A Bayesian approach to optimal sensor placement for structural health monitoring with application to active sensing

This paper introduces a novel approach for optimal sensor and/or actuator placement for structural health monitoring (SHM) applications. Starting from a general formulation of Bayes risk, we derive a global optimality criterion within a detection theory framework. The optimal configuration is then established as the one that minimizes the expected total presence of either type I or type II error during the damage detection process. While the approach is suitable for many sensing/actuation SHM processes, we focus on the example of active sensing using guided ultrasonic waves by implementing an appropriate statistical model of the wave propagation and feature extraction process. This example implements both pulse-echo and pitch-catch actuation schemes and takes into account line-of-site visibility and non-uniform damage probabilities over the monitored structure. The optimization space is searched using a genetic algorithm with a time-varying mutation rate. We provide three actuator/sensor placement test problems and discuss the optimal solutions generated by the algorithm.