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In this paper we focus on sensor placement for output-only modal analysis, where the objective is to choose those sensor locations yielding a minimal variance in the identification of modal parameters from measurement data. It is heuristically shown that the variance of modal parameters estimated with data-driven subspace identification can be approximated solely based on the process and the measurement noise properties with the Kalman filter and the underlying system model, and is independent of data which are not available at the experimental design stage. The performance of the proposed approach is illustrated on an extensive Monte Carlo simulation for an illustrative example of a mechanical chain system.

International audience; Evaluating natural frequencies for damage detection and localization is a standard procedure in non-destructive testing (NDT) and structural health monitoring (SHM). In particular, for cables and other prestressed tendons, natural frequencies exhibit high sensitivities to structural changes, which is often demonstrated by comparing the frequencies before and after damage occurred, e.g., using probability of detection (POD) or probability of localization (POL) curves. In this paper, an approach is developed to predict POD/POL curves without any data from the damaged state. The method is based on data from the undamaged state and a numerical model, which is utilized to obtain sensitivity vectors that linearize the relation between frequency changes and changes in structural parameters. At the same time, statistical uncertainties in the frequency estimation process are considered. Based on this method, a cable monitoring strategy is suggested, where sensitivity vectors are first used to calibrate decisive cable properties using model updating, followed by a performance assessment through POD/POL curves, and a continuous damage detection and localization based on statistical tests. The synergic effects of the presented methods are demonstrated by means of a numerical case study on a prestressed cable, where data from a single uni-axial vibration sensor is evaluated. The results indicate that changes in stiffness and axial forces can be distinguished using localization tests, but additional sensors and features are necessary for damage localization along the cable.

International audience; The 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.

International audience; Structural health monitoring is a promising technology to automatically detect structural changes based on permanently installed sensors. Vibration-based methods that evaluate the global system response to ambient excitation are suited to diagnose changes in boundary conditions, i.e., changes in member prestress or imposed displacements. In this paper, these changes are evaluated based on sensitivity-based statistical tests, which are capable of detecting and localizing parametric structural changes. The main contribution is the analytical calculation of sensitivity vectors for changes in boundary conditions (i.e., changes in prestress or support conditions) based on stress stiffening, and the combination with a numerically efficient algorithm, i.e., Nelson's method. One of the main advantages of the employed damage diagnosis algorithm is that, although it uses physical models for damage detection, it considers the uncertainty in the data-driven features, which enables a reliabilitybased approach to determine the probability of detection. Moreover, the algorithm can be trained and the probability of detecting future damages can be predicted based on data and a model from the undamaged structure, in an unsupervised learning mode, making it particularly relevant for unique structures, where no data from the damaged state is available. For proof of concept, a numerical case study is presented. The study assesses the loss of prestress in a two-span reinforced concrete beam and showcases suitable validation approaches for the sensitivity calculation.

International audience; Modal 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.

International audience; Damage detection and damage localization constitute two pillars of Structural Health Monitoring that are highly relevant for applications to large-scale structures. Damage detection is usually achieved through statistical tests of data-driven residuals that monitor changes of a structure from its baseline behaviour. Damage localization investigates changes in damage residuals with respect to parameterized structural models through sensitivity vectors. Among the classic damage-sensitive features used for residual generation are subspace angles and principal components obtained from data spaces, whose evaluation for a decision about damage often boils down to novelty analysis, or statistical likelihood ratio tests. Modal parameter estimates are also employed for this purpose; however, most of the existing approaches appear to neglect the uncertainties related to their estimation. This paper fills this gap and presents a residual for damage detection and damage localization that is based on the difference of modal parameters obtained from data collected in some baseline and some test state of the structural system. The proposed scheme is evaluated in numerical simulations validating its robustness for damage detection and damage localization.

International audience; The first phase of each structural monitoring project is the operational evaluation. Its purpose is to define relevant damage mechanisms and environmental conditions, to consider the data acquisition limitations on site, and to justify the investment. Subsequently, relevant measurement quantities and damagesensitive features are selected, but very few systematic approaches exist in the literature on how to select the most appropriate features. The presented paper fills this gap and develops an approach to select damage-sensitive features based on probability of detection (POD) curves. The POD curves are generated based on a novel method for statistical damage detection tests that requires a finite element model and vibration data from the undamaged structure. However, no data is required from the damaged state, making it particularly suited for unique or large and complex engineering structures. The approach explicitly considers the uncertainties in the features due to unknown loads, measurement noise, and short measurement durations. Although global damage-sensitive features are considered, such as modal parameters and subspace-based residuals, the detectability is evaluated for local structural components. The paper includes a proof of concept study on a laboratory structure. The results demonstrate that the developed method successfully finds the feature with the highest damage detectability for a chosen damage scenario, and that the detectability varies depending on the monitored local component.

International audience; The interpretation of stabilization diagrams is a classical task in operational modal analysis, and has the goal to obtain the set of physical modal parameters from estimates at the different model orders of the diagram. The diagrams are contaminated by spurious modes that appear due to the unknown (non-white) ambient excitation and sensor noise, as well as possible over-modelling. Under the premise that spurious modes will vary and physical modes will remain quite constant at different model orders, the focus is to retrieve the physical modes that constitute the identified model, while rejecting the non-physical, spurious modes. Over the last decade, extensive research has been devoted for developing automated strategies facilitating their interpretation. To this end, the interpretation is in principle disconnected from the identification method and boils down to three stages i.e., clearing the diagram from the spurious mode estimates, aggregating the modal parameter estimates in modal alignments and the final parameter choice. Besides the point estimates of the modal parameters, also their confidence bounds are available with some identification methods, such as subspace identification. These uncertainties provide useful information for an automated interpretation of the stabilization diagrams. First, modes with high uncertainty are most likely non-physical modes. Second, the confidence bounds provide a natural threshold for the automated extraction of modal alignments, avoiding the requirement of a deterministic threshold regarding the allowable variation within an alignment. In this paper, a strategy is presented for the automated mode extraction considering their uncertainties, based on clustering a statistical distance measures between the modes. The relevance of the uncertainty consideration in the automated extraction will be demonstrated on vibration data from two bridges.

International audience; This article describes an approach to evaluate the minimum localizable damage for stochastic subspace-based damage diagnosis. Localizability is defined as the sensitivity to small and local damages (detectability), the ability to narrow down the exact damage location (localization resolution) and the test response of undamaged parameters (false localization alarms). For the analysis, damage is defined as a change in model-based design parameters, for example, material constants or cross-sectional values in a finite element model. Subsequently, the parameter changes are linked to changes in the global damage-sensitive features using sensitivity vectors, and inherent uncertainties (due to stochastic loads and measurement noise) are quantified. This way, local structural parameters can be tested for changes using statistical hypothesis tests, such as the general likelihood ratio and the statistical minmax localization test. Due to the numerical conditioning of the damage localization problem, the sensitivity vectors have to be clustered before damage can be localized. Sensitivity clustering corresponds to a substructuring of the finite element model, where the number of clusters (the localization resolution) is a user-defined input parameter. The main results of this paper are mathematical criteria to calculate the damage detectability and the false alarm susceptibility for different localization resolutions. Moreover, an automated substructuring routine is described that finds the optimal substructure arrangement as a compromise between high damage detectability, high localization resolution, and low false alarm susceptibility. For proof of concept, a numerical case study is presented, where the damage localizability is determined and validated for a cable-stayed bridge.