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The stochastic dynamic damage locating vector approach is a vibration-based damage localization method based on a finite element model of a structure and output-only measurements in both reference and damaged states. A stress field is computed for loads in the null space of a surrogate of the change in the transfer matrix at the sensor positions for some values in the Laplace domain. Then, the damage location is related to positions where the stress is close to zero. Robustness of the localization information can be achieved by aggregating results at different values in the Laplace domain. So far, this approach, and in particular the aggregation, is deterministic and does not take the uncertainty in the stress estimates into account. In this paper, the damage localization method is extended with a statistical framework. The uncertainty in the output-only measurements is propagated to the stress estimates at different values of the Laplace variable, and these estimates are aggregated based on statistical principles. The performance of the new statistical approach is demonstrated both in a numerical application and a lab experiment, showing a significant improvement of the robustness of the method due to the statistical evaluation of the localization information.

A theorem on damage localization from flexibility changes has been proven recently,
where it has been shown that the image of the change in flexibility δF between
damaged and reference states of a structure is a basis for the influence lines of stress
resultants at the damaged locations. This damage localization approach can operate on
output-only vibration measurements from damaged and reference states, and a finite
element model of the structure in reference state is required. While the localization
approach is based on purely mechanical principles, an estimate of the image of δF is
required from the data that is subject to statistical uncertainty due to unknown noise
excitation and finite data length. In this paper, this uncertainty is quantified from the
measurements and a statistical framework is added for the decision about damaged
elements. The combined approach is successfully applied to a numerical simulation
and to a cantilever beam in a lab experiment.

For the last decades vibration based identification of damage on civil Engineering structures has become an important issue for maintenance operations on transport infrastructure.
Research in that field has been rapidly expanding from classic modal Parameter estimation using measured excitation to modern operational monitoring. Here the difficulty is to regard to the specific environmental and operational influence to the structure under observation. In this paper, two methods accounting for statistical and/or operational uncertainties are applied to measurement data of a progressive damage test on a prestressed concrete bridge. On the base of covariance driven Stochastic Subspace Identification (SSI) an algorithm is developed to monitor and automatically compute confidence intervals of the obtained modal parameters. Furthermore, a null space based non-parametric damage detection method, utilizing a statistical χ2 type test is applied to the measurement data. It can be shown that for concrete bridges the proposed methodology is able to clearly indicate the presence of structural damage, if the damage leads to a change of the structural system.

For the last decades vibration based damage detection of engineering structures has become an important issue for maintenance operations on transport infrastructure. Research in vibration based structural damage detection has been rapidly expanding from classic modal parameter estimation to modern operational monitoring. Methodologies from control Engineering especially of aerospace applications have been adopted and converted for the application on civil structures. Here the difficulty is to regard to the specific environmental and operational influence to the structure under observation. A null space based damage detection algorithm is tested for its sensitivity to structural damage of a prestressed concrete road bridge. Specific techniques and extensions of the algorithm are used to overcome difficulties from the size of the structure which is associated with the number of recorded sensor channels as well as from the operational disturbances by a nearby construction site. It can be shown that for concrete bridges the proposed damage detection methodology is able to clearly indicate the presence of structural damage, if the damage leads to a significant change of the structural system. Small damage which do not result in a System change when not activated by loading, do not lead to a modification of the dynamic response behavior and for that cannot be detected with the proposed global monitoring method.

In Operational Modal Analysis, the modal parameters (natural frequencies, damping ratios and mode shapes) obtained from Stochastic Subspace Identification (SSI) of a structure, are afflicted with statistical uncertainty. For evaluating the quality of the obtained results it is essential to know the respective confidence intervals of these figures. In this paper we present algorithms that automatically compute the confidence intervals of modal parameters obtained from covarianceand data-driven SSI of a structure based on vibration measurements. They are applied to the monitoring of the modal parameters of a prestressed concrete highway bridge during a progressive damage test that was accomplished within the European research project IRIS. Results of the covariance- and data-driven SSI are compared.

