Advances in communication, location, identification and evaluation for shock sources - Research Article
Dynamic target template matching for railway catenary suspension motion detection in wind area
International Journal of Distributed Sensor Networks 2018, Vol. 14(9) Ó The Author(s) 2018 DOI: 10.1177/1550147718797956 journals.sagepub.com/home/dsn
Wei Zhou1,2,3,4, Heting Xiao1,2,3,4, Zhonggang Wang1,2,3,4, Lin Chen1,2,3,4 and Shaoqing Fu1,2,3,4
Abstract A dynamic target template matching method was proposed to identify railway catenary suspension movements of wind-induced vibration in wind area. Catenary positioning point was taken as the target template, which was compared with equal-sized image sequentially using the proposed matching difference. And, three-dimensional contour map of matching difference value at each sub-area was obtained, where the target pixel coordinates were determined by the minimum matching difference value. Considering the complex imaging condition, the target template was updated by the detected target image to sense the gradual change of illumination conditions like brightness and contrast. Furthermore, to eliminate detecting errors due to wind-induced camera vibration, both static and moving target templates were identified for acquiring the absolute motion of the moving target. Finally, validation test was performed with animation in PowerPoint. The calculated target displacement agrees well with theoretical motion with maximum relative error of 1.8%. And experiment application was conducted at site by analyzing the relationship between detecting displacement and wind speed. Results indicate that the proposed dynamic target template matching method can meet required engineering precision and provide an effective way for wind-vibration safety research of railway catenary system in wind area. Keywords Railway catenary, visual detection, template matching, wind-induced vibration, anti-wind safety
Date received: 3 February 2018; accepted: 25 July 2018 Handling Editor: Gongnan Xie
Introduction 1
Wind-induced catenary vibration can sometimes lead to serious safety problems when the relative position between catenary wire and pantograph deviates tremendously from normal range.1–6 Severe pantographcatenary impacts and malposition may occur due to large catenary wire displacement subjected to strong wind loads, which brings hidden danger to fatigue failure of catenary-pantograph components, and possibly give rise to system malfunction and even operation safety issues. This relates to a high degree of interest in the motion-detecting technologies of catenary wires.
School of Traffic and Transportation Engineering, Central South University, Changsha, China 2 Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Changsha, China 3 Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha, China. 4 National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha, China Corresponding author: Zhonggang Wang, School of Traffic and Transportation Engineering, Central South University, 68 Shao-Shan South Road, Changsha 410075, Hunan, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 Deviation maximums detected in different incoming wind flows can provide reliable evidence for evaluating anti-wind performance of railway catenary and thus optimizing operation regulations like the appropriate running speed limit in wind area with both train and pantograph-catenary safety taken into account. Here, motion-detecting technologies are discussed in two categories: on-vehicle means for pantographcatenary attitudes and ground measurements for windinduced catenary vibrations. In published research, motion status detection for pantograph, catenary, and their coupled system mainly employs contactless measurement due to their complex and severe service environment. In conditions like harsh blown-sand, high electromagnetic field interference, and strong working vibrations, it is impossible to adopt contact means like draw-wire or thimble displacement sensors for motion detection since there is no installing reference for sensors, and relative position between pantograph and catenary varies in all freedoms randomly. Hence, onvehicle detections are more likely to use laser beam detectors or vision cameras to sense the change of relative position between pantograph and catenary wire, where detecting facilities are mostly installed above the train at a certain safe distance from pantographcatenary contact position. Of all statistical data onto pantograph-catenary motion detection, the study of machine vision method accounts for more than 80% of the cases. Researchers got excellent algorithms with respect to target recognition to explain the movements of pantograph referred to train or catenary wire,7–15 but not referred to the ground. To better understand mechanical behavior of pantograph-catenary system, it is essential to know exactly how pantograph reacts referred to ground, how catenary reacts referred to ground, and how they react referred to each other. Z Lu et al.16 put forward a vision-recognition methodology using four visual-detecting sensors at positions of a car to detect relative movements between the vehicle and rail track, which are indispensable parameters for pantograph-ground relative movements detection. For ground detection of catenary vibrations, the direct option is to use acceleration sensors right on top of catenary wire or at the positioning point of catenary cantilever structure. However, it requires extraordinary reliability and durability of the sensor to calculate the displacement of catenary wire by second integration, when subjected to multi-directional vibrations and complex electromagnetic interference, not to mention the risk of passive influence on train operation safety if the sensor falls down when the installation failure occurs. To take care of this issue, W Zhou and H Tian17 proposed a vision detection method where areaarray CCD (charge-coupled device) cameras were installed on top of catenary column at the same height of wire, observing multi-points of catenary wire marked
