Quadratic model updating with symmetry, positive definiteness, and no spill-over

Delin Chlj*, Moody Chu, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticle

38 Scopus citations

Abstract

Updating a system modeled as a real symmet ric quadratic eigenvalue problem to match observed spectral information has been an important task for practitioners in different disciplines. It is often desirable in the process to match only the newly measured data without tampering with the other unmeasured and often unknown eigenstructure i nherent in the original model. Such an updating, known as no spill-over, has been critical yet chall enging in practice. Only recently, a mathematical theory on updating with no spill-over has begun to be understood. However, other imperative issues such as maintaining positive definiteness in t he coefficient matrices remain to be addressed. This paper highlights several theoretical aspects about updating that preserves both no spill-over and positive definiteness of the mass and the stiffness matrices. In particular, some necessary and sufficient conditions for the solvability conditions are established in this investigation.

Original languageEnglish
Pages (from-to)546-564
Number of pages19
JournalSIAM Journal on Matrix Analysis and Applications
Volume31
Issue number2
DOIs
StatePublished - 28 Dec 2009

Keywords

  • Eigenstructure assignment
  • Inverse eigenvalue problem
  • Model updating
  • Positive definiteness
  • Quadratic model
  • Spill-over

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