2.5.5.      Effective Independence

The effective independence (EI) algorithm is based on maximizing the amount of “information” available from the measured DOF in a modal test. The amount of “information” is defined as the determinant of the Fisher Information Matrix (FIM) defined as follows:

                                                     (2.5.5-1)

Kammer [8] has shown that the contribution of each DOF to this determinant can be measured by the diagonal of the following matrix:

                                                (2.5.5-2)

Because it is not feasible to calculate the full matrix in Equation (2.5.5-2), we instead sum the columns of the following matrix:

                                             (2.5.5-3)

The effective independence algorithm is an iterative algorithm that starts from a large set of DOF and eliminates those DOF with the smallest contribution to the information matrix at each step. This algorithm typically does not do a good job of selecting a DOF set that results in an accurate Guyan mass reduction, but it can be improved significantly by premultiplying the mode shapes by the square root of the mass matrix. If the initial set is all DOF, the initial FIM in this case is the self-orthogonality matrix, and should be the identity. As DOF are eliminated the mass matrix is not reduced so the link between the FIM and the self-orthogonality is lost. However, the fact that each mode shape coefficient is weighted by its corresponding mass still improves the performance of the algorithm. The major advantage of the EI algorithm, when compared with the IGR and MWEI algorithms is the fact that it never requires calculation of static shapes or reduction of the mass matrix. This makes the algorithm much more efficient and therefore applicable to very large (100,000+ DOF) initial sets.