Identification and monitoring of stochastic linear subsystems with unknown local nonlinearities via output injection

Neha Aswal, Adrien Mélot, Laurent Mevel, Qinghua Zhang

Abstract: Most civil and mechanical structures exhibit nonlinear stochastic behaviour, which is difficult to model accurately, but necessary for conventional model-based structural health monitoring techniques. Although various methods have been developed to estimate nonlinear systems, they require information about the external excitation and are susceptible to sensor noise and modelling inaccuracies. This knowledge is challenging to acquire in practice. Hence, this article presents a novel nonlinearity model-agnostic approach to detect damage in mechanical systems with localized nonlinearities. The proposed method utilizes output injection to reject the unknown nonlinearities as if they were unknown disturbances. By applying an existing disturbance rejection technique, the need for a priori knowledge about the functional form of nonlinearities is avoided. Besides, a switching strategy is employed to determine the most probable location of the nonlinearities, thereby eliminating the need for a priori knowledge about their location. The method makes use of interacting particle Kalman filter, where the particle filter estimates the parameters (health indices) in order to detect possible damage while the Kalman filter simultaneously estimates the states. The efficiency of the proposed method is demonstrated with the help of numerical experiments on a spring–mass–damper oscillator chain with attached localized nonlinearity. The proposed approach is further validated against experimental data of jointed beams.