Phase space reconstruction and Koopman operator based linearization of nonlinear model for damage detection of nonlinear structures

Vibration responses of structures with inherent nonlinear behaviors can degrade the performance of linear theory based damage detection methods. This paper integrates the phase space reconstruction and Koopman operator to provide a linear representation of strongly nonlinear systems. Similar to the modal analysis of linear systems, the linearized model allows for handling nonlinear vibration responses as a superposition of the discovered nonlinear coordinate basis. This property provides opportunities to identify the structural condition change of structures with initial nonlinearity. The eigen-frequencies extracted from the Koopman operator are served as damage features. The performance of using the eigen-frequencies from dynamic mode decomposition for nonlinear structural damage detection is compared with the natural frequencies obtained from fast Fourier transformation and the time-frequency analysis method to emphasize the superiority of the proposed approach. Two experimental structures exhibiting inherent nonlinearity, namely, a magneto-elastic system and a precast segment beam, are employed to demonstrate the feasibility and effectiveness of using the proposed method for identifying condition change of nonlinear structures. Results demonstrate that the presented nonlinearity linearization framework and the damage feature defined in this study are suitable for reliably identifying the occurrence of structural damage and condition change in structures with inherent nonlinearities.