Recovery of non-stationary free field based on pressure and acceleration measurements in a noisy environment

In order to remove the non-stationary incoming field from the back side of the measurement plane and the scattered field caused by the incoming wave falling on the surface of the target source, a recovery method of the non-stationary free field with the pressure and particle acceleration measurements is proposed. First, the mixed time-evolving pressure and particle acceleration calculated by the finite difference technique on one measurement plane are obtained. Then, two physical relations are employed to deduce a forward complete recovery formulation of the target source in the noisy environment. One relation contains two impulse response functions relating the time-wavenumber pressure spectrum to particle acceleration and pressure spectrums, respectively, and the other is the surface reflection coefficient of the target source relating the scattered field to the incoming field. Finally, the time-evolving pressure radiated by the target source in free-field is recovered. A circular piston fixed on an infinite rigid baffle and two monopole sources are designed in a numerical simulation to test the performance of the proposed method. The simulation results attest that the proposed method not only can recover the time-evolving pressure radiated by the target source in free-field at any space points, but also recover the space distribution of the non-stationary sound field of the target source in free-field at different time instants effectively.