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Reliability analysis of deteriorating structural systems requires the solution of time-variant reliability problems.
In the general case, both the capacity of and the loads on the structure vary with time. This analysis can be approached by approximation through a series of time-invariant reliability problems, which is a potentially effective strategy for cases where direct solutions of the time-variant reliability problem are challenging, e.g. for structural systems with many elements or arbitrary load processes. In this contribution, we thoroughly Review the formulation of the equivalent time-invariant reliability problems and extend this approximation to structures for which inspection and monitoring data is available. Thereafter, we present methods for efficiently evaluating the reliability over time. In particular, we propose the combination of sampling-based methods with a FORM (first-order reliability method) approximation of the series system reliability problem that arises in the computation of the lifetime reliability. The framework and algorithms are demonstrated on a set of numerical examples, which include the computation of the reliability conditional on inspection data.
Inspection and maintenance contribute significantly to the lifetime cost of bridges. There is significant potential in using information obtained through structural health monitoring to update predictive models of the condition and performance of such structures, and thus ena-ble an improved decision-making regarding inspection and maintenance activities. Within the AISTEC project funded by the German Federal Ministry of Education and Research, we develop vibration-based structural health monitoring systems aimed at continuously provid-ing information on the structural condition of bridges. Environmental variations such as changing ambient temperatures can significantly influence the dynamic characteristics of bridges and thus mask the effect of structural changes and damages. It remains a challenge to account for such influences in structural health monitoring. To study the effect of ambient temperatures on the dynamic characteristics of beam structures, we monitor the vibration response of a reinforced concrete beam in the uncracked and cracked state at varying tem-peratures in a climate chamber. We postulate a set of competing parameterized probabilistic structural models, which explicitly account for the effect of varying ambient temperatures on the mechanical properties of the system. We then combine the information provided by the structural models with the information contained in the recorded vibration data to learn the parameters of the temperature-dependent structural models and infer the plausible state of the beam using Bayesian system identification and model class selection.
Gradual or sudden changes in the state of structural systems caused, for example, by deterioration or accidental load events can influence their load-bearing capacity. Structural changes can be inferred from static and/or dynamic response data measured by structural health monitoring systems. However, they may be masked by variations in the structural response due to varying environmental conditions. Particularly, the interaction of nominally load-bearing components with nominally non-load bearing components exhibiting characteristics that vary as a function of the environmental conditions can significantly affect the monitored structural response. Ignoring these effects may hamper an inference of structural changes from the monitoring data. To address this issue, we adopt a probabilistic model-based framework as a basis for developing digital twins of structural systems that enable a prediction of the structural behavior under varying ambient condition. Within this framework, different types of data obtained from real the structural system can be applied to update the digital twin of the structural system using Bayesian methods and thus enhance predictions of the structural behavior. In this contribution, we implement the framework to develop a digital twin of a simply supported steel beam with an asphalt layer. It is formulated such that it can predict the static response of the beam in function of its temperature. In a climate chamber, the beam was subject to varying temperatures and its static response wass monitored. In addition, tests are performed to determine the temperature-dependent properties of the asphalt material. Bayesian system identification is applied to enhance the predictive capabilities of the digital twin based on the observed data.
Changes in the measured response of structural systems can be an indication of structural damages. However, such changes can also be caused by the effect of varying environmental conditions. To detect, localize and quantify changes or damages in structural systems subject to varying environmental conditions, physics-based models of the structural systems have to be applied which explicitly account for the influence of ambient conditions on the structural behavior. Data obtained from the structural systems should be used to calibrate the models and update predictions. Bayesian system identification is an effective framework for this task. In this paper, we apply this framework to learn the parameters of two competing structural models of a reinforced concrete beam subject to varying temperatures based on static response data. The models describe the behavior of the beam in the uncracked and cracked condition. The data is collected in a series of load tests in a climate chamber. Bayesian model class selection is then applied to infer the most plausible condition of the beam conditional on the available data.
Structural health monitoring (SHM) intends to improve the management of engineering structures. The number of successful SHM projects – especially SHM research projects – is ever growing, yielding added value and more scientific insight into the management of infrastructure asset. With the advent of the data age, the value of accessible data becomes increasingly evident. In SHM, many new data-centric methods are currently being developed at a high pace. A consequent application of research data management (RDM) concepts in SHM projects enables a systematic management of raw and processed data, and thus facilitates the development and application of artificial intelligence (AI) and machine learning (ML) methods to the SHM data. In this contribution, a case study based on an institutional RDM framework is presented. Data and metadata from monitoring the structural health of the Maintalbrücke Gemünden for a period of 16 months are managed with the RDM system BAM Data Store, which makes use of the openBIS data management software. An ML procedure is used to classify the data. Feature engineering, feature training and resulting data are performed and modelled in the RDM system.
