Sensing sheets: Optimal arrangement of dense array of sensors for an improved probability of damage detection

Reliable early-stage damage detection and localization ideally requires continuous sensing over large areas with dense arrays of sensors, and that is the reason for the creation of sensing sheets based on large area electronics, which contains a large number of densely spaced unit sensors. However, although the sensors are densely spaced, there are some empty spaces between them and these spaces are not sensitive to minute damage. This raises three fundamental questions addressed in this article: How do the sizes of the non-instrumented areas influence the reliability in damage detection? What is the most efficient arrangement of the sensors in the sensing sheet? Given the size of the sensing sheet and given the combined size of all the sensors, is it more efficient to use small amount of large sensors, or large amount of small sensors? A probabilistic approach has been taken to address these questions. Analytical expressions were derived first, followed with the generation and validation of Monte Carlo simulations. Then the probability that the sensing sheet with a given surface area and given number, size, and spacing of unit sensors can detect a crack with a given size was derived. Based on these probability of detection functions, it was possible to assess the reliability of sensing sheets for crack detection and to establish general principles for the design of sensing sheets so that the probability of detection is maximized. The presented probability of detection analysis can be modified and applied beyond the scope of the sensing sheet project to other sensor networks used in strain-based structural health monitoring.