Acoustic Scattering Field Reconstruction Using Truncated Total Least Square Algorithm
Abstract
Acoustic scattering-field reconstruction of structures with arbitrary shape is the research basis of the scattering characteristics for underwater targets. Firstly, using boundary element method (BEM) and acoustic radiation modes (ARMs) solution in fluid domain, it is proved that the scattering pressures can be expressed by ARMs. Secondly, the acoustic field distribution modes (AFDMs) are constructed by ARMs and a new acoustic transfer matrix (ATM) which is acquired by the simplification of the traditional ATM. At the same time, the scattering pressures can be expressed as the product of the AFDMs and the modal expansion coefficients. Thus, the scattering reconstruction problem is converted into the exact solution problem of the modal expansion coefficients. Aiming at the existing noise of both the pressures at measuring point and AFDMs, the total least square (TLS) algorithm is introduced to acquire the accurate solution. Further, considering the ill-conditioned AFDMs matrix, the truncated total least square (TTLS) algorithm is introduced to solve the modal expansion coefficients. Simulation results show that the capability of resisting noise contamination is limited for the reconstruction algorithm based on TLS and that the reconstruction algorithm based on TTLS has a better denoising performance than the TLS one. At the same time, for smaller wave numbers, the modal orders for reconstruction at different noise levels are approximately equal and the reconstruction errors are small. The simulation results also demonstrate that the reconstruction algorithm based on TTLS has a better denoising performance at smaller wave numbers than at higher wave numbers. For the higher wave numbers, the modal orders for reconstruction decrease and the reconstruction errors increase with the decrease of the signal-to-noise ratio (SNR). For the backward reconstruction at smaller wave numbers, the influence to reconstruction results, which arises from structure complexity ascending and evanescent waves existing, should be considered when the reconstruction surfaces are near the structures.
