Structural Engineering and Mechanics

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Probabilistic damage detection of structures with uncertainties under unknown excitations based on Parametric Kalman filter with unknown Input

  • Liu, Lijun (Department of Civil Engineering, Xiamen University) ;
  • Su, Han (Department of Civil Engineering, Xiamen University) ;
  • Lei, Ying (Department of Civil Engineering, Xiamen University)
  • Received : 2017.04.04
  • Accepted : 2017.05.12
  • Published : 2017.09.25
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Abstract

System identification and damage detection for structural health monitoring have received considerable attention. Various time domain analysis methodologies based on measured vibration data of structures have been proposed. Among them, recursive least-squares estimation of structural parameters which is also known as parametric Kalman filter (PKF) approach has been studied. However, the conventional PKF requires that all the external excitations (inputs) be available. On the other hand, structural uncertainties are inevitable for civil infrastructures, it is necessary to develop approaches for probabilistic damage detection of structures. In this paper, a parametric Kalman filter with unknown inputs (PKF-UI) is proposed for the simultaneous identification of structural parameters and the unmeasured external inputs. Analytical recursive formulations of the proposed PKF-UI are derived based on the conventional PKF. Two scenarios of linear observation equations and nonlinear observation equations are discussed, respectively. Such a straightforward derivation of PKF-UI is not available in the literature. Then, the proposed PKF-UI is utilized for probabilistic damage detection of structures by considering the uncertainties of structural parameters. Structural damage index and the damage probability are derived from the statistical values of the identified structural parameters of intact and damaged structure. Some numerical examples are used to validate the proposed method.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of China (NSFC), Natural Science Foundation of Fujian Provincial, Shanghai Municipal science and Technology Committee

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