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Damage Identification and Localization Using Dynamic Data and Its Principal Components

Rahai, Mohammad | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49434 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Bakhshi, Ali; Esfandiari, Akbar
  7. Abstract:
  8. Damage identification and localization using dynamic data and its Principal Components The objective of this study is to demonstrate the application of SVD-based principal component analysis performed on moving windows of transfer function. It uses the sensitivities of measured responses in frequency domain, its singular values and right eigenvectors for FE model updating in an efficient way, by developing a quasi-linear sensitivity equation of structural response. The benefit of applying PCA for dynamical systems comes from its ability to detect and rank the dominant coherent spatial and frequency-dependent information of dynamic response. The challenge of using modal parameters of structure for damage detection is that they may change highly by variation of operational conditions and structural uncertainties. Hence, most vibration-based model updating techniques only give good results in well-controlled laboratory conditions preventing the noise to mask the information on the damage state of structure. In this regard, proper selection of measured frequency points for updating of noisy data with low damage levels were have been addressed in this paper. Finally, validation of this method is evaluated using numerical simulations and a beam experiment. Since no exact solution exists here, this overdetermined system of equations should be solved by Least Square numerical methods such as “Brut force” inversion, Pseudo-inversion using SVD, Gaussian elimination solution or QR factorization. The quality of predicted damage depends on several factors including the sensor types and locations, excitation types and locations, measurement and modeling error, updating frequency points, appropriate weighting techniques to avoid forming ill-conditioned systems, observability of unknown parameters and numerical methods used for solution of the system of equations. In this paper, some of individual equations in were omitted because of low sensitivities to the unknown parameters and magnification of adverse effects of measurement errors. For avoiding the least-squares solution to be dominated by the equations with the largest coefficients, both sides of equations were multiplied by a scale factor as a weighting approach. Therefore, in this paper, each row of sensitivity matrix equation was be weighted by the inverse of its second norm. Given a set of sensor locations and frequency points, for parameter estimations, it is necessary to have the highest value of change in the response due to changes in the unknown structural parameters
  9. Keywords:
  10. Damage Detection ; Singular Value Decomposition (SVD) ; Sensitivity Equations ; Least Squares Method ; Frequency Response ; Finite Element Method ; Principal Component Analysis (PCA)

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