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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.
The local asymptotic approach is promising for vibration-based fault diagnosis when associated to a subspace-based residual function and efficient hypothesis testing tools. It has the ability of detecting small changes in some chosen system parameters. In the residual function,the left null space of the observability matrix associated to a reference model is confronted to the Hankel matrix of output covariances estimated from test data. When this left null space is not perfectly known from a model, it should be replaced by an estimate from data to avoid model errors in the residual computation. In this paper, the asymptotic distribution of the resulting data-driven residual is analyzed and its covariance is estimated, which includes also the covariance related to the reference null space estimate. The advantages of the data-driven residual are demonstrated in a numerical study, and the importance of including the covariance of the reference null space estimate is shown, which increases the detection Performance.
This paper addresses how the value of damage detection Information depends on key Parameters of the Structural Health Monitoring (SHM) system including number of sensors and sensor locations. The Damage Detection System (DDS) provides the information by comparing ambient vibration measurements of a (healthy) reference state with measurements of the current structural system. The performance of DDS method depends on the physical measurement properties such as the number of sensors, sensor positions, measuring length and sensor type, measurement noise, ambient excitation and sampling frequency, as well as on the data processing algorithm including the chosen type I error for the indication threshold. The quantification of the value of Information (VoI) is an expected utility based Bayesian decision analysis method for quantifying the difference of the expected economic benefits with and without information. The (pre-)posterior probability is computed utilizing the Bayesian updating theorem for all possible indications. If changing any key parameters of DDS, the updated probability of system failure given damage detection information will be varied due to different indication of probability of damage, which will result in changes of value of damage detection information. The DDS system is applied in a statically determinate Pratt truss bridge girder. Through the analysis of the value of information with different SHM system characteristics, the settings of DDS can be optimized for minimum expected costs and risks before implementation.
This paper addresses the effects of the deterioration on the value of damage detection information. The quan-tification of the value of damage detection information for deteriorated structures is based on Bayesian pre-posterior decision analysis, comprising structural system performance models, consequence, benefit and costs models and damage detection information models throughout the service life of a structural system. The value of damage detection information accounts for the relevance and precision of the information to ensure the structural integrity and to reduce the potential structural system risks and expected costs throughout the ser-vice life before implementing damage detection system. With the developed approach, the value of damage detection information for a statically determinate Pratt truss bridge girder subjected to different deterioration models is calculated. The analysis shows the impact of the deterioration model parameters on the value of damage detection information. The results can be used to develop optimal maintenance strategies before im-plementation of the damage detection system.
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.
The Stochastic Dynamic Damage Locating Vector (SDDLV) approach is a vibration-based damage localization method based on both a finite element model of a structure and modal parameters estimated
from output-only measurements in the damage and reference states. A statistical version of the Approach takes into account the inherent uncertainty due to noisy measurement data. In this paper, the effect of temperature fluctuations on the performance of the method is analyzed in a model-based approach using a finite element model with temperature dependent parameters. Robust damage localization is carried out by rejecting the temperature influence on the identified modal parameters in the damaged state. The algorithm is illustrated on a simulated structure.
The subject of damage localization is an important issue for Structural Health Monitoring (SHM) particularly in mechanical or civil structures under ambient excitation. In this paper, the statistical subspacebased damage localization method has been applied on a benchmark application, namely a 1/200 scale model of the Saint-Nazaire Bridge, which is a cable-stayed bridge located on the Loire River near the river’s mouth. The employed damage localization method combines data-driven features with physical parameter information from a finite element model in statistical tests, avoiding typical ill-conditioning problems of FE model updating. Damage is introduced in the mockup for cable failures on some of the 72 cables. The purpose of the experiment is to assess the capability of damage assessment methods to find a cable failure.
Temperature variation can be a nuisance that perturbs vibration based structural health monitoring (SHM) approaches for civil engineering structures. In this paper, temperature affected vibration data is evaluated within a stochastic damage detection framework, which relies on a null space based residual. Besides two existing temperature rejection approaches – building a reference state from an averaging method or a piecewise method – a new approach is proposed, using model interpolation. In this approach, a general reference model is obtained from data in the reference state at several known reference temperatures. Then, for a particular tested temperature, a local reference model is derived from the general reference model. Thus, a well fitting reference null space for the formulation of a residual is available when new data is tested for damage detection at an arbitrary temperature. Particular attention is paid to the computation of the residual covariance, taking into account the uncertainty related to the null space matrix estimate. This improves the test performance, contrary to prior methods, for local and global damages, resulting in a higher probability of detection (PoD) for the new interpolation approach compared to previous approaches.
The Stochastic Dynamic Damage Locating Vector (SDDLV) approach is a vibration-based damage localization method based on both a finite element model of a structure and modal parameters estimated from output-only measurements in the damage and reference states. A statistical version of the Approach takes into account the inherent uncertainty due to noisy measurement data. In this paper, the effect of temperature fluctuations on the performance of the method is analyzed in a model-based approach using a finite element model with temperature dependent parameters. Robust damage localization is carried out by rejecting the temperature influence on the identified modal parameters in the damaged state. The algorithm is illustrated on a simulated structure.
The subject of damage localization is an important issue for Structural Health Monitoring (SHM) particularly in mechanical or civil structures under ambient excitation. In this paper, the statistical subspacebased damage localization method has been applied on a benchmark application, namely a 1/200 scale model of the Saint-Nazaire Bridge, which is a cable-stayed bridge located on the Loire River near the river’s mouth. The employed damage localization method combines data-driven features with physical parameter information from a finite element model in statistical tests, avoiding typical ill-conditioning problems of FE model updating. Damage is introduced in the mockup for cable failures on some of the 72 cables. The purpose of the experiment is to assess the capability of damage assessment methods to find a cable failure.
