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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.
This paper addresses the quantification of the value of damage detection system and algorithm information on the basis of Value of Information (VoI) analysis to enhance the benefit of damage detection information by providing the basis for its optimization before it is performed and implemented. The approach of the quantification the value of damage detection information builds upon the Bayesian decision theory facilitating the utilization of damage detection performance models, which describe the information and its precision on structural system level, facilitating actions to ensure the structural integrity and facilitating to describe the structural system performance and its functionality throughout the service life. The structural system performance is described with its functionality, its deterioration and its behavior under extreme loading. The structural system reliability given the damage detection information is determined utilizing Bayesian updating. The damage detection performance is described with the probability of indication for different component and system damage states taking into account type 1 and type 2 errors. The value of damage detection information is then calculated as the difference between the expected benefits and risks utilizing the damage detection information or not. With an application example of the developed approach based on a deteriorating Pratt truss system, the value of damage detection information is determined,demonstrating the potential of risk reduction and expected cost reduction.
Damage detection systems (DDS) provide information of the structural system integrity in contrast to e.g. local information by inspections or non-destructive testing techniques. In this paper, an approach is developed and demonstrated to utilize DDS information to update the structural system reliability and to integrate this information in structural system risk and utility analyses. For this aim, a novel performance modelling of DDS building upon their system characteristics and non-destructive testing reliability is introduced. The DDS performance modelling accounts for a measurement system in combination with a damage detection algorithm attached to a structural system in the reference and damage states and is modelled with the probability of indication accounting for type I and II errors. In this way, the basis for DDS performance comparison and assessment is provided accounting for the dependencies between the damage states in a structure. For updating of the structural system reliability, an approach is developed based on Bayesian updating facilitating the use of DDS information on structural system level and thus for a structural system risk analysis. The structural system risk analysis encompasses the static, dynamic, deterioration, reliability and consequence models, which provide the basis for the system model for calculating the direct risks due to component failure and the indirect risks due to system failure. Two case studies with the developed approach demonstrate a high Value of DDS Information due to risk and expected cost reduction.
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.
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.