fine alignment optimization stage, the disclosed objective is to align the synthesized video-based strain maps with the structure of the ground truth strain maps derived from DAS data. On top of the normalized cross-correlation, the disclosers have found that Dice loss is particularly well-suited for this alignment task due to its focus on the overlap between predicted and ground truth regions of interest. The disclosers define a threshold that can discriminate regions with high absolute value of strain rate amplitude. the disclosers define the set of elements that surpassed the threshold in the predicted array as A and the corresponding set of elements in the ground truth as B. Then the Dice loss is formulated as follows: , where

[0260] However, the disclosers encountered some challenges during the disclosed empirical experience. Specifically, synthesized data can include outliers from incorrect detection of moving vehicles, while ground truth data may contain noise not present in the synthesized data. To deal with these challenges the disclosers use Huber loss which reduce the influence of outliers without giving them too significant attention, but also has a continuous and smooth gradient. The Huber loss is defined as: (34).

[0261] Automatic Calibration of DAS and Camera Results

[0262] We show the results of the proposed system for DAS and camera calibration. The scene takes place on a two way straight road. The road does not have significant turns, ups and downs. The camera has been set on a roof of a nearby building so there is a large distance and an angle between the camera and the road. The entire scene is about 20 minutes long, but we are going to focus on only 1 minute. Our use-case involves 2 buses driving in opposite directions (on different lanes) in different times (the camera doesn’t capture the moment they pass by eachFRAMO-P050-WO other). This is emphasized because, based on Equations 1-3, driving in different lanes is essential to avoid obtaining a symmetric solution, as the single-lane problem lacks convexity. The present disclosure demonstrates that this one-minute segment provides sufficient data to accurately estimate the fiber locations.

[0263] DAS Signals Pre-Processing

[0264] After decimation and activating F-K filtering over the DAS data, the disclosers get the strain map shown in figure 15. As expected, the disclosers can see that at each channel, there are rise and fall of the strain rate values when the vehicle passing by the channel.

[0265] Fiber Optic Locations Initialization

[0266] The disclosers use YOLO to detect and track vehicles of the scene. Then the disclosers generate synthesized strain map based on the video. the disclosers start from guessed locations and run the initialization process to get better approximation of the initial fiber locations.

[0267] Strain Rate Map Fine Alignment Optimization

[0268] After initializing the approximate channels locations, the disclosers then optimized the locations to get better estimation of the fiber structure and curvature. The disclosers ran the second stage of the disclosed optimizer with the following parameters: • Learning rate: 0.1 • Epochs: 2000 • Cosine annealing that reaches 0.001 with restarts every 200 epochs • Integrity regularizer upper bound: 1.02 [m] • Integrity regularizer lower bound: 0.75 [m] • Regularizers coefficients: 5.0 • Loss functions coefficients: 1.0.

[0269] This configuration allows significant changes in the segmentation map while maintaining the physical integrity of the solution. Visualizations of the results can be seen with respect to figures 18 – 21. Figures 18 and 19 present the final estimation of the fiber locations, showing that the optimizer successfully captured the fiber’s curves. Figures 20 and 21 illustrate the significant changes in the generated strain map, which is now aligned with the DAS-based strain map at figure 15.FRAMO-P050-WO

[0270] Automatic Calibration of DAS and Camera Evaluation

[0271] The results were evaluated using four methods: convergence of the segmentation alignment, channel locations comparison with manual calibration, loss comparison with manual calibration and a field tour with the infrastructure project manager from Tel Aviv University.

[0272] a) Convergence Graph: The convergence graph shows a rapid decrease in loss over the first 100 epochs. Due to the annealing strategy the disclosers employed, the convergence point shifts slightly until stabilizing. The loss, which includes the loss functions and regularizers presented at V-B2 and V-B1, decreases significantly, from 13.4 to 0.63, indicating a high degree of alignment between the two strain maps.

[0273] b) Fiber Locations Comparison with Manual Calibration Results: A comparison with manual calibration demonstrates that the automatic calibration not only closely aligns with the manual results—showing an average distance difference of approximately 1.8 meters—but also provides more granular details. Figure 24 illustrates the projected locations from both methods.

[0274] Visual inspection reveals that 1) the fiber locations from both methods are quite similar; and 2) the manual calibration is less informative, capturing only 36 out of the 90 channels that should have been measured.

