A model updating method for undamped structural systems

作者：Yuan Yongxin^*

来源：Journal of Computational and Applied Mathematics, 2008, 219(1): 294-301.

DOI：10.1016/j.cam.2007.07.025

• model updating
• undamped structural systems
• matrix decomposition
• generalized inverses of matrices
• best approximation

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given a full column rank matrix X epsilon R-n x p, a diagonal matrix Lambda epsilon R-p x p and matrices K-0 epsilon R-r x r, M-0 epsilon R-r x r, find n x n matrices K . M such that parallel to K X - M X Lambda parallel to = min, s.t. K(vertical bar l, r vertical bar) = K-0. M(vertical bar l. r vertical bar) = M-0, where K(vertical bar l, r vertical bar) and M(vertical bar l, r vertical bar) are, respectively, the r x r leading principal submatrices of K and M. We then consider a best approximation problem: Given n x n matrices Ka. M-a with K-a(vertical bar l, r vertical bar) = K-0. M-a(vertical bar l, r vertical bar) = M-0, find ((K) over cap, (M) over cap) epsilon S-E such that parallel to K-a - (K) over cap parallel to(2) + parallel to M-a - (M) over cap parallel to(2) = inf ((K . M)epsilon SE) (parallel to K-a - K parallel to(2) + parallel to M-a - M parallel to(2)), where S-E is the solution set of LSP. We show that the best approxiniation solution ((K) over cap, (M) over cap) is unique and derive an explicit formula for it.

• 出版日期2008-9-15
• 单位江苏大学