Variance Computation of MAC and MPC for Real-Valued Mode Shapes from the Stabilization Diagram

Recent advances in efficient variance computation of modal parameter estimates from the output-only subspace-based identification algorithms make the modal parameter variance a practical modal indicator, indicating the accuracy of the estimation. A further modal indicator is the Modal Assurance Criterion (MAC), for which a recently developed uncertainty quantification scheme estimates the variance at a fixed model order. The Modal Phase Collinearity (MPC) is another popular indicator, for which an uncertainty scheme is currently missing. Unlike other modal parameters, which are Gaussian distributed, estimates of MAC and MPC are close to the border of their respective distribution support and cannot be approximated as a Gaussian random variable. This paper addresses the respective uncertainty quantification of MAC and MPC. The results are validated in the context of operational modal analysis (OMA) of a spring mass system.