Uncertainty quantification of input matrices and transfer function in input/output subspace system identification. (15th March 2022) - Greś, Szymon; Döhler, Michael; Jacobsen, Niels-Jørgen; Mevel, Laurent
Abstract: The transfer function of a linear mechanical system can be defined in terms of the quadruplet of state-space matrices ( A, B, C, D ) that can be identified from input and output measurements with subspace-based system identification methods. The estimation of the quadruplet has been well studied in the literature from both theoretical and practical viewpoints. Nonetheless, a practical algorithm for uncertainty quantification of its estimation errors and the uncertainty of the resultant parametric transfer function is missing in the context of subspace identification. For several output-only and input/output subspace methods, the covariance related to the matrices ( A, C ) and to the resulting modal parameters can be effectively obtained with recently developed first-order perturbation-based schemes, while the corresponding uncertainty quantification for the input-related matrices ( B, D ) is missing. In this paper, explicit expressions for the covariance related to matrices ( B, D ) are developed, and applied to the covariance estimation of the resulting transfer function. The proposed schemes are validated on a simulated data of a mechanical system and are applied to laboratory measurements of a plate. Highlights: The transfer function is defined from the state-space matrices A, B, C, D. When computed from input/output data, their estimates are afflicted with uncertainty. Expressions to estimate the covariance of (B, D) are derived for two subspace methods. Expresions to quantify uncertainty of a transfer function estimate are developed. The proposed uncertainty quantification schemes are applied to a shaker test.