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This paper deals with uncertainty considerations in damage diagnosis using the stochastic subspace-based damage detection technique. With this method, a model is estimated from data in a (healthy) reference state and confronted to measurement data from the possibly damaged state in a hypothesis test. Previously, only the uncertainty related to the measurement data was considered in this test, whereas the uncertainty in the estimation of the reference model has not been considered. We derive a new test framework, which takes into account both the uncertainties in the estimation of the reference model as well as the uncertainties related to the measurement data. Perturbation theory is applied to obtain the relevant covariances. In a numerical study the effect of the new computation is shown, when the reference model is estimated with different accuracies, and the performance of the hypothesis tests is evaluated for small damages. Using the derived covariance scheme increases the probability of detection when the reference model estimate is subject to high uncertainty, leading to a more reliable test.
Automatic vibration-based structural health monitoring has been recognized as a useful alternative or addition to visual inspections or local non-destructive testing performed manually. It is, in particular, suitable for mechanical and aeronautical structures as well as on civil structures, including cultural heritage sites. The main challenge is to provide a robust damage diagnosis from the recorded vibration measurements, for which statistical signal processing methods are required. In this chapter, a damage detection method is presented that compares vibration measurements from the current system to a reference state in a hypothesis test, where data9
related uncertainties are taken into account. The computation of the test statistic on new measurements is straightforward and does not require a separate modal identification. The performance of the method is firstly shown on a steel frame structure in a laboratory experiment. Secondly, the application on real measurements on S101 Bridge is shown during a progressive damage test, where damage was successfully detected for different damage scenarios.
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.
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.
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.
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.
Subspace-based detection of fatigue damage on jacket support structures of offshore wind turbines
(2014)
The paper describes the application of the Stochastic Subspace-based Damage Detection (SSDD) method on model structures for an utilization of this approach on offshore wind turbine structures. Aim of the study was therefore to analyze the usability and efficiency of the detection method as well as to determine an optimized set of parameter for realistic damage on support structures of wind energy turbines. Based on results of an experimental fatigue test on a Steel frame laboratory structure a strategy for a numerical verification of the experimentally evolved damage detection was developed, utilizing a time integration approach to simulate the dynamic response. In a second Step the identified modeling and computing methodology is used to numerically investigate the ability to detect damage in real size structural components of offshore wind turbines.
Altematively to common modal analysis as tool for detectmg changes between a reference and an actual (possibly damaged) structural state, the subspace-based damage detection method has been developed in recent years and successfully adopted to test application data sets. Characteristic for that method is that instead of analyzing modal parameters, a Statistical test with respect to changes of a dynamic signature of structural response is introduced. Therefor, a Gaussian residual vector is extracted from the subspace of an output only Vibration data covariance matrix within the reference state. The paper describes the application of this damage detection method within a laboratory fatigue test on a Steel frame structure. Aim of the investigation was to analyze the usability and efficiency of the detection method for realistic damage on carrying structures of wind energy turbines. In a second Step, a numerical model of the lab test structure is developed and validated. Thus, a comparable numerical Simulation of the fatigue damage detection was feasible and the accuracy of the Simulation procedure could be verified. The present study describes the first Step in a two-step approach for quantifying and optimizing fundamental characteristics of SHM Systems for offshore wind turbine structures concerning a required number of sensors and their optimal location.
Damage detection can be performed by detecting changes in the modal parameters between a reference state and the current (possibly damaged) state of a structure from measured output-only vibration data. Alternatively, a subspace-based damage detection test has been proposed and applied successfully, where changes in the modal parameters are detected, but the estimation of the modal parameters themselves is avoided. Like this, the test can run in an automated way directly on the vibration measurements. However, it was assumed 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. A new version of the test has been derived recently that is robust to such changes in the ambient excitation. In this paper, the robust test is recalled and its performance is evaluated both on numerical simulations and a real application, where a steel frame structure is artificially damaged in the lab.