Carlo Cappello

Expected Utility Theory for Monitoring-Based Decision-Making

The main purpose of structural health monitoring (SHM) is to obtain information about the state of a structure in order to guide bridge management decisions. Nevertheless, in practice, once a rigorous estimate of the structural state is available, decisions are usually made based on the decision-makers intuition or experience. In this paper, we present the implementation of expected utility theory (EUT) in those civil engineering decision problems in which decision-makers have to act based on the output of SHM. EUT is an analytical quantitative framework that allows the identification of the financially most convenient decisions, based on the possible outcomes of each action and on the probabilities of each structural state occurring. The advantage of the presented implementation is the optimization of decision strategies in SHM. In the paper, we first formalize the solution of single-stage decision processes, in which the decision-maker has to take only one action. Then, we formalize the solution of multistage decision processes, in which multiple actions may be taken over time. Finally, using an example based on a case study, we describe the variables involved in the analysis of SHM decision problems, discuss the possible results, and address the issues that may arise in the application of EUT in real-life settings.

A viscoelastic model for the long-term deflection of segmental prestressed box girders

Most of segmental prestressed concrete box girders exhibit excessive multidecade deflections unforeseeable by past and current design codes. To investigate such a behavior, mainly caused by creep and shrinkage phenomena, an effective finite element (FE) formulation is presented in this article. This formulation is developed by invoking the stationarity of an energetic principle for linear viscoelastic problems and relies on the Bazant creep constitutive law. A case study representative of segmental prestressed concrete box girders susceptible to creep is also analyzed in the article, that is, the Colle Isarco viaduct. Its FE model, based on the aforementioned energetic formulation, was successfully validated through the comparison with monitoring field data. As a result, the proposed 1D FE model can effectively reproduce the past behavior of the viaduct and predict its future behavior with a reasonable run time, which represents a decisive factor for the model implementation in a decision support system.

On estimating the accuracy of monitoring methods using Bayesian error propagation technique

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.

Fusion of monitoring data from cable-stayed bridge

This contribution illustrates an application of Bayesian logic to monitoring data analysis and structural condition state inference. The case study is a cable-stayed bridge 260 m long spanning the Adige River ten kilometers north of the town of Trento, Italy. It is a statically indeterminate structure, consisting of a steel-concrete composite deck, supported by 12 stay cables. Structural redundancy, possible relaxation losses and an as-built condition differing from design, suggest that longterm load redistribution between cables can be expected. To monitor load redistribution, the owner decided to install a monitoring system that combines built-on-site elasto-magnetic and fiber-optic sensors. In this article, we discuss a rational way to improve the accuracy of the load variation, estimated using the elasto-magnetic sensors, taking advantage of the fiber-optic sensors 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 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.

Structural health monitoring of the Colle Isarco Viaduct

This paper presents a monitoring system, partially installed on the Colle Isarco Viaduct, and a finite element model used to explain past behaviour and predict future behaviour. The whole monitoring system consists of: a topographic network to measure displacements, thermocouples to detect temperature, fibre optic sensors to measure strains, and, lastly, load cells to check the tension magnitude in new post-tensioning cables. The use of such a monitoring system leads to have a complete history of deflections, providing all the necessary data for an accurate interpretation of results. Furthermore, a finite element model, based on an energetic formulation for linear viscoelastic problems, is adopted to reproduce the observed time profile and, mainly, to predict the future behaviour.

Calibration of Elasto-Magnetic Sensors on In-Service Cable-Stayed Bridges for Stress Monitoring

The recent developments in measurement technology have led to the installation of efficient monitoring systems on many bridges and other structures all over the world. Nowadays, more and more structures have been built and instrumented with sensors. However, calibration and installation of sensors remain challenging tasks. In this paper, we use a case study, Adige Bridge, in order to present a low-cost method for the calibration and installation of elasto-magnetic sensors on cable-stayed bridges. Elasto-magnetic sensors enable monitoring of cable stress. The sensor installation took place two years after the bridge construction. The calibration was conducted in two phases: one in the laboratory and the other one on site. In the laboratory, a sensor was built around a segment of cable that was identical to those of the cable-stayed bridge. Then, the sample was subjected to a defined tension force. The sensor response was compared with the applied load. Experimental results showed that the relationship between load and magnetic permeability does not depend on the sensor fabrication process except for an offset. The determination of this offset required in situ calibration after installation. In order to perform the in situ calibration without removing the cables from the bridge, vibration tests were carried out for the estimation of the cables’ tensions. At the end of the paper, we show and discuss one year of data from the elasto-magnetic sensors. Calibration results demonstrate the simplicity of the installation of these sensors on existing bridges and new structures.

The conditional value of information of SHM: what if the manager is not the owner?

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.

On predicting monitoring system effectiveness

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.

Quantifying the benefit of structural health monitoring : what if the manager is not the owner?

Only very recently our community has acknowledged that the benefit of structural health monitoring 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. Typically, it is assumed that there is one decision-maker for all decisions, that is, deciding on both the investment on the monitoring system and the operation of the structure. The aim of this work is to formalize a rational method for quantifying the value of information when two different actors are involved in the decision chain: the manager, who makes decisions regarding the structure, based on monitoring data; and the owner, who chooses whether to install the monitoring system or not, before having access to these data. The two decision-makers, even if both rational and exposed to the same background information, may still act differently because of their different appetites for risk. To illustrate how this framework works, we evaluate a hypothetical VoI for the Streicker Bridge, a pedestrian bridge in Princeton University campus equipped with a fiber optic sensing system, assuming that two fictional characters, Malcolm and Ophelia, are involved: Malcolm is the manager who decides whether to keep the bridge open or close it following to an incident; Ophelia is the owner who decides whether to invest on a monitoring system to help Malcolm making the right decision. We demonstrate that when manager and owner are two different individuals, the benefit of monitoring could be greater or smaller than when all the decisions are made by the same individual. Under appropriate conditions, the monitoring VoI could even be negative, meaning that the owner is willing to pay to prevent the manager to use the monitoring system.

Monitoring-based decision support system for optimal management of Colle Isarco viaduct

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.