Modal Identification of Bridges Using Mobile Sensors with Sparse Vibration Data
Publication: Journal of Engineering Mechanics
Volume 146, Issue 4
Abstract
Dynamic sensor networks have the potential to significantly increase the speed and scale of infrastructure monitoring. Structural health monitoring (SHM) methods have been long developed under the premise of utilizing fixed sensor networks for data acquisition. Over the past decade, applications of mobile sensor networks have emerged for bridge health monitoring. Yet, when it comes to modal identification, there remain gaps in knowledge that have ultimately prevented implementations on large structural systems. This paper presents a structural modal identification methodology based on sensors in a network of moving vehicles: a large-scale data collection mechanism that is already in place. Vehicular sensor networks scan the bridge’s vibrations in space and time to build a sparse representation of the full response, i.e., an incomplete data matrix with a low rank. This paper introduces modal identification using matrix completion (MIMC) methods to extract dynamic properties (frequencies, damping, and mode shapes) from data collected by a large number of mobile sensors. A dense matrix is first constructed from sparse observations using alternating least-square (ALS) then decomposed for structural modal identification. This paper shows that the completed data matrix is the product of a spatial matrix and a temporal matrix from which modal properties can be extracted via methods such as principal component analysis (PCA). Alternatively, an impulse-response structure can be embedded into the temporal matrix and then natural frequencies and damping ratios are determined using Newton’s method with an inverse Hessian approximation. For the case of ambient vibrations, the natural excitation technique (NExT) is applied and then structured optimization (Newton’s method) is performed. Both approaches are evaluated numerically, and results are compared in terms of data sparsity, modal property accuracy, and postprocessing complexity. Results show that both techniques extract accurate modal properties, including high-resolution mode shapes from sparse dynamic sensor network data; they are the first to provide a complete modal identification using data from a large-scale dynamic sensor network.
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Data Availability Statement
Models and codes generated and used during the study are available from the corresponding author by request.
Acknowledgments
Research funding is partially provided by the National Science Foundation through Grant CMMI-1351537 by the Hazard Mitigation and Structural Engineering program, Grants CCF-1618717 and CCF-1740796, and by a grant from the Commonwealth of Pennsylvania, Department of Community and Economic Development, through the Pennsylvania Infrastructure Technology Alliance (PITA). The authors would like to thank Anas S.p.A, Allianz, Brose, Cisco, Dover Corporation, Ford, the Amsterdam Institute for Advanced Metropolitan Solutions, the Fraunhofer Institute, the Kuwait-MIT Center for Natural Resources and the Environment, LabCampus, RATP, Singapore-MIT Alliance for Research and Technology (SMART), SNCF Gares & Connexions, UBER, and all the members of the MIT Senseable City Lab Consortium for supporting this research.
References
Alexander, L., S. Jiang, M. Murga, and M. C. González. 2015. “Origin–destination trips by purpose and time of day inferred from mobile phone data.” Transp. Res. Part C: Emerging Technol. 58 (Part B): 240–250. https://doi.org/10.1016/j.trc.2015.02.018.
Allemang, R. J., and D. L. Brown. 1982. “A correlation coefficient for modal vector analysis.” In Vol. 1 of Proc., 1st Int. Modal Analysis Conf., 110–116. Orlando, FL: SEM.
Anjomshoaa, A., F. Duarte, D. Rennings, T. Matarazzo, P. de Souza, and C. Ratti. 2018. “City scanner: Building and scheduling a mobile sensing platform for smart city services.” IEEE Internet Things J. 5 (6): 4567–4579. https://doi.org/10.1109/JIOT.2018.2839058.
Au, S.-K. 2011. “Fast Bayesian FFT method for ambient modal identification with separated modes.” J. Eng. Mech. 137 (3): 214–226. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000213.
Barabasi, A.-L. 2005. “The origin of bursts and heavy tails in human dynamics.” Nature 435 (7039): 207. https://doi.org/10.1038/nature03459.
Brincker, R., L. Zhang, and P. Andersen. 2001. “Modal identification of output-only systems using frequency domain decomposition.” Smart Mater. Struct. 10 (3): 441. https://doi.org/10.1088/0964-1726/10/3/303.
Cai, J.-F., E. J. Candès, and Z. Shen. 2010. “A singular value thresholding algorithm for matrix completion.” SIAM J. Optim. 20 (4): 1956–1982. https://doi.org/10.1137/080738970.
Candès, E. J., and B. Recht. 2009. “Exact matrix completion via convex optimization.” Found. Comput. Math. 9 (6): 717. https://doi.org/10.1007/s10208-009-9045-5.
