Optimal sensor placement through Bayesian experimental design: effect of measurement error and number of sensors

Sensors networks for the health monitoring of structural systems ought to be designed to render both accurate estimations of the relevant mechanical parameters and an affordable experimental setup. Therefore, the number, type and location of the sensors have to be chosen so that the uncertainties related to the estimated health are minimized. Several deterministic methods based on the sensitivity of measures with respect to the parameters to be tuned are widely used. Despite their low computational cost, these methods do not take into account the uncertainties related to the measurement process. In former studies, a method based on the maximization of the information associated with the available measurements has been proposed and the use of approximate solutions has been extensively discussed. Here we propose a robust numerical procedure to solve the optimization problem: in order to reduce the computational cost of the overall procedure, Polynomial Chaos Expansion and a stochastic optimization method are employed. The method is applied to a flexible plate. First of all, we investigate how the information changes with the number of sensors; then we analyze the effect of choosing different types of sensors (with their relevant accuracy) on the information provided by the structural health monitoring system.