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Bridge frequency estimation strategies using smartphones

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Bridges are susceptible to deterioration and damage as they age and should be routinely assessed to evaluate their integrity and safety for service. Traditionally, structural monitoring has comprised visual inspections, however this is both time and labor intensive. Researchers have shown that sensors on moving vehicles may provide insight into the dynamic behavior of bridges. Accelerometers within smartphones may serve as the sensors from which data is collected; thus, enabling massive data collection from a fleet of potential monitoring vehicles. This paper presents four postprocessing strategies for estimating bridge frequencies from smartphone acceleration data streams with no a priori information about the mass or stiffness of the bridge or vehicle. These techniques utilize the DFT and MUSIC algorithms to calculate vehicle acceleration frequency spectrums from which the fundamental bridge vibration frequency may be estimated. Both single-vehicle and crowdsourced postprocessing techniques are investigated. Utilizing the MUSIC algorithm within a crowdsourcing framework, the correct bridge frequency was identified in all analytical simulations within 4% error, representing a significant increase in performance over single-vehicle estimations made using MUSIC. The effect of user interaction with the smartphone is studied by including superimposed acceleration signals on 25–100% of analytical results; the superimposed user events included a dropped smartphone and talking on a smartphone. Increasing the percentage of noisy signals in the pool of evaluated accelerations generally reduces performance with the exception of crowdsourced estimations made using the MUSIC algorithm, which proved to be robust against user interaction with the smartphone.

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  1. ASCE (2017) 2017 Infrastructure Report Card

  2. Doebling SW, Farrar CR, Prime MB (1997) A summary review of vibration-based damage identification methods. Technical report, Los Alamos National Laboratory

  3. Jiang X, Ma ZJ, Ren W-X (2012) Crack detection from the slope of the mode shape using complex continuous wavelet transform. Comput Civ Infrastruct Eng 27:187–201.

    Article  Google Scholar 

  4. Sohn H, Farrar CR, Hemez F, Czarnecki J (2002) A review of structural health monitoring literature 1996–2001. Technical report. Los Alamos National Laboratory

  5. Arangio S, Bontempi F (2010) Soft computing based multilevel strategy for bridge integrity monitoring. Comput Civ Infrastruct Eng 25:348–362.

    Article  Google Scholar 

  6. Mehrjoo M, Khaji N, Moharrami H, Bahreininejad A (2008) Damage detection of truss bridge joints using artificial neural networks. Expert Syst Appl 35:1122–1131.

    Article  Google Scholar 

  7. Zapico JL, González MP, Worden K (2003) Damage assessment using neural networks. Mech Syst Signal Process 17:119–125.

    Article  Google Scholar 

  8. Hazra B, Sadhu A, Roffel AJ, Narasimhan S (2012) Hybrid time-frequency blind source separation towards ambient system identification of structures. Comput Civ Infrastruct Eng 27:314–332.

    Article  Google Scholar 

  9. Story BA, Fry GT (2014) Methodology for designing diagnostic data streams for use in a structural impairment detection system. J Bridg Eng 19:04013020.

    Article  Google Scholar 

  10. Story BA, Fry GT (2014) A Structural impairment detection system using competitive arrays of artificial neural networks. Comput Civ Infrastruct Eng 29:180–190

    Article  Google Scholar 

  11. Xiang J, Liang M (2012) Wavelet-based detection of beam cracks using modal shape and frequency measurements. Comput Civ Infrastruct Eng 27:439–454.

    Article  Google Scholar 

  12. Cantero D, Hester D, Brownjohn J (2017) Evolution of bridge frequencies and modes of vibration during truck passage. Eng Struct 152:452–464.

    Article  Google Scholar 

  13. Cantero D, O’Brien EJ (2013) The non-stationarity of apparent bridge natural frequencies during vehicle crossing events. FME Trans 41:279–284

    Google Scholar 

  14. Cerda F, Garrett J, Bielak J et al (2012) Indirect structural health monitoring in bridges: scale experiments. In: Proceedings of bridge maintenance, safety, management, resilience, and sustainability. Lago di Como, pp 346–353

  15. Kim C, Chang K, Mcgetrick PJ et al (2017) Utilizing moving vehicles as sensors for bridge condition screening. A laboratory verification. Sens Mater 29:153.

    Article  Google Scholar 

  16. Kim C-W, Isemoto R, McGetrick P et al (2014) Drive-by bridge inspection from three different approaches. Smart Struct Syst 13:775–796.

    Article  Google Scholar 

  17. Kim J, Lynch JP (2012) Experimental analysis of vehicle bridge interaction using a wireless monitoring system and a two-stage system identification technique. Mech Syst Signal Process 28:3–19.

    Article  Google Scholar 

  18. Kong X, Cai CS, Kong B (2016) Numerically extracting bridge modal properties from dynamic responses of moving vehicles. J Eng Mech 142:04016025.