Die Infrastruktursysteme der Industriestaaten erfordern heute und in Zukunft ein effizientes Management bei alternder Bausubstanz, steigenden Lasten und gleichbleibend hohem Sicherheitsniveau. Digitale Technologien bieten ein großes Potenzial zur Bewältigung der aktuellen und künftigen Herausforderungen im Infrastrukturmanagement. Im BMBF-geförderten Projekt Bewertung alternder Infrastrukturbauwerke mit digitalen Technologien (AISTEC) wird untersucht, wie unterschiedliche Technologien und deren Verknüpfung gewinnbringend eingesetzt werden können. Am Beispiel der Maintalbrücke Gemünden werden ein sensorbasiertes Bauwerksmonitoring, bildbasierte Inspektion mit durch Kameras ausgestatteten Drohnen (UAS) und die Verknüpfung digitaler Bauwerksmodelle umgesetzt. Die aufgenommenen Bilder dienen u. a. als Grundlage für spätere visuelle Anomaliedetektionen und eine 3D-Rekonstruktion, welche wiederum für die Kalibrierung und Aktualisierung digitaler Tragwerksmodelle genutzt werden. Kontinuierlich erfasste Sensordaten werden ebenfalls zur Kalibrierung und Aktualisierung der Tragwerksmodelle herangezogen. Diese Modelle werden als Grundlage für Anomaliedetektionen und perspektivisch zur Umsetzung von Konzepten der prädiktiven Instandhaltung verwendet. Belastungsfahrten und historische Daten dienen in diesem Beitrag der Validierung von kalibrierten Tragwerksmodellen.
The reliability of deteriorating structures at time t is quantified by the probability that failure occurs within the period leading up to time t. This probability is often referred to as cumulative failure probability and is equal to the cumulative distribution function of the time to failure. In structural reliability, an estimate of the cumulative failure probability is obtained based on probabilistic Engineering models of the deterioration processes and structural performance. Information on the condition and the loading contained in inspection and monitoring data can be included in the probability estimate through Bayesian updating. Conditioning the
probability of failure on the inspection or monitoring outcomes available at time t (e.g. detections or no detection of damages) can lead to a reduction in that probability.
Such a drop in the cumulative failure probability might seem counterintuitive since the cumulative failure probability is a non-decreasing function of time. In this paper, we illustrate—with the help of a numerical example—that such a drop is possible because the cumulative probability before and after the updating is not based on the same information, hence not on the same probabilistic model.
Identifying optimal inspection and repair strategies for offshore jacket structures is a challenging task. We pre-sent an approach, which is based on recent developments in the field of risk-based operation and maintenance planning at the structural system level. The approach utilizes heuristics to define inspection and repair strate-gies at the system level and to reduce the search space of possible strategies. For each defined strategy, the expected service life cost of inspection, repair and failure is evaluated based on simulated inspection and re-pair histories. Subset simulation is applied to compute the conditional repair and failure probabilities required for this analysis. It also forms the basis for simulating inspection and repair histories. The strategy that mini-mizes the expected service life cost is the optimal one in the set of pre-selected strategies. The underlying condition and performance model accounts for the stochastic dependence among the deterioration states of the different structural elements and the structural redundancy. The approach is demonstrated in a case study considering a jacket-type frame. In this study, we essentially vary the inspection interval, the minimum num-ber of inspected components and the target reliability, and identify the combination that minimizes the ex-pected total service life cost.
Monitoringsysteme erfassen kontinuierlich Bauwerksdaten wie z.B. Bauwerksbeschleunigungen, auf deren Grundlage Bauwerksschäden mit Hilfe von SHM-Methoden quantifiziert werden können. Mit den gewonnenen Informationen über den aktuellen Bauwerkszustand können Vorhersagen des Bauwerkszustandes und der Bauwerkszuverlässigkeit aktualisiert und erforderliche Inspektionen und Instandhaltungsmaßnahmen vorausschauend geplant werden. Im BMBF-Forschungsvorhaben AISTEC entwickeln der Fachbereich 7.2 „Ingenieurbau“ innovative Monitoringverfahren zur Systemidentifikation und automatischen Detektion, Lokalisierung und Quantifizierung von Schäden an Infrastrukturbauwerken anhand von gemessenen dynamischen und statischen Bauwerksdaten. Im Rahmen dieses Projektes werden die Verfahren an der Maintalbrücke bei Gemünden angewendet, welche Teil der ICE-Strecke Hannover-Würzburg ist. In diesem Vortrag wird das für die Maintalbrücke Gemünden geplante und umgesetzte Monitoingsystem vorgestellt.