[0275] Next, the disclosers calculated the distances between the fiber locations from the two methods. For each manually measured channel, the disclosers calculated the distance to the nearest auto-measured channel: • Mean distance: 1.802 m • Standard deviation: 0.911 m • Maximum distance: 2.984 m • Minimum distance: 0.437 m

[0276] Loss Comparison with Manual Calibration Results: the disclosers apply the loss functions previously introduced to strain maps generated from both the manual and automated calibration results. Since manual calibration provides less detailed information, the disclosers use linear interpolation to produce higher-quality strain maps. Losses are compared across 9 different minutes where strain maps for both methods are generated and evaluated against the DAS-basedFRAMO-P050-WO ground-truth strain maps for the corresponding minute. The calculated losses for both methods were nearly identical. The results are shown in Table 2, below: minute auto manual index calibration calibration loss loss 0 0.61 0.55 1 0.52 0.55 2 0.86 0.87 3 0.77 0.76 4 0.78 0.82 5 0.76 0.75 6 0.59 0.51 7 0.67 0.78 8 0.77 0.76 Table 2. Loss Comparison between Automated and Manual Calibration Methods Over 9 Minutes of the Scene

[0277] Overall, the results from automatic calibration are consistent with those from the manual method. Both methods confirm that the fiber is located on the same sidewalk, and the estimated locations of channels closer to the camera are nearly identical. However, some variations in exact locations were observed, particularly near and beyond the bus station, which is farther from the camera. While the precise cause of these deviations is unclear, several potential factors could be contributing to the differences: • The camera’s position might have influenced the accuracy of location estimates for distant channels, affecting both calibration methods. For instance, in automatedFRAMO-P050-WO calibration, detection accuracy for distant vehicles was lower compared to those closer to the camera. • Using a single camera impacts the quality of projection. As discussed herein, a homography transformation is applied with the assumption of a constant z-axis in 3D coordinates. This assumption may cause slight deviations in the results. • Manual calibration might not be as precise, and the channel numbering may be biased.

[0278] d) Field Tour With The Infrastructure Project Manager: During a field tour with the infrastructure project manager, the disclosers observed that the fiber is positioned closer to the road, near the sidewalk edge, and that there is a curve after the bus stop. These findings are consistent with the disclosed results.

[0279] Verify Physical Solution

[0280] The disclosers verified that the solution is physically feasible in two manners: reasonable trajectory in terms of curves and distance between consecutive channels.

[0281] Distance Between Consecutive Channels: The expected distance between consecutive channels is approximately 1 meter, with minimal deviation between consecutive channel pairs. Upon analyzing these distances, the following was calculated: • Mean distance: 0.87 m • Standard deviation: 0.0076 m.

[0282] The mean distance being close to 1 meter is consistent with the disclosed expectations. The slight deviation could be attributed to twists and curves between the channels that are not captured in the results. Additionally, the low standard deviation indicates minimal variation, as anticipated. Overall, the distances between consecutive channels are reasonable, supporting the physical validity of the solution.

[0283] Fiber Trajectory and Curvature: Verification of the fiber’s trajectory and curvature reveals that the radius of curvature is significantly above the acceptable limit, with a calculated value of ρ = 79130.92 m.

[0284] Assuming that the fiber’s diameter is approximately 25-50 mm, the minimum allowable radius of curvature should range from 250-500 mm (according to the Fiber Optic Association Reference Guide). The resulting fiber trajectory exhibits a much larger radius of curvature, indicating that the solution is physically feasible in terms of bending constraints.FRAMO-P050-WO

[0285] Performance And Analysis

[0286] In this section, the disclosers analyze the performance of the disclosed optimization algorithm by comparing results from a 1-minute scene involving two buses driving in opposite directions with those from a 9-minute scene with various vehicles, including buses and cars. To ensure a fair comparison, the disclosers filtered out all vehicles other than buses in the 9-minute scene. To compare the 9-minute scene with the 1-minute scene, the disclosers ran the second stage of the optimization process on the initialized fiber locations (see section V-A) with identical hyperparameters: • Learning rate: 0.1FRAMO-P050-WO • Epochs: 2000 • Cosine annealing that reaches 0.001 with restarts every 200 epochs • Integrity regularizer upper bound: 1.02 m • Integrity regularizer lower bound: 0.75 m • Regularizers coefficients: 5.0 • Loss functions coefficients: 1.0.

[0287] This configuration was designed to allow significant adjustments and emphasize the fiber structure and curves. the disclosers evaluated the results using the same comparison methods as previously described herein. Specifically, the disclosers first compared the fiber locations resulting from the two methods, and then the disclosers compared their respective losses. Figure 25 shows the fiber channel locations for the two runs. Results from the 9-minute scene (with buses only) are shown in lightest gray, and results from the 1-minute scene are shown in gray. As reference, manual calibration is depicted in dark gray.

[0288] Visual inspection reveals that 1) the fiber locations of all methods are quite similar; and 2) there are cases where the results from the 9- minute scene are closer to the manual calibration results, and some cases that the 1-minute scene results are closer.

[0289] The disclosers calculated the distances between the results based on 9 minutes scene to the manual calibration results. For each manually measured channel, the disclosers calculated the distance to the nearest auto-measured channel: • Mean distances 1.91 m • Standard deviation of the distances 1.04 m • Maximum distance 3.56 m • Minimum distance 0.35 m.

