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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.
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.
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.
The Influence of brittle Daniels system characteristics on the value of load monitoring information
(2016)
This paper addresses the influence of deteriorating brittle Daniels system characteristics on the value of structural health monitoring (SHM). The value of SHM is quantified as the difference between the life cycle benefits with and without SHM. A value of SHM analysis is performed within the framework of the Bayesian pre-posterior decision theory and requires (1) structural performance modelling and prediction, (2) structural integrity management models, (3) the (pre-posterior) modelling of SHM and (4) the coupling of SHM and the structural performance models. The pre-posterior decision theoretical framework facilitates that the value of SHM can be quantified before the SHM system is quantified and before data are acquired. The results of this study support decisions to select structural systems for which the SHM strategy load monitoring is optimal.
An efficient approach to reliability analysis of deteriorating structural systems is presented, which considers stochastic dependence among element deterioration. Information on a deteriorating structure obtained through inspection or monitoring is included in the reliability assessment through Bayesian updating of the system deterioration model. The updated system reliability is then obtained through coupling the updated deterioration model with a probabilistic structural model. The underlying high-dimensional structural reliability problems are solved using subset simulation, which is an efficient and robust sampling-based algorithm suitable for such analyses. The approach is demonstrated in two case studies considering a steel frame structure and a Daniels system subjected to high-cycle fatigue.
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.
Dieser Bericht beschreibt ein Systemmodell für eine integrale Ermittlung und Prognose der Schadens- und Zustandsentwicklung der Elemente eines Brückensystems unter Berücksichtigung von Ergebnissen aus Inspektionen und Überwachung. Das Systemmodell wurde anhand eines ausgesuchten Spannbetonüberbaus in einzelliger Kastenbauweise entwickelt. Es besteht aus zwei integralen Teilmodellen: ein Modell zur Beschreibung des Systemschädigungszustandes und ein Modell zur Beschreibung der Standsicherheit. Für die Modellierung des stochastischen Systemschädigungszustandes eines Brückensystems werden dynamische Bayes'sche Netze (DBN) vorgeschlagen. Dieser Ansatz ermöglicht es, alle relevanten Schädigungsprozesse und deren stochastische Abhängigkeiten zu berücksichtigen. Ein wesentlicher Vorteil dieses Ansatzes ist es, dass DBN ideal dafür geeignet sind, Bayes'sche Aktualisierungen auf Grundlage von Informationen aus Inspektionen und Überwachungsmaßnahme auf eine effiziente und robuste Art und Weise durchzuführen. Der DBN-Ansatz ist deshalb für die Entwicklung von Software für das Erhaltungsmanagement von alternden Brückenbauwerken, die vom Benutzer keine vertieften Kenntnisse der Zuverlässigkeitstheorie verlangt, ideal geeignet. Für die Modellierung der Standsicherheit eines alternden Kastenträgers wird vereinfachend Biegeversagen des globalen Längssystems betrachtet. Zur Berechnung der maximalen Traglast eines Kastenträgers infolge des Systemschädigungszustandes wird ein plastisch-plastisches Verfahren eingesetzt, wobei die Beanspruchungen mittels der Fließgelenktheorie unter Ausnutzung der plastischen Beanspruchbarkeit der Querschnitte des Kastenträgers ermittelt werden. Ein Kastenträger versagt, wenn sich durch die Ausbildung einer ausreichend großen Anzahl von Fließgelenken eine kinematische Kette ausbildet. Dieser Modellierungsansatz berücksichtigt Redundanzen, die sich aus der plastischen Beanspruchbarkeit der Querschnitte und der statischen Unbestimmtheit eines Kastenträgers ergeben. Zum Nachweis der praktischen Einsetzbarkeit des entwickelten Systemmodells wurde ein Software-Prototyp entwickelt, der eine intuitiv benutzbare graphische Benutzeroberfläche (Front-End) mit einem Berechnungskern (Back-End) koppelt. Die aktuelle Version des Software-Prototyps implementiert ein Modell der chloridinduzierten Bewehrungskorrosion und ein Tragwerksmodell, welches das Verfahrens der stetigen Laststeigerung zur Bestimmung der maximalen Traglast des Kastenträgers auf der Grundlage eines Finite-Elemente-Modells umsetzt. Zur Durchführung von Bayes'schen Aktualisierungen des Systemschädigungszustandes auf der Grundlage des DBN-Modells implementiert der Prototyp den Likelihood-Weighting-Algorithmus. Die entwickelte Architektur des Prototyps ermöglicht eine Erweiterung der Software um weitere Schädigungsprozesse. Der entwickelte Software-Prototyp ermöglicht Benutzern ohne vertiefte Kenntnisse der Zuverlässigkeitstheorie eine Berechnung des Einflusses von Bauwerksinformationen auf den Systemschädigungszustand und die Tragsicherheit eines Kastenträgers. Auf dieser Grundlage können effiziente Inspektions- und Überwachungsmaßnahmen identifiziert und das Erhaltungsmanagement optimiert werden.
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.