模糊特征目标的相对熵识别法

张虎彪; 王星; 徐宇恒; 吴笑天; 胡文辉

doi:10.13700/j.bh.1001-5965.2020.0237

模糊特征目标的相对熵识别法

doi: 10.13700/j.bh.1001-5965.2020.0237

1.
空军工程大学航空工程学院，西安 710038
2.
中国人民解放军 95174部队，武汉 430000

详细信息

通讯作者:
E-mail：13399289501@189.cn

中图分类号: TN971；C934
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- 被引次数: 0
出版历程
- 收稿日期: 2020-06-02
- 录用日期: 2020-10-09
- 网络出版日期: 2020-10-21
- 整期出版日期: 2023-12-31

Relative entropy method in target recognition with fuzzy features

1.
Aeronautics Engineering College，Air Force Engineering University，Xi’an 710038，China
2.
95174 Troops of the PLA，Wuhan 430000，China

More Information

Corresponding author: E-mail：13399289501@189.cn

摘要

摘要:
针对模糊特征的目标识别问题，提出了一种结合模糊建模和改进CRITIC方法的相对熵识别方法。计算多个时刻观测值的统计特征，通过模糊建模将观测值转化为模糊数；基于模糊数距离测度，定义并计算目标特征值和观测值之间的相似度；对CRITIC方法进行改进，提出一种目标特征客观权重的求解方法；根据相似度和特征权重，使用相对熵排序法得到识别结果。仿真结果显示：模糊特征能够更好地体现识别中的不确定性，所提方法对模糊特征的目标识别率高，实时性和鲁棒性好，具有一定的应用价值。
- 相对熵 /
- 模糊数 /
- CRITIC /
- 多属性决策 /
- 目标识别
Abstract:
A relative entropy method combining fuzzy modeling and improved CRITIC was presented to recognize targets with fuzzy features. The observed values from multiple times were converted into fuzzy numbers through fuzzy modeling based on the statistical characteristics of multiple sets of the observed values. As a result of measuring the distance between the fuzzy numbers, similarities between the values of the target feature and the observed values were determined. The improved CRITIC was proposed to calculate the objective weights of the target features. According to the feature weights and the similarities between the target feature values and the observed values, the recognition result was obtained by the relative entropy evaluation method. The simulation results indicate that the uncertainty in target recognition is better reflected by the fuzzy features, and the proposed method has a high target recognition rate for the target with fuzzy features with good real-time and robustness, which has a certain application value.
- relative entropy /
- fuzzy number /
- CRITIC /
- multiple attribute decision making /
- target recognition

HTML全文

图 1 目标识别问题的多属性决策模型

Figure 1. Multiple attribute decision making model in target recognition

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图 2 模糊特征目标的相对熵识别法流程

Figure 2. Process of relative entropy method in target recognition for fuzzy feature targets

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图 3 目标特征权重的均值

Figure 3. Average weights of target features

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图 4 识别率随观测值组数变化曲线

Figure 4. Recognition rate relationship with number of sets of observed values

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图 5 同时存在正常数据和奇异点时识别率随观测值组数变化曲线

Figure 5. Recognition rate relationship with number of sets of observed values with both normal data and outliers

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表 1 空中目标模糊数据库

Table 1. Fuzzy database of air targets

目标	F₁/(km·h⁻¹)	F₂/(m·s⁻²)	F₃/km	F₄/GHz
T₁	(800,900,1050)	(0,1.2,3.0)	(10.0,12.5,15.0)	(13.05,13.20,13.35)
T₂	(580,700,800)	(0,0.7,2.8)	(10.0,12.0,14.0)	(14.50,14.70,14.90)
T₃	(400,600,955)	(0,0.5,2.0)	(7.5,9.0,12.0)	(2.30,2.40,2.50)
T₄	(905,1200,1800)	(0,4.0,8.0)	(13.0,16.0,18.0)	(9.25,9.35,9.45)
T₅	(710,1100,1500)	(0,3.2,6.0)	(8.0,13.0,14.0)	(9.20,9.30,9.40)

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表 2 不同相似度指标下的识别率

Table 2. Recognition rate of different similarity metrics

M	识别率/%
M	似然函数法	顶点法	L₂-metric 距离法
1.0	73.43	99.58	99.77
1.1	70.80	98.70	99.08
1.2	67.78	97.22	97.76