Chang, M., and S. N. Pakzad. 2014. “Observer Kalman filter identification for output-only systems using interactive structural modal identification toolsuite.” J. Bridge Eng. 19 (5): 04014002. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000530.
Chopra, A. K. 2017. Dynamics of structures theory and applications to earthquake engineering. Hoboken, NJ: Pearson.
Dorvash, S., and S. Pakzad. 2013. “Stochastic iterative modal identification algorithm and application in wireless sensor networks.” Struct. Control Health Monit. 20 (8): 1121–1137. https://doi.org/10.1002/stc.1521.
Eisen, M., A. Mokhtari, and A. Ribeiro. 2017. “Large scale empirical risk minimization via truncated adaptive newton method.” Preprint, submitted May 22, 2017. http://arxiv.org/abs/1705.07957.
Eshkevari, S. S., and S. Pakzad. 2019. “Bridge structural identification using moving vehicle acceleration measurements.” In Vol. 2 of Dynamics of civil structures, 251–261. Cham, Switzerland: Springer.
Eshkevari, S. S., and S. N. Pakzad. 2020. “Signal reconstruction from mobile sensors network using matrix completion approach.” In Vol. 8 of Topics in modal analysis and testing, 61–75. Cham, Switzerland: Springer.
Eshkevari, S. S., T. J. Matarazzo, and S. N. Pakzad. 2020. “Bridge modal identification using acceleration measurements within moving vehicles.” Preprint, submitted January 6, 2020. http://arxiv.org/abs/2001.01797.
Eshkevari, S. S., M. Takác, S. N. Pakzad, and S. S. Eshkevari. 2019. “High resolution bridge mode shape identification via matrix completion approach.” Struct. Health Monit. https://doi.org/10.12783/shm2019/32499.
Gensun, F. 1996. “Whittaker–Kotelnikov–Shannon sampling theorem and aliasing error.” J. Approximation Theory 85 (2): 115–131. https://doi.org/10.1006/jath.1996.0033.
González, A., E. J. OBrien, and P. McGetrick. 2012. “Identification of damping in a bridge using a moving instrumented vehicle.” J. Sound Vib. 331 (18): 4115–4131. https://doi.org/10.1016/j.jsv.2012.04.019.
Gurney, K. R., et al. 2015. “Climate change: Track urban emissions on a human scale.” Nat. News 525 (7568): 179. https://doi.org/10.1038/525179a.
Jain, P., P. Netrapalli, and S. Sanghavi. 2013. “Low-rank matrix completion using alternating minimization.” In Proc., 45th Annual ACM Symp. on Theory of Computing, 665–674. New York: Association for Computing Machinery.
James, G., T. G. Carne, and J. P. Lauffer. 1995. “The natural excitation technique (NExT) for modal parameter extraction from operating structures.” Modal Anal. Int. J. Anal. Exp. Modal Anal. 10 (4): 260.
Jerri, A. J. 1977. “The Shannon sampling theorem—Its various extensions and applications: A tutorial review.” Proc. IEEE. 65 (11): 1565–1596. https://doi.org/10.1109/PROC.1977.10771.
Jolliffe, I. 2011. “Principal component analysis.” In International encyclopedia of statistical science, 1094–1096. Cham, Switzerland: Springer.
Juang, J.-N., and R. S. Pappa. 1985. “An eigensystem realization algorithm for modal parameter identification and model reduction.” J. Guidance Control Dyn. 8 (5): 620–627. https://doi.org/10.2514/3.20031.
Keenahan, J., E. J. OBrien, P. J. McGetrick, and A. Gonzalez. 2014. “The use of a dynamic truck–trailer drive-by system to monitor bridge damping.” Struct. Health Monit. 13 (2): 143–157. https://doi.org/10.1177/1475921713513974.
Kleywegt, A., and K. Sinha. 1994. Tools for bridge management data analysis. Washington, DC: Transportation Research Board.
Kramer, B., and A. A. Gorodetsky. 2018. “System identification via cur-factored Hankel approximation.” SIAM J. Sci. Comput. 40 (2): A848–A866. https://doi.org/10.1137/17M1137632.
Kramer, B., and S. Gugercin. 2016. “Tangential interpolation-based eigensystem realization algorithm for MIMO systems.” Math. Comput. Modell. Dyn. Syst. 22 (4): 282–306. https://doi.org/10.1080/13873954.2016.1198389.
Krishnan, S. S., Z. Sun, A. Irfanoglu, S. J. Dyke, and G. Yan. 2011. “Evaluating the performance of distributed approaches for modal identification.” In Vol. 7981 of Sensors and smart structures technologies for civil, mechanical, and aerospace systems 2011, 79814M. Bellingham, WA: International Society for Optics and Photonics.
