Bayesian multi-parameter estimation using the mechanical equivalent of logical inference

In this work we illustrate how the mathematics of rational thinking is formally equivalent to that of structural mechanics. Concepts from the wold of logic, such as accuracy, uncertainty, Maximum a Posteriori (MAP) and rationality correspond, in the world of mechanics, to stiffness, flexibility, equilibrium and conservativeness. For instance, a linear Gaussian N-parameter estimation problem can be solved through a N-dof linear elastic system, as the analogy goes along these lines: the parameters covariance matrix is the system's flexibility matrixthe Fishers information is the stiffness matrixthe negative log-distribution of the parameters is the elastic potential energy of the systemthe Maximum a Posteriori (MAP) is the state of static equilibrium. In principle, based on this analogy, we could reproduce any logical inference problem with a finite element model, and make a judgment by finding its equilibrium state. We will show application of this analogy to a number of civil engineering inference problems, including Bayesian estimation, Bayesian networks and Kalman filter

Quantifying the benefit of SHM: can the VoI be negative?

The benefit of Structural Health Monitoring (SHM) can be properly quantified using the concept of Value of Information (VoI), i.e. the difference between the utilities of operating the structure with and without the monitoring system. In calculating the VoI, a commonly understood assumption is that all decisions 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 use it, and they may behave differently because of their different risk aversion. We demonstrate that in a decision-making process where the two individuals involved share exactly the same information, but behave differently, the VoI can be negative. Indeed, even if the two agents have an agreement a priori, due to their different behaviors, their optimal actions can diverge after the installation of the monitoring system. This scenario could generate a negative Vol from the owners perspective. In this work, we propose a qualitative and quantitative formulation to evaluate when and under which circumstances the VoI can be negative, if the owner differs from the manager with respect to their risk prioritization. Moreover, we apply this formulation on a real-life case study concerning the Streicker Bridge (Princeton, NJ). The results demonstrate that when the owner, because of the managers different behaviour, is forced to undertake an action he would not chose, his VoI becomes negative, i.e. it is not convenient for him to install the monitoring system. 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 managers behavior toward risk is different from the owners own, and so are his management decisions

Quantifying the benefit of structural health monitoring: can the value of information be negative?

The benefit of Structural Health Monitoring (SHM) can be properly quantified using the concept of Value of Information (VoI), which is, applied to an SHM case, the difference between the utilities of operating the structure with and without the monitoring system. The aim of this contribution is to demonstrate that, in a decision-making process where two different individuals are involved in the decision chain, i.e. the owner and the manager of the structure, the VoI can be negative. Indeed, even if the two decision makers are both rational and exposed to the same background information, their optimal actions can diverge after the installation of the monitoring system due to their different appetite for risk: this scenario could generate a negative VoI, which corresponds exactly to the amount of money the owner is willing to pay to prevent the manager using the monitoring system. In this paper, starting from a literature review about how to quantify the VoI, a mathematical formulation is proposed which allows one to assess when and under which specific conditions, e.g. appropriate combination of prior information and utility functions, the VoI becomes negative. Moreover, to illustrate how this framework works, a hypothetical VoI is evaluated for the Streicker Bridge, a pedestrian bridge on the Princeton University campus equipped with a fiber optic sensing system: the results show how the predominant factor that determines a negative VoI is the different risk appetite of the two decision makers, owner and manager

Consequences of representativeness bias on SHM-based decision-making

Judging the state of a bridge based on SHM observations is an inference process, which should be rationally carried out using a logical approach. However, it is often observed that real-life decision makers depart from this ideal model of rationality, judge and decide using common sense, and privilege fast and frugal heuristics to rational analytic thinking. For instance, confusion between condition state and safety of a bridge is one of the most frequently observed examples in bridge management. The aim of this paper is to describe mathematically this observed biased judgement, a condition that is broadly described by Kahneman and Tversky’s representativeness heuristic. Particularly, the paper examines how this heuristic affects the interpretation of data, providing a deeper understanding of the differences between a method affected by cognitive biases and the classical rational approach. Based on the literature review, three different models reproducing an individual behaviour distorted by representativeness are identified. These models are applied to the case of a transportation manager who wrongly judges a particular bridge unsafe simply because deteriorated, regardless its actual residual load-carrying capacity. It is demonstrated that the application of any of the three heuristic judgment models correctly predicts that the manager will mistakenly judge the bridge as unsafe based on the observed condition state. It is not objective of the paper to suggest that representativeness should be used instead of rational logic, however, understanding how real-life managers actually behave is of paramount importance when setting a general policy for bridge maintenance

How heuristic behaviour can affect SHM-based decision problems?