Structural health monitoring with statistical methods during progressive damage test of S101 Bridge
(2014)

For the last decades vibration based damage detection of engineering structures has become an important issue for maintenance operations on transport infrastructure. Research in vibration based structural damage detection has been rapidly expanding from classic modal parameter estimation to modern operational monitoring. Since structures are subject to unknown ambient excitation in operation conditions, all estimates from the finite data measurements are of statistical nature. The intrinsic uncertainty due to finite data length, colored noise, non-stationary excitations, model order reduction or other operational influences needs to be considered for robust and automated structural health monitoring methods. In this paper, two subspace-based methods are considered that take these statistical uncertainties into account, first modal parameter and their confidence interval estimation for a direct comparison of the structural states, and second a statistical null space based damage detection test that completely avoids the identification step. The performance of both methods is evaluated on a large scale progressive damage test of a prestressed concrete road bridge, the S101 Bridge in Austria. In an on-site test, ambient vibration data of the S101 Bridge was recorded while different damage scenarios were introduced on the bridge as a benchmark for damage identification. It is shown that the proposed damage detection methodology is able to clearly indicate the presence of structural damage, if the damage leads to a change of the structural system.

Fault detection and isolation can be handled by many different approaches. This paper builds upon a hypothesis test that checks whether the mean of a Gaussian random vector has become non-zero in the faulty state, based on a chi2 test. For fault isolation, it has to be decided which components in the parameter set of the Gaussian vector have changed, which is done by variants of the chi2 hypothesis test using the so-called sensitivity and minmax approaches. While only the sensitivity of the tested parameter component is taken into account in the sensitivity approach, the sensitivities of all parameters are used in the minmax approach, leading to better statistical properties at the expense of an increased computational burden. The computation of the respective test variable in the minmax test is cumbersome and may be ill-conditioned especially for large parameter sets, asking hence for a careful numerical evaluation. Furthermore, the fault isolation procedure requires the repetitive calculation of the test variable for each of the parameter components that are tested for a change, which may be a significant computational burden. In this paper, dealing with the minmax problem, we propose a new efficient computation for the test variables, which is based on a simultaneous QR decomposition for all parameters. Based on this scheme, we propose an efficient test computation for a large parameter set, leading to a decrease in the numerical complexity by one order of magnitude in the total number of parameters. Finally, we show how the minmax test is useful for structural damage localization, where an asymptotically Gaussian residual vector is computed from output-only vibration data of a mechanical or a civil structure.

Operational modal analysis and vibration based damage detection of engineering
structures have become important issues for Structural Health Monitoring (SHM) and
maintenance operations, e.g. on transport infrastructure. Methods from control
engineering have been adopted and converted for the application on civil structures.
Approaches like subspace-based system identification combine excellent theoretical
properties under the unknown excitation properties of a structure with practical
usefulness.
In this paper, the implementation of covariance-driven stochastic subspace
identification (SSI) on the smart wireless sensor platform PEGASE is described.
Special care is taken about the fast implementation of this technique since the
computations are embedded on the platform and perform in real-time. The most
efficient and current version of subspace algorithms has been implemented. Efficiency
and memory consumption are primary criteria in this implementation.
First validated results will be given for each step of the algorithms: crosscorrelation
on natural inputs signal from sensors; Hankel matrix output; SSI
implementation using the LAPACK library to get a SVD, pseudo-inverse, eigenvalues
etc. Results validation has been correlated between PEGASE implementation and the
previous processing in static situation: the same data was collected by wired sensors
and data-loggers, then, later, processed on a PC using traditional Matlab software.
In parallel, from an engineering point of view, a description of the PEGASE
wireless platform will be given: generic usage, wide capacities, embedded Digital
Signal Processing (DSP) processor and Library over a small embedded Linux
Operating System, a very accurate synchronization principle based on a GPS/PPS
principle, etc. Perspectives about a complete technical in-situ installation will also be
given.

In the last ten years, monitoring the integrity of the civil infrastructure has been an active research topic, including in connected areas as automatic control. It is common practice to perform damage detection by detecting changes in the modal parameters between a reference state and the current (possibly damaged) state from measured vibration data. Subspace methods enjoy some popularity in structural 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, a subspace-based fault detection residual has been recently proposed and applied successfully, where the estimation of the modal parameters in the possibly damaged state is avoided. However, most works assume that the unmeasured ambient excitation properties during measurements of the structure in the reference and possibly damaged condition stay constant, which is hardly satisfied by any application. This paper addresses the problem of robustness of such fault detection methods. It is explained why current algorithms from literature fail when the excitation covariance changes and how they can be modified. Then, an efficient and fast subspace-based damage detection test is derived that is robust to changes in the excitation covariance but also to numerical instabilities that can arise easily in the computations. Three numerical applications show the efficiency of the new approach to better detect and separate different levels of damage even using a relatively low sample length.