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.

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使用截断总最小二乘算法重建声散射场

任意形状结构的声散射场重建是水下目标散射特性的研究基础。首先，利用流体域中的边界元法（BEM）和声辐射模式（ARMs）求解，证明了散射压力可以用ARMs表示。其次，声场分布模式（AFDMs）由ARMs和通过对传统ATM的简化获得的新的声学传递矩阵（ATM）构建。同时，散射压力可以表示为AFDMs和模态膨胀系数的乘积。因此，散射重建问题转化为模态展开系数的精确解问题。针对测点压力和AFDM存在的噪声，引入总最小二乘（TLS）算法以获得准确的解决方案。此外，考虑到病态的AFDMs矩阵，引入截断总最小二乘（TTLS）算法来求解模态展开系数。仿真结果表明，基于TLS的重构算法抗噪声污染的能力有限，基于TTLS的重构算法比TLS算法具有更好的去噪性能。同时，对于较小的波数，不同噪声水平下重构的模态阶数近似相等，重构误差较小。仿真结果还表明，基于TTLS的重建算法在较小波数下比在较高波数下具有更好的去噪性能。对于较高的波数，重构的模态阶数随着信噪比（SNR）的降低而降低，重构误差增加。对于较小波数的后向重建，当重建表面靠近结构时，应考虑结构复杂性上升和渐逝波存在对重建结果的影响。