Kurata, M., J. Kim, Y. Zhang, J. P. Lynch, G. Van Der Linden, V. Jacob, E. Thometz, P. Hipley, and L.-H. Sheng. 2011. “Long-term assessment of an autonomous wireless structural health monitoring system at the new Carquinez suspension bridge.” In Vol. 7983 of Nondestructive characterization for composite materials, aerospace engineering, civil infrastructure, and homeland security 2011, 798312. Bellingham, WA: International Society for Optics and Photonics.
Li, W.-M., Z.-H. Jiang, T.-L. Wang, and H.-P. Zhu. 2014. “Optimization method based on generalized pattern search algorithm to identify bridge parameters indirectly by a passing vehicle.” J. Sound Vib. 333 (2): 364–380. https://doi.org/10.1016/j.jsv.2013.08.021.
Lin, C., and Y. Yang. 2005. “Use of a passing vehicle to scan the fundamental bridge frequencies: An experimental verification.” Eng. Struct. 27 (13): 1865–1878. https://doi.org/10.1016/j.engstruct.2005.06.016.
Lynch, J. P., and K. J. Loh. 2006. “A summary review of wireless sensors and sensor networks for structural health monitoring.” Shock Vib. Dig. 38 (2): 91–130. https://doi.org/10.1177/0583102406061499.
Malekjafarian, A., P. J. McGetrick, and E. J. OBrien. 2015. “A review of indirect bridge monitoring using passing vehicles.” Shock Vib. 2015: 286139. https://doi.org/10.1155/2015/286139.
Malekjafarian, A., and E. J. OBrien. 2014. “Identification of bridge mode shapes using short time frequency domain decomposition of the responses measured in a passing vehicle.” Eng. Struct. 81 (Dec): 386–397. https://doi.org/10.1016/j.engstruct.2014.10.007.
Marulanda, J., J. M. Caicedo, and P. Thomson. 2017. “Modal identification using mobile sensors under ambient excitation.” J. Comput. Civ. Eng. 31 (2): 04016051. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000619.
Massaro, E., C. Ahn, C. Ratti, P. Santi, R. Stahlmann, A. Lamprecht, M. Roehder, and M. Huber. 2017. “The car as an ambient sensing platform [point of view].” Proc. IEEE. 105 (1): 3–7. https://doi.org/10.1109/JPROC.2016.2634938.
Matarazzo, T. J., and S. N. Pakzad. 2016a. “Structural identification for mobile sensing with missing observations.” J. Eng. Mech. 142 (5): 04016021. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001046.
Matarazzo, T. J., and S. N. Pakzad. 2016b. “Truncated physical model for dynamic sensor networks with applications in high-resolution mobile sensing and bigdata.” J. Eng. Mech. 142 (5): 04016019. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001022.
Matarazzo, T. J., and S. N. Pakzad. 2018. “Scalable structural modal identification using dynamic sensor network data with STRIDEX.” Comput.-Aided Civ. Infrastruct. Eng. 33 (1): 4–20. https://doi.org/10.1111/mice.12298.
Matarazzo, T. J., P. Santi, S. N. Pakzad, K. Carter, C. Ratti, B. Moaveni, C. Osgood, and N. Jacob. 2018. “Crowdsensing framework for monitoring bridge vibrations using moving smartphones.” Proc. IEEE. 106 (4): 577–593. https://doi.org/10.1109/JPROC.2018.2808759.
Maymon, S., and A. V. Oppenheim. 2011. “Sinc interpolation of nonuniform samples.” IEEE Trans. Signal Process. 59 (10): 4745–4758. https://doi.org/10.1109/TSP.2011.2160054.
McGetrick, P. J., C.-W. Kim, A. González, and E. J. Brien. 2015. “Experimental validation of a drive-by stiffness identification method for bridge monitoring.” Struct. Health Monit. 14 (4): 317–331. https://doi.org/10.1177/1475921715578314.
Mei, Q., and M. Gül. 2018. “A crowdsourcing-based methodology using smartphones for bridge health monitoring.” Struct. Health Monit. 18 (5–6): 1602–1619. https://doi.org/10.1177/1475921718815457.
Mei, Q., M. Gül, and M. Boay. 2019. “Indirect health monitoring of bridges using Mel-frequency cepstral coefficients and principal component analysis.” Mech. Syst. Sig. Process. 119 (Mar): 523–546. https://doi.org/10.1016/j.ymssp.2018.10.006.
Moheimani, S. R., D. Halim, and A. J. Fleming. 2003. Vol. 10 of Spatial control of vibration: Theory and experiments. Singapore: World Scientific.
