Distributed pressure estimation using a piezoelectric array in a cone structure for hypersonic applications

In structures where direct pressure measurement is impossible, dynamic pressure can still be estimated from the vibrational response of the system. Nevertheless, because this is an inverse load identification problem, several critical challenges must be overcome to ensure good accuracy and consistency in the estimated pressure field. Namely, to avoid poor numerical conditioning, many sensors must be used to overdetermine the system, especially to reconstruct a spatially varying distributed pressure input. To address this challenge, we perform numerical and experimental investigations into distributed pressure estimation using a large piezoelectric sensor array. To estimate the pressure, we construct a distributed pressure basis using the mode shapes of the structure, creating a model that relates each basis function to the piezoelectric sensor output. During operation, we regularize and invert this model to obtain the weighting of each basis function and reconstruct the distributed pressure on the structure. We show how the number and placement of sensors can be optimized to improve accuracy, and we determine the required number of sensors for a given frequency and wavelength of p