Bayesian Optimal Sensor Placement for Modal Identification of Civil Infrastructures

A Bayesian optimal experimental design (OED) method is proposed in this work for estimating the best locations of sensors in structures so that the measured data are most informative for estimating reliably the structural modes. The information contained in the data is measured by the Kullback-Leibler (K-L) divergence between the prior and posterior distribution of the model parameters taken in modal identification to be the modal coordinates. The optimal sensor placement that maximizes the expected K-L divergence is shown also to minimize the information entropy of the posterior distribution. Unidentifiability issues observed in existing formulations when the number of sensors is less than the number of identified modes, are resolved using a non-uniform prior in the Bayesian OED. An insightful analysis is presented that demonstrates the effect of the variances of Bayesian priors on the optimal design. For dense mesh finite element models, sensor clustering phenomena are avoided by integrating in the methodology spatially correlated prediction error models. A heuristic forward sequential sensor placement algorithm and a stochastic optimization algorithm are used to solve the optimization problem in the continuous physical domain of variation of the sensor locations. The theoretical developments and algorithms are applied for the optimal sensor placement design along the deck of a 537 m concrete bridge.