Enhanced identification of bridge modal parameters using contact residuals from three-connected vehicles: Theoretical study

Yi He, Judy P. Yang*, Zhitao Yan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this study, using two residual contact responses from three-connected moving vehicles is proposed to enhance the identification of bridge modal parameters. Based on the analytical formulation of the residual contact-point accelerations, the contact-point accelerations are back-calculated from the vertical accelerations of three vehicles, from which the magnitudes of pavement irregularity-related frequencies can be largely reduced in the two residual contact responses. From the residual contact responses, the bridge frequencies are identified by conducting FFT spectrum analysis, while the damping ratios are estimated using curve fitting of the free-decay components extracted by random decrement technique and variational mode decomposition. Unlike the incomplete construction of the mode shapes of a bridge using one residual response from two-connected vehicles, the proposed method can retrieve the complete mode shapes of a bridge. Since the two contact residual accelerations can be expressed as the interpolation of bridge mode shapes, the latter can be retrieved by performing the singular value decomposition of the residual response matrix. To recover the invalid measured data in retrieving the bridge mode shapes, the singular value thresholding algorithm is applied. The effectiveness and robustness of the method are validated by the numerical examples considering a wide range of practical conditions, particularly, with the merit of application to various boundary conditions of bridges in comparison with the commonly adopted technique.

Original languageEnglish
Pages (from-to)1320-1335
Number of pages16
StatePublished - Aug 2023


  • Bridge modal parameters
  • Pavement irregularity
  • Residual contact-point response
  • Singular value thresholding
  • Vehicle scanning method


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