Frequency Response Functions, Uncertainty Estimates, Localization of Resonances, and Model Validation

Non-parametric estimates play an important role in frequency domain identification of higher-order dynamical systems. Accurate measurements of the frequency response can be used as an intermediate step towards a parametric transfer function model, or provide an effective mechanism for model validation. This paper concerns several aspects of nonparametric frequency domain identification. We review developments in frequency response estimation for a class of linear or weakly nonlinear systems. We examine some properties of the associated confidence bounds. We describe an approach to localize resonant behavior without estimating a parametric model first, and demonstrate its use on experimental data of a steel beam. As models become more complex and diverse in response to the challenges of modern control strategies there will be an increasing need for a greater range of model validation procedures. We draw attention to the appearance of multiple testing problems in system identification, propose one method and contrast with another approach found in the statistics literature.