International Journal of Distributed Sensor Networks by red square-shaped targets. Suggested recognition algorithm receives good accuracy and reliability, but risks still exist when the designed targets installed on wire lose connection due to long service fatigue failures. In this work, an improved detecting method is proposed without special designed targets in observation. Natural connections of catenary wire and droppers are picked as moving targets, and background featured points are regarded as static targets to compensate detecting errors due to wind-induced column vibrations. The key point of proposed method is the template matching operator for both moving and static targets, as well as the environment-adaptive template refreshing principle adopted to fit in complicated imaging conditions. A brief introduction of visual detection scheme is given in section ‘‘Detecting scheme.’’ Image recognition algorithm for both moving target and static target is investigated in section ‘‘Detecting model,’’ where grayscale difference matching operator was formulated and contour plotted with observed image in section ‘‘Matching difference formulation.’’ Principle of how dynamic matching template is updated by the identified target is introduced in section ‘‘Dynamic target template update,’’ and modification of detection error resulted from camera vibration using static background target is further studied in section ‘‘Stabilizing algorithm.’’ Then, in section ‘‘Validation,’’ validation of the suggested method was conducted through a simple but effective experiment, where rectangle moving path of a circle target was defined in PowerPoint. By comparison between theoretical data and detected motion data with camera shaking during observation when the shape and color of both moving target and static target change, the reliability, accuracy, and robustness of the suggested method were analyzed. Finally, experiment application was conducted and the relationship between detected displacement and environmental wind speed was analyzed.
Detecting scheme This program is supported by Windproof Safety of Electrified Railway Catenary Research Project in Xinjiang Uighur autonomous region. Catenary motion detection site locates at a transit section from bridge wind barrier to railway deep cut at one end of Sangequan Grand Bridge in Nanjiang railway line. Historical maximum wind speed at site can reach 60 m/ s, which definitely has negative influence on catenary service performance no matter whether the train moves pass this section or not. Frequent wind-induced vibrations result in fatigue failures of key catenary components. In addition, at deep-cut section, terrain at both sides of railway is much higher than the train itself. And in a certain distance from beginning of deep-cut
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Figure 1. Catenary motion-detecting scheme on-site.
section, train operation fault like pantograph-catenary disconnection occurs frequently because of complex wind-induced vertical uplift to catenary wire. Hence, both catenary spans at this section, with half on the bridge and the other in deep cut, are visually inspected by cameras installed on catenary column. And the environmental wind speed is measured by wind speed sensors installed at the same height of bridge, about 50 m distance away from the railway bridge, as shown in Figure 1. Unlike wind-deviation detection in literature,18–23 connections between droppers and catenary wire as well as messenger wire were treated as moving targets in this work. Reflective paint was used on the connection to enhance its identifiability. Detecting area-array CCD cameras were installed between catenary cantilever mounting points where the best viewpoint and illumination conditions can be acquired. Infrared light sources were employed for each camera during
nighttime to inspect moving target and static target without affecting train operation by mistaking visible lighting source as the train signal light.
Detecting model In camera imaging model, all calculations are formulated in front projection, where the projection plane is in front of the projective center. Since catenary suspension connection targets are mostly circular, the shape of which is not suitable for rotational angle calculation, only translational freedom in planar 2-direction is taken into account. Here, the actual transverse displacement of target is denoted as DX, and actual vertical displacement is denoted as DY. The transverse pixel displacement of target is denoted as Dx, and pixel vertical displacement is denoted as Dy. Object distance to projective center is denoted as u, and focal distance of camera is denoted as f. The geometrical relationship
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Figure 2. Actual and pixel offsets under front projection.
