Sensor placement for calibration of spatially varying model parameters

This paper presents a sensor placement optimization framework for the calibration of spatially varying model parameters. To account for the randomness of the calibration parameters over space and across specimens, the spatially varying parameter is represented as a random field. Based on this representation, Bayesian calibration of spatially varying parameter is investigated. To reduce the required computational effort during Bayesian calibration, the original computer simulation model is substituted with Kriging surrogate models based on the singular value decomposition (SVD) of the model response and the Karhunen-Loeve expansion (KLE) of the spatially varying parameters. A sensor placement optimization problem is then formulated based on the Bayesian calibration to maximize the expected information gain measured by the expected Kullback-Leibler (K-L) divergence. The optimization problem needs to evaluate the expected K-L divergence repeatedly which requires repeated calibration of the spatially varying parameter, and this significantly increases the computational effort of solving the optimization problem. To overcome this challenge, an approximation for the posterior distribution is employed within the optimization problem to facilitate the identification of the optimal sensor locations using the simulated annealing algorithm. A heat transfer problem with spatially varying thermal conductivity is used to demonstrate the effectiveness of the proposed method.