The A22 Colle Isarco Viaduct is one of the most important infrastructural links in Italy, of strategic importance on the European route E45, connecting Northern Europe to Italy. A disruption of this bridge caused by a damage event would result in a critical increase in traffic congestion, with negative consequences for users and environment. To optimize its management after a possible damaging event, we developed an innovative decision support system (DSS), based on the data from a multi-technology structural monitoring system, which includes a robotized topographic system, a fibre optic sensor network and a thermometer network. The DSS analyses the monitoring data, assesses the probabilities that the bridge is damaged or not by using formal Bayesian inference, and identifies the optimal action according to the axioms of expected utility theory (EUT). This DSS is one of the first of its kind developed in Europe and can help in optimizing the traffic management along the A22 highway while enhancing users’ safety and reducing the bridge maintenance costs. It highlights in real time abnormal states of the bridge and allows the owner to act promptly with inspection, maintenance or repair, only when strictly necessary. We developed this DSS in collaboration with Autostrada del Brennero SpA, and although designed for a specific case study, its scope is very broad and can be applied to any problem of infrastructure management which requires optimal decision based on uncertain information under safety and economic constraints.
Only very recently our community has acknowledged that the benefit of Structural Health Monitoring (SHM) can be properly quantified using the concept of Value of Information (VoI). The VoI is the difference between the utilities of operating the structure with and without the monitoring system, usually referred to as preposterior utility and prior utility. In calculating the VoI, a commonly understood assumption is that all the decisions to concerning system installation and operation are taken by the same rational agent. In the real world, the individual who decides on buying a monitoring system (the owner) is often not the same individual (the manager) who will actually use it. Even if both agents are rational and exposed to the same background information, they may behave differently because of their different risk aversion. We propose a formulation to evaluate the VoI from the owner’s perspective, in the case where the manager differs from the owner with respect to their risk prioritisation. Moreover, we apply the results on a real-life case study concerning the Streicker Bridge, a pedestrian bridge on Princeton University campus, in USA. This framework aims to help the owner in quantifying the money saved by entrusting the evaluation of the state of the structure to the monitoring system, even if the manager’s behaviour toward risk is different from the owner’s own, and so are his or her management decisions. The results of the case study confirm the difference in the two ways to quantify the VoI of a monitoring system.
Decision making investigates choices that have uncertain consequences and that cannot be completely predicted. Rational behavior may be described by the so-called expected utility theory (EUT), whose aim is to help choosing among several solutions to maximize the expectation of the consequences. However, Kahneman and Tversky developed an alternative model, called prospect theory (PT), showing that the basic axioms of EUT are violated in several instances. In respect of EUT, PT takes into account irrational behaviors and heuristic biases. It suggests an alternative approach, in which probabilities are replaced by decision weights, which are strictly related to the decision maker’s preferences and may change for different individuals. In particular, people underestimate the utility of uncertain scenarios compared to outcomes obtained with certainty, and show inconsistent preferences when the same choice is presented in different forms. The goal of this paper is precisely to analyze a real case study involving a decision problem regarding the Streicker Bridge, a pedestrian bridge on Princeton University campus. By modelling the manager of the bridge with the EUT first, and with PT later, we want to verify the differences between the two approaches and to investigate how the two models are sensitive to unpacking probabilities, which represent a common cognitive bias in irrational behaviors.
KEYWORDS: Bayesian inference, Logic, Structural health monitoring, Structural engineering, Mechanics, Fiber optics sensors, Bridges, Probability theory, Data modeling, Structural design, Pattern recognition, Sensors, Chemical elements
Structural health monitoring requires engineers to understand the state of a structure from its observed response. When
this information is uncertain, Bayesian probability theory provides a consistent framework for making inference.
However, structural engineers are often unenthusiastic about Bayesian logic and prefer to make inference using
heuristics. Herein we propose a quantitative method for logical inference based on a formal analogy between linear
elastic mechanics and Bayesian inference with Gaussian variables. We start by discussing the estimation of a single
parameter under the assumption that all of the uncertain quantities have a Gaussian distribution and that the relationship
between the observations and the parameter is linear. With these assumptions, the analogy is stated as follows: the
expected value of the considered parameter corresponds to the position of a bar with one degree of freedom and
uncertain observations of the parameter are modelled as linear elastic springs placed in series or parallel. If we want to
extend the analogy to multiple parameters, we simply have to express the potential energy of the mechanical system
associated to the inference problem. The expected value of the parameters is then calculated by minimizing that potential
energy. We conclude our contribution by presenting the application of mechanical equivalent to a real-life case study in
which we seek the elongation trend of a cable belonging to Adige Bridge, a cable-stayed bridge located North of Trento,
Italy.
While the objective of structural design is to achieve stability with an appropriate level of reliability, the design of systems for structural health monitoring is performed to identify a configuration that enables acquisition of data with an appropriate level of accuracy in order to understand the performance of a structure or its condition state. However, a rational standardized approach for monitoring system design is not fully available. Hence, when engineers design a monitoring system, their approach is often heuristic with performance evaluation based on experience, rather than on quantitative analysis. In this contribution, we propose a probabilistic model for the estimation of monitoring system effectiveness based on information available in prior condition, i.e. before acquiring empirical data. The presented model is developed considering the analogy between structural design and monitoring system design. We assume that the effectiveness can be evaluated based on the prediction of the posterior variance or covariance matrix of the state parameters, which we assume to be defined in a continuous space. Since the empirical measurements are not available in prior condition, the estimation of the posterior variance or covariance matrix is performed considering the measurements as a stochastic variable. Moreover, the model takes into account the effects of nuisance parameters, which are stochastic parameters that affect the observations but cannot be estimated using monitoring data. Finally, we present an application of the proposed model to a real structure. The results show how the model enables engineers to predict whether a sensor configuration satisfies the required performance.
This paper illustrates an application of Bayesian logic to monitoring data analysis and structural condition state
inference. The case study is a 260 m long cable-stayed bridge spanning the Adige River 10 km north of the town of
Trento, Italy. This is a statically indeterminate structure, having a composite steel-concrete deck, supported by 12 stay
cables. Structural redundancy, possible relaxation losses and an as-built condition differing from design, suggest that
long-term load redistribution between cables can be expected. To monitor load redistribution, the owner decided to
install a monitoring system which combines built-on-site elasto-magnetic and fiber-optic sensors. In this note, we discuss
a rational way to improve the accuracy of the load estimate from the EM sensors taking advantage of the FOS
information. More specifically, we use a multi-sensor Bayesian data fusion approach which combines the information
from the two sensing systems with the prior knowledge, including design information and the outcomes of laboratory
calibration. Using the data acquired to date, we demonstrate that combining the two measurements allows a more
accurate estimate of the cable load, to better than 50 kN.
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