Improved subspace method with application in linear time-varying structural modal parameter identification

An improved subspace method using ensemble response sequence was developed. The original method can identify the pseudo-modal parameter of time-varying structure efficiently, but is sensitive to the noise severely. Considering that the key of this method is to find a matrix whose eigenvalues are the same to the system matrix, the process of finding this matrix was converted to a Least Square (LS) problem. Using generalized observability instead of the output matrix, an improved method was obtained, where the sensitivity to noise was abated, but the computational complexity increased. The orthogonality of the left singular matrix was once considered, the process of computing the pseudo-inverse of the matrix in LS problem was simplified into finding the transposed itself to greatly reduce the computational complexity. The improved method was verified via identifying pseudo-modal parameters of a 2DOF spring-mass model with three kinds of time-varying stiffness.