[0290] Similarly, the disclosers calculated the distances between the results based on 1 minute scene to the manual calibration results: • Mean distances 1.8 m • Standard deviation of the distances 0.9 m • Maximum distance 2.93 m • Minimum distance 0.41 m.FRAMO-P050-WO

[0291] Loss Comparison: the disclosers applied the loss function presented herein over the generated strain maps based on the 9 minute calibration results and the 1 minute calibration results enables to compare the losses for all 9 minutes of both methods. batch automated 9 automated 1 index minute minute 0 0.57 0.54 1 0.73 0.72 2 0.68 0.69 3 0.73 0.74 4 0.73 0.73 5 0.73 0.74 6 0.58 0.59 7 0.85 0.84 8 0.69 0.70 Table 3. Comparison of Automated 9 Minute Calibration and Automated 1 Minute Calibration Loss for Each Minute.

[0292] Overall, the losses are comparable, showing no clear advantage for either method in terms of loss calculations. These results suggest that high-quality, smaller datasets can yield results comparable to, or even better than, those from larger datasets. This conclusion has significant implications for performance, user experience, and the requirements of the disclosed approach, emphasizing that smaller, high-quality datasets can be as effective, if not more effective, than larger ones.

[0293] Discussion

[0294] Automatic Calibration of DAS and Camera EvaluationFRAMO-P050-WO

[0295] The present disclosure relates to the spatial calibration between DAS and camera systems. The disclosed proposed solution builds upon previous research in traffic analysis using DAS. The present disclosure presents a system capable of analyzing a short video recording of street traffic alongside corresponding DAS measurements from a nearby fiber. The system can accurately reconstruct the fiber’s trajectory, achieving a deviation of only 1-2 meters over distant channels relative to the camera, and essentially providing a proof of concept for this purpose. Additionally, the disclosed system can determine the fiber’s trajectory within minutes, using only a few minutes of informative scene data (video and DAS). In fact, the disclosers demonstrated that just 1 minute of well-captured data is sufficient to achieve quite accurate results.

[0296] The disclosers focused on data involving bus traffic due to the high SNR produced by seismic waves from buses, which generate noticeable strains on the fiber’s strain map. Future work could examine the limitations of the disclosed system, particularly whether data from car traffic alone can also achieve accurate results. Further improvements could be made by refining the recording settings, such as optimizing the camera angle or using stereo recordings to improve depth estimation. Additionally, the disclosed system does not account for the coiling of optical fibers, which is a common practice during deployment. Addressing this challenge could enhance the system’s ability to generalize and ensure the full integrity of the calibration process. Furthermore, the disclosed system can be used to augment data for other DAS applications by mass-producing synthesized DAS data that can be consistent with a specific (real, or fake) fiber-optic deployment. the disclosers believe that the disclosed novel solution to the spatial calibration problem will serve as a foundation for any future use of fiber optic sensing technologies.

[0297] Performance and Methodology

[0298] The presently disclosed results demonstrate high accuracy for detection and classification, exceeding 94%, along with a low false alarm rate (about 1.5%). Such performance was achieved through a data collection strategy that involved recording for several hours and extrapolating to a whole week. Spatially, the disclosers recorded 80 meters of the road and extrapolated for the remaining 270 meters. This approach allowed generation of comprehensive statistics and analysis on vehicle counting, classification, and speed estimation.

[0299] From Sensing to Smart City applicationsFRAMO-P050-WO

[0300] To assess the disclosed model’s performance and its advantages, the disclosers analyze vehicle statistics throughout the week. Specifically, the disclosers apply the trained model to unseen DAS recordings to obtain distributed statistics on vehicle traffic along the fiber. Figure 6 presents the vehicle counts for four different days of the week for the whole fiber distance (about 350 meters).

[0301] The analysis uncovers a variety of intriguing trends, including the usual start time of the workday, the average vehicle density, and the ratio of buses to cars. This emphasizes the street’s heavy usage by buses, consistent with at least ten different regularly operating bus lines along this route. Saturday, the rest day in Israel, exhibits an entirely different pattern: a slow rise in activity, fewer vehicles, and almost no buses. Friday afternoon, which is approximately the time at which bus service stops, also shows a very clear reduction in bus usage.

[0302] Assumptions and Limitations

[0303] Data Quality and Model Robustness: A significant challenge encountered was the presence of noise in the labels. Interestingly, the model occasionally demonstrated an inherent ability to reduce noise effects. To further mitigate this source of noise, the disclosers proposed a method to smooth the detection map. Despite the high performance of the model, the disclosers believe that improving the labeling quality will dramatically improve its performance and generalization abilities.

[0304] Strain-Rate Shape and Gaussian Envelope Analysis: the disclosers examined the relationship between the strain-rate shape and the Gaussian envelope, finding similarities but not consistent equivalence. Comparisons with analytical functions revealed discrepancies, arising from deviations from the disclosed initial assumptions, as described earlier. the disclosers addressed these limitations through empirical tuning of the Gaussian envelope, which proved effective in practical applications. It possible that with larger, properly labeled datasets, more complete signal representations that further resemble the expected analytical behavior can be utilized and leveraged for more accurate results.

