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

Abstract

In the present work, two issues that can complicate a damage detection process are considered: the uncertainties and the intrinsically nonlinear behavior. To deal with these issues, a stochastic version of the Volterra series is proposed as a baseline model, and novelty detection is applied to distinguish the condition of the structure between a reference baseline state (presumed “healthy”) and damaged. The studied system exhibits nonlinear behavior even in the reference condition, and it is exposed to a type of damage that causes the structure to display a nonlinear behavior with a different nature than the initial one. In addition, the uncertainties associated with data variation are taken into account in the application of the methodology. The results confirm that the monitoring of nonlinear coefficients and nonlinear components of the system response enables the method to detect the presence of the damage earlier than the application of some linear-based metrics. Besides that, the stochastic treatment enables the specification of a probabilistic interval of confidence for the system response in an uncertain ambient, thus providing more robust and reliable forecasts.

Bayesian model identification of higher-order frequency response functions for structures assembled by bolted joints

“…Since the nonlinear system in equation ( 26) has terms up to the cubic order, it is used η = 3 contributions to compute the higher-order FRFs [16,17,32]. Thus, applying the harmonic probing method to map the three-dimensional kernel in frequencies ω 1 , ω 2 and ω 3 , the derived higher-order FRF yields:…”

Nonlinear structural damage detection using output‐only Volterra series model

“…The nonlinear proportion will increase with the severity of damage; thus, structural damage can be effectively detected by analyzing the nonlinearity in dynamic responses introduced by the degradation of structural integrity. A damage-sensitive index, which has already been successfully applied to detect the nonlinear damage, 25,37 including breathing crack and bolt loosen, is described as…”

“…Prawin and Rao 26 developed an adaptive filter‐based Volterra series model estimation method and applied it to the nonlinear parameter identification of multiple degrees‐of‐freedom (DOFs) system subjected to a harmonic load. Villani et al 25 proposed a stochastic Volterra series model and experimentally verified the feasibility of using this method in evaluating the state of structure with initial nonlinearity subjected to chirp excitations. The weak hysteresis behavior, that is, vortex‐induced vibration (VIV) can be accurately approximated by Volterra series model with the finite‐order polynomial.…”

“…It has been intensively demonstrated [16][17][18] that the damage-induced nonlinearity degree will increase with the damage severity, which provides a new damage assessment perspective by quantifying the proportion of nonlinearity component presented in vibration responses. In the past decade, many methods, for example, Wiener-Hammerstein models, 19 nonlinear ARMA (NARMA) model, 20 frequency-domain subspace identification, 21 principal component analysis (PCA), 22 deep learning 23 and Volterra series model 24,25 have been developed to effectively characterize nonlinearities with the system input and output data. Among those methods, Volterra series model has been demonstrated to have the feasibility and applicability in estimating the nonlinear properties presented in mechanical systems.…”

Damage detection of nonlinear structures using probability density ratio estimation

“…(2017) proposed to use a Volterra series model, which is a generalization of the linear convolution representing the linear and nonlinear responses of a dynamical system in a separable way. The Volterra series model has been further studied in relation to uncertainties and experimental data in the last 2 years (Villani et al., 2019, 2020; Villani, Todd et al., 2019). However, the Volterra series model relies on input signals, making it impractical for applications on large civil engineering structures, where the input is generally unknown.…”