Research on adaptive step size algorithm of marine streamline controlled by information entropy
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摘要: 海洋流场的流线构造与放置对于认识和理解海洋流场具有重要意义。在流线绘制过程中，积分步长的选择至关重要，能够直接影响流线放置效果。固定步长算法由于无法适应曲率不断变化的情形往往不被采用，以往自适应步长流线算法存在自由度低以及多尺度适用性差的问题。针对上述问题，本文首次将信息熵引入到步长计算中，提出了信息熵控制的海洋流线自适应步长算法。该算法首先通过计算流场信息熵得到熵场，然后依据熵值大小将流场划分为高熵区域和低熵区域，并为每个积分点赋予新的步长，使得流场可以根据变化剧烈程度自适应调整步长大小，即高熵区域（变化剧烈的区域）步长较小，低熵区域（变化平缓的区域）步长较大。实验结果表明，本文算法能够显著增加变化剧烈区域的积分点数目和流线条数，更好地绘制特征处的流线细节，同时在不会影响放置效果的前提下减少了非重要区域的积分点数目和流线条数以提高计算效率，相比以往自适应步长算法显著提高了步长调节的自由度以及尺度适用性，可以应用于不同尺度的海洋流场。Abstract: Abstrart: The streamline construction and placement of the marine flow field is of great significance for recognizing and understanding the marine flow field. In the process of streamline drawing, the selection of integration step is very important, which can directly affect the effect of streamline placement. The fixed step size algorithm is often not used because it cannot adapt to the changing curvature. The previous adaptive step size streamline algorithm has the problems of low degree of freedom and poor multi-scale applicability. In view of the above problems, this paper introduces information entropy into the step size calculation for the first time, and proposes an adaptive step size algorithm of marine streamline controlled by information entropy. Firstly, the entropy field is obtained by calculating the information entropy of the flow field, and then the flow field is divided into high entropy region and low entropy region according to the entropy value, and each integration point is given a new step size, so that the flow field can adaptively adjust the step size according to the intensity of change, that is, the step size of the high entropy region (the region with sharp change) is smaller, and the step size of the low entropy region (the region with gentle change) is larger. The experimental results show that the proposed algorithm can significantly increase the number of integration points and streamlines in the rapidly changing region, better draw the details of the streamline at the feature, and reduce the number of integration points and streamlines in the unimportant region without affecting the placement effect to improve the computational efficiency. Compared with the previous adaptive step size algorithm, the proposed algorithm significantly improves the degree of freedom of step size adjustment and the scale applicability, and can be applied to different scales of marine flow field.
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图 1 不同种子点放置效果
a.基于特征的种子点放置；b.随机种子点放置；c.均匀种子点放置
Fig. 1 Placement effect of different seed points
a. Places seed points based on features; b. Randomly places seed points; c. Evenly places seed points
图 3 二维流场图及二维熵场图
a.b.c. 二维流场图；d.e.f. 二维熵场图
Fig. 3 Two-dimensional flow field map and two-dimensional entropy field map
a.b.c. Two-dimensional flow field map; d.e.f. two-dimensional entropy field map
图 4 不同固定步长下流线放置效果
a.步长为0.2的固定步长算法；b.步长为0.3的固定步长算法
Fig. 4 Streamline placement effects with different fixed step sizes
a. fixed-step algorithm with a step size of 0.2; b. fixed-step algorithm with a step size of 0.3
图 6 流场A流线放置效果对比
a.步长为0.1的固定步长算法；b.步长为0.2的固定步长算法；c.步长为0.3的固定步长算法；d.考虑速度方向变化的自适应步长算法；e.改进后的AMFCA算法算法；f.本文算法
Fig. 6 Comparison of flow field A streamline placement results
a. fixed-step algorithm with a step size of 0.1; b. fixed-step algorithm with a step size of 0.2; c. fixed-step algorithm with a step size of 0.3; d. adaptive step size algorithm that takes into account changes in velocity direction; e. improved AMFCA algorithm; f. this paper's algorithm
图 7 流场A流线图、温度图和海表面高度图
a.流线图；b.温度图；c.海表面高度图
Fig. 7 Streamline map, temperature map and sea surface height map of flow field A
a. Streamline map; b. Temperature map; c. Sea surface height map
图 8 流场B流线放置效果对比
a.步长为0.1的固定步长算法；b.步长为0.2的固定步长算法；c.步长为0.3的固定步长算法；d.考虑速度方向变化的自适应步长算法；e.改进后的AMFCA算法算法；f.本文算法
Fig. 8 Comparison of flow field B streamline placement results
a. fixed-step algorithm with a step size of 0.1; b. fixed-step algorithm with a step size of 0.2; c. fixed-step algorithm with a step size of 0.3; d. adaptive step size algorithm that takes into account changes in velocity direction; e. improved AMFCA algorithm; f. this paper's algorithm
图 9 流场B流线图、温度图和海表面高度图
a.流线图；b.温度图；c.海表面高度图
Fig. 9 Streamline map, temperature map and sea surface height map of flow field B
a. Streamline map; b. Temperature map; c. Sea surface height map
图 10 流线图相似性对比
a.本文实验结果（流场A）；b.卫星数据流线图（流场A）；c.本文实验结果（流场B）；d.卫星数据流线图（流场B）
Fig. 10 Similarity comparison of streamline map
a. Experimental results in this paper(flow field A); b. Streamline map of satellite data(flow field A); c. Experimental results in this paper(flow field B); d. Streamline map of satellite data(flow field B)
图 11 步长空间分布图
a.流场A部分区域步长空间分布图；b.流场B部分区域步长空间分布图
Fig. 11 Step size spatial distribution map
a. Step size spatial distribution map of flow field A; b. Step size spatial distribution map of flow field B
图 12 三种自适应步长算法对比结果
a.本文算法；b.考虑速度方向变化的自适应步长算法；c.改进后的AMFCA算法
Fig. 12 Comparison of three adaptive step size algorithms
a. this paper's algorithm; b. adaptive step size algorithm that takes into account changes in velocity direction; c. improved AMFCA algorithm
表 1 流场A区域一中不同算法对比结果
Tab. 1 Comparison results of different algorithms in region 1 of flow field A
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表 2 流场A区域二中不同算法对比结果
Tab. 2 Comparison results of different algorithms in region 2 of flow field A
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表 3 流场B区域一中不同算法对比结果
Tab. 3 Comparison results of different algorithms in region 1 of flow field B
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表 4 流场B区域二中不同算法对比结果
Tab. 4 Comparison results of different algorithms in region 2 of flow field B
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表 5 流场A不同算法结果运行时间
Tab. 5 Running time of different algorithm results of flow field A
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