[0305] Transferability and Scalability: the disclosed approach demonstrates promising transferability to new sites. While the disclosers used 9 recording hours for optimal training, the disclosers found that only a few hours of data collection could yield at least 90% of the optimal performance given nominal traffic conditions. Similar scalability was observed in the spatialFRAMO-P050-WO domain, where training on half of the visually-covered fiber (40 m instead of 80m) was sufficient for accurate predictions (at least 90% of the optimal performance) over larger distances (the whole 350 meters). These results suggest that the disclosed approach could be readily adapted to new fiber layouts with minimal site-specific data collection.

[0306] Model Assumptions and Real-World Applications: A key assumption in the disclosed model is the parallel alignment of the fiber to the road, which may not always be true in real-world scenarios. This assumption allowed for a spatially invariant model, such as a fully Convolutional Neural Network. In other embodiments, spatial encoding techniques or non- spatially-invariant architectures could be used to extend the model’s ability to analyze differently the input for different locations, for example, For cases where the fiber is not parallel to the road. It is also important to note that in practical deployments, the presence of fiber spools is very common, and may introduce complications. However, these can be readily detected and excluded from the DAS map, either through tap testing or other channel mapping methods, thus minimizing their impact on overall performance.

[0307] Classification Limitations: The presented method supports a general number of classes, including cars and heavy vehicles (trucks and buses). The street under study had a high frequency of cars and buses but fewer trucks, motorcycles, and pedestrians. In addition, the weights of buses may significantly vary based on the number of passengers and whether the bus is articulated or not. Furthermore, the low signal-to-noise ratio (SNR) in detecting lighter objects, such as pedestrians, presents a challenge that may require more sensitive interrogators and specialized processing techniques.

[0308] Additional Considerations

[0309] In certain embodiments, the disclosed traffic monitoring system may be enhanced with supplemental data sources beyond DAS and video. For example, GPS data originating from in-vehicle sensors may be used to provide additional vehicle location information. These GPS inputs can be aligned with DAS signal patterns and video-based object detections through spatio- temporal correlation. In particular, vehicle coordinates obtained via GPS may be used to calibrate or validate the spatial alignment between DAS channels and video-derived vehicle trajectories. This approach enables fusion of multi-modal signals to improve the accuracy andFRAMO-P050-WO robustness of vehicle classification, speed estimation, and spatial localization along the fiber optic cable.

[0310] Additionally, the system may incorporate a Kalman filter or other state estimation module to fuse real-time outputs from DAS-based detection, video-based tracking, and GPS- based localization. These data sources can be used during the training phase to improve alignment, reduce ambiguity in labeling vehicle attributes, and generate more accurate supervisory signals. For instance, GPS data may help disambiguate overlapping objects or correct for occlusion in video detection. While the present disclosure trains the DAS model using video data alone, the incorporation of supplemental data sources such as GPS during training may increase model robustness and generalization, allowing the trained DAS model to operate independently without reliance on such data after deployment. This flexibility enables the system to scale across environments with differing data availability, while maintaining high classification performance from DAS signals alone.

[0311] CONCLUSION

[0312] The disclosers present a hybrid approach, leveraging both visual and DAS data, for traffic monitoring in an urban environment. The disclosed methodology enables precise detection, classification, and counting through neural networks applied to DAS data, with a training stage guided by video recordings. The disclosed approach highlights the potential of combining fiber-optic sensors with visual cues, focusing on practicality and scalability, protecting privacy, and minimizing infrastructure expenses, making it a feasible choice for real- world traffic monitoring.

[0313] In certain embodiments, the disclosed system performs a computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input. According to other embodiments, the model may also be trained with additional data such as GPS data, or other acoustic or light-based data. The method begins by receiving, by a processor, DAS training data that represents strain or strain rate measured along a fiber optic cable. Simultaneously, the method includes receiving, by the processor, video training data from a training camera that captures video of a stretch of road covered by the same segment of fiber optic cable used to collect the DAS training data; for example, the camera may be co-located with the fiber. The system then applies, by the processor, a machine learning-based objectFRAMO-P050-WO detection model—which, according to some embodiments, may include convolutional neural networks (CNNs) such as YOLO, or equivalent real-time object detection models—to the video training data to generate vehicle attribute data labels. These vehicle attribute data labels may include a vehicle’s position or track, a classification label (e.g., car, bus, truck, motorcycle), a bounding box, a timestamp, velocity or heading estimates, or a unique object identifier. Next, the method aligns, by the processor, the vehicle attribute data labels with corresponding portions of the DAS training data in both space and time. The processor then trains a neural network model—which may include deep learning architectures such as UNet, ResNet, or other CNN- based segmentation networks—using the aligned DAS training data and vehicle attribute data labels to associate DAS signal patterns with vehicle classification outcomes. As used herein, vehicle classification outcomes refer to predicted labels indicating the type or category of vehicle responsible for the observed DAS signal pattern, such as passenger car, heavy truck, bus, motorcycle, or background noise. This training process produces a trained DAS model, which is then stored in a memory. In deployment, the system applies, by the processor, the trained DAS model to incoming operational DAS data from the fiber optic cable to detect and classify vehicles. Finally, the processor can output model output comprising vehicle detection or classification results based solely on the operational DAS data. The trained DAS model is capable of generating such model output without requiring input of operational video data.

