Variance estimation of modal parameters from input/output covariance-driven subspace identification

International audienceFor Operational Modal Analysis (OMA), the vibration response of a structure from ambient and unknown ex-citation is measured and used to estimate the modal parameters. For OMA with eXogenous inputs (OMAX), some of the inputs are known in addition, which are considered as realizations of a stochastic process. When identifying the modal parameters from noisy measurement data, the information on their uncertainty is most relevant. Previously, a method for variance estimation has been developed for the output-only case with covariance-driven subspace identification. In this paper, a recent extension of this method for the in-put/output covariance-driven subspace algorithm is discussed. The resulting variance expressions are easy to evaluate and computationally tractable when using an efficient implementation. Based on Monte Carlo simulations, the quality of identification and the accuracy of variance estimation are evaluated. It is shown how the input information leads to better identification results and lower uncertainties

Quantification of statistical uncertainties in subspace-based operational modal analysis and their applications

International audienceModal parameters are estimated from vibration data, thus they are inherently afflicted with statistical uncertainties due to the unknown ambient excitation and measurement noise. While the point estimates of the modal parameters can be obtained with several system identification methods, only few of them also provide the associated uncertainties. The quantification of these uncertainties is important for many applications, since they are a means to assess the precision of the estimates, and to evaluate if changes between different datasets are statistically significant or not. As such, they are an added value in modern modal analysis practice and used in applications to e.g., damage detection and localization, reliability analysis, modal tracking and model calibration. For subspace-based system identification, efficient methods for uncertainty quantification have been developed for the last 15 years, yielding reliable estimates of the uncertainties at reasonable computational cost. They cover a wide range of subspace methods and their application areas. In this paper, an overview of the developments is given and the importance of the knowledge of the uncertainties is illustrated

Efficient Structural System Reliability Updating with Subspace-Based Damage Detection Information

International audienceDamage detection systems and algorithms (DDS and DDA) provide information of the structural system integrity in contrast to e.g. local information by inspections or non-destructive testing techniques. However, the potential of utilizing DDS information for the structural integrity assessment and prognosis is hardly exploited nor treated in scientific literature up to now. In order to utilize the information provided by DDS for the structural performance, usually high computational efforts for the pre-determination of DDS reliability are required. In this paper, an approach for the DDS performance modelling is introduced building upon the non-destructive testing reliability which applies to structural systems and DDS containing a strategy to overcome the high computational efforts for the pre-determination of the DDS reliability. This approach takes basis in the subspace-based damage detection method and builds upon mathematical properties of the damage detection algorithm. Computational efficiency is gained by calculating the probability of damage indication directly without necessitating a pre-determination for all damage states. The developed approach is applied to a static, dynamic, deterioration and reliability structural system model, demonstrating the potentials for utilizing DDS for risk reduction

Robust Subspace Based Fault Detection

Subspace methods enjoy some popularity, especially in mechanical engineering, where large model orders have to be considered. In the context of detecting changes in the structural properties and the modal parameters linked to them, some subspace based fault detection residual has been recently proposed and applied successfully. However, most works assume that the unmeasured ambient excitation level during measurements of the structure in the reference and possibly damaged condition stays constant, which is not satisfied by any application. This paper addresses the problem of robustness of such fault detection methods. An efficient subspace-based fault detection test is derived that is robust to excitation change but also to numerical instabilities that could arise easily in the computations. Furthermore, the fault detection test is extended to the Unweighted Principal Component subspace algorithm.Les méthodes des sous espaces jouissent d'une certaine popularité, notamment en ingénierie mécanique, où des modèles de grande taille sont à considérer. Dans l'objectif de détecter des changements dans les propriétés structurelles - ainsi que dans les paramètres modaux associés, un résidu sous espace pour la détection de pannes a été récemment proposé, puis appliqué avec succès. Cependant, généralement, une hypothèse restrictive est présupposée, c'est à dire que les propriétés de l'excitation ambiante et non mesurée restent constantes entre les états de référence et les états possiblement endommagés de la structure. Cette hypothèse n'est pas valide pour la plupart des cas d'étude. Ce travail adresse le problème de la robustesse d'un tel résidu. Un nouveau résidu numériquement plus efficace et plus robuste est proposé. De plus, ce test de détection est adapté à d'autres classes que les méthodes des sous espaces par covariance

Fault Isolation and Quantification from Gaussian Residuals with Application to Structural Damage Quantification

International audienceFault detection for structural health monitoring has been a topic of much research during the last decade. Localization and quantification of damages, which are linked to fault isolation, have proven to be more challenging, and at the same time of higher practical impact. While damage detection can be essentially handled as a data-driven approach, localization and quantification require a strong connection between data analysis and physical models. This paper builds upon a hypothesis test that checks if the mean of a Gaussian residual vector – whose parameterization is linked to possible damage locations – has become non-zero in the faulty state. It is shown how the damage location and extent can be inferred and robust numerical schemes for their estimation are derived based on QR decompositions and minmax approaches. Finally, the relevance of the approach is assessed in numerical simulations of two structures

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

Efficient Multi-Order Uncertainty Computation for Stochastic Subspace Identification

International audienceStochastic Subspace Identification methods have been extensively used for the modal analysis of mechanical, civil or aeronautical structures for the last ten years. So-called stabilization diagrams are used, where modal parameters are estimated at successive model orders, leading to a graphical procedure where the physical modes of the system are extracted and separated from spurious modes. Recently an uncertainty computation scheme has been derived allowing the computation of uncertainty bounds for modal parameters at some given model order. In this paper, two problems are addressed. Firstly, a fast computation scheme is proposed reducing the computational burden of the uncertainty computation scheme by an order of magnitude in the model order compared to a direct implementation. Secondly, a new algorithm is proposed to derive efficiently the uncertainty bounds for the estimated modes at all model orders in the stabilization diagram. It is shown that this new algorithm is both computationally and memory efficient, reducing the computational burden by two orders of magnitude in the model order

Uncertainty quantification for monitoring of civil structures from vibration measurements

International audienceHealth Monitoring of civil structures can be performed by detecting changes in the modal parameters of a structure, or more directly in the measured vibration signals. For a continuous monitoring the excitation of a structure is usually ambient, thus unknown and assumed to be noise. Hence, all estimates from the vibration measurements are realizations of random variables with inherent uncertainty due to (unknown) process and measurement noise and finite data length. In this talk, a strategy for quantifying the uncertainties of modal parameter estimates from a subspace-based system identification approach is presented and the importance of uncertainty quantification in monitoring approaches is shown. Furthermore, a damage detection method is presented, which is based on the direct comparison of the measured vibration signals without estimating modal parameters, while taking the statistical uncertainty in the signals correctly into account. The usefulness of both strategies is illustrated on data from a progressive damage action on a prestressed concrete bridge