Reconstruction of nonstationary sound field based on group sparsity time domain equivalent source method

Abstract

To improve the accuracy and stability of reconstruction of nonstationary sound field, a novel time domain equivalent source method based on non-convex overlapping group sparsity (NOGS-TESM) is proposed. In the proposed NOGS-TESM, the time-varying pressure in the near field is first modeled by a set of equivalent sources positioned inside the vibrating structure. Then, the NOGS regularization is applied for solving the inverse problem, and a novel algorithm derived on the basis of Majorize-Minimization theory is utilized to obtain the optimal solution of equivalent sources strengths. Finally, the optimal equivalent sources strengths at all times are substituted into a time-domain convolution to calculate the time-varying pressure of reconstruction surface. The proposed NOGS-TESM enriches the prior information by considering the group sparsity of spatial pressure distribution, and enhances the accuracy of estimated equivalent sources strength via its alternative calculation of l0−norm. A vibrating plate to produce a nonstationary sound field, which is designed as a numerical simulation, and the time-varying pressures of measurement surface are input into the proposed NOGS-TESM. The quantitative and qualitative comparisons confirm that the proposed NOGS-TESM can greatly reconstruct the non-stationary sound field in time–space domains, and its reconstruction accuracy is higher than that of TESM with Tikhonov regularization (TR-TESM). Meanwhile, several parameters, for example, the noise and position of equivalent source surface, are discussed in detail, and the superiorities of the proposed NOGS-TESM in terms of stability and robustness are proved by comparing to TR-TESM. The predominance of the proposed NOGS-TESM is further validated by conducting one experiment on the vibrating steel plate.