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

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

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

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