Nonparametric data-driven modeling of linear systems: estimating the frequency response and impulse response function

The aim of this article is to give a tutorial overview of frequency response function (FRF) or impulse response (IR) function measurements of linear dynamic systems. These nonparametric system identification methods provide a first view on the dynamics of a system. As discussed in “Summary,” the article discusses three main points. The first replaces classic FRF measurement techniques based on spectral analysis methods with more advanced, recently developed algorithms. User guidelines will be given to select the best among these methods according to four specific user situations: 1) measurements with a high or low signal-to-noise ratio (SNR), 2) systems with smooth or fast-varying transfer functions as a function of the frequency, 3) batch or real-time processing, and 4) low or high computational cost. The second main point is to store the reference signal together with the data. This will be very useful whenever there are closed loops in the system to be tested, including interactions between the generator and the setup. The final point is to use periodic excitations whenever possible. Periodic excitations provide access to a full nonparametric noise model, even under closed-loop experimental conditions. Combining periodic signals with the advanced methods presented in this article provides access to high-quality FRF measurements, while the measurement time is reduced by eliminating disturbing transient effects.