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Smart Structures and Systems
  Volume 15, Number 3, March 2015 , pages 717-733

Assessment of modal parameters considering measurement and modeling errors
Qindan Huang, Paolo Gardoni and Stefan Hurlebaus

    Modal parameters of a structure are commonly used quantities for system identification and damage detection. With a limited number of studies on the statistics assessment of modal parameters, this paper presents procedures to properly account for the uncertainties present in the process of extracting modal parameters. Particularly, this paper focuses on how to deal with the measurement error in an ambient vibration test and the modeling error resulting from a modal parameter extraction process. A bootstrap approach is adopted, when an ensemble of a limited number of noised time-history response recordings is available. To estimate the modeling error associated with the extraction process, a model prediction expansion approach is adopted where the modeling error is considered as an \"adjustment\" to the prediction obtained from the extraction process. The proposed procedures can be further incorporated into the probabilistic analysis of applications where the modal parameters are used. This study considers the effects of the measurement and modeling errors and can provide guidance in allocating resources to improve the estimation accuracy of the modal data. As an illustration, the proposed procedures are applied to extract the modal data of a damaged beam, and the extracted modal data are used to detect potential damage locations using a damage detection method. It is shown that the variability in the modal parameters can be considered to be quite low due to the measurement and modeling errors; however, this low variability has a significant impact on the damage detection results for the studied beam.
Key Words
    modal parameters; measurement error; modeling error; bootstrap; sample size
Qindan Huang: Department of Civil Engineering, The University of Akron, Akron, OH 44325-3905, USA
Paolo Gardoni: Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign,
Urbana, IL 61801-2352, USA
Stefan Hurlebaus: Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843-3136, USA

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