Time-Variant Frequency Response Function Measurements on Weakly Nonlinear, Arbitrarily Time-Varying Systems Excited by Periodic Inputs

In quite some applications, the linear dynamics of the system under test evolve over time in a smooth nonperiodic manner. The dynamic behavior of such systems is uniquely described by the time-variant frequency response function (TV-FRF). However, since most real-life systems behave nonlinearly to some extent, it is important to detect and quantify the deviation between the ideal linear time-variant (LTV) framework and the true non-LTV dynamics. Therefore, in this paper, a nonparametric estimation procedure is developed for detecting and quantifying the noise level and the level of the nonlinear distortions in TV-FRF measurements using random-phase multisine excitations. As a result, the users can decide whether or not the LTV framework is accurate enough to describe the true dynamics in their particular application. The proposed measurement procedure is illustrated on a time-variant electronic circuit.