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

In a noisy environment, the interested sound field is interfused with 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. In order to remove the non-stationary incoming and scattered fields simultaneously, 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 are firstly measured on one measurement plane, where the particle acceleration is obtained by the finite difference approximation with the aid of an auxiliary measurement plane; 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 spectra, respectively, and the other is the surface reflection coefficient of the target source relating the scattered field to the incoming field. Finally, the mixed pressure and particle acceleration are substituted into the recovery formulation, and the time-evolving pressure radiated by the target source in free-field is recovered. Thereby, the proposed method possesses a significant feature of real-time recovery of the non-stationary free field. 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. An experiment with two speakers embedded in a planar steel plate and a speaker is further employed to verify the validity of the proposed method.