Info Rail displacement measurement in shaking table tests via a method integrating KLT feature tracker and extended Kalman filter

Abstract

Shaking table tests are widely used to evaluate seismic effects on railway structures, but accurately measuring rail displacement remains a significant challenge owing to the nonlinear characteristics of large displacements, ambient noise interference, and limitations in displacement meter installation. In this paper, a novel method that integrates the Kanade-Lucas-Tomasi (KLT) feature tracker with an extended Kalman filter (EKF) is presented for measuring rail displacement during shaking table tests. The method employs KLT feature tracker and a random sample consensus algorithm to extract and track key feature points, while EKF optimally estimates dynamic states by accounting for system noise and observation errors. Shaking table test results demonstrate that the proposed method achieves an acceleration root mean square error of 0.300 m/s² and a correlation with accelerometer data exceeding 99.7%, significantly outperforming the original KLT approach. This innovative method provides a more efficient and reliable solution for measuring rail displacement under large nonlinear vibrations.

Keywords

shaking table test / rail displacement / computer vision / Kanade-Lucas-Tomasi (KLT) feature tracker / extended Kalman filter (EKF)

References

[1] ZHU Y, WEI Y X. Earthquake damage characteristics of Wenchuan earthquake railway engineering and consideration on seismic design countermeasures[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(S1):3378-3386. (in Chinese)

[2] ZHU G Y. Analysis of spatial deformation of ballasted track and running safety under earthquake[D]. Chengdu: Southwest Jiaotong University, 2014. (in Chinese)

[3] ESMAEILI M, NOGHABI H H. Investigating seismic behavior of ballasted railway track in earthquake excitation using finite-element model in three-dimensional space[J]. Journal of Transportation Engineering, 2013, 139(7): 697-708.

[4] Ministry of Construction of the People’s Republic of China. Code for seismic design of railway engineering: GB 50111—2006[S]. Beijing: Ministry of Construction of the People’s Republic of China, 2006. (in Chinese)

[5] WANG Y L. Dynamic response analysis of vehicle-line-bridge in the end area of long-span bridge and study on track ride comfort[D]. Beijing: China Academy of Railway Sciences, 2023. (in Chinese)

[6] PENG D H. Mechanism of post-seismic track irregularity for high-speed railway bridge and its control measure[D]. Changsha: Central South University, 2023. (in Chinese)

[7] XU C C. Study on deformation characteristics of ballasted track under earthquake action[D]. Chengdu: Southwest Jiaotong University, 2011. (in Chinese)

[8] KOSEKI J, KODA M, MATSUO S, et al. Damage to railway earth structures and foundations caused by the 2011 off the Pacific Coast of Tohoku Earthquake[J]. Soils and Foundations, 2012, 52(5): 872-889.

[9] WANG C G. Study on response mechanism and analysis method of high-speed railway track structure under earthquake action[D]. Qingdao: Qingdao University of Technology, 2023. (in Chinese)

[10] GAO C H, JI J B, YAN W M, et al. Developments of shaking table technology in China[J]. China Civil Engineering Journal, 2014, 47(8): 9-19. (in Chinese)

[11] ZHANG T, GAO B, FAN K X, et al. Study on flexible material in the sidewall of rigid model box in shaking table test[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(10): 2415-2424. (in Chinese)

[12] YU H T, ZHANG J H, YUAN Y, et al. Design and analysis of shaking table test on shield tunnel-shaft junction[J]. China Journal of Highway and Transport, 2017, 30(8): 183-192. (in Chinese)

[13] BOWNESS D, LOCK A C, POWRIE W, et al. Monitoring the dynamic displacements of railway track[J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2007, 221(1): 13-22.

[14] XIAO Z Z, LIANG J, YU D H, et al. Rapid three-dimension optical deformation measurement for transmission tower with different loads[J]. Optics and Lasers in Engineering, 2010, 48(9): 869-876.

[15] ZHU Y Y, LI J H, ZHU L, et al. Visual enhancement-based bridge detection algorithm and technique[J]. Journal of Southeast University (Natural Science Edition), 2024, 54(4): 902-910. (in Chinese)

[16] MIAO Z. Study on the state of interlayer structure of ballastless track based on digital image processing[D]. Shanghai: Shanghai University of Engineering Science, 2020. (in Chinese)

[17] KIM J, JEONG Y, LEE H, et al. Marker-based structural displacement measurement models with camera movement error correction using image matching and anomaly detection[J]. Sensors, 2020, 20(19): 5676.

[18] WANG X C, ZHONG L S, WANG Y, et al. Track longitudinal displacement measurement method based on binocular vision[J]. Science Technology and Engineering, 2022, 22(27): 12167-12174. (in Chinese)

[19] CHENG J M, JIN H, ZHENG Z J, et al. Welding seam groove recognition of steel structure on construction site based on machine vision[J]. Journal of Southeast University (Natural Science Edition), 2023, 53(1): 86-93. (in Chinese)

[20] CHENG J M, JIN H, ZHENG Z J, et al. Real-time detection method for weld feature of construction site steel structure based on top-down paradigm[J]. Journal of Southeast University (Natural Science Edition), 2023, 53(6): 1100-1110. (in Chinese)

[21] LIAO R X, WU T, ZHANG Y M, et al. Vision-based vessel detection for vessel-bridge collision warnings under complex scenes[J]. Journal of Southeast University (English Edition), 2024, 40(1): 33-40.

