Samuel da Silva

Luis Gustavo Giacon Villani, Samuel da Silva, Americo Cunha

The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.

Luis Gustavo Gioacon Villani, Samuel da Silva, Americo Cunha et al.

The damage detection problem becomes a more difficult task when the intrinsically nonlinear behavior of the structures and the natural data variation are considered in the analysis because both phenomena can be confused with damage if linear and deterministic approaches are implemented. Therefore, this work aims the experimental application of a stochastic version of the Volterra series combined with a novelty detection approach to detect damage in an initially nonlinear system taking into account the measured data variation, caused by the presence of uncertainties. The experimental setup is composed by a cantilever beam operating in a nonlinear regime of motion, even in the healthy condition, induced by the presence of a magnet near to the free extremity. The damage associated with mass changes in a bolted connection (nuts loosed) is detected based on the comparison between linear and nonlinear contributions of the stochastic Volterra kernels in the total response, estimated in the reference and damaged conditions. The experimental measurements were performed on different days to add natural variation to the data measured. The results obtained through the stochastic proposed approach are compared with those obtained by the deterministic version of the Volterra series, showing the advantage of the stochastic model use when we consider the experimental data variation with the capability to detect the presence of the damage with statistical confidence. Besides, the nonlinear metric used presented a higher sensitivity to the occurrence of the damage compared with the linear one, justifying the application of a nonlinear metric when the system exhibits intrinsically nonlinear behavior.