[0314] According to certain embodiments, the model output can include a synthetic strain rate map that is generated using the vehicle attribute data labels and a physical fiber layout model. The synthetic strain rate map can be computed from a video tensor that associates detected vehicles with estimated mass and three-dimensional location, and a fiber object that associates DAS sampling channels with corresponding 3D coordinates. This map helps approximate what the DAS system should detect based on video-derived information.

[0315] According to certain embodiments, the model output can include a synthetic image of the DAS data. This synthetic image can depict a classified vehicle as a time-varying strain pattern mapped onto a spatial representation of the fiber optic cable, allowing users to visualize vehicle movement and classification along the cable.

[0316] According to certain embodiments, the DAS training data received by the processor can include phase-shift measurements, which are sampled at regular spatial intervalsFRAMO-P050-WO along the fiber optic cable. These measurements capture acoustic strain or strain rate as sensed by the DAS.

[0317] According to certain embodiments, applying the object detection model to the video training data can involve detecting and tracking objects across multiple video frames using a pre-trained CNN such as YOLO. When the model misses detections in certain frames, object locations can be interpolated using the object’s unique tracking identifier. A consistent classification label can be assigned to each object based on the most frequently predicted class over time.

[0318] According to certain embodiments, aligning vehicle attribute data labels with DAS training data involves determining a homography between vehicle positions in ground- plane coordinates (derived from the video data) and DAS signal locations. This transformation enables spatial synchronization between visual and acoustic data. The homography described above can be refined by minimizing a calibration loss function, which includes a Dice loss that measures spatial overlap and a regularization term that penalizes sharp discontinuities in the alignment.

[0319] The homography transformation can further be constrained using a physical fiber layout model. This model can encode the geometric path of the fiber optic cable and provides additional physical context for accurate alignment. In some embodiments, the physical fiber layout model imposes continuity and curvature constraints on the homography, helping ensure the resulting alignment respects real-world cable topology and physical properties.

[0320] According to certain embodiments, spatio-temporal calibration can be performed to align vehicle attribute data labels with DAS training data. This can involve striking the ground at a series of known anchor locations along the fiber optic cable, recording both DAS responses and video timestamps, and using a projection matrix and an assumed burial depth to align DAS channels to a world coordinate frame.

[0321] According to certain embodiments, vehicle attribute data labels can be generated by applying an object detection model to the video data to detect and classify moving objects. Static objects, such as parked cars, are discarded because they do not produce DAS signal patterns. The system determines the closest fiber location for each object and generates aFRAMO-P050-WO probability-based detection map using a Gaussian envelope. This detection map is then normalized using a softmax activation function.

[0322] According to certain embodiments, training the neural network model can further include various preprocessing and calibration steps. These can include: (i) decimating and applying a two-dimensional FK filter to the DAS training data; (ii) tracking and classifying moving vehicles while interpolating missing detections and removing static objects; (iii) computing a homography transformation; and (iv) refining fiber alignment using a calibration optimization implemented via stochastic gradient descent.

[0323] In certain embodiments, the DAS training data is preprocessed prior to training the neural network model. This preprocessing step can help reduce noise and improve the relevance of signal patterns. According to some embodiments, preprocessing can include applying a median filter to the DAS training data to smooth out spurious spikes or outliers. In other embodiments, preprocessing can also involve applying a low-pass filter, which removes high-frequency noise and preserves the signal features of interest.

[0324] In some embodiments, preprocessing includes applying a two-dimensional FK filter to enhance signal quality by removing unwanted components from the data based on frequency and wave number characteristics. The FK filtering process can further include performing a two-dimensional Fourier transform, applying a custom band-pass filter (e.g., to exclude signals with a wave number above 0.045 and velocities outside 2.5–25 m / s), and then performing an inverse transform to return to the time-space domain. The preprocessing can also comprise resampling the DAS training data, which allows for temporal or spatial alignment or normalization prior to training. According to certain embodiments, the neural network model can be trained using a cross-entropy loss function for classification tasks to penalize incorrect predictions.

[0325] According to some embodiments, additional training steps can include applying a manifold smoothness constraint to the directional gradients of the model output to help ensure smoother predictions across neighboring locations and time windows. After training, for each position and time, the class with the highest posterior probability can be selected to generate a final classification map from the model output.FRAMO-P050-WO

[0326] According to some embodiments, the trained DAS model can be deployed on a field system that operates without access to any operational video or GPS data, relying solely on operational DAS data for vehicle detection and classification. In deployment, the trained DAS model can continuously generate real-time vehicle classification results as it processes the incoming DAS signal stream.

[0327] According to certain embodiments, the model output can be aggregated over time intervals and spatial segments along the fiber to produce a map-based traffic report.

[0328] According to certain embodiments, the neural network model can be trained using a cross-entropy loss function for classification tasks to penalize incorrect predictions. Training can further include data augmentation by horizontally flipping DAS data windows. This mimics time reversal and helps reduce bias from traffic directionality. Data augmentation during training can also include vertical flipping of DAS windows, which effectively reverses the spatial order of the data and can help improve generalization.