[22] STEPHEN G A, BROWNJOHN J M W, TAYLOR C A. Measurements of static and dynamic displacement from visual monitoring of the Humber Bridge[J]. Engineering Structures, 1993, 15(3): 197-208.

[23] OLASZEK P. Investigation of the dynamic characteristic of bridge structures using a computer vision method[J]. Measurement, 1999, 25(3): 227-236.

[24] PRIEST J A, POWRIE W, YANG L, et al. Measurements of transient ground movements below a ballasted railway line[J]. Géotechnique, 2010, 60(9): 667-677.

[25] MURRAY C A, TAKE W A, HOULT N A. Measurement of vertical and longitudinal rail displacements using digital image correlation[J]. Canadian Geotechnical Journal, 2015, 52(2): 141-155.

[26] HAN Y R. Realization and engineering application of dynamic displacement monitoring system based on image method[D]. Wuhan: Wuhan University of Technology, 2012. (in Chinese)

[27] CUI Y. Structural displacement and strain monitoring method based on digital image and feature points[D]. Harbin: Harbin Institute of Technology, 2014. (in Chinese)

[28] ZHANG W. Research and development of bridge deflection monitoring system based on image processing[D]. Nanjing: Nanjing University of Science and Technology, 2020. (in Chinese)

[29] GUO J, ZHU C A. Dynamic displacement measurement of large-scale structures based on the Lucas-Kanade template tracking algorithm[J]. Mechanical Systems and Signal Processing, 2016, 66: 425-436.

[30] FENG M Q, FUKUDA Y, FENG D M, et al. Nontarget vision sensor for remote measurement of bridge dynamic response[J]. Journal of Bridge Engineering, 2015, 20(12): 04015023.

[31] WANG X G, LIANG J, YOU W, et al. 3D full field displacement measurement of seismic shaking table experiment[J]. Journal of Applied Optics, 2016, 37(4): 567-572.

[32] WANG S, ZHANG L J, YIN G J. Defect identification method for steel surfaces based on improved YOLOv5[J]. Journal of Southeast University (English Edition), 2024, 40(1): 49-57.

[33] HUDSON A, WATSON G, LE PEN L, et al. Remediation of mud pumping on a ballasted railway track[J]. Procedia Engineering, 2016, 143: 1043-1050.

[34] MA Z Q, WANG Y S, SONG Z B. The image detection of wheel-rail relative lateral displacement based on laser[J]. Journal of Graphics, 2017, 38(4):623-628. (in Chinese)

[35] YANG T. Research on wheel-rail contact relationship of train based on image processing[D]. Lanzhou: Lanzhou Jiatong University, 2020. (in Chinese)

[36] CHONG A X, YIN H, LIU Y T, et al. Research on longitudinal displacement measurement method of seamless rail based on binocular vision[J]. Chinese Journal of Scientific Instrument, 2019, 40(11): 82-89. (in Chinese)

[37] HU J Y, WANG Y, YAN Y J, et al. Vehicle state estimation based on limited memory random weighted extended Kalman filter[J]. Journal of Southeast University (Natural Science Edition), 2022, 52(2): 387-393. (in Chinese)

[38] LOU Y X, CHEN S D, LU J, et al. Calculation method for pavement macrotexture depth based on improved Kalman filter algorithm[J]. Journal of Southeast University (Natural Science Edition), 2019, 50(1):129-136. (in Chinese)

[39] WON J, PARK J W, SONG M H, et al. Robust vision-based displacement measurement and acceleration estimation using RANSAC and Kalman filter[J]. Earthquake Engineering and Engineering Vibration, 2023, 22(2): 347-358.

[40] SHAN J Z, ZHANG H Z, BAI Z X, et al. Interstory drift response identification of structures based on vision and vibration data fusion[J]. Journal of Southeast University (Natural Science Edition), 2025, 55(1): 41-50. (in Chinese)

[41] XIONG C B, SUN C B, NIU Y B. Fusion estimation of structural dynamic displacement based on vision-and acceleration-based measurements[J]. Journal of Tianjin University (Science and Technology), 2024, 57(9): 891-901. (in Chinese)

[42] YAO Y. Damage identification of frame structure based on proper orthogonal decomposition and Kalman filter[D]. Baoding: Hebei University, 2023. (in Chinese)

[43] ZHAO J, BAO Y Q, GUAN Z G, et al. Video-based multiscale identification approach for tower vibration of a cable-stayed bridge model under earthquake ground motions[J]. Structural Control and Health Monitoring, 2019, 26(3): e2314.

Funding

National Key Research and Development Program of China(2021YFB2600600); National Key Research and Development Program of China(2021YFB2600601); National Natural Science Foundation of China(52408456); China Postdoctoral Science Foundation(2022M720533); College Students’ Innovative Entrepreneurial Training Plan Program(202410710009); Key Research and Development Program of Shaanxi, China(2024SF-YBXM-659)