A value-of-information-based optimal sensor placement design framework for cost-effective structural health monitoring (with application to miter gate monitoring)

Structural health monitoring (SHM) involves collecting information to assess the health of a structure, typically to guide risk-informed maintenance decision-making or predict limit state behavior throughout its lifespan. Although the value of information (VoI) obtained from an SHM system can facilitate improved decision-making, it is important to estimate its overall utility by considering the costs involved in designing, developing, installing, maintaining, and operating the system. A feasible SHM system provides greater expected returns resulting from data-informed lifecycle management decisions than the cost of the SHM system design, fabrication, deployment, operation, and maintenance. That is, since data acquisition is a precursor to data-informed decision-making, the design of an SHM system governs its feasibility. Such cost-benefit analyses are a current topic of research in the SHM community. One approach that has been proposed for these analyses is a preposterior decision analysis using the VoI metric. In this paper, we propose a sensor optimization framework that maximizes the VoI over the structure's lifecycle, constrained by a pre-decided maintenance policy. We use two different VoI metrics: the traditional expected VoI and a gambling-theory-inspired normalized expected-savings-to-investmentrisk ratio. We introduce three time-normalized, unitless VoI metrics that are valuable for evaluating the performance of an SHM design over an extended period. Furthermore, we consider the effect of different risk profiles on the overall optimal sensor design, recognizing that the cost of decision-making depends on the utility and risk perception of the decision-maker. We conduct a detailed analysis on the marginal utility gain of gathered information as we add more sensors, observing the utility to diminish in line with the law of diminishing returns as the information content increases. This framework is applied to the design of an SHM system used for monitoring miter gates.