Mode shape expansion with consideration of analytical modelling errors and modal measurement uncertainty

Hua Peng Chen, Kong Fah Tee, Yiqing Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)


Mode shape expansion is useful in structural dynamic studies such as vibration based structural health monitoring; however most existing expansion methods can not consider the modelling errors in the finite element model and the measurement uncertainty in the modal properties identified from vibration data. This paper presents a reliable approach for expanding mode shapes with consideration of both the errors in analytical model and noise in measured modal data. The proposed approach takes the perturbed force as an unknown vector that contains the discrepancies in structural parameters between the analytical model and tested structure. A regularisation algorithm based on the Tikhonov solution incorporating the L-curve criterion is adopted to reduce the influence of measurement uncertainties and to produce smooth and optimised expansion estimates in the least squares sense. The Canton Tower benchmark problem established by the Hong Kong Polytechnic University is then utilised to demonstrate the applicability of the proposed expansion approach to the actual structure. The results from the benchmark problem studies show that the proposed approach can provide reliable predictions of mode shape expansion using only limited information on the operational modal data identified from the recorded ambient vibration measurements.
Original languageEnglish
Pages (from-to)485-499
Number of pages15
JournalSmart Structures and Systems
Issue number4
Publication statusPublished - 1 Jan 2012


  • Canton Tower benchmark problem
  • Measurement uncertainty
  • Mode shape expansion
  • Modelling errors
  • Perturbed force
  • Regularisation algorithm

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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