Page 20 - 《应用声学》2022年第4期

518 2022 年 7 月

如表 2 所示，使用多特征向量约束的匹配场算法中， [7] Richardson A M, Nolte L W. A posteriori probability
在估计拷贝场互谱矩阵时，随机多项式展开方法的 source localization in an uncertain sound speed, deep
ocean environment[J]. The Journal of the Acoustical So-
时间开销不到蒙特卡洛统计方法的7%。
ciety of America, 1999, 89(5): 2280–2284.
[8] Byrne C L. A stable data-adaptive method for matched-
表 2 多特征向量约束匹配场声源定位算法的时间开销 field array processing in acoustic waveguides[J]. The Jour-
Table 2 The time cost of the MV-EPC source nal of the Acoustical Society of America, 1990, 87(6):
localization algorithms 2493–2502.
[9] 杨坤德, 马远良. 基于扇区特征向量约束的稳健自适应匹配场
算法中互谱矩阵的 蒙特卡洛 随机多项式 处理器 [J]. 声学学报, 2006, 31(5): 399–409.
估计方法 统计方法 展开法 Yang Kunde, Ma Yuanliang. Robust adaptive matched
field processing with sector eigenvector constraints[J].
时间/h 417.2 28.8
Acta Acustica, 2006, 25(3): 243–257.
[10] Chandler H A, Feuillade C, Smith G B. Sector-focused
3 结论 processing for stabilized resolution of multiple acoustic
sources[J]. The Journal of the Acoustical Society of Amer-
ica, 1995, 97(4): 2159–2172.
本文提出了一种基于复声压随机多项式展开
[11] James K R, Dowling D R. A probability density func-
的多特征向量约束不确定场声源定位方法。通过将 tion method for acoustic field uncertainty analysis[J]. The
随机声压表示成随机多项式展开的形式，提高了估 Journal of the Acoustical Society of America, 2005, 118(5):
计拷贝场复声压互谱矩阵的计算效率。在浅海、低 2802–2810.
[12] James K R, Dowling D R. A method for approximat-
频、海水声速存在起伏时，多特征向量约束的匹配
ing acoustic-field-amplitude uncertainty caused by envi-
场声源定位算法在定位性能 (定位准确率和输出峰 ronmental uncertainties[J]. The Journal of the Acoustical
均比)上优于线性匹配器和最小方差无失真匹配器， Society of America, 2008, 124(3): 1465–1476.
[13] James K R, Dowling D R. Pekeris waveguide comparisons
算法在估计拷贝场复声压互谱矩阵时，与蒙特卡洛
of methods for predicting acoustic field amplitude uncer-
统计方法相比，使用随机多项式展开方法会使得算 tainty caused by a spatially uniform environmental un-
法在定位性能略逊于前者，但计算效率比之提升一 certainty(L)[J]. The Journal of the Acoustical Society of
个数量级。 America, 2011, 129(2): 589–592.
[14] Xiu D, Karniadakis G E. The Wiener-Askey polynomial
chaos for stochastic differential equations[J]. SIAM Jour-
nal on Scientific Computing, 2002, 24(2): 619–644.
参 考 文 献 [15] Creamer D B. On closure schemes for polynomial chaos
expansions of stochastic differential equations[J]. Waves
[1] 杨坤德. 水声阵列信号的匹配场处理 [M]. 西安: 西北工业大 in Random and Complex Media, 2008, 18(2): 197–218.
学出版社, 2008: 165–166, 207. [16] Blatman G, Sudret B. Adaptive sparse polynomial chaos
[2] Krolik J L, Hodgkiss W S. Matched field source localiza- expansion based on least angle regression[J]. Journal of
tion in an uncertain environment using constraints based Computational Physics, 2011, 230(6): 2345–2367.
on sound-speed perturbations[C]. Oceans, IEEE, 2002. [17] Eldred M S. Recent advances in non-intrusive poly-
[3] Shorey J A, Nolte L W, Krolik J L. Computationally effi- nomial chaos and stochastic collocation method
cient Monte Carlo estimation algorithms for matched field for uncertainty analysis and design[C]. 50 th
processing in uncertain ocean environments[J]. Journal of AIAA/ASME/ASCE/AHS/ASC Structures, Structural
Computational Acoustics, 1994, 2(3): 285–314. Dynamics, and Materials Conference, 2009.
[4] Schmidt H, Baggeroer A B, et al. Environmentally toler- [18] Ma X, Zabaras N. An adaptive high-dimensional stochas-
ant beamforming for high-resolution matched field pro- tic model representation technique for the solution of
cessing: deterministic mismatch[J]. The Journal of the stochastic partial differential equations[J]. Journal of
Acoustical Society of America, 1990, 88(4): 1851–1862. Computational Physics, 2010, 229(10): 3884–3915.
[5] Krolik J L. Matched-field minimum variance beamforming [19] Hosder S, Walters R W, Balch M. Efficient sam-
in a random ocean channel[J]. The Journal of the Acous- pling for non-intrusive polynomial chaos applica-
tical Society of America, 1992, 92(3): 1408–1419. tions with multiple uncertain input variables[C]. 48 th
[6] Shorey J A, Nolte L W. Wideband optimal a posteri- AIAA/ASME/ASCE/AHS/ASC Structures, Structural
ori probability source localization in an uncertain shal- Dynamics, and Materials Conference, 2007.
low ocean environment[J]. The Journal of the Acoustical [20] Augustin F, Gilg A, Paffrath M, et al. An accuracy com-
Society of America, 1998, 103(1): 355–361. parison of polynomial chaos type methods for the propa-