Direct Least-Squares Formulation of a Stiffness Adjustment Method

The matrix pencil nearness problem in structural dynamic model updating

“…Based on the localization of modeling errors, it is a common practice to adjust partial elements of the analytical mass and stiffness matrices M a and K a using the measured test data. Methods of preserving the connectivity of the structural dynamic model can be found in [20][21][22][23][24][25][26][27][28]. The problem of updating simultaneously both the analytical mass and stiffness matrices with a submatrix pencil constraint using the vibration test data has been considered by Jiang et al [29].…”

A constrained matrix least-squares problem in structural dynamics model updating

“…Problems of finding the best approximation to a given matrix subject to different kinds of linear constraints, symmetry and positive semidefiniteness are discussed in [4,5,6,7,8,9,10,11,12,13,14,15]. Problems containing zero/nonzero pattern constraint and linear constraints can be found in [16,17,18,19,5,20,21]. Recently, Yuan [22] considered problem (1) using subgradient algorithm for two different models.…”

Matrix linear variational inequality approach for finite element model updating

“…To overcome this shortcoming, Kabe [10] developed an algorithm preserving the connectivity of the structural model. Caesar and Peter [11], Kammer [12], Smith and Beattie [13,14], Zhang and Zerva [15], Halevi and Bucher [16], Sako and Kabe [17] presented some improvements of Kabe's method. But Kabe's method and its improvements fail to guarantee that the updated stiffness matrix is positive semidefinite.…”