[0329] The system can also augment training data by randomly dropping vehicle attribute data labels to simulate occlusions or missing detections in real-world video data. Simulated Gaussian noise can also be injected into the DAS training data to further enhance the model's robustness against noisy input during deployment.

[0330] According to the disclosure, the disclosed methods and systems can achieve vehicle detection accuracy exceeding 90% when evaluated on held-out DAS training data. The trained DAS model can also estimate vehicle speed by analyzing how detected vehicle locations progress over time within the operational DAS data. This speed estimation can be corrected using alignment parameters derived from prior calibration between the DAS training data and the video training data.

[0331] In some embodiments, the model output can include a detection map that represents a probability distribution over several vehicle classes and a noise class. The detection map can also include a class probability vector at each position and time window along the fiber, indicating confidence in the predicted classifications. These class probability vectors can further include a confidence score representing the likelihood of each vehicle classification outcome. Model output can be filtered using a confidence threshold derived from these class probability vectors, discarding low-confidence predictions.FRAMO-P050-WO

[0332] According to some embodiments, the trained DAS model can be configured to detect the presence of a vehicle without necessarily assigning a vehicle classification. According to certain embodiments, the vehicle attribute data labels may include any of: vehicle location, classification label, bounding box, and timestamp.

[0333] According to some embodiments, the trained DAS model can optionally also be applied to operational video data received from a co-located video camera and / or GPS data. In this mode, the system may output vehicle detection or classification results based on DAS data as well as additional video data and / or GPS data.

[0334] In some embodiments, the spatial layout of the fiber optic cable can be estimated from seismic signal patterns using the vehicle attribute data labels. The fiber alignment process can begin with a pre-optimization phase that iteratively tests candidate fiber positions along a perpendicular axis to the road, selecting the configuration that maximizes cross-correlation between simulated and actual DAS maps. This initialization can be further refined using a gradient-based optimization process. In some embodiments, the system can generate simulated DAS strain rate maps and minimize a composite loss function that includes fidelity to observed data and physical regularization constraints.

[0335] In certain embodiments, a traffic monitoring system can include a non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform the method disclosed herein.

[0336] In some embodiments, a method is provided for training the DAS model, including receiving DAS and video training data, generating vehicle attribute data labels, aligning them with DAS data, and training the neural network to produce a model that outputs results from DAS data alone. A traffic monitoring system trained according to this method can include a fiber optic cable, a processor and memory storing the trained DAS model, and an output module for visualizing the model output. The system can operate using only operational DAS data and can generate time-resolved maps indicating vehicle classification outcomes.

[0337] In some embodiments, the video training data can be received from more than one training camera, with each training camera positioned to capture video of a segment of roadway covered by at least a portion of the same fiber optic cable that supplies the DAS training data. The use of multiple cameras can increase coverage and improve the quality of vehicle attributeFRAMO-P050-WO data labels across complex road geometries. In certain embodiments, the training step further comprises training, by the processor, the neural network model using the aligned DAS training data, vehicle attribute data labels, and localization information from GPS. A Kalman filter can be applied to fuse the GPS data with the video training data and DAS training data to improve alignment during training. This enables the trained DAS model to associate DAS signal patterns with vehicle classification outcomes and location outcomes, where location outcomes refer to the estimated physical position of the vehicle relative to the fiber optic cable. In some embodiments, the trained DAS model is configured to operate in real-time by continuously processing operational DAS data to generate updated vehicle detection or classification results as new data is received.

[0338] Drawing Legend

[0339] Figure 26 illustrates an embodiment of a traffic monitoring system 100 trained using both DAS and video data but which is operable without requiring operational video input. The system includes a computing device 1 comprising a processor 2 and memory 3. The memory 3 stores a trained DAS model trained on DAS and video input and instructions which, when executed by processor 2, cause the system to receive operational DAS data from a fiber optic cable 106 deployed along a spatial path 107. The DAS data 108 is processed to generate model output 104 indicating vehicle detection or classification results. The output module 105 delivers these results in real-time. In some embodiments, the DAS model can be initially trained using a combination of DAS data, video training data, and GPS training data in accordance with present disclosure. However, after training, the system can operate solely on DAS data, without requiring input from an operational video camera.

[0340] References

[0341] All publications, patents, patent applications and other references cited in this application are incorporated herein by reference in their entirety for all purposes to the same extent as if each individual publication, patent, patent application or other reference was specifically and individually indicated to be incorporated by reference in its entirety for all purposes. Citation of a reference herein shall not be construed as an admission that such is prior art to the present invention.FRAMO-P050-WO

[0342] [2] Philippe Jousset et al. “Dynamic Strain Determination Using Fibre-Optic Cables Allows Imaging of Seismological and Structural Features”. In: Nature communication (2018).