psychologists call these differences cognitive biases. Many heuristic behaviors have been studied and demonstrated, with applications in various fields such as psychology, cognitive science, economics and finance, but not yet to SHM-based decision problems. SHM-based decision making is particularly susceptible to the representativeness heuristic, where simplified rules for updating probabilities can distort the decision makers perception of risk. In this work, we examine how this heuristic affects the interpretation of data, providing a deeper understanding of the differences between a heuristic method affected by cognitive biases and the classical approach. Our study is conducted both theoretically through comparison with formal Bayesian methods as well as empirically through the application to a real-life case study in the field of civil engineering. With this application we demonstrate the heuristic framework and we show how this cognitive bias affects decision-making by distorting the representation of information provided by SHM.The main purpose of structural health monitoring (SHM) is to provide accurate and real-time information about the state of a structure, which can be used as objective inputs for decision-making regarding its management. However, SHM and decision-making occur at various stages. SHM assesses the state of a structure based on the acquisition and interpretation of data, which is usually provided by sensors. Conversely, decision-making helps us to identify the optimal management action to undertake. Generally, the research community recognizes people tend to use irrational methods for their interpretation of monitoring data, instead of rational algorithms such as Bayesian inference. People use heuristics as efficient rules to simplify complex problems and overcome the limits in rationality and computation of the human brain. Even though the results are typically satisfactory, they can differ from results derived from a rational proces

