Improved (non-)parametric identification of dynamic systems excited by periodic signals—The multivariate case

Recently [1] a method has been developed to suppress nonparametrically the noise (and system) transients (leakage errors) in frequency response function and noise (co-)variance estimates of single-input, single-output systems excited by periodic signals. This paper extends the results of [1] to multiple-input, multiple-output systems where all inputs and outputs are disturbed by noise (i.e. an errors-in-variables framework). Two methods are presented: the first starts from multiple experiments with uncorrelated sets of inputs, and makes no assumption about the frequency response matrix (FRM); while the second only requires one single experiment, but assumes that the FRM can locally be approximated by a polynomial. Both methods estimate simultaneously the FRM, the noise level, and the level of the nonlinear distortions. For lightly damped systems, the proposed methods either significantly reduce the experiment duration or, for a given measurement time, significantly increase the frequency resolution of the FRM estimate. If the noise (and/or system) transients are the dominant error sources, then the proposed methods also significantly reduce the covariance matrix of the FRM estimates. The use of the nonparametric noise covariance estimates for parametric transfer function modelling is also discussed in detail.