    Article  Google Scholar 

  19. Li WM, Jiang ZH, Wang TL, Zhu HP (2014) Optimization method based on generalized pattern search algorithm to identify bridge parameters indirectly by a passing vehicle. J Sound Vib 333:364–380.

    Article  Google Scholar 

  20. Lin CW, Yang YB (2005) Use of a passing vehicle to scan the fundamental bridge frequencies: an experimental verification. Eng Struct 27:1865–1878.

    Article  Google Scholar 

  21. Malekjafarian A, McGetrick PJ, O’Brien EJ (2015) A review of indirect bridge monitoring using passing vehicles. Shock Vib.

    Article  Google Scholar 

  22. Malekjafarian A, O’Brien EJ (2014) Application of output-only modal method in monitoring of bridges using an instrumented vehicle. In: Civil Engineering Research in Ireland. Belfast, UK

  23. Malekjafarian A, O’Brien EJ (2014) Identification of bridge mode shapes using short time frequency domain decomposition of the responses measured in a passing vehicle. Eng Struct 81:386–397.

    Article  Google Scholar 

  24. Malekjafarian A, O’Brien EJ (2017) On the use of a passing vehicle for the estimation of bridge mode shapes. J Sound Vib 397:77–91.

    Article  Google Scholar 

  25. McGetrick PJ, González A, OBrien EJ (2009) Theoretical investigation of the use of a moving vehicle to identify bridge dynamic parameters. Insight Non Destr Test Cond Monit 51:433–438.

    Article  Google Scholar 

  26. O’Brien EJ, Malekjafarian A (2015) Identification of bridge mode shapes using a passing vehicle. In: 7th International conference structure health monitor intelligence infrastructure, Torino, Italy, July, 2015

  27. Siringoringo DM, Fujino Y (2012) Estimating bridge fundamental frequency from vibration response of instrumented passing vehicle: analytical and experimental study. Adv Struct Eng 15:417–433.

    Article  Google Scholar 

  28. Yang YB, Chang KC (2009) Extracting the bridge frequencies indirectly from a passing vehicle: parametric study. Eng Struct 31:2448–2459.

    Article  Google Scholar 

  29. Yang YB, Chang KC (2009) Extraction of bridge frequencies from the dynamic response of a passing vehicle enhanced by the EMD technique. J Sound Vib 322:718–739.

    Article  Google Scholar 

  30. Yang YB, Chang KC, Li YC (2013) Filtering techniques for extracting bridge frequencies from a test vehicle moving over the bridge. Eng Struct 48:353–362.

    Article  Google Scholar 

  31. Yang YB, Cheng MC, Chang KC (2013) Frequency variation in vehicle–bridge interaction systems. Int J Struct Stab Dyn 13:1350019.

    Article  MathSciNet  MATH  Google Scholar 

  32. Yang YB, Li YC, Chang KC (2014) Constructing the mode shapes of a bridge from a passing vehicle: a theoretical study. Smart Struct Syst 13:797–819.

    Article  Google Scholar 

  33. Yang YB, Lin CW (2005) Vehicle–bridge interaction dynamics and potential applications. J Sound Vib 284:205–226.

    Article  Google Scholar 

  34. Yang YB, Lin CW, Yau JD (2004) Extracting bridge frequencies from the dynamic response of a passing vehicle. J Sound Vib 272:471–493.

    Article  Google Scholar 

  35. Yang YB, Yang JP (2018) State-of-the-art review on modal identification and damage detection of bridges by moving test vehicles. Int J Struct Stab Dyn 18:1850025.

    Article  Google Scholar 

  36. Zhu XQ, Law SS (2015) Structural health monitoring based on vehicle–bridge interaction: accomplishments and challenges. Adv Struct Eng 18:1999–2015.

    Article  Google Scholar 

  37. Sitton JD, Zeinali Y, Rajan D, Story BA (2020) Frequency estimation on two-span continuous bridges using dynamic responses of passing vehicles. J Eng Mech 146:04019115.

    Article  Google Scholar 

  38. Oshima Y, Funamizu Y, Sugiura K (2015) Stochastic characteristics of estimated frequencies in bridge–vehicle interactions. J Civ Struct Heal Monit 5:263–273.

    Article  Google Scholar 

  39. Elhattab A, Uddin N, OBrien E (2016) Drive-by bridge damage monitoring using bridge displacement profile difference. J Civ Struct Heal Monit 6:839–850.

    Article  Google Scholar 

  40. Tan C, Elhattab A, Uddin N (2017) “Drive-by’’ bridge frequency-based monitoring utilizing wavelet transform. J Civ Struct Heal Monit 7:615–625.

    Article  Google Scholar 

  41. Feldbusch A, Sadegh-Azar H, Agne P (2017) Vibration analysis using mobile devices (smartphones or tablets). Procedia Eng 199:2790–2795.

    Article  Google Scholar 

  42. McGetrick PJ, Hester D, Taylor SE (2017) Implementation of a drive-by monitoring system for transport infrastructure utilising smartphone technology and GNSS. J Civ Struct Heal Monit 7:175–189.

