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.

翻译：当分析中考虑结构固有的非线性行为及数据的自然变异时，损伤检测问题变得更加困难，因为若采用线性确定性方法，这两种现象都可能与损伤相混淆。因此，本研究旨在实验应用随机版本的Volterra级数，结合新颖性检测方法，在考虑由不确定性引起的测量数据变异的情况下，检测初始非线性系统中的损伤。实验装置由一个悬臂梁构成，即使在健康状态下，由于自由端附近存在磁铁，其运动也处于非线性状态。通过比较参考状态与损伤状态下估计的随机Volterra核在总响应中的线性与非线性贡献，检测了螺栓连接处（螺母松动）质量变化相关的损伤。实验测量在不同日期进行，以增加测量数据的自然变异。通过所提出的随机方法获得的结果与确定性Volterra级数版本的结果进行了比较，结果表明在考虑实验数据变异时，随机模型具有优势，能够以统计置信度检测损伤的存在。此外，与线性度量相比，所使用的非线性度量对损伤的发生表现出更高的敏感性，这证明了当系统表现出固有非线性行为时应用非线性度量的合理性。