Nonlinear modal analysis using pattern recognition

The main objective of nonlinear modal analysis is to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. Most theories regarding structural modal analysis are centred on the linear modal analysis which has proved to now to be the method of choice for the analysis of linear dynamic structures. However, for the majority of other structures, where the effect of nonlinearity becomes significant, then 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 by learning the nonlinear manifold between the variables.