Damage detection of nonlinear structures using probability density ratio estimation

This study focuses on vibration-based damage detection for a structure that has nonlinear behavior even in the undamaged state. Based on the vibration responses of a single sensor, a non-Gaussian multivariate probability density function (PDF) is developed and used as a feature. The change between the PDF of the undamaged state and that of a potentially damaged state is used to indicate the damage. Since what of interest is the change of the PDF, instead of estimating the two PDFs separately, the ratio of them is estimated directly using a density ratio estimation method. In addition, principal component analysis is applied to reduce the dimensionality of the PDFs. The effectiveness and advantages of the proposed method are demonstrated in two case studies: an experimental nonlinear beam and simulations of an offshore wind turbine subjected to nonlinear pile-soil interaction. Compared with a second-order statistical method, the proposed method shows better damage detection performance due to the integration of higher order statistical information.