Optimal Input Excitation Design for Nonparametric Uncertainty Quantification of Multi-Input Multi-Output Systems

摘要

In this paper, the impact of various input excitation scenarios on two different MIMO linear non-parametric modeling schemes is investigated in the frequency-domain. It is intended to provide insight into the optimal experiment design that not only provides the best linear approximation (BLA) of the frequency response functions (FRFs), but also delivers the means for assessing the variance of the estimations. Finding the mathematical representations of the variances in terms of the estimation coherence and noise/nonlinearity contributions are of critical importance for the frequency-domain system identification where the objective function needs to be weighted in the parametrization step. The input excitation signal design is tackled in two cases, i.e., multiple single-reference experiments based on the zero-mean Gaussian and the colored noise signal, the random-phase multisine, the Schroeder multisine, and minimized crest factor multisine; and multi-reference experiments based on the Hadamard matrix, and the so-called orthogonal multisine approach, which additionally examines the coupling between the input channels. The time-domain data from both cases are taken into the classical H1 spectral analysis as well as the robust local polynomial method (LPM) to extract the BLAs. The results are applied for data-driven modeling of a flexible beam as a model of a flexible robotic arm.