Bayesian virtual sensing in structural dynamics

Structural monitoring and control utilize vibration measurements acquired by a sensor network. Combined empirical and analytical virtual sensing is introduced to estimate full-field dynamic response of a structure using a limited number of sensors. Bayesian empirical virtual sensing technique is developed to obtain less noisy estimates of sensor data. Then, analytical virtual sensing utilizes the expansion algorithm to compute the full-field response. If the sensor noise is known, virtual sensors are more accurate than the corresponding physical measurements with any number of sensors in the network. Often, the measurement error has to be estimated. The upper bound of the sensor noise variance is derived, and the effect of the noise estimation error on the accuracy of virtual sensors is studied. Numerical simulations are performed for a structure subject to unknown random excitation in order to validate the proposed virtual sensing algorithms. Displacement and strain sensor networks with different numbers of sensors and different noise models are studied.