This paper deals with vibration-based damage localization and quantification from output-only measurements. We describe an approach which operates on a data-driven residual vector that is statistically evaluated using information from a finite element model, without updating the parameters of the model. First, the damaged elements are detected in statistical tests, and second, the damage is quantified only for the damaged elements. We propose a new residual vector in this context that is based on the transfer matrix difference between reference and damaged states, and compare it with a previously introduced subspace-based residual. We show localization and quantification on both residuals in simulations.
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.
Damage detection and localization in civil or mechanical structures is a subject of active development and research. A few vibration‐based methods have been developed so far, requiring, for example, modal parameter estimates in the reference and damaged states of the investigated structure, and for localization in addition a finite element model. For structures in operation, temperature has been shown to be a major nuisance to the efficiency of such methods because the modal parameters are varying not only with damage but also due to temperature variations. For detection, a few rejection approaches have been developed. Besides the increased complexity, environmental variation is hardly taken into account in localization approaches. In this paper, we propose a sensitivity‐based correction of the identified modal parameters in the damaged state with respect to the temperature field in the reference state, on the basis of a sensitivity analysis with respect to temperature dependent Parameters of the finite element model in the reference state. The approach is then applied to the stochastic dynamic damage locating vector method, where its improved performance under nonuniform temperature variations is shown in a numerical application on a beam.
Environmental based perturbations influence significantly the ability to identify structural dam-age in Structural Health Monitoring. Strategies are needed to classify such effects and consider them appropri-ately in SHM. It has to be considered if seasonal effects just mask the structural response or if temperature itself correlates to a weakening of the structure. Various methods have been developed and analyzed to separate environmental based effects from damage induced changes in the measures. Generally, two main approaches have emerged from research activity in this fields: (a) statistics-based tools analyzing patterns in the data or in computed parameters and (b) methods, utilizing the structural model of the bridge considering environmental as well as damage-based changes of stiffness values. With the background of increasing affordability of sensing and computing technology, effort should be made to increase sensitivity, reliability and robustness of proce-dures, separating environmental from damage caused changes in SHM measures. The contribution describes an attempt to evaluate both general strategies, their advantages and drawbacks. In addition, two vibration moni-toring procedures are introduced, allowing for temperature-based perturbations of the monitoring data.
A method to determine the influencing parameters of a structural and damage detection system is proposed based on the value of Information analysis. The value of information analysis utilizes the Bayesian pre-posterior decision theory to quantify the value of damage detection system for the structural integrity management during service life. First, the influencing parameters of the structural system, such as deterioration type and rate are introduced for the performance of the prior probabilistic system model. Then the influencing parameters on the damage detection system performance, including number of sensors, sensor locations, measurement noise, and the Type-I error are investigated. The preposterior probabilistic model is computed utilizing the Bayes’ theorem to update the prior system model with the damage indication information. Finally, the value of damage detection system is quantified as the difference between the maximum utility obtained in pre-posterior and prior analysis based on the decision tree analysis, comprising structural probabilistic models, consequences, as well as benefit and costs analysis associated with and without monitoring. With the developed approach, a case study on a statically determinate Pratt truss bridge girder is carried out to validate the method. The analysis shows that the deterioration rate is the most sensitive parameter on the effect of relative value of information over the whole service life. Furthermore, it shows that more sensors do not necessarily lead to a higher relative value of information; only specific sensor locations near the highest utilized components lead to a high relative value of information; measurement noise and the Type-I error should be controlled and be as small as possible. An optimal sensor employment with highest relative value of information is found. Moreover, it is found that the proposed method can be a powerful tool to develop optimal service life maintenance strategies—before implementation—for similar bridges and to optimize the damage detection system settings and sensor configuration for minimum expected Costs and risks.
Fault detection for linear parameter varying systems under changes in the process noise covariance
(2020)
Detecting changes in the eigenstructure of linear systems is a comprehensively investigated subject. In particular, change detection methods based on hypothesis testing using Gaussian residuals have been developed previously. In such residuals, a reference model is confronted to data from the current system. In this paper, linear output-only systems depending on a varying external physical parameter are considered. These systems are driven by process noise, whose covariance may also vary between measurements. To deal with the varying parameter, an interpolation approach is pursued, where a limited number of reference models – each estimated from data measured in a reference state – are interpolated to approximate an adequate reference model for the current parameter. The problem becomes more complex when the different points of interpolation correspond to different noise conditions. Then conflicts may arise between the detection of changes in the eigenstructure due to a fault and the detection of changes due to different noise conditions. For this case, a new change detection approach is developed based on the interpolation of the eigenstructure at the reference points. The resulting approach is capable of change detection when both the external physical parameter and the process noise conditions are varying. This approach is validated on a numerical simulation of a mechanical system.
Fault detection for linear parameter varying systems under changes in the process noise covariance
(2020)
Detecting changes in the eigenstructure of linear systems is a comprehensively investigated subject. In particular, change detection methods based on hypothesis testing using Gaussian residuals have been developed previously. In such residuals, a reference model is confronted to data from the current system. In this paper, linear output-only systems depending on a varying external physical parameter are considered. These systems are driven by process noise, whose covariance may also vary between measurements. To deal with the varying parameter, an interpolation approach is pursued, where a limited number of reference models -- each estimated from data measured in a reference state -- are interpolated to approximate an adequate reference model for the current parameter. The problem becomes more complex when the different points of interpolation correspond to different noise conditions. Then conflicts may arise between the detection of changes in the eigenstructure due to a fault and the detection of changes due to different noise conditions. For this case, a new change detection approach is developed based on the interpolation of the eigenstructure at the reference points. The resulting approach is capable of change detection when both the external physical parameter and the process noise conditions are varying. This approach is validated on a numerical simulation of a mechanical 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.
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.