Nonlinear modal analysis via non-parametric machine learning tools

Modal analysis is an important tool in the structural dynamics community; it is widely utilised to understand and investigate the dynamical characteristics of linear structures. Many methods have been proposed in recent years regarding the extension to nonlinear analysis, such as nonlinear normal modes or the method of normal forms, with the main objective being to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. In fact, for the majority of structures where the effect of nonlinearity becomes significant, nonlinear modal analysis is a necessity. The objective of the current paper is to demonstrate a machine learning approach to output-only nonlinear modal decomposition using kernel independent component analysis and locally linear-embedding analysis. The key element is to demonstrate a pattern recognition approach which exploits the idea of independence of principal components from the linear theory by learning the nonlinear manifold between the variables. In this work, the importance of output-only modal analysis via "blind source" separation tools is highlighted as the excitation input/force is not needed and the method can be implemented directly via experimental data signals without worrying about the presence or not of specific nonlinearities in the structure.