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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.
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.
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.
The statistical subspace-based damage detection technique has shown promising theoretical and practical results for vibration-based structural health monitoring. It evaluates a subspacebased residual function with efficient hypothesis testing tools, and has the ability of detecting small changes in chosen system parameters. In the residual function, a Hankel matrix of Output covariances estimated from test data is confronted to its left null space associated to a reference model. The hypothesis test takes into account the covariance of the residual for decision making. Ideally, the reference model is assumed to be perfectly known without any uncertainty, which is not a realistic assumption. In practice, the left null space is usually estimated from a reference data set to avoid model errors in the residual computation. Then, the associated uncertainties may be non-negligible, in particular when the available reference data is of limited length. In this paper, it is investigated how the statistical distribution of the residual is affected when the reference null space is estimated. The asymptotic residual distribution is derived, where its refined covariance term considers also the uncertainty related to the reference null space estimate. The associated damage detection test closes a theoretical gap for real-world applications and leads to increased robustness of the method in practice. The importance of including the estimation uncertainty of the reference null space is shown in a numerical study
and on experimental data of a progressively damaged steel frame.
Structural health monitoring (SHM) of civil structures often is limited due to changing environmental conditions, as those changes affect the structural dynamical properties in a similar way like damages can do. In this article, an approach for damage detection under changing temperatures is presentedand applied to a beam structure. The used stochastic subspace-based algorithm relies on a reference null space estimate, which is confronted to data from the testing state in a residual function. For damage detection the residual is evaluated by means of statistical hypothesis tests. Changes of the system due to temperature effects are handled with a model interpolation approach from linear parameter varying system theory. From vibration data measured in the undamaged state at some few reference temperatures, a model of the dynamic system valid for the current testing temperature is interpolated. The reference null space and the covariance matrix for the hypothesis test is computed from this interpolated model. This approach has been developed recently and was validated in an academic test case on simulations of a mass-spring-damper. In this paper, the approach is validated experimentally on a beam structure under varying temperature conditions in a climate chamber. Compared to other approaches, the interpolation approach leads to significantly less false positive alarms in the reference state when the structure is exposed to different temperatures, while faults can still be detected reliably.
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.