between actual and pixel displacement of target can be depicted as shown in Figure 2. Mathematical relationship between actual displacement {DX, DY} and imaging pixel displacement {Dx, Dy} in orthogonal directions can be formulated in equation (1)
DX DY
=
u=f 0
0 u=f
Dx Dy
ð1Þ
For the issue studied in this work, it is unnecessary to determine the focal distance u and object distance f before working since it demands high accuracy to do the distance measurement from camera projective center to different targets. It is supposed that the target size LR in different directions represents the actual displacement and its imaging pixel size LP represents the pixel displacement in equation (1); self-calibration coefficient KC is then calculated by simply measuring actual size and corresponding imaging pixel size of targets, as shown in equation (2); here, KC = 2.7 mm/pixel KC =
u LR = f LP
ð2Þ
Catenary motion-detecting model is constructed incorporating equations (1) and (2), from which we find that the key issue of motion detection is to identify the imaging pixel coordinates of the concerned catenary target. Varying target pixel coordinates in sequence images represent its motion displacement when taking the initial image as reference, as shown in Figure 3. Thus, a detailed introduction of target recognition algorithm subjected to complex imaging conditions will be given in the following sections.
Target template matching Image processing issues about catenary recognition have been extensively studied. M Zhao24 developed a real-time image processing module with TMS320 DM642 as the core processing chip. His study aims at catenary characteristic extraction, pantograph-catenary
Figure 3. Actual and pixel dimensions of the connecting parts of contact suspension.
arc, and disconnection as well as abrasion detection in a way of image processing algorithm, where complex image background noise, uneven illumination, and high vehicle running speed are taken into account. Advantages of both high sampling rate of linear-array CCD camera and high percentage of coverage of areaarray CCD camera are considered in the study, but the accuracy of image processing is somewhat affected when illumination on object changes. J Liu et al.25 presented an image enhancement technique for catenary images obtained on top of a moving train based on wavelet transform and fuzzy contrast algorithm. Proposed method enhances image clarity and enriches conveyed image information and meets the requirement of human visual sensing and computer analysis, which can serve as an effective way to accurately assess catenary current-carrying status. JH Kim et al.26 proposed an optimized image dehazing algorithm for hazy images and videos as the overcompensation of degraded contrast may truncate pixel values and cause information loss. A cost function consisting of the contrast term and information loss is formulated, by which the contrast and information can be optimally preserved and enhanced. The proposed method in this literature can be an effective aid for catenary image quality enhancement. X Yan27 developed a non-contact-style detection system for high-speed electrified railway catenary, which is installed on the roof of moving train and completely disengaged with high-voltage equipment. Adaptive threshold and twice binary approaches are used for image preprocessing, tracking distinguished techniques are adopted to eliminate interference targets. Yet, detection errors due to vehicle vibration are not taken into account. S Tabayashi et al.28 developed a non-contact measurement system for wear and contact force between pantograph and catenary using image processing. Detection schemes and models were described where line sensors and CCD cameras were both used to measure such parameters like catenary wearing, height, gradient, and contact force. The developed system was installed on
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Figure 4. Target template matching in image processing region.
rooftop of vehicle in practice and experimental results were further analyzed. As mentioned above, image recognition methodologies about catenary parameters have been extensively studied. Image processing algorithm proposed in this article focuses on dynamic target template matching and sub-region template traversing, as an aid to enhance motion-detecting efficiency and reliability of catenary wire targets in complex imaging conditions. Motion detection algorithm with respect to target template matching consists of the following steps. 1. Image processing region definition. Positioning point of catenary suspension is regarded as target feature point. We consider the motion boundary limit in transverse and vertical direction of the centered target, respectively, denoted as XLIM and YLIM, as shown in Figure 4. Target movements even in the least favorable wind environment will not exceed this defined motion boundary, which can be calculated by theoretical formula between historical maximum wind speed and catenary deviation on-site. Hence, image processing region is designed to be the same size of target motion. Target recognition algorithm is operated only within the image processing region to improve its execution efficiency. 2. Target template definition. The target template of catenary positioning point has relative small size compared to image processing boundary, whereas the pixel size should neither be too small to contain all necessary information on the target nor be too large to eliminate background pixel interference to accurate motion identification. Thus, the target template region, rectangular shape defined, should not exceed target pixel size. Here, transverse and vertical pixel size of target template is symbolized, respectively, as xLIM and yLIM.
