A Bayesian optimal sensor placement (OSP) framework is presented for virtual sensing in structures using output-only vibration measurements. Particularly, this probabilistic OSP scheme aims to enhance the reconstruction of dynamical responses (e.g., accelerations, displacements, strain, stresses) for updating structural reliability and safety, as well as fatigue lifetime prognosis. The OSP framework is formulated using information theory. The information gained from a sensor configuration is defined as the Kullback-Liebler divergence (KL-div) between the prior and posterior distributions of the response quantities of interest (QoI). The Gaussian nature of the response estimate for linear models of structures is employed, and the information gain is characterized in terms of the reconstruction error covariance matrix. A Kalman-based input-state estimation technique is integrated within an existing OSP strategy, aiming to obtain estimates of response QoI and their uncertainties. The design variables include the location, type and number of sensors. Heuristic algorithms are used to solve optimization problem and provide computationally efficient solutions. The effectiveness of the method is demonstrated using an example from structural dynamics.
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