Interpolation of forced structural responses from non-uniform sparse measurements

This paper presents a method for interpolating a sparse set of nonuniformly spaced velocity measurements on the surface of a vibrating structure. The method utilizes knowledge of the physical nature of the vibrating structure specified in terms of a given bound on the energy of the excitation forces, estimated mobilities of the structure and a known set of sparse velocity measurements. To minimize the maximum possible error of the estimated surface velocities. The method employs an estimation approach derived from the theory of optimal signal recovery. Results are presented which demonstrate the performance of the method on interpolating surface velocities of a rectangular plate. With only four randomly selected point velocity measurements out of 209 possible locations. The method estimates the structural surface velocity with a normalized error of only -45 dB. The ability to achieve this performance with a small number of sensors makes this method important for many active noise control applications where an accurate measure of structural surface velocity is required to predict the radiated acoustic field