Bayesian optimal sensor placement for crack identification in structures using strain measurements

A Bayesian framework is presented for finding the optimal locations of strain sensors in a plate with a crack with the goal of identifying the crack properties, such as crack location, size, and orientation. Sensor grids of different type and size are considered. The Bayesian optimal sensor placement framework is rooted in information theory, and the optimal grid is the one which maximizes the expected information gain (Kullback-Liebler divergence) between the prior and posterior probability density functions of the crack parameters. The uncertainty in the crack parameters is accounted for naturally within the Bayesian framework through the prior probability density functions. The framework is demonstrated for a thin plate with crack, subjected to static loading. A finite element model is used to simulate the strain distributions in the plate given the crack properties. To verify the effectiveness of the proposed optimal sensor placement methodology, the estimated optimal sensor grids are used to perform Bayesian crack identification using simulated data. Parametric analyses are carried out giving emphasis on the effect of the number of sensors, grid type, and experimental data noise levels in the identification results.