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Quantification of the posterior utilities of SHM campaigns on an orthotropic steel bridge deck
(2019)

This paper contains a quantification and decision theoretical optimization of the posterior utilities for several options for monitoring campaigns on the particular case of fatigue life predictions of an orthotropic steel deck. The monitoring campaigns are defined by varying monitoring durations and phases. The decision analysis is performed with real data from the Structural Health Monitoring (SHM) of the Great Belt Bridge (Denmark) which, among others, consist of measured strains, pavement temperatures and traffic intensities. The fatigue loading prediction model is based on regression models linking daily averaged pavement temperatures, daily aggregated heavy-traffic Counts and derived S-N fatigue damages, all of them derived from the outcomes of different monitoring campaigns. A probabilistic methodology is utilized to calculate the fatigue reliability profiles of selected instrumented welded joints. The posterior utilities of SHM campaigns are then quantified by considering the structural fatigue reliability, various monitoring campaigns and the corresponding cost-benefit models. The decisions of identifying the optimal monitoring campaign and of extending the service life or not in conjunction with monitoring results are modelled. The optimal monitoring campaign is identified - retrospectively - by maximizing the expected benefits and minimize risks in dependency of the monitoring duration and the monitoring associated costs. The results, despite relying on a number of simplistic assumptions, pave the way towards the use of pre-posterior decision support to optimise the design of monitoring campaigns for similar bridges, with an overall goal to proof the cost efficiency of SHM approaches to civil infrastructure management.

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 article introduces an approach and framework for the quantification of the value of structural health monitoring (SHM) in the context of the structural risk and integrity management for systems. The quantification of the value of SHM builds upon the Bayesian decision and utility theory, which facilitates the assessment of the value of information associated with SHM. The principal approach for the quantification of the value of SHM is formulated by modeling the fundamental decision of performing SHM or not in conjunction with their expected utilities. The expected utilities are calculated accounting for the probabilistic performance of a system in conjunction with the associated structural integrity and risk management actions throughout the life cycle, the associated benefits, structural risks, and costs and when performing SHM, the SHM information, their probabilistic outcomes, and costs. The calculation of the expected utilities necessitates a comprehensive and rigorous modeling, which is introduced close to the original formulations and for which analysis characteristics and simplifications are described and derived. The framework provides the basis for the optimization of the structural risk and integrity management based on utility gains including or excluding SHM and inspection information. Studies of fatigue deteriorating structural Systems and their characteristics (1) provide decision Support for the performance of SHM, (2) explicate the influence of the structural component and system characteristics on the value of SHM, and (3) demonstrate how an integral optimization of SHM and inspection strategies for an efficient structural risk and integrity management can be performed.

Fires in road tunnels constitute complex scenarios with interactions between the fire, tunnel users and safety measures. More and more methodologies for risk analysis quantify the consequences of these scenarios with complex models. Examples for complex models are the computational fluid dynamics model Fire Dynamics Simulator (FDS) and the microscopic evacuation model FDS+Evac. However, the high computational effort of complex models often limits the number of scenarios in practice. To balance this drawback, the scenarios are often simplified. Accordingly, there is a challenge to consider complex scenarios in risk analysis.
To face this challenge, we improved the metamodel used in the methodology for risk analysis presented on ISTSS 2016. In general, a metamodel quickly interpolates the consequences of few scenarios simulated with the complex models to a large number of arbitrary scenarios used in risk analysis. Now, our metamodel consists of the projection array-based design, the moving least squares method, and the prediction interval to quantify the metamodel uncertainty. Additionally, we adapted the projection array-based design in two ways: the focus of the sequential refinement on regions with high metamodel uncertainties; and the combination of two experimental designs for FDS and FDS+Evac.
To scrutinise the metamodel, we analysed the effects of three sequential refinement steps on the metamodel itself and on the results of risk analysis. We observed convergence in both after the second step (ten scenarios in FDS, 192 scenarios in FDS+Evac). In comparison to ISTSS 2016, we then ran 20 scenarios in FDS and 800 scenarios in FDS+Evac. Thus, we reduced the number of scenarios remarkably with the improved metamodel. In conclusion, we can now efficiently integrate complex scenarios in risk analysis. We further emphasise that the metamodel is broadly applicable on various experimental or modelling issues in fire safety engineering.

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.

Inspections are an efficient means of enhancing the reliability of redundant structural Systems subjected to fatigue. To investigate the effect of such inspections, we represent the deterioration state of a Daniels System by means of a probabilistic fatigue crack growth model of all elements, which considers stochastic dependence among element fatigue behavior. We include inspection results in the calculation of the System collapse probability through Bayesian updating of the System deterioration state. Based on this approach, we calculate the collapse probability of a deteriorating Daniels System conditional on different inspection strategies in terms of inspection coverage and inspection times. The acceptability of an inspection strategy is verified by comparing the calculated collapse probabilities with maximum acceptable System failure probabilities. This study is a Step towards identifying optimal inspection strategies for redundant structural Systems subjected to fatigue.