Identification of restoring force non-linearity from a system's response to a white-noise excitation

—A single degree-of-freedom system with a white-noise excitation is considered. The problem is to detect a non-linearity of the system's restoring force and to estimate its level from measured steady-state response. Three alternative methods are considered, one of which is based on estimating probability density, and two others on spectral analysis of the response. The analytical background for these methods is outlined. In particular, the procedure of cross-correlating amplitudes of the resonant response component and of its integer multiple component is proposed. The results of verification of the methods by computer simulation are presented.