Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties

Abstract

Systems and structures are generally assumed to behave linearly and in a noise-free environment. This is in practice not perfectly the case. First, nonlinear phenomena can appear and second, the presence of noise is unavoidable for all experimental measurements. Nonlinearities can be considered as a deterministic process in the sense that in the absence of noise the output signal depends only on the input signal. Noise is purely stochastic: in the absence of an input signal, the output signal is not null and cannot be predicted at any arbitrary instant. It turns out that these two issues are coupled: all the noise that is not correctly removed from the measurements could be misinterpreted as nonlinearities, and if nonlinearities are not accurately estimated, they will end up within the noise signal and information about the system under study will be lost. The underlying idea consists here in extracting the maximum of available linear and nonlinear deterministic information from measurements without misinterpreting noise.