Uncertainty quantification for the Modal Phase Collinearity of complex mode shapes. (1st May 2021) - Greś, Szymon; Döhler, Michael; Andersen, Palle; Mevel, Laurent
Highlights: The Modal Phase Collinearity (MPC) indicates the complexity of a mode shape. Its statistical distribution depends on the complexity of the mode shape. The MPC distribution based on complex mode shapes estimates can be approximated as Gaussian. An algorithm to compute confidence intervals of the resulting Gaussian approximation is proposed. The resulting confidence intervals are validated in numerical simulations and applied to an offshore mast. Abstract: The Modal Phase Collinearity (MPC) is a modal indicator designed to decide whether the mode shape used in its computation is a real or complex-valued vector. Its estimate inherits the statistical properties of the corresponding mode shape estimate. While the statistical framework for the uncertainty quantification of modal parameters is well-known and developed in the context of subspace-based system identification methods, uncertainty quantification for the MPC estimate has not been carried out yet. In this paper, the uncertainty quantification of the MPC estimates is developed when the corresponding mode shapes are complex-valued vectors. In this case, the theoretical value of the MPC is strictly lower than 1 and it is shown that the distribution of the MPC estimate can be approximated as Gaussian. The computation of its variance and the resulting confidence intervals of the MPC estimate are developed. The proposed framework is validated in Monte Carlo simulations and illustrated on experimental data of an offshore structure.