Robust optimal sensor placement for operational modal analysis based on maximum expected utility

Optimal sensor placement is essentially a decision problem under uncertainty. The maximum expected utility theory and a Bayesian linear model are used in this paper for robust sensor placement aimed at operational modal identification. To avoid nonlinear relations between modal parameters and measured responses, we choose to optimize the sensor locations relative to identifying modal responses. Since the modal responses contain all the information necessary to identify the modal parameters, the optimal sensor locations for modal response estimation provide at least a suboptimal solution for identification of modal parameters. First, a probabilistic model for sensor placement considering model uncertainty, load uncertainty and measurement error is proposed. The maximum expected utility theory is then applied with this model by considering utility functions based on three principles: quadratic loss, Shannon information, and K-L divergence. In addition, the prior covariance of modal responses under band-limited white-noise excitation is derived and the nearest Kronecker product approximation is employed to accelerate evaluation of the utility function. As demonstration and validation examples, sensor placements in a 16-degrees-of-freedom shear-type building and in Guangzhou TV Tower under ground motion and wind load are considered. Placements of individual displacement meter, velocimeter, accelerometer and placement of mixed sensors are illustrated.