Damage detection in an uncertain nonlinear beam based on stochastic Volterra series

TL;DR

This work tackles structural health monitoring for systems with intrinsic nonlinear behavior under uncertainty. It introduces a stochastic Volterra series with random Kautz bases to model uncertain nonlinear dynamics and to detect damages such as breathing cracks with probabilistic confidence. Two damage-detection routes are developed: one based on Volterra kernel coefficients and another on kernel contributions, both using Mahalanobis distance with KDE thresholds for novelty testing. The results on a nonlinear beam model show the nonlinear indicators reliably distinguish damage from data variation, highlighting the method's robustness and potential for experimental validation.

Abstract

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.

Figures (18)

• Figure 1: Description of the Volterra kernels identification approach used, based on Monte Carlo simulations.
• Figure 2: Description of the damage detection approach based on stochastic Volterra series.
• Figure 3: Nonlinear system simulated in the reference condition.
• Figure 4: Time-frequency diagram of the response for different levels of input amplitude, considering the reference condition (Healthy).
• Figure 5: Nonlinear system simulated in the damaged condition.