Uncertainty quantification in data-driven stochastic subspace identification

A crucial aspect in system identification is the assessment of the accuracy of the identified system matrices. Stochastic Subspace Identification (SSI) is a widely used approach for the identification of linear systems from output-only data because it combines a high computational robustness and efficiency with a high estimation accuracy. Practical approaches for estimating the (co)variance of system matrices that are identified using SSI exist for the case where the system matrices are obtained from the shift-invariant structure of the extended observability matrix. However, in data-driven SSI, the system matrices are often obtained in a different way, using identified state sequences. This case is treated in the present work, for three common types of weighting. First, it is shown that the estimated system matrices depend entirely on sample output correlation estimates, the covariance of which can be straightforwardly estimated. Subsequently, a linear sensitivity analysis of the data-driven SSI algorithm is performed, such that the covariance of the identified system matrices can be also computed. A memory efficient implementation is obtained by computing the related Jacobian only implicitly. An extensive numerical validation, covering a range of parameter choices, demonstrates the accuracy of the estimated variance of the identified system description. Finally, the practical use of the method in the context of operational modal analysis is demonstrated in an experimental case study.