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The interference characteristics of normal modes in low-frequency broadband sound can be applied to source localization and environmental parameter inversion in shallow water. However, the identification ambiguity of interference normal mode pairs generally occurs in practical applications due to unknown source position, some weakly-excited normal modes, mismatched environmental model, etc. For the applications of a horizontal line array, a model-based processing approach is proposed to determine the orders of the interference normal mode pairs based on the intrinsic dispersion characteristics of interference normal mode pairs in the received signals and the range-independent properties of the array beam output angles. Firstly, the normal mode pair filtering is achieved by using the WARPING transform of the signal autocorrelation function in the element domain of the horizontal line array. Then, the arrival angles of the filtered interference normal mode pairs are estimated by using array beamforming. Finally, the estimated beam output angles are matched with the replica values computed by sound field model. The approach is verified by using the explosive pulse signals received by the seafloor-deployed 32-element horizontal line array at the North Yellow Sea in 2011. Furthermore, some simulations are involved to analyze the effects of environmental parameter mismatches including water sound speed profile, sea bottom parameters and water depth on the identification performance of interference normal mode pairs. The results show that the water depth is a major factor influencing the extracted values of the beam output angles of interference normal mode pairs. The approach might fail when the water depth mismatch exceeds 14% of the practical value. However, the effects of water sound speed profile mismatch and sea bottom parameters mismatch are negligible. The effect of signal-to-noise ratio in the element domain on a horizontal line array is also simulated in order to analyze the limitation of identification performance, which shows that the required signal-to-noise ratio in the element domain should be more than 2 dB.
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Keywords:
- shallow water waveguide /
- interference normal mode pair /
- WARPING transform /
- modal identification /
- horizontal line array
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Niu H Q, He L, Li Z L, Zhang R H, Nan M X 2014 Acta Acoust. 39 1
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Li J W, Lu L C, Guo S M, Ma L 2017 Acta Phys. Sin. 66 204301
Google Scholar
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Google Scholar
[9] 王冬, 郭良浩, 刘建军, 戚聿波 2016 65 104302
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Wang D, Guo L H, Liu J J, Qi Y B 2016 Acta Phys. Sin. 65 104302
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Qi Y B, Zhou S H, Zhang R H, Zhang B, Ren Y 2014 Acta Phys. Sin. 63 044303
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Google Scholar
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Google Scholar
Li X M, Piao S C, Zhang M H, Liu Y Q, Zhou J B 2017 Acta Phys. Sin. 66 184301
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Google Scholar
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Google Scholar
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Google Scholar
Qi Y B, Zhou S H, Zhang R H, Ren Y 2015 Acta Phys. Sin. 64 074301
Google Scholar
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Google Scholar
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[21] 戚聿波, 周士弘, 任云, 刘建军, 王德俊, 冯希强 2015 声学学报 40 144
Qi Y B, Zhou S H, Ren Y, Liu J J, Wang D J, Feng X Q 2015 Acta Acoust. 40 144
[22] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) p1
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图 1 不同源深时接收信号自相关函数WARPING变换谱图 (a)源深33 m; (b)源深60 m
Figure 1. WARPING transform spectral of received signal autocorrelation functions at different source depths: (a) Source depth 33 m; (b) source depth 60 m.
图 2 干涉简正模波束输出角度理论值与提取值的对比
Figure 2. Comparison of beam output angles between the theoretical and extracted values of the interference normal mode pairs.
图 3 声速剖面
Figure 3. Sound speed profile.
图 4 WARPING变换频谱 (a)全部信号; (b)距离25.26 km 处接收的数据
Figure 4. WARPING transform spectrum: (a) All signals; (b)the signal at range of 25.26 km.
图 5 距离25.26 km处信号两组干涉简正模成分波束输出角度提取值与理论值的对比 (a)第一组干涉简正模; (b)第二组干涉简正模
Figure 5. Comparison of the measured and computed beam output angles of the normal mode pairs at the range of 25.26 km: (a) The first normal mode pair; (b) the second normal mode pair.
图 6 (1, 2)阶干涉简正模判别结果及其概率 (a)判别结果; (b)概率统计结果
Figure 6. The discrimination of normal mode pair (1, 2) and its probability: (a) The discrimination of result; (b) probability.
图 8 (1, 4)阶干涉简正模判别结果及其概率 (a)判别结果; (b)概率统计结果
Figure 8. The discrimination of normal mode pair (1, 4) and its probability: (a) The discrimination of result; (b) probability.
图 7 (1, 3)阶干涉简正模判别结果及其概率 (a)判别结果; (b)概率统计结果
Figure 7. The discrimination of normal mode pair (1, 3) and its probability: (a) The discrimination of result;(b)probability.
