Direct optimisation based model selection and parameter estimation using time-domain data for identifying localised nonlinearities

A major difficulty when modelling nonlinear structures from experimental vibration data is to determine the type of nonlinear functions that will better predict their dynamic response. In this paper we address this issue by developing a recursive framework in which the characteristics and parameters of nonlinear structures are identified using measured input and output time-domain data. Forward-backward and exhaustive search regression algorithms are exploited based on optimisation techniques to recursively select and quantify the best nonlinear functions from a predefined library of nonlinear terms. The framework assumes localised nonlinearities for which their location is assumed to be known. The proposed methodology is demonstrated using numerical and experimental examples of single and multi-degree-of-freedom systems. The results presented highlight key advantages of the proposed method including: the capability of treating multi-degree of freedom nonlinear systems holding different types of localised nonlinearities, and the capability of selecting nonlinear terms with a light computational effort and with limited number of time samples.