[0343] [5] Michele Berlingerio et al. “AllAboard: a system for exploring urban mobility and optimizing public transport using cellphone data”. In: Machine Learning and Knowledge Discovery in Databases: European Con- ference, ECML PKDD 2013, Prague, Czech Republic, September 23-27, 2013, Proceedings, Part III 13. Springer.2013, pp.663–666.

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Claims

FRAMO-P050-WO CLAIMS 1. A computer-implemented method for monitoring traffic using a distributed acoustic sensing (DAS) model trained with video input, the method comprising: receiving, by a processor, DAS training data representing strain or strain rate along a fiber optic cable; receiving, by the processor, video training data from a training camera co-located with at least a portion of the fiber optic cable; applying, by the processor, a machine learning-based object detection model to the video training data to generate vehicle attribute data labels; aligning, by the processor, the vehicle attribute data labels with corresponding portions of the DAS training data in space and time; training, by the processor, a neural network model using the aligned DAS training data and vehicle attribute data labels to associate DAS signal patterns with vehicle classification outcomes, thereby producing a trained DAS model; storing the trained DAS model in a memory; applying, by the processor, the trained DAS model to operational DAS data received from the fiber optic cable to detect and classify vehicles; and outputting, by the processor, model output comprising vehicle detection or classification results based on the operational DAS data; wherein the trained DAS model can generate model output without input of operational video data.

2. The method of claim 1: wherein the model output comprises a synthetic strain rate map generated using vehicle attribute data labels and a physical fiber layout model; wherein the synthetic strain rate map is computed from a video tensor associating detected vehicles with their estimated mass and 3D location and a fiber object associating DAS sampling channels with 3D coordinates; and wherein the synthetic strain rate map is generated from video training data recorded concurrently with the DAS training data and is used for fiber localization by comparison to the DAS training data.FRAMO-P050-WO 3. The method of claim 1: wherein the model output comprises a synthetic image of the operational DAS data projected onto a synthetic strain rate map, the synthetic image depicting a classified vehicle as a time-varying strain pattern mapped to a spatial layout of the fiber optic cable; and wherein the synthetic strain rate map is generated from video training data recorded concurrently with the DAS training data and is used for fiber localization by comparison to the DAS training data.

4. The method of claim 1, wherein the DAS training data comprises phase-shift measurements sampled at regular intervals along the fiber optic cable.

5. The method of claim 1, wherein the machine learning-based object detection model is a convolutional neural network trained to detect multiple vehicle classes.

6. The method of claim 1, wherein applying the object detection model to the video training data further comprises: (i) detecting and tracking objects across video frames using a pre-trained object detection model; (ii) interpolating missing object locations in frames where detections are absent using tracked object identifiers; and (iii) assigning a consistent classification label to each tracked object based on the most frequently predicted class across frames.

7. The method of claim 1, wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises determining a homography between ground-plane vehicle positions derived from the video training data and DAS signal locations within the DAS training data.

8. The method of claim 7, wherein the homography is refined by minimizing a calibration loss function comprising a Dice loss and a regularization term penalizing spatial discontinuity.

9. The method of claim 7, wherein the homography is further constrained using a physical fiber layout model representing the geometry of the fiber optic cable.

10. The method of claim 9, wherein the physical fiber layout model enforces continuity and curvature constraints on the homography alignment.FRAMO-P050-WO 11. The method of claim 1, wherein aligning the vehicle attribute data labels with corresponding portions of the DAS training data comprises performing a spatio-temporal calibration comprising: striking the ground at a plurality of anchor locations along the fiber optic cable; recording DAS responses at each strike; and aligning DAS channels to world coordinates using a projection matrix and an assumed fiber burial depth.

12. The method of claim 1, wherein generating the vehicle attribute data labels from the video training data comprises: applying a machine learning-based object detection model to the video training data to detect and classify moving objects; discarding static objects that do not produce DAS signal patterns; identifying, for each detected object, a location along the fiber optic cable that minimizes a distance metric relative to DAS signal channels; generating a detection map representing a probability distribution over time and fiber location using a Gaussian envelope function; and normalizing the detection map using a softmax activation function.

13. The method of claim 1, wherein training the neural network model further comprises at least one of: (i) preprocessing the DAS training data using decimation and two-dimensional FK filtering to reduce noise and enhance signal quality; (ii) generating vehicle attribute data labels from the video training data by: (a) applying a machine learning-based object detection model to track and classify moving vehicles; (b) removing static objects not expected to produce DAS signal patterns; and (c) interpolating missing detections based on tracking continuity; (iii) computing a homography matrix to transform detected vehicle positions from image coordinates to a three-dimensional coordinate system aligned with the fiber optic cable; and (v) refining fiber alignment using a calibration optimization process implemented via stochastic gradient descent.FRAMO-P050-WO 14. The computer-implemented method according to claim 1, wherein the DAS training data is preprocessed prior to training the neural network model.

15. The method of claim 14, wherein the preprocessing comprises applying a median filter.

16. The method of claim 14, wherein the preprocessing comprises applying a low- pass filter.

17. The method of claim 14, wherein the preprocessing comprises applying a two- dimensional FK filter.

18. The method of claim 1, wherein the neural network model is trained using a cross-entropy loss.

19. The computer-implemented method according to claim 1, wherein the neural network model comprises a convolutional neural network with a UNet architecture.

