Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: An experimental application

Abstract

Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: an experimental application. Mechanical Systems and Signal Processing, Elsevier, 2019, 128, pp.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.

On the detection of a nonlinear damage in an uncertain nonlinear beam using stochastic Volterra series

“…The Monte Carlo method was chosen because it is easier to perform when the deterministic algorithm is known. 23,43 More information about the random Kautz functions and the process of the random Volterra kernels estimation may be found in Villani et al 36,38 Damage detection based on novelty detection…”

“…A method based on a stochastic version of the Volterra series, with the use of the random kernel's coefficients and contributions as damage detection features, combined with a novelty detection technique, was applied to solve the problem. Unlike what has been shown in the previous works published, 36,38 the kernel coefficients and the kernel contributions approaches were applied together, considering a unique index to monitor the structural condition, aiming to augment the robustness of the method. Moreover, a theoretical distribution was introduced to the Mahalanobis distance computed in the reference condition to reduce the possible problems related to the use of the kernel density estimator previously assumed.…”

“…Then, in Villani et al (2019) 38 the authors showed the experimental application of the approach based on the Volterra kernels' contributions to detect damage in an intrinsically nonlinear beam, considering data variation related to the reassembly of the experimental setup. However, the damage simulated was associated with the loss of mass that reflected in the variation of the natural frequencies of the equivalent linear system.…”

“…To be familiar with the Volterra series model application in damage detection problems, find the motivation to the study of the nonlinear phenomena in the procedure, and have more details about the Volterra series reformulation to predict the nonlinear responses considering data variation, the interested reader is referred to seeing Bruce et al (2017) 37 , Villani et al (2019) 36 and Villani et al (2019) 38 . The present paper will be centered on the primary differentiation between the approach used here, and the one analyzed previously and in the experimental results obtained with the application of the method contemplating an initially uncertain nonlinear system subjected to the presence of damage that provokes nonlinear phenomena to the structure behavior, that was not done before.…”

On the use of the GP-NARX model for predicting hysteresis effects of bolted joint structures

“…In this work, the shaker amplifier's voltage signal is used as input data for training, verification, and validation of the GP-NARX model. This approach is considered as excitation once this signal is constant over a frequency range [42]. Also, to take into account the data fluctuation observed in Fig.…”