5 and bottom direction. Traversing mode in both directions works in a rolling way from [1;xLIM,1;yLIM] to [2;xLIM + 1,2;yLIM + 1], other than the moving way from [1;xLIM,1;yLIM] to [xLIM + 1;2xLIM, yLIM + 1;2yLIM]. Calculations at each traversing position represent the matching extent of matching area compared to target template. Apparently, the smaller is the grayscale difference between each other, the greater is the degree of matching. With all matching difference values calculated, which will be introduced in the following section, the matching difference minimum of traversing position is taken as the target point. Corresponding pixel coordinates after modification in template pixel length and width are used to compute the target movements by subtracting its initial position from the coordinates in windless condition. 4. Image sequences processing. The next image frame is read and processed as back in step 3. Calculations of matching difference between matching area and both moving/static targets are again performed. This image processing continues until all image sequences have been processed. Matching difference formulation. Matching difference is defined to describe the pixel grayscale difference between target template and equal-sized matching area. Formulation of the difference must demonstrate the overall difference level of all pixel points, respectively, in matching area and target template. Therefore, the square of grayscale difference value between pixel point in target template and point of matching area in same location is taken as the grayscale difference level for single pixel point, as shown in Figure 5. Then, the summation of grayscale difference level of all pixel points per unit pixel area and the square root are calculated as the matching difference formula shown in equation (3)
Dðk, lÞ =
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi PyLIM PxLIM 0 i=1 j = 1 D ði, jÞ xLIM yLIM
where D#(i, j) = (GOBJ(i,j) 2 GIMG(i,j)]2. GOBJ(i, j) and GIMG(i, j) denote the grayscale value of pixel point at coordinate (i, j), respectively, in target template and image matching area. Parameters k and l denote the pixel coordinate in two directions of the present matching area. In consideration of target template size, parameters k and l can be calculated as shown in equation (4) k = 1;YLIM yLIM + 1
3. Matching difference calculation. Calculation of matching degree based on pixel grayscale difference between target template and same-sized matching area starts from top left corner of image processing region to the right
ð3Þ
l = 1;XLIM xLIM + 1
ð4Þ
To illustrate the matching difference distribution of processing image, the target template of one image
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Figure 5. Schematic diagram of traversal matching and matching difference calculation.
Figure 6. The 3D contour plot of matching difference between target template and matching area within image processing region.
frame is taken to calculate the matching difference within image processing region in rolling traversing mode from top left to bottom right. After matching difference traversing over all image processing region, the three-dimensional (3D) matching difference contour map, where x and y coordinates are related to image
pixel in width and height, respectively, is plotted as shown in Figure 6. As it can be seen from the matching difference contour map, the minimum peak of 3D map indicates the least difference between corresponding image and target template. And pixel coordinates of that minimum
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Figure 7. Grayscale characteristic of positioning target in different illumination conditions.
Figure 8. Algorithm steps of dynamic target template updating.
peak really count for the real target position. Traversing pixel coordinates of identified target are denoted as (k0, l0), then the modified target pixel coordinates are calculated with target template size taken into account, as shown in equation (5) yLIM 2 xLIM lOBJ = l0 + 2
kOBJ = k0 +
ð5Þ
Dynamic target template update. Problem occurs when an unchangeable target template according to its initial status is consistently used. As illumination conditions on-site change in different periods of time during day and night, grayscale characteristic of pixels in target area varies a lot from the initial target template, which brings a lot of trouble to perform difference calculation between present image and initial target template. It becomes impossible to find the target when actual target in present image frame looks totally different from the initial target template, as shown in Figure 7.
From monitoring images at different times, it can be observed that white color feature of the target becomes the best at daytime before 13:00. However, target color becomes grayscale due to poor illumination condition from 14:00 to 18:00. And target color turns white again because of infrared lighting source after 19:00 at nighttime. As it can be seen, target identifiability becomes much better without complex background interference during night. In target template matching process, prominent difference of target area at different times leads to recognition failure if the initial unchangeable target template is being compared all the time. Thus, it is necessary to update the target template by replacing it with the recognized target at each processing step from image frame, in order that the catenary positioning target can be identified accurately in sensing the gradual change of illumination condition. Dynamic target template update is realized in the following steps as depicted in Figure 8. To improve target recognition efficiency for a single image frame, a threshold for matching difference is
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Figure 9. Static background template during daytime (image on left) and nighttime (image on right).
