Random decrement technique for detection and characterization of nonlinear behavior

When performing operational modal analysis, the mechanical system being investigated is assumed to be linear. If this assumption is not true, errors could be made when estimating the modal parameters of the system. There are no generally accepted robust analysis procedures available that can verify or validate the assumption of linearity in an output-only setting. In the present study, a method of detecting nonlinear behavior from a random response signal is proposed. The method is based on the random decrement (RD) technique, which involves identifying triggering points (TPs) in a measured response signal. The proposed procedure is to identify a set of TPs, where each member of the set represents a unique initial condition. A RD signature is then calculated for each set member of TPs. For the response of a linear system, all RD signatures are equal regardless of the initial conditions. For a nonlinear system, not all RD signatures will be equal for different initial conditions. Detection of nonlinear behavior is then possible by using principal component analysis and a parameterization of RD signatures to analyze the sameness of all the RD signatures in the set. The proposed analysis procedure is investigated with numerical and experimental test cases of a single-degree-of-freedom stick-slip system. Results show that it is possible to distinguish between linear and nonlinear behavior using this method. It is also possible to characterize which aspect of the system the nonlinear behavior relates to.