Estimating Bridge Modal Parameters from Residual Response of Two-Connected Vehicles

Yi He, Judy P. Yang*, Jiuquan Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Purpose: This study presents a method to estimate the bridge frequencies, damping ratios and mode shapes from the responses of two connected single-axle vehicles. As the bridge pavement roughness is the main excitation for a passing vehicle, the roughness-related components can seriously overshadow the bridge modal parameters contained in the vehicle responses. Although the residual response from two-connected vehicles has been adopted to remove the roughness-related components in the identification of bridge frequencies, the estimation of bridge damping ratios and mode shapes from the residual response is not fully explored yet. Methods: A semi-analytical solution is first derived to understand the frequency content of a contact-point residual response; then, the two contact-point responses are back-calculated from the vehicle responses. Subsequently, the singular spectrum analysis is conducted to exact the bridge frequency-related mono-components, from which the bridge damping ratios are estimated by curve-fitting while the mode shapes are constructed by Hilbert transform. Results: The numerical results show that the proposed method enables the estimation of the first two bridge damping ratios and the construction of the first mode shape with satisfactory accuracy. Conclusion: The proposed method can effectively remove the adverse effect of pavement roughness and efficiently construct the mode shapes of bridge in consideration of bridge damping ratios.

Original languageEnglish
JournalJournal of Vibrational Engineering and Technologies
StateAccepted/In press - 2022


  • Contact-point response
  • Hilbert transform
  • Modal parameter identification
  • Pavement roughness
  • Singular spectrum analysis
  • Vehicle scanning method


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