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非嵌入式随机多项式展开法是目前性能最优的一种不确定声场快速算法，但配点的选择对算法计算精度影响较大，且当计算随不确定海洋环境参数变化剧烈的声场输出时，需采用分段概率配点法等特殊方法处理. 基于Kriging模型提出了一种新的浅海不确定声场快速算法. 首先给出了该算法的理论推导，然后通过数值计算验证了算法性能，并给出具体的物理解释. 结果表明：在同等条件下，新算法的计算精度较非嵌入式随机多项式展开法更高；无需针对声场输出随不确定海洋环境参数的变化情况采取特殊处理过程；克服了非嵌入式随机多项式展开法为提高计算精度将随机多项式展开至非常高的阶数，从而增加计算量的不足；较非嵌入式随机多项式展开法，其样本点的选择简单易行，且可直接计算误差. 因此，本文算法较非嵌入式随机多项式展开法普适性更强.Non-intrusive polynomial chaos expansion (NPCE) method is a fast algorithm with the best performances for an uncertain acoustic filed currently, in which the selection of collocation points is an important factor for the computational accuracy, and some special processing methods such as piecewise probabilistic collocation method, should be adopted when the outputs of acoustic field vary severely with uncertain ocean environmental parameters. A new fast algorithm for uncertain acoustic filed in shallow-water is proposed based on Kriging model. The theoretical description of the new algorithm is given, and numerical simulations are conducted to verify the performances of the proposed algorithm. The physical interpretations are given in detail. The results demonstrate that the proposed algorithm is more accurate than the NPCE method under the same conditions, and any special processing method does not need to be adopted when the outputs of acoustic field vary severely with the uncertain ocean environmental parameters. The weakness of NPCE method can be overcome by the proposed algorithm, which is that the computational cost increases with the stochastic polynomial expanding to a higher order for enhancing the computational accuracy. The selection of sample point of the proposed algorithm is simpler and easier than that of NPCE method, and the calculation errors can be given directly. Thus, the proposed algorithm is more universal than NPCE method.
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Keywords:
- uncertain acoustic field /
- Kriging model /
- fast algorithm /
- universality
[1] Cheng G L, Zhang M M 2013 Acta Acoust. 38 294 (in Chinese) [程广利, 张明敏 2013 声学学报 38 294]
[2] Liu Z W, Sun C, Du J Y 2013 Acta Phys. Sin. 62 064303 [刘宗伟, 孙超, 杜金燕 2013 62 064303]
[3] Livingston E S, Goff J A, Finette S, Abbot P, Lynch J F, Hodgkiss W S 2006 IEEE J. Ocean. Eng. 31 245
[4] Kevin R J 2009 Ph. D. Dissertation (Michigan: University of Michigan)
[5] Kevin R J, David R D 2008 J. Acoust. Soc. Am. 124 1465
[6] Steven F 2005 J. Acoust. Soc. Am. 117 997
[7] Khine Y Y, Steven F, Dennis B C 2010 J. Comp. Acoust. 18 397
[8] Dennis B, Creamer 2006 J. Acoust. Soc. Am. 119 1979
[9] Kevin R J, David R 2011 J. Acoust. Soc. Am. 129 589
[10] Cheng G L, Zhang M M 2013 Tech. Acoust. 32 7 (in Chinese) [程广利, 张明敏 2013 声学技术 32 7]
[11] Cheng G L, Zhang M M 2013 J. Harbin Engineer. Univ. 34 21 (in Chinese) [程广利, 张明敏 2013 哈尔滨工程大学学报 34 21]
[12] Deutsch C V, Wilde B J 2013 Int. J. Coal Geology 112 87
[13] Yin D W, Li B W, Wang Y H, Feng X J 2011 Acta Aeronaut. Astronaut. Sin. 25 99 (in Chinese) [尹大伟, 李本威, 王永华, 冯向军 2011 航空学报 25 99]
[14] Kwak S, Kin H K, Cha J W 2013 Transactions of the Korean Institute of Electrical Engineering 62 177
[15] Su Y H, Yang H B 2012 Chin. J. Appl. Mech. 29 705 (in Chinese) [苏永华, 杨红波 2012 应用力学学报 29 705]
[16] Wang L X, Fang D Z, Zhang M Y 2006 Handbook of Math (Beijing: Higher Education Press) p497 (in Chinese) [王连祥, 方德植, 张鸣镛 2006 数学手册 (北京: 高等教育出版社) 第497页]
[17] Martin J D 2009 J. Mech. Design 1 1
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[1] Cheng G L, Zhang M M 2013 Acta Acoust. 38 294 (in Chinese) [程广利, 张明敏 2013 声学学报 38 294]
[2] Liu Z W, Sun C, Du J Y 2013 Acta Phys. Sin. 62 064303 [刘宗伟, 孙超, 杜金燕 2013 62 064303]
[3] Livingston E S, Goff J A, Finette S, Abbot P, Lynch J F, Hodgkiss W S 2006 IEEE J. Ocean. Eng. 31 245
[4] Kevin R J 2009 Ph. D. Dissertation (Michigan: University of Michigan)
[5] Kevin R J, David R D 2008 J. Acoust. Soc. Am. 124 1465
[6] Steven F 2005 J. Acoust. Soc. Am. 117 997
[7] Khine Y Y, Steven F, Dennis B C 2010 J. Comp. Acoust. 18 397
[8] Dennis B, Creamer 2006 J. Acoust. Soc. Am. 119 1979
[9] Kevin R J, David R 2011 J. Acoust. Soc. Am. 129 589
[10] Cheng G L, Zhang M M 2013 Tech. Acoust. 32 7 (in Chinese) [程广利, 张明敏 2013 声学技术 32 7]
[11] Cheng G L, Zhang M M 2013 J. Harbin Engineer. Univ. 34 21 (in Chinese) [程广利, 张明敏 2013 哈尔滨工程大学学报 34 21]
[12] Deutsch C V, Wilde B J 2013 Int. J. Coal Geology 112 87
[13] Yin D W, Li B W, Wang Y H, Feng X J 2011 Acta Aeronaut. Astronaut. Sin. 25 99 (in Chinese) [尹大伟, 李本威, 王永华, 冯向军 2011 航空学报 25 99]
[14] Kwak S, Kin H K, Cha J W 2013 Transactions of the Korean Institute of Electrical Engineering 62 177
[15] Su Y H, Yang H B 2012 Chin. J. Appl. Mech. 29 705 (in Chinese) [苏永华, 杨红波 2012 应用力学学报 29 705]
[16] Wang L X, Fang D Z, Zhang M Y 2006 Handbook of Math (Beijing: Higher Education Press) p497 (in Chinese) [王连祥, 方德植, 张鸣镛 2006 数学手册 (北京: 高等教育出版社) 第497页]
[17] Martin J D 2009 J. Mech. Design 1 1
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