OBrien, E. J., and A. Malekjafarian. 2016. “A mode shape-based damage detection approach using laser measurement from a vehicle crossing a simply supported bridge.” Struct. Control Health Monit. 23 (10): 1273–1286. https://doi.org/10.1002/stc.1841.
Pakzad, S. N., G. L. Fenves, S. Kim, and D. E. Culler. 2008. “Design and implementation of scalable wireless sensor network for structural monitoring.” J. Infrastruct. Syst. 14 (1): 89–101. https://doi.org/10.1061/(ASCE)1076-0342(2008)14:1(89).
Pakzad, S. N., G. V. Rocha, and B. Yu. 2011. “Distributed modal identification using restricted auto regressive models.” Int. J. Syst. Sci. 42 (9): 1473–1489. https://doi.org/10.1080/00207721.2011.563875.
Peeters, B., and G. De Roeck. 2001. “Stochastic system identification for operational modal analysis: A review.” J. Dyn. Syst. Meas. Contr. 123 (4): 659–667. https://doi.org/10.1115/1.1410370.
Poncelet, F., G. Kerschen, J.-C. Golinval, and D. Verhelst. 2007. “Output-only modal analysis using blind source separation techniques.” Mech. Syst. Sig. Process. 21 (6): 2335–2358. https://doi.org/10.1016/j.ymssp.2006.12.005.
Schanze, T. 1995. “Sinc interpolation of discrete periodic signals.” IEEE Trans. Signal Process. 43 (6): 1502–1503. https://doi.org/10.1109/78.388863.
Smith, I. F. 2016. “Studies of sensor data interpretation for asset management of the built environment.” Front. Built Environ. 2: 8. https://doi.org/10.3389/fbuil.2016.00008.
Sony, S., S. Laventure, and A. Sadhu. 2019. “A literature review of next-generation smart sensing technology in structural health monitoring.” Struct. Control Health Monit. 26 (3): e2321. https://doi.org/10.1002/stc.2321.
Tachet, R., O. Sagarra, P. Santi, G. Resta, M. Szell, S. Strogatz, and C. Ratti. 2017. “Scaling law of urban ride sharing.” Sci. Rep. 7: 42868. https://doi.org/10.1038/srep42868.
Tachet, R., P. Santi, S. Sobolevsky, L. I. Reyes-Castro, E. Frazzoli, D. Helbing, and C. Ratti. 2016. “Revisiting street intersections using slot-based systems.” PLoS One. 11 (3): e0149607. https://doi.org/10.1371/journal.pone.0149607.
Vazifeh, M. M., P. Santi, G. Resta, S. Strogatz, and C. Ratti. 2018. “Addressing the minimum fleet problem in on-demand urban mobility.” Nature 557 (7706): 534. https://doi.org/10.1038/s41586-018-0095-1.
Wang, H., F. Calabrese, G. Di Lorenzo, and C. Ratti. 2010. “Transportation mode inference from anonymized and aggregated mobile phone call detail records.” In Proc., 13th Int. IEEE Conf. on Intelligent Transportation Systems, 318–323. New York: IEEE.
Wang, P., T. Hunter, A. M. Bayen, K. Schechtner, and M. C. González. 2012. “Understanding road usage patterns in urban areas.” Sci. Rep. 2: 1001. https://doi.org/10.1038/srep01001.
Wilson, E. L., M.-W. Yuan, and J. M. Dickens. 1982. “Dynamic analysis by direct superposition of Ritz vectors.” Earthquake Eng. Struct. Dyn. 10 (6): 813–821. https://doi.org/10.1002/eqe.4290100606.
Wright, S., and J. Nocedal. 1999. Numerical optimization. New York: Springer.
Yang, Y., and K. Chang. 2009. “Extracting the bridge frequencies indirectly from a passing vehicle: Parametric study.” Eng. Struct. 31 (10): 2448–2459. https://doi.org/10.1016/j.engstruct.2009.06.001.
Yang, Y.-B., C. Lin, and J. Yau. 2004. “Extracting bridge frequencies from the dynamic response of a passing vehicle.” J. Sound Vib. 272 (3–5): 471–493. https://doi.org/10.1016/S0022-460X(03)00378-X.
Zachariah, D., M. Sundin, M. Jansson, and S. Chatterjee. 2012. “Alternating least-squares for low-rank matrix reconstruction.” IEEE Signal Process Lett. 19 (4): 231–234. https://doi.org/10.1109/LSP.2012.2188026.
Zhu, C., R. H. Byrd, P. Lu, and J. Nocedal. 1997. “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization.” ACM Trans. Math. Software (TOMS). 23 (4): 550–560. https://doi.org/10.1145/279232.279236.
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Received: Mar 4, 2019
Accepted: Aug 27, 2019
Published online: Jan 28, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 28, 2020
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