20. The method of claim 1, wherein training the neural network model further comprises applying a manifold smoothness constraint on directional gradients of the model output.

21. The method of claim 1, wherein the trained DAS model is operable without access to operational video data.

22. The method of claim 21, wherein the model output is aggregated over time intervals and fiber segments to generate a map-based traffic report.

23. The method of claim 1, further comprising augmenting the DAS training data by randomly dropping vehicle attribute data labels.

24. The method of claim 1, further comprising augmenting the DAS training data by injecting simulated Gaussian noise.

25. The method of claim 1, wherein the fiber optic cable location is automatically calibrated without manual annotation of a physical fiber layout model.

26. The method of claim 25, wherein the automatic calibration optimizes a predicted fiber path under physical constraints of curvature and continuity defined by the physical fiber layout model.

27. The method of claim 1, further comprising estimating vehicle speed based on the temporal progression of detected vehicle locations within the operational DAS data.FRAMO-P050-WO 28. The method of claim 27, wherein the speed estimation is corrected using alignment parameters derived from calibration between the video training data and the DAS training data.

29. The method of claim 1, wherein the model output comprises a detection map including a class probability vector at each position and time window along the fiber.

30. The method of claim 29, wherein the class probability vector comprises a confidence score representing the likelihood of a vehicle classification outcome.

31. The computer-implemented method according to claim 30, wherein the outputting step further comprises filtering model output using a confidence threshold derived from the class probability vector.

32. The method of claim 1, wherein the trained DAS model is configured to detect the presence of a vehicle without determining a vehicle classification.

33. The computer-implemented method according to claim 1, wherein the vehicle attribute data labels comprise at least one of a vehicle location, a classification label, a bounding box, or a timestamp.

34. The computer-implemented method according to claim 1, further comprising: applying, by the processor, the trained DAS model to operational video data received from an operational video camera co-located with at least a portion of the fiber optic cable to detect and classify vehicles; and outputting, by the processor, model output comprising vehicle detection or classification results based on the operational DAS data and the operational video data.

35. The method of claim 1, further comprising: initializing fiber optic channel locations for alignment using a pre-optimization procedure that iteratively evaluates candidate fiber positions along a perpendicular axis relative to the road direction, wherein the initialization maximizes a normalized cross-correlation between simulated strain rate maps and processed DAS training data.

36. The method of claim 35, further comprising: refining the initialized fiber optic channel locations using a gradient-based optimization process comprising:FRAMO-P050-WO generating simulated strain rate maps based on vehicle distances from candidate fiber positions; and minimizing a composite loss function comprising data fidelity and physical regularization terms, including constraints on channel spacing integrity and path continuity.

37. The method of claim 1, wherein training the neural network model further comprises augmenting the DAS training data by performing at least one of: horizontally flipping DAS training data windows; and vertically flipping DAS training data windows.

38. A traffic monitoring system comprising a non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to perform the method of any of claims 1–37.

39. A computer-implemented method for training a distributed acoustic sensing (DAS) model using video input, the method comprising: receiving, by a processor, DAS training data representing strain or strain rate along a fiber optic cable; receiving, by the processor, video training data from a training camera co-located with at least a portion of the fiber optic cable; applying, by the processor, a machine learning-based object detection model to the video training data to generate vehicle attribute data labels; aligning, by the processor, the vehicle attribute data labels with corresponding portions of the DAS training data in space and time; training, by the processor, a neural network model using the aligned DAS training data and the vehicle attribute data labels to associate DAS signal patterns with vehicle classification outcomes, thereby producing a trained DAS model; and outputting the trained DAS model, wherein the trained DAS model is configured to generate model output based solely on operational DAS data, without requiring operational video data.

40. A traffic monitoring system trained according to the method of claim 47, the system comprising:FRAMO-P050-WO a fiber optic cable configured to generate DAS data representing strain or strain rate along a spatial path; a processor operatively coupled to a memory storing a trained DAS model; wherein the trained DAS model is configured to: receive, as input, operational DAS data sampled from the fiber optic cable; generate model output comprising vehicle detection or classification results based solely on the operational DAS data; and an output module configured to generate a time-resolved detection map indicating vehicle classification outcomes over the monitored area.

41. The method of claim 1, wherein the video training data is received from more than one training camera, each training camera co-located with at least a portion of the fiber optic cable.

42. The method of claim 1, wherein the training step further comprises training, by the processor, the neural network model using the aligned DAS training data, vehicle attribute data labels, and localization information from GPS, wherein a Kalman filter is applied to fuse the GPS data with the video training data and DAS training data to improve alignment, thereby producing a trained DAS model that associates DAS signal patterns with vehicle classification and location outcomes.

43. The method of claim 1, wherein the trained DAS model is configured to operate in real- time by processing incoming operational DAS data continuously to generate vehicle detection or classification results.

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