In this contribution, we consider two applications in which probabilistic approaches can potentially complement or enhance the design and assessment of offshore wind turbine foundations. First, we illustrate in a numerical example that probabilistic modelling can be helpful in dealing with chang-es in turbine locations during the planning phase of an offshore wind farm. In this case, spatial probabilistic modelling of the ground conditions enables (a) an inference of the soil properties at the modified turbine location from field data collected at different locations across an offshore wind farm site and (b) an optimisation of further site investigations. Second, we discuss the uncer-tainties and risks associated with the installation of large diameter monopiles in soils with hetero-geneities such as strong layers and/or embedded boulders. Subsequently, we present a concept for modelling, understanding, and managing these risks based on a probabilistic model of the subgrade conditions, monopile, and subgrade-pile-interaction.
In this presentation, we discuss the potential of probabilistic approaches to the design and assessment of offshore foundations. The potential is demonstrated in a numerical example considering a laterally loaded monopile. As an outlook, we present a concept for managing the risk associated with installing large monopiles.
In this presentation, a framework for integrating vibration-based structural health monitoring data into the optimization of inspection and maintenance of deteriorating structural systems is presented. The framework is demonstrated in an illustrative example considering a steel frame subject to fatigue.
Im AISTEC Projekt erforscht der FB 7.2 Verfahren zur Bewertung von Verkehrsbrücken auf der Gruandlage von sensorbasierten Bauwerksmessungen. In diesem Vortrag wird ein Überlick über die Forschungsarbeiten des FB 7.2 präsentiert. Des Weiteren wird ein Ausblick zur quantitativen Integration von sensorbasierten Bauwerksmessungen in die risiko-basierte prädiktive Planung von Inspektionen und Reparaturen von Ingenieurbauwerken gegeben.
Fatigue is one of the main deterioration processes affecting the performance of welded steel support structures of wind turbines in offshore wind farms. In this contribution, we present a probabilistic physics-based fatigue deterioration model of a wind farm that accounts for the stochastic dependence among the fatigue behavior of different hotspots at turbine and wind farm level. The dependence exists because of uncertain common influencing factors such as similar material properties, fabrication qualities and load conditions. These system effects signify that an inspection of one hotspot provides indirect information of the condition of the remaining hotspots and thus enable an optimization of the inspection effort for a wind farm.
The wind farm model consists of two levels: A turbine support structure (level 1 system model) is represented by its fatigue hotspots and their stochastic dependence. The fatigue performance of a hotspot is described by a probabilistic fracture mechanics (FM) fatigue model. The probabilistic model of the parameters of the FM fatigue model is calibrated based on design data and is thus directly linked to the design of the turbine support structures. Dependence among the fatigue performances of different hotspots in a turbine support structure is modeled by introducing correlations between the stochastic parameters of the FM fatigue models. A wind farm (level 2 system model) consists of different turbine support structures (level 1 system models). Additional correlations are introduced at wind farm level to account for the dependence among the fatigue behavior of hotspots belonging to different turbine support structures. The wind farm model enables the computation of (marginal) hotspot fatigue reliabilities, system fatigue reliabilities of individual turbine support structures and the system fatigue reliability of an entire wind farm. The probabilistic model of the parameters of the two-level system model can be consistently updated with inspection outcomes using Bayesian methods. The updated probabilistic model of the model parameters then forms the basis for updating the estimates of the fatigue reliabilities.
We implement the wind farm model in a software tool named SysPark. The tool provides the means for planning inspections at wind farm level using an adaptive reliability-based threshold approach. In this approach, the first inspection campaign is planned in the year before the fatigue failure rates of the hotspots with the lowest fatigue reliabilities exceed a threshold failure rate. Once inspection results become available, the probabilistic model of the parameters of the wind farm model is updated. If repairs are performed, the wind farm model is additionally modified to describe the behavior of the repaired hotspots. The updated and modified model then enables the planning of the next inspection campaign and so on. The software tool is demonstrated in a case study considering a generic wind farm consisting of turbines with jacket support structures.
The reliability of deteriorating structures at time t is quantified by the probability that failure occurs within the period leading up to time t. This probability is often referred to as cumulative failure probability and is equal to the cumulative distribution function of the time to failure. In structural reliability, an estimate of the cumulative failure probability is obtained based on probabilistic engineering models of the deterioration processes and structural performance. Information on the condition and the loading contained in inspection and monitoring data can be included in the probability estimate through Bayesian updating. Conditioning the probability of failure on the inspection or monitoring outcomes available at time t (e.g. detections or no detection of damages) can lead to a reduction in that probability.
Such a drop in the cumulative failure probability might seem counterintuitive since the cumulative failure probability is a non-decreasing function of time. In this paper, we illustrate—with the help of a numerical example—that such a drop is possible because the cumulative probability before and after the updating is not based on the same information, hence not on the same probabilistic model.