    Article  Google Scholar 

  43. Mei Q, Gül M, Boay M (2019) Indirect health monitoring of bridges using Mel-frequency cepstral coefficients and principal component analysis. Mech Syst Signal Process 119:523–546

    Article  Google Scholar 

  44. Mei Q, Gül M (2019) Monitoring populations of bridges in smart cities using smartphones. Structures Congress 2019, Orlando, FL, April, 2019

  45. Sadeghi Eshkevari S, Pakzad SN, Takac M, Matarazzo TJ (2020) Modal identification of bridges using mobile sensors with sparse vibration data. J Eng Mech 146:04020011

    Article  Google Scholar 

  46. Salawu OS (1996) Detection of structural damage through changes in frequency: a review. Eng Struct 19(9):718–723

    Article  Google Scholar 

  47. Moradalizadeh M (1990)Evaluation of crack defects in framed structures using resonant frequency techniquesM. Phil. Thesis, University of Newcastle Upon Tyne

  48. Slastan J, Pietrzko S (1993) Changes of RC-beam modal parameters due to cracks. In: Proceedings of 11th international modal analysis conference, vol 1. pp 70–76

  49. Brownjohn JMW (1988) Assessment of structural integrity by dynamic measurements. Ph.D. Thesis, University of Bristol

  50. Begg RD, Mackenzie AC, Dodds CJ, Loland O (1976) Structural integrity monitoring using digital processing of vibration signals. In: Proceedings of 8th offshore technology conference

  51. Alampalli S, Fu G, Abdul Aziz I (1992) Modal analysis as a bridge inspection tool. In: Proceedings of 10th international modal analysis conference, vol 2. pp 1359–1366

  52. Biswas M, Pandey AK, Samman MM (1990) Diagnostic experimental spectral/modal analysis of a highway bridge. Int J Anal Exp Model Anal 5(1):33–42

    Google Scholar 

  53. Schmidt RO (1986) Multiple emitter location and signal parameter. IEEE Trans Antennas Propag 34:276–280

    Article  Google Scholar 

  54. Barabell AJ, Capon J, DeLong DF et al (1998) Performance comparison of superresolution array processing algorithms. Lexington, Massachusetts

    Google Scholar 

  55. Jiang X, Adeli H (2007) Pseudospectra, MUSIC, and dynamic wavelet neural network for damage detection of highrise buildings. Int J Numer Methods Eng 71:606–629

    Article  Google Scholar 

  56. Amezquita-Sanchez JP, Adeli H (2015) A new music-empirical wavelet transform methodology for time-frequency analysis of noisy nonlinear and non-stationary signals. Digit Signal Process A Rev J 45:55–68.

    Article  Google Scholar 

  57. Amezquita-Sanchez JP, Park HS, Adeli H (2017) A novel methodology for modal parameters identification of large smart structures using MUSIC, empirical wavelet transform, and Hilbert transform. Eng Struct 147:148–159.

    Article  Google Scholar 

  58. Mazzoni S, McKenna F, Scott MH, Fenves GL (2006) OpenSees command language manual

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The authors would like to thank the undergraduate researchers Christopher Stenzel and Hussam Khresat in the SMU Structural Engineering Laboratory and the GISD Summer Research Fellows (Anthony Aiyedun, Joseline Contreras, Arath Dominguez, Michelle Mendoza, Sarina Mohanlal, Caleb Vinson) for assistance with vehicle customization and experimental design. This research is supported through a research and education partnership with Garland Independent School District.


Smart Infrastructure Innovation Initiative (S3i) Program with Garland ISD.

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All authors contributed to this research and the writing of this article. BS and DR conceptualized and developed the method. JS developed the numerical models and experimental setup and performed all simulations and experiments.

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Correspondence to Brett A. Story.

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Appendix: User interaction signals

Appendix: User interaction signals

In an ideal diagnostic scenario, a smartphone would be stationary within a vehicle traversing a bridge. In reality, user interaction may occur. As a first-order approximation to including user interaction among vehicle signals, several experiments were performed to investigate superposition of two user events (i.e., Talk and Drop events) on vehicular vibration signals. For both user events, the following acceleration responses were recorded experimentally from a smartphone in a vehicle:

  1. 1.

    Driving along flat ground with no user events performed;

  2. 2.

    The user event while the car was stationary;

  3. 3.

    The user event while the car was driven along flat ground.


Fig. 11
figure 11

Time history comparison for drop event

11 and

Fig. 12
figure 12

Time history comparison for talking event

12 compare the superposition of signal types 1 and 2 with signal type 3 for both Drop and Talk events. To a first-order approximation, the superposition of individual events upon vehicle signals resembles the response of the smartphone to a user event during vehicle movement.

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Sitton, J.D., Rajan, D. & Story, B.A. Bridge frequency estimation strategies using smartphones. J Civil Struct Health Monit 10, 513–526 (2020).

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