A nonlinear decomposition and regulation method for nonlinearity characterization

Nonlinearity detection and characterization for crack-/damage-related fault evaluation/detection is a hot engineering topic. This study investigates a novel and systematic nonlinear decomposition and regulation method for nonlinearity characterization. It is shown that, using the proposed output decomposition and regulation, the even-order nonlinearity and crack-incurred nonlinearity (not a simple even-order nonlinearity although at its initial stage) can all be effectively evaluated by the magnitude of the second-order harmonic response, and the latter is a linear function of the crack severity and can be accurately estimated with the proposed method. Theoretical analysis, example studies, finite element modeling, and experiment validation are provided to demonstrate the advantages and effectiveness of the proposed method in characterizing nonlinear dynamics incurred by initial crack or damage. The theory and methods of this study would provide a useful and alternative frequency-domain approach for nonlinear signal processing in crack/damage evaluation, nonlinearity detection and characterization, and can benefit a broad spectrum of engineering practice.