Brücken werden durch Inspektionen und teilweise durch Monitoring überwacht, um Daten und Informationen über den Zustand und die Einwirkungen zu sammeln. Auf deren Grundlage werden Entscheidungen hinsichtlich Maßnahmen zur Gewährleistung der Sicherheit und Verfügbarkeit getroffen. In diesem Vortrag werden die Potentiale der Digitalisierung zur Unterstützung und Verbesserung der Brückenüberwachung diskutiert. Insbesondere werden die Bereiche Datenmanagement, Brückenmodellierung und Entscheidungsfindung betrachtet.
The current practice of operating and maintaining deteriorating structural systems ensures acceptable levels of structural reliability, but it is not clear how efficient it is. Changing the current prescriptive approach to a risk-based approach has great potential to enable a more efficient management of such systems. Risk-based optimization of operation and maintenance strategies identifies the strategy that optimally balances the cost for controlling deterioration in a structural system with the achieved risk reduction. Inspections and monitoring are essential parts of operation and maintenance strategies. They are typically performed to reduce the uncertainty in the structural condition and inform decisions on future operation and maintenance actions. In risk-based optimization of operation and maintenance strategies, Bayesian updating is used to include information contained in inspection and monitoring data in the prediction of the structural reliability. All computations need to be repeated many times for different potential inspection and monitoring outcomes. This motivates the development of robust and efficient approaches to this computationally challenging task.
The reliability of deteriorating structural systems is time-variant because the loads on them and their capacities change with time. In most practical applications, the reliability analysis of deteriorating structural systems can be approached by dividing their lifetime into discrete time intervals. The time-variant reliability problem can then be represented by a series of time-invariant reliability problems. Using this methodology as a starting point, this thesis proposes a novel approach to compute the time-variant reliability of deteriorating structural systems for which inspection and monitoring data are available. The problem is formulated in a nested way in which the prediction of the structural condition is separated from the computation of the structural reliability conditional on the structural condition. Information on the structural condition provided by inspections and monitoring is included in the reliability assessment through Bayesian updating of the system deterioration model employed to predict the structural condition. The updated system reliability is obtained by coupling the updated deterioration model with a probabilistic structural model utilized to calculate the failure probability conditional on the structural condition. This approach is the first main outcome of this thesis and termed nested reliability analysis (NRA) approach. It is demonstrated in two numerical examples considering inspected and monitored steel structures subject to high-cycle fatigue.
An alternative – recently developed – approach, which also follows the strategy of discretizing time, describes deteriorating structural systems with hierarchical dynamic Bayesian networks (DBN). DBN combined with approximate or exact inference algorithms also enable the computation of the time-variant reliability of deteriorating structural systems conditional on information provided by inspection and monitoring data. In this thesis – as a proof of concept – a software prototype is developed based on the DBN approach, which can be used to assess the reliability of a corroding concrete box girder for which half-cell potential measurements are available. This is the second main outcome of this thesis.
Both approaches presented in this thesis enable an integral reliability analysis of inspected and monitored structures that accounts for system effects arising from (a) the correlation among deterioration states of different structural elements, (b) the interaction between element deterioration and system failure, and (c) the indirect information gained on the condition of all unobserved structural elements from inspecting or monitoring the condition of some structural elements. Thus, both approaches enable a systemwide risk-based optimization of operation and maintenance strategies for deteriorating structural systems.
The NRA approach can be implemented relatively easily with subset simulation, which is a sequential Monte Carlo method suitable for estimating rare event probabilities. Subset simulation is robust and considerably more efficient than crude Monte Carlo simulation. It is, however, still sampling-based and its efficiency is thus a function of the number of inspection and monitoring outcomes, as well as the value of the simulated event probabilities. The current implementation of the NRA approach performs separate subset simulation runs to estimate the reliability at different points in time. The efficiency of the NRA approach with subset simulation can be significantly improved by exploiting the fact that failure events in different years are nested. The lifetime reliability of deteriorating structural systems can thus be computed in reverse chronological order in a single subset simulation run.
The implementation of the DBN approach is much more demanding than the implementation of the NRA approach but it has two main advantages. Firstly, the graphical format of the DBN facilitates the presentation of the model and the underlying assumptions to stakeholders who are not experts in reliability analysis. Secondly, it can be combined with exact inference algorithms. In this case, its efficiency neither depends on the number of inspection and monitoring outcomes, nor on the value of the event probabilities to be calculated. However, in contrast to the NRA approach with subset simulation, the DBN approach with exact inference imposes restrictions on the number of random variables and the dependence structure that can be implemented in the model.