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表 3 不同权重计算方法下的识别率

Table 3. Recognition rate of different weight calculation %

权重计算	识别率
等权重法	96.90
熵权法	96.96
CRITIC 方法	96.35
改进CRITIC 方法	97.92

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表 4 不同多属性决策方法下的识别率

Table 4. Recognition rate of different multiple attribute decision making methods %

方法	识别率
TOPSIS	97.62
灰色关联TOPSIS	95.35
相对熵排序法	97.94

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表 5 不同观测值组数下的识别率

Table 5. Recognition rate of different sets of observations

N	识别率/%	N	识别率/%
2	94.42	13	99.80
3	95.93	14	99.87
4	97.05	15	99.91
5	97.86	16	99.91
6	98.34	17	99.94
7	98.82	18	99.96
8	99.17	19	99.96
9	99.39	20	99.97
10	99.60	21	99.98
11	99.70	22	99.98
12	99.75

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表 6 不同目标数量和观测值组数下的运行时间

Table 6. Running time of different numbers of targets and sets of observations

N	运行时间/ms
N	n_T=2	n_T=3	n_T=4	n_T=5
2	0.337	0.375	0.407	0.447
3	0.333	0.375	0.410	0.447
4	0.332	0.370	0.408	0.449
5	0.330	0.377	0.410	0.450
6	0.333	0.374	0.409	0.450
7	0.334	0.381	0.409	0.447
8	0.334	0.377	0.413	0.446

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表 7 不同特征数量和观测值组数下的运行时间

Table 7. Running time of different numbers of features and sets of observations

N	运行时间/ms
N	n_F=1	n_F=2	n_F=3	n_F=4
2	0.094	0.169	0.222	0.270
3	0.091	0.167	0.218	0.271
4	0.093	0.167	0.218	0.271
5	0.089	0.168	0.223	0.273
6	0.091	0.166	0.214	0.268
7	0.093	0.167	0.221	0.274
8	0.094	0.166	0.215	0.272

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表 8 不同观测值组数下的虚警率

Table 8. False alarm rate of different sets of observations

N	虚警率/%					平均虚警率/%
N	T₁	T₂	T₃	T₄	T₅	平均虚警率/%
2	5.00	6.70	6.17	6.58	6.39	6.17
3	3.71	5.19	5.32	5.45	5.39	5.01
4	2.93	4.76	4.57	4.41	4.26	4.19
5	2.37	4.11	4.06	3.89	3.99	3.68
6	1.48	3.37	3.66	3.48	3.49	3.10
7	1.05	3.23	2.97	3.14	3.50	2.78
8	0.74	2.76	2.58	2.76	2.65	2.30

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表 9 只存在奇异点时不同观测值组数下的识别率

Table 9. Recognition rate with different sets of observations when only outliers exist

N	识别率/%
N	M=1.2	M=1.4	M=1.6	M=1.8	M=2.0
2	40.53	36.60	32.04	28.40	24.11
3	40.18	34.59	32.40	29.62	26.36
4	44.90	41.20	37.69	34.22	28.18
5	47.78	42.54	38.31	34.07	30.01
6	49.88	43.46	39.95	36.44	31.39
7	49.62	45.03	41.23	36.58	31.62
8	51.74	45.28	41.10	37.15	32.04

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表 10 同时存在正常数据和奇异点时不同观测值组数下的识别率

Table 10. Recognition rate of different sets of observations with both normal data and outliers

N	识别率/%
N	M=1.0	M=1.2	M=1.4	M=1.6	M=1.8	M=2.0
2	97.73	93.94	89.10	82.67	75.52	68.64
3	98.85	94.91	89.22	81.03	72.15	63.47
4	99.41	95.72	89.30	80.19	69.58	60.31
5	99.71	96.51	89.81	79.31	67.55	57.57
6	99.83	97.04	89.97	78.46	65.55	55.27
7	99.91	97.18	90.43	77.77	64.09	55.73
8	99.95	97.52	90.86	76.83	62.86	52.68

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表 11 不同奇异点偏离程度下的识别率

Table 11. Recognition rate of different deviation degrees of outliers

N	识别率/%
N	M=1.2	M=1.4	M=1.6	M=1.8	M=2.0
2	40.65	36.97	32.30	28.24	24.22
3	39.95	34.66	32.38	29.57	26.94
4	44.90	41.59	37.36	33.93	28.34
5	47.47	42.39	38.47	34.49	29.80
6	49.67	43.45	40.09	35.87	31.28
7	50.29	45.06	41.03	36.30	31.61
8	51.62	45.48	40.99	37.29	31.88

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