Uncertainty quantification of input matrices and transfer function in input/output subspace system identification

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. •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.