defined as T. When the matching difference between target template and matching image area becomes less than threshold T, the traversing matching image area is treated as the target. The suggested image threshold method can enhance processing efficiency to a certain extent because it is unnecessary to traverse all pixels in processing region and then find the minimum peak. When matching difference value below threshold is observed, target position is expected. To obtain the optimal threshold T, all image frames over 24-h period during the day and at night were processed to calculate the minimum matching difference. The maximum of these minimum matching differences of 24-h image frames was then determined as the threshold T (here, T = 5). This optimal threshold T was again substituted into all image frames to calculate the deviation between recognized target position by optimal threshold and theoretical target position, and the deviation between the identified target positions is calculated by corresponding minimum matching difference. Calculating results indicate that the maximum deviation is within 1 pixel, that is, only 2.7 mm in engineering dimension. Results show that the suggested optimal difference threshold contributes to the best recognition results both in processing efficiency and accuracy.
Stabilizing algorithm Strong environmental wind produces column vibration where detecting cameras were installed on it. To measure accurate catenary motion, vibration-induced false displacement of moving target must be eliminated. As mentioned in literature,29 pixel coordinates change of both moving target and static target is the same due to camera vibration in windless condition. And this change mainly involves transverse and vertical direction because of wind-vibration mechanical behavior of catenary column. From this perspective, a static target is observed to calculate the false pixel displacement because of camera vibration, through which the absolute pixel displacement of moving suspension targets can be modified.
Here, we take the mileage plate on steel portal structure as the static target. On one hand, image of the static target demonstrates a signboard with numbers on it at daytime and a white light-reflecting plate at nighttime. This typical image characteristic makes the static target template prominently identifiable, as shown in Figure 9. On the other hand, the mileage plate can be regarded as static point even in the strongest wind because of large rigidity of the steel portal structure. Taking the mileage plate shown in Figure 9 as target template, camera vibration–induced displacement of the static target is then calculated by employing the same image processing model introduced in section ‘‘Target template matching.’’ Transverse and vertical false displacements of static target are denoted as Dxstatic_i and Dystatic_i, respectively. In the same image frame, transverse and vertical identified displacements of moving target at suspension positioning point are denoted as Dxmoving_i and Dymoving_i, respectively. Hence, the absolute displacements of suspension positioning target referred to static background are calculated in equation (6) DXi = KC Dxmoving i Dxstatic i DYi = KC Dymoving i Dystatic i
ð6Þ
where DXi and DYi indicate transverse and vertical displacement (unit in mm), respectively, of suspension target from image frame i#, taking static background as reference. KC is the self-calibration coefficient of moving target as described in equation (2).
Validation It is difficult to implement validation of the suggested method since there is no effective way to precisely measure the movement of catenary suspension target, which is counted as the theoretical movement for comparison. Thus, a simple but effective validation of the suggested method is proposed here via PowerPoint, a demonstration software developed by Microsoft Corporation. In editing page, a dark blue circle is set as the moving
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Figure 10. Validation test scheme: (a) validation test setup, moving target at (b) initial top right corner position, (c) top left corner position, (d) bottom left corner position, (e) bottom right corner position, and (f) moving target back at top right corner position.
target, the moving path of which is designed in a closed rectangle. The moving target moves clockwise from start to end in 5 s. At the same time, a grayscale diamond shape is set as the static target at the center of moving area. No moving path is set on static target. In order to simulate the shape change and color change of detecting target caused by different illumination conditions, the circular moving target size is reduced from 100% to 70%, and its color is gradually changed from dark blue to light blue during the whole moving process. With respect to the static diamond target, its size is magnified from 100% to 140%, and the color within it is changed gradually from gray to purple. Validating simulation of test setup and moving target at different corner node positions is shown in Figure 10.