图 9 环境参数失配对(1,2)阶干涉简正模波束输出角度值的影响 (a)海水声速剖面失配; (b)海底参数失配; (c)海深失配
Figure 9. The effect of environmental parameter mismatches on the beam output angles of the normal mode pair (1,2): (a)Sound speed profile mismatch; (b) sea bottom parameter mismatch; (c)water depth mismatch.
图 10 信噪比对干涉简正模成分波束输出角度提取值的影响 (a)角度差均方根值与信噪比关系; (b) 2 dB时角度提取值与理论值
Figure 10. The effect of SNR on the beam output angles of the normal mode pair: (a) The mean square error of the angle varies with SNR; (b) the extracted and theretical values at 2 dB.
表 1 海底底质参数选择
Table 1. Sea bottom parameters
海底声速/m·s–1 海底密度/g·cm–3 吸收系数/dB·λ–1 1530 1.20 0.30 1550 1.50 0.20 1606 1.65 0.09 1700 1.80 0.05 
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[1] Bonnel J, Nicolas B, Mars J I, Walker S C 2010 J. Acoust. Soc. Am. 128 719
Google Scholar
[2] Bonnel J, Chapman N R 2011 J. Acoust. Soc. Am. 130 EL101
Google Scholar
[3] 牛海强, 何利, 李整林, 张仁和, 南明星 2014 声学学报 39 1
Niu H Q, He L, Li Z L, Zhang R H, Nan M X 2014 Acta Acoust. 39 1
[4] Li Z L, Zhang R H 2007 Chin. Phys. Lett. 24 471
Google Scholar
[5] Li F H, Zhang B, Guo Y G 2014 Chin. Phys. Lett. 31 47
[6] Bonnel J, Ying-Tsong L, Eleftherakis D, Goff J A, Dosso S, Chapman R, Miller J H, Potty G R 2018 J. Acoust. Soc. Am. 143 405
Google Scholar
[7] 李佳蔚, 鹿力成, 郭圣明, 马力 2017 66 204301
Google Scholar
Li J W, Lu L C, Guo S M, Ma L 2017 Acta Phys. Sin. 66 204301
Google Scholar
[8] Lopatka M, Touzé G L, Nicolas B, Cristol X, Mars J I, Fattaccioli D 2010 J. Adv. Signal Proc. 2010 304103
Google Scholar
[9] 王冬, 郭良浩, 刘建军, 戚聿波 2016 65 104302
Google Scholar
Wang D, Guo L H, Liu J J, Qi Y B 2016 Acta Phys. Sin. 65 104302
Google Scholar
[10] Bonnel J, Thode A 2013 J. Acoust. Soc. Am. 19 070066
[11] 戚聿波, 周士弘, 张仁和, 张波, 任云 2014 63 044303
Google Scholar
Qi Y B, Zhou S H, Zhang R H, Zhang B, Ren Y 2014 Acta Phys. Sin. 63 044303
Google Scholar
[12] 李晓曼, 张明辉, 张海刚, 朴胜春, 刘亚琴, 周建波 2017 66 094302
Google Scholar
Li X M, Zhang M H, Zhang H G, Piao S C, Liu Y Q, Zhou J B 2017 Acta Phys. Sin. 66 094302
Google Scholar
[13] 李晓曼, 朴胜春, 张明辉, 刘亚琴, 周建波 2017 66 184301
Google Scholar
Li X M, Piao S C, Zhang M H, Liu Y Q, Zhou J B 2017 Acta Phys. Sin. 66 184301
Google Scholar
[14] Zhou S H, Qi Y B, Ren Y 2014 Sci. China-Phys. Mech. Astron. 57 225
Google Scholar
[15] Baraniuk R G, Jones D L 1995 IEEE Trans. Signal Process. 43 2269
Google Scholar
[16] Touzé L, Nicolas B, Mars J I, Lacoume J L 2009 IEEE Trans. Signal Process. 57 1783
Google Scholar
[17] 戚聿波, 周士弘, 张仁和, 任云 2015 64 074301
Google Scholar
Qi Y B, Zhou S H, Zhang R H, Ren Y 2015 Acta Phys. Sin. 64 074301
Google Scholar
[18] 戚聿波, 周士弘, 张仁和 2016 65 134301
Google Scholar
Qi Y B, Zhou S H, Zhang R H 2016 Acta Phys. Sin. 65 134301
Google Scholar
[19] Jensen F B, Kuperman W A, Porter M B, Schmidt H 2011 Computational Ocean Acoustics (2nd Ed.) (NewYork: Springer) p408
[20] Bender C M, Orszag S A 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill) p276
[21] 戚聿波, 周士弘, 任云, 刘建军, 王德俊, 冯希强 2015 声学学报 40 144
Qi Y B, Zhou S H, Ren Y, Liu J J, Wang D J, Feng X Q 2015 Acta Acoust. 40 144
[22] Porter M B 1991 The KRAKEN Normal Mode Program (La Spezia: SACLANT Undersea Research Centre) p1
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