Complex eigenvector scaling from mass perturbations

• Adoption of the normal mode model when modal complexity is high leads to undue error.
• Significant modal complexity can arise in low damped systems with closely spaced poles.
• A method to normalize latent vectors from output only ID is derived and properties are clarified.
• The trade between bias and variance in a stochastic setting is examined analytically.
• Gains over a sensitivity solution in the nonlinear case are highlighted.

This paper presents an approach to normalize experimentally extracted complex eigenvectors so that their outer product gives transfer function residues. The approach, an implementation of the mass perturbation strategy, is exact for arbitrary perturbation magnitudes and number of sensors when the modal space is complete and is robust against modal truncation. It is shown that improvements over a sensitivity solution are significant when the relation between the eigenvalue and the perturbation magnitude is strongly nonlinear.