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Smart Structures and Systems
  Volume 10, Number 4, October-November 2012, pages 485-499

Mode shape expansion with consideration of analytical modelling errors and modal measurement uncertainty
Hua-Peng Chen, Kong Fah Tee and Yi-Qing Ni

    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.
Key Words
    mode shape expansion; modelling errors; perturbed force; measurement uncertainty; regularisation algorithm; Canton Tower benchmark problem
Hua-Peng Chen and Kong Fah Tee : School of Engineering, University of Greenwich, Chatham Maritime, Kent, ME4 4TB, UK
Yi-Qing Ni : Department of Civil and Structural Engineering, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong

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