Robust damage detection in uncertain nonlinear systems - Villani, Luis Gustavo Giacon (2019)
Structural Health Monitoring (SHM) methodologies aim to develop techniques able to detect, localize, quantify and predict the progress of damages in civil, aerospatial and mechanical structures. In the hierarchical process, the damage detection is the first and most important step. Despite the existence of numerous methods of damage detection based on vibration signals, two main problems can complicate the application of classical approaches: the nonlinear phenomena and the uncertainties. This thesis demonstrates the importance of the use of a stochastic nonlinear model in the damage detection problem considering the intrinsically nonlinear behavior of mechanical structures and the measured data variation. A new stochastic version of the Volterra series combined with random Kautz functions is proposed to predict the behavior of nonlinear systems, considering the presence of uncertainties. The stochastic model proposed is used in the damage detection process based on hypothesis tests. Firstly, the method is applied in a simulated study assuming a random Duffing oscillator exposed to the presence of a breathing crack modeled as a bilinear oscillator. Then, an experimental application considering a nonlinear beam subjected to the presence of damage with linear characteristics (loss of mass in a bolted connection) is performed, with the direct comparison between the results obtained using a deterministic and a stochastic model. Finally, an experimental application considering a nonlinear beam subjected to the presence of nonlinear damage (a breathing crack) is carried out. In all the applications, the comparison between the use of linear and nonlinear models is held, revealing the better results obtained when one considers the nonlinearities in the analysis. Furthermore, although the reference stochastic model is always the same, the methodology to detect the damage changes from one application to another, showing the evolution of the proposed approach during the research. The method presented satisfactory results in all the conditions studied, representing an improvement in the damage detection area considering nonlinearities and uncertainties at the same time.