Detecting camera in validation is DS-2CD5A24 FWD-IZH, manufactured by Hikvision. Image sampling rate is set to 24 image frames per second, which surely reaches low-frequency characteristic requirement of wind-induced vibration of catenary suspension (mostly 1.2–1.8 Hz). The detecting camera was mounted on top of a tripod, at the same height of computer screen. During the validation test, tripod vibration was generated at the bottom where a vibration test bench works at a frequency of 0.5 Hz. The vibration frequency is determined according to detection results of static target, so as to simulate the vibration behavior of catenary column. Adopting the proposed method using minimum matching difference, identified transverse pixel
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Figure 11. Pixel displacement curve in x- and y-directions of the moving target and static target. Displacement of (a) moving target in x-direction, (b) moving target in y-direction, (c) static target in x-direction, and (d) static target in y-direction.
Figure 12. The contrast chart of detected and theoretical pixel displacement of moving target.
displacement in x-direction and vertical pixel displacement in y-direction of both moving target and static target are shown in Figure 11. Detected displacement of moving target referred to static target is revised according to equation (6). Then, the pixel displacement curves between detected offset and theoretical offset of moving target can be obtained as shown in Figure 12. From the validation test, we can conclude that the detected pixel displacement curve of moving target agrees well with the theoretical displacement curve. The maximum detecting error between motion path from proposed method and theoretical definition is within 3.5 pixels in two directions, the relative error of which is within 1.8%. Validation shows that the proposed dynamic target template matching method can completely meet required engineering precision.
Experiment application Adopting the suggested detection scheme mentioned above, wind-induced vibration of catenary suspension target at positioning point was observed at railway mileage of K20 + 599, where the detecting camera was mounted on top of the catenary column at one end of Sangequan Grand Bridge in Nanjiang railway line. Environmental wind data were collected via wind speed sensor, which was installed 50 m distance away from the railway bridge. Detecting results of wind-induced displacement of catenary suspension target were calculated in two directions including transverse direction which is perpendicular to the railway line horizontally and vertical direction which is perpendicular to the ground. Environmental wind speed data were processed in 10min averaged way. Experiment data were selected for
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Figure 13. Transverse displacement versus wind speed curve.
Figure 14. Vertical displacement versus wind speed curve.
24 h from 5:00 on 24 September 2017. The curve of detecting transverse displacement versus 10-min mean wind speed is depicted in Figure 13 and that of detecting vertical displacement versus 10-min mean wind speed is depicted in Figure 14. In the period of experiment as depicted in Figure 13, the environmental wind grew from 16 m/s to the maximum of 41 m/s and then dropped to 14 m/s. The maximum detecting transverse displacement of catenary suspension target can reach 12.9 and 217.7 mm. The maximum vertical displacement can reach 86.7 and 221.3 mm, which is apparently greater than transverse displacement. Testing displacement extent comparison between two directions agrees well with the law that vertical rigidity of catenary suspension positioning point is much smaller than transverse rigidity due to the spring device arranged at the bottom of positioner in vertical direction. Besides, detecting wind-induced displacement becomes bigger as environmental wind speed grows and the peak moment of both displacement and wind speed coincides with each other. From
this perspective, the suggested method can realize windinduced displacement detection of catenary suspension and thus provide important experiment data for windvibration safety research of electrified railway system in wind area.
Conclusion 1.
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The matching difference, defined based on root mean square (rms) of pixel grayscale between target template and same-sized traversing image area, can effectively represent the recognition matching extent between image and target. The smaller the matching difference becomes, the bigger the matching extent is. Suggested dynamic target template update, which replaces the target template with the recognized target at each processing step from image frame, can identify the catenary
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positioning target accurately by sensing the gradual change of illumination condition. In this way, the suggested method becomes more adaptable to complex illumination conditions like environmental brightness and contrast. Stabilizing algorithm, taking a static target as the target template to calculate its false displacement because of camera vibration, aims at eliminating vibration-induced false displacement of the moving target, whereby revising the absolute pixel displacement of moving target referred to static background. Validation test indicates that the detected pixel displacement curve of moving target by proposed method agrees well with theoretical displacement curve. The maximum relative error of target motion path between proposed method and theoretical definition is within 1.8%. Detected wind-induced displacement via experiment application is consistent with variation of environmental wind speed. Validation and application results prove that the proposed dynamic target template matching method can completely meet required engineering precision and thus provide an effective way for windvibration safety research of railway catenary system in wind area.
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Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
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Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is financially supported by the Technology Research and Development Program of China Railway Corporation (grant no. 2017J010-B).
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