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

IWSHM 2017 : 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

Supporting rational decision-making in civil engineering

The management of civil engineering structures, such as bridges and dams, is fundamental for ensuring their continued safe and economical operation, where decisions such as whether or not to suspend operations are based on uncertain knowledge concerning the state of the structure. Modern development in technology has made available several accurate monitoring devices providing Structural Health Information, that can be used to support such decision-making through more informed assessment of the structural state. The wide-spread adoption of these devices has led to the development of Structural Health Monitoring (SHM) decision support system, to identify appropriate courses of action based on observed data from the monitoring system. Essentially, it is a two-step process, which includes the judgment of the structural state based on the SHM information, and the decision about the optimal action based on the knowledge of the structural state. When engineering knowledge concerning the state of the system is uncertain, as the monitoring system does not directly observe the state of the structure, Bayesian inference and Expected Utility Theory provide the only consistent way to judge and to make decisions, respectively, as all alternative inferential methods for decision support are susceptible to logical inconsistency.;However, we must recognize that in the real world the process followed by decision makers may be distorted. The goal of the research proposed in this contribution is twofold: we investigate how heuristic behaviours may affect human judgment and decision-making in civil engineering, and also how decision-making can be distorted when multiple agents, even rational but with different appetites for risk, are involved in the decision chain. Firstly, most agents in everyday life apply heuristic approaches rather than a formal Bayesian procedure in order to make inference to support decisions. In particular, without the use of formal algorithms to support rational interpretation of data, humans apply simple strategies or mental processes to interpret data, which are prone to systemic errors. This may happen with data that come from various data sources, such as SHM but also engineering expert knowledge. Innovative frameworks to support rational decision-making are then required, in order to minimize the risk of biased judgments or decisions. For instance, being able to predict the behavior of an irrational manager is necessary when we set a general policy for bridge management, and we know that someone else who is going to enact the policy may behave irrationally.;In this doctoral thesis, we start reviewing the literature of heuristics and cognitive biases in order to identify the most relevant as regards human judgment and decision-making for civil engineering structures. We identify Kahneman and Tversky's representativeness as a heuristic for which SHM-based decision-making is particularly susceptible, where simplified rules for updating probabilities can distort the decision maker's perception of risk. Therefore, we reproduce mathematically this observed irrational behavior to investigate how it distorts human judgment. In addition, it is recognized that heuristic behaviors may affect expert knowledge. Consequently, we propose a method for eliciting engineering expert knowledge in order to assess civilengineering structures: the process is required in order to support the collection of valid and reliable data, by minimizing the adverse impact of cognitive biases. Secondly, the decision process can be distorted when multiple agents are involved, not only in the case of irrational behaviors, where the distortion is expected, but even in the case of rational behaviors. Indeed, decision makers may differ in their decisions under uncertainty according to their different appetites for risk. Again, predicting the behavior of managers is required for instance when there is a management policy for which the final decision of an agent has to consider the opinion of other decision makers, who may behave differently.;In this thesis, we formalize an innovative rational method for quantifying the value of information (VoI) of SHM when two different agents are involved in the decision chain: this framework allows one to investigate how decisions may be distorted due to the different appetites for risk of decision makers. In addition, we understand that the interaction between rational agents with different appetites for risk may lead to a negative VoI, which is unexpected since it means that the monitoring information may be perceived as damaging. Therefore, we develop a mathematical formulation to investigate under which specific circumstances it is possible to achieve this unexpected outcome. Finally, all the studied theories and proposed frameworks are applied respectively to various civil engineering case studies. In summary: we evaluate the structural safety of a common type of bridge of the Autonomous Province of Trento stock, in Italy; we investigate the system reliability of the Mountain Chute dam and generating station in Ontario, Canada; we analyse the management of a pedestrian bridge in Princeton University campus equipped with a monitoring system, in USA. These applicationsallow us to demonstrate the operationalizability of the methods developed in this thesis, and to prove their relevance in various civil engineering case studies.The management of civil engineering structures, such as bridges and dams, is fundamental for ensuring their continued safe and economical operation, where decisions such as whether or not to suspend operations are based on uncertain knowledge concerning the state of the structure. Modern development in technology has made available several accurate monitoring devices providing Structural Health Information, that can be used to support such decision-making through more informed assessment of the structural state. The wide-spread adoption of these devices has led to the development of Structural Health Monitoring (SHM) decision support system, to identify appropriate courses of action based on observed data from the monitoring system. Essentially, it is a two-step process, which includes the judgment of the structural state based on the SHM information, and the decision about the optimal action based on the knowledge of the structural state. When engineering knowledge concerning the state of the system is uncertain, as the monitoring system does not directly observe the state of the structure, Bayesian inference and Expected Utility Theory provide the only consistent way to judge and to make decisions, respectively, as all alternative inferential methods for decision support are susceptible to logical inconsistency.;However, we must recognize that in the real world the process followed by decision makers may be distorted. The goal of the research proposed in this contribution is twofold: we investigate how heuristic behaviours may affect human judgment and decision-making in civil engineering, and also how decision-making can be distorted when multiple agents, even rational but with different appetites for risk, are involved in the decision chain. Firstly, most agents in everyday life apply heuristic approaches rather than a formal Bayesian procedure in order to make inference to support decisions. In particular, without the use of formal algorithms to support rational interpretation of data, humans apply simple strategies or mental processes to interpret data, which are prone to systemic errors. This may happen with data that come from various data sources, such as SHM but also engineering expert knowledge. Innovative frameworks to support rational decision-making are then required, in order to minimize the risk of biased judgments or decisions. For instance, being able to predict the behavior of an irrational manager is necessary when we set a general policy for bridge management, and we know that someone else who is going to enact the policy may behave irrationally.;In this doctoral thesis, we start reviewing the literature of heuristics and cognitive biases in order to identify the most relevant as regards human judgment and decision-making for civil engineering structures. We identify Kahneman and Tversky's representativeness as a heuristic for which SHM-based decision-making is particularly susceptible, where simplified rules for updating probabilities can distort the decision maker's perception of risk. Therefore, we reproduce mathematically this observed irrational behavior to investigate how it distorts human judgment. In addition, it is recognized that heuristic behaviors may affect expert knowledge. Consequently, we propose a method for eliciting engineering expert knowledge in order to assess civilengineering structures: the process is required in order to support the collection of valid and reliable data, by minimizing the adverse impact of cognitive biases. Secondly, the decision process can be distorted when multiple agents are involved, not only in the case of irrational behaviors, where the distortion is expected, but even in the case of rational behaviors. Indeed, decision makers may differ in their decisions under uncertainty according to their different appetites for risk. Again, predicting the behavior of managers is required for instance when there is a management policy for which the final decision of an agent has to consider the opinion of other decision makers, who may behave differently.;In this thesis, we formalize an innovative rational method for quantifying the value of information (VoI) of SHM when two different agents are involved in the decision chain: this framework allows one to investigate how decisions may be distorted due to the different appetites for risk of decision makers. In addition, we understand that the interaction between rational agents with different appetites for risk may lead to a negative VoI, which is unexpected since it means that the monitoring information may be perceived as damaging. Therefore, we develop a mathematical formulation to investigate under which specific circumstances it is possible to achieve this unexpected outcome. Finally, all the studied theories and proposed frameworks are applied respectively to various civil engineering case studies. In summary: we evaluate the structural safety of a common type of bridge of the Autonomous Province of Trento stock, in Italy; we investigate the system reliability of the Mountain Chute dam and generating station in Ontario, Canada; we analyse the management of a pedestrian bridge in Princeton University campus equipped with a monitoring system, in USA. These applicationsallow us to demonstrate the operationalizability of the methods developed in this thesis, and to prove their relevance in various civil engineering case studies

An elicitation process to quantify Bayesian networks for dam failure analysis

Bayesian Networks support the probabilistic failure analysis of complex systems, e.g. dams and bridges, needed for a better understanding of the system reliability and for taking mitigation actions. In particular, they are useful in representing graphically the interactions among system components, while the quantitative strength of the interrelationships between the variables is measured using conditional probabilities. However, due to a lack of objective data it often becomes necessary to rely on expert judgment to provide subjective probabilities to quantify the model. This paper proposes an elicitation process that can be used to support the collection of valid and reliable data with the specific aim of quantifying a Bayesian Network, while minimizing the adverse impact of biases to which judgment is commonly subjected. To illustrate how this framework works, it is applied to a real-life case study regarding the safety of the Mountain Chute Dam and Generating Station, which is located on the Madawaska River in Ontario, Canada. This contribution provides a demonstration of the usefulness of eliciting engineering expertise with regard to system reliability analysis