﻿ 等效阵长对声压线阵声呐空间增益的影响分析
 舰船科学技术  2017, Vol. 39 Issue (9): 123-128 PDF

1. 海军潜艇学院，山东 青岛 266000;
2. 中国人民解放军31001部队，北京 100000

Impact analysis of equivalent array length on spatial gain of pressure hydrophone array sonar
WANG Sen1, WANG Yu2, WANG Yi-chuan1, GAO Xin1
1. Navy Submarine Academy, Qingdao 266000, China;
2. No. 31001 Unit of PLA, Beijing 100000, China
Abstract: The simulation analysis of relationship between beam forming results and equivalent array length of array sonar has been done, in order to study the factors that influence spatial gain of pressure hydrophone array sonar with a fixed number of arrays. Firstly, the array sonar models of linear array, circle array, semicircular array and tai-ji array have been established. The mathematical expression of equivalent array length is defined and the comparison has been done. Secondly, the conception of –3 dB beam width is defined. The inverse relationship between equivalent array length and –3 dB beam width is obtained through the Monte-Carlo experiments. Finally, the results of beam forming simulation with multiple objective are contrasted and the relationship between spatial gain and equivalent array length is affirmed.
Key words: pressure hydrophone array sonar     equivalent array length     semicircular array     beam width
0 引　言

1 线阵声呐模型 1.1 直线阵

 图 1 线阵声呐模型 Fig. 1 Array sonar model of linear array
1.2 圆阵

 图 2 圆阵声呐模型 Fig. 2 Array sonar model of circle array
1.3 半圆阵

 图 3 半圆阵声呐模型 Fig. 3 Array sonar model of semicircular array
1.4 太极阵

 图 4 太极阵声呐模型 Fig. 4 Array sonar model of Tai-ji array
2 等效阵长 2.1 坐标系

 图 5 计算坐标系 Fig. 5 Coordinate system of calculation
2.2 阵型比较

 图 6 四种线阵声呐阵型比较 Fig. 6 Comparison of arrays

2.3 等效阵长的计算

 ${L_E} = \max \left| {{{x'}_i} - {{x'}_j}} \right|\text{，}\;\;\;\;i,j \in [0,N - 1]\text{。}$ (1)

 图 7 等效阵长比较 Fig. 7 Comparison of equivalent array length

3 空间增益分析 3.1 波束形成

 ${S_i}(t) = A\cos \left\{ {2\pi f\left[ {t + {\tau _i}(\theta )} \right]} \right\}\text{，}$ (2)

 ${\tau _i}(\theta ) = {y'_i}/c\text{，}\;\;\;i = 0,1,2, \cdots ,N - 1\text{，}$ (3)

 ${S_i}\left[ {t - {\tau _i}(\varphi )} \right] = A\cos \left\{ {2\pi f\left[ {t + {\Delta _i}(\theta )} \right]} \right\}\text{，}$ (4)

 ${\Delta _i}(\theta ) = {\tau _i}(\theta ) - {\tau _i}(\varphi )\text{。}$ (5)

 $G(\theta ) = \frac{1}{N}{\left\{ {E\left[ {{S^2}(t)} \right]} \right\}^{1/2}}\text{。}$ (6)

 图 8 信号0°入射仿真 Fig. 8 The target bearing is 0°

 图 9 信号45°入射仿真 Fig. 9 The target bearing is 45°

 图 10 信号90°入射仿真 Fig. 10 The target bearing is 90°

3.2 波束宽度

 ${\theta _{ - 3{\rm dB}}} = \left| {{\theta _ + } - {\theta _ - }} \right|\text{。}$ (7)

 图 11 信号22°入射仿真 Fig. 11 The target bearing is 22°

 图 12 信号90°入射仿真 Fig. 12 The target bearing is 90°

 图 13 信号180°入射仿真 Fig. 13 The target bearing is 180°

 图 14 波束宽度变化曲线 Fig. 14 The changing of beam width

 图 15 波束宽度变化曲线局部放大图 Fig. 15 The detail of beam width changing

 图 16 信号167°入射仿真 Fig. 16 The target bearing is 167°
3.3 多目标仿真

 图 17 直线阵多目标仿真 Fig. 17 The simulation of linear array

 图 18 圆阵多目标仿真 Fig. 18 The simulation of circular array

 图 19 半圆阵多目标仿真 Fig. 19 The simulation of semicircular array

 图 20 太极阵多目标仿真 Fig. 20 The simulation of Tai-ji array

4 结　语

1）线阵声呐的等效阵长与波束宽度之间具有反比关系，即某个方位的等效阵长越大，波束形成后的波束宽度越窄，方位分辨能力越强。

2）同等阵元个数情况下，半圆阵线阵声呐既不存在直线阵的左右舷模糊问题，又具有优于圆阵和太极阵的方位分辨能力，空间增益性能最佳。

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