Covariance-driven subspace identification: A complete input–output approach

In most of the available input-output covariance-driven subspace identification approaches the knowledge of the input is exploited for eigenstructure identification only. In the authors’ opinion a complete input-output identification method should also cater for the estimation of the input matrix B and the direct feedthrough matrix D of the state-space model. In this paper, a multivariate subspace-based formulation in the time domain for modal parameter identification using covariances is developed. A novel covariance-based procedure for estimating the input matrix B and the direct feedthrough matrix D is derived, with the aim of proposing a complete input-output covariance-driven identification method applicable in the same way as its well-established data-driven counterpart. Detailed implementation issues are given and the method is validated through a 15 DOFs numerical example. As an advantage, when some user-defined parameters are increased to obtain more accurate estimates or in case of very large data sets, the covariance-driven method is not suffering from the memory limitation problems that may affect the data-driven method, due to the storing and managing of large data matrices. This is also demonstrated in the numerical example. The method is tested on an experimental application consisting of a thin-walled metallic structure: with a comparable computational effort, results are very similar to those obtained by applying a data-driven method.