Uncertainty propagation in subspace methods for operational modal analysis under misspecified model orders

International audienceThe quantification of statistical uncertainty in modal parameter estimates has become a standard tool, used in applications to, e.g., damage diagnosis, reliability analysis, modal tracking and model calibration. Although efficient multi-order algorithms to obtain the (co)variance of the modal parameter estimates with subspace methods have been proposed in the past, the effect of a misspecified model order on the uncertainty estimates has not been investigated. In fact, the covariance estimates may be inaccurate due to the presence of small singular values in the supposed signal space. In this paper we go back to the roots of the uncertainty propagation in subspace methods and revise it to account for the case when a part of the noise space is erroneously added to the signal space. What is more, the proposed scheme adapts a different approach for the sensitivity analysis of the signal space, which improves the numerical efficiency. The performance is illustrated on an extensive Monte Carlo simulation of a simple mechanical system and applied to real data from a bridge

Crack-damage quantification based on stochastic optimization of finite element models with data-driven features

International audienceThe vibration-based Structural Health Monitoring plays a central role in ensuring the safe operation of infrastructures by monitoring their structural integrity based on data collected by sensors. While damage detection has reached maturity, the localization and the quantification of small-scale damage remain an open challenge. To address it, both the localization and the quantification of damage are often posed as an updating problem of a Finite Element Model (FEM) of the operating structure, minimizing the misfit between some features computed from response measurements of a faulty structure and its FEM in a reference, healthy condition. This paper investigates the choice of the features for the design of the objective function to quantify structural cracks. For this purpose, a FEM of a beam with a transverse crack is developed and parametrized by the second moment of area of the elements to locate and quantify the crack-related damage. Subsequently, the impact on the choice of the objective function is discussed based on a small-samples Monte Carlo study

Statistical optimization for subspace-based damage quantification

International audienceThe purpose of model updating is to minimize the misfit between the structural response measurements and an assumed numerical model. In the context of damage quantification, this misfit is characterized by some features computed from the response data measured on the faulty structure, and its Finite Element (FE) model in the healthy condition. The FE model is parameterized so that the estimated features are related to the physical parameters of the model. Therein, the parameterization size may be large. As a consequence of low instrumentation, different parameters can have a similar effect on the estimated features, resulting in non uniqueness of the updating problem solutions, even taking into account the inherent uncertainty errors, originating both from the model and the measurements. In this paper a model updating-based damage quantification strategy is proposed. It involves the minimization of two Hankel matrices, one computed from the data and another from the optimized model. The difference between those two matrices is studied, in particular in the practical case where the ambient excitation is unknown. It yields a statistical residual, whose deviations from zero can be evaluated through a statistical test. The resulting optimization is based on the Generalized Likelihood Ratio test as an objective function and uses its 95 per cent quantile as a measure of closeness for a stopping criterion for the optimization. Moreover, the large size of the finite element model to optimize compared to the low instrumentation has to be taken into account by clustering the parameter space. This clustering is proceeded using the well known stochastic subspace-based damage localisation method. The proposed framework is validated on simulations of a simple mechanical system

Hankel matrix-based Mahalanobis distance for fault detection robust towards changes in process noise covariance

International audienceStatistical subspace-based change detection residuals have been developed to infer a change in the eigenstructure of linear systems. Their statistical properties have been properly evaluated in the case of a known reference and constant noise properties. Previous residuals have favored the family of null space-based approaches, whereas the possibility of using other metrics such as the Mahalanobis distance has been omitted. This paper investigates the development and study of such a norm under the premise of a varying noise covariance. Its statistical properties have been studied and tested on a numerical example of a mechanical system