Inverse mode problems for real and symmetric quadratic models

Matthew M. Lin, Bo Dong, Moody T. Chu

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)

摘要

Many natural phenomena can be modeled by a second-order dynamical system Mÿ + Cẏ + Ky = f (t), where y(t) stands for an appropriate state variable and M, C, K are time-invariant, real and symmetric matrices. In contrast to the classical inverse vibration problem where a model is to be determined from natural frequencies corresponding to various boundary conditions, the inverse mode problem concerns the reconstruction of the coefficient matrices (M,C,K) from a prescribed or observed subset of natural modes. This paper set forth a mathematical framework for the inverse mode problem and resolves some open questions raised in the literature. In particular, it shows that given merely the desirable structure of the spectrum, namely given the cardinalities of real or complex eigenvalues but not of the actual eigenvalues, the set of eigenvectors can be completed via solving an under-determined nonlinear system of equations. This completion suffices to construct symmetric coefficient matrices (M,C,K) whereas the underlying system can have arbitrary eigenvalues. Generic conditions under which the real symmetric quadratic inverse mode problem is solvable are discussed. Applications to important tasks such as updating models without spill-over or constructing models with positive semi-definite coefficient matrices are discussed.

原文English
文章編號065003
期刊Inverse Problems
26
發行號6
DOIs
出版狀態Published - 2010

All Science Journal Classification (ASJC) codes

  • 理論電腦科學
  • 訊號處理
  • 數學物理學
  • 電腦科學應用
  • 應用數學

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