Variance estimation of modal parameters from output-only and input/output subspace-based system identification

An important step in the operational modal analysis of a structure is to infer on its dynamic behavior through its modal parameters. They can be estimated by various modal identification algorithms that fit a theoretical model to measured data. When output-only data is available, i.e. measured responses of the structure, frequencies, damping ratios and mode shapes can be identified assuming that ambient sources like wind or traffic excite the system sufficiently. When also input data is available, i.e. signals used to excite the structure, input/output identification algorithms are used. The use of input information usually provides better modal estimates in a desired frequency range. While the identification of the modal mass is not considered in this paper, we focus on the estimation of the frequencies, damping ratios and mode shapes, relevant for example for modal analysis during in-flight monitoring of aircrafts. When identifying the modal parameters from noisy measurement data, the information on their uncertainty is most relevant. In this paper, new variance computation schemes for modal parameters are developed for four subspace algorithms, including output-only and input/output methods, as well as data-driven and covariance-driven methods. For the input/output methods, the known inputs are considered as realizations of a stochastic process. Based on Monte Carlo validations, the quality of identification, accuracy of variance estimations and sensor noise robustness are discussed. Finally these algorithms are applied on real measured data obtained during vibrations tests of an aircraft.