基于AHP-DST融合专家先验知识的BN参数学习

doi:10.16182/j.issn1004731x.joss.24-0658

摘要/Abstract

摘要：

针对小样本数据集条件下采用单一专家先验知识可能存在不确定性导致BN参数学习精度不高问题，设计了一种基于AHP-DST融合专家先验知识的BN参数学习方法。利用层次分析法的思想结合证据理论合成规则计算出专家综合先验知识；将专家综合先验知识加入到正态分布中，与单调性约束相结合得到虚拟样本信息；将虚拟样本信息加入到贝叶斯估计中得到网络参数估计值。在不同样本量条件下进行仿真验证，结果表明：在样本数据较小时，所提方法的KL散度始终优于其他4种方法，运行时间则略高于其他两种方法，总体上，所提算法综合性能优于其他4种方法，更适用于样本数据量较小的情况。将所提方法应用于空中目标对海面舰艇的攻击意图识别中，仿真结果能够较好的反应实际情况，进一步验证了方法的有效性和可行性。

关键词: 贝叶斯网络, 参数学习, 小数据集, 层次分析法, 证据理论, 单调性约束

Abstract:

Aiming at the problem of low accuracy of BN parameter learning due to the uncertainty of a single expert prior knowledge under the condition of small sample data set, a BN parameter learning method based on AHP-DST fusion expert prior knowledge was designed. The synthetic prior knowledge of experts was calculated by using the thought of analytic hierarchy process combined with the rules of evidence theory synthesis. The expert comprehensive prior knowledge was added to the normal distribution and combined with the monotonicity constraint to obtain the virtual sample information. The virtual sample information was added to the Bayesian estimation to get the network parameter estimate. The simulation results show that the KL divergence of the proposed method is always better than that of the other four methods when the sample data is small, and the running time is slightly higher than that of the other two methods. In general, the comprehensive performance of the proposed algorithm outperforms the other four methods, and it is more suitable for the case of small sample data. The proposed method is applied to the identification of the attack intention of the air target on the surface ship, and the simulation results can reflect the actual situation well, which further verifies the effectiveness and feasibility of the method.

Key words: Bayesian network, parameter learning, small dataset, analytic hierarchy process, evidence theory, monotonic constraint

中图分类号:

TP181

陈海洋,吝红凯,任智芳等 . 基于AHP-DST融合专家先验知识的BN参数学习[J]. 系统仿真学报, 2025, 37(11): 2778-2792.

Chen Haiyang,Lin Hongkai,Ren Zhifang,et al . Bayesian Network Parameter Learning Based on AHP-DST Fusion of Expert Prior Knowledge[J]. Journal of System Simulation, 2025, 37(11): 2778-2792.

图/表 25

图1

表1

图2

表2

表3

表4

专家1认知判断矩阵

专家1	$P 1$	$P 2$	$Θ$
$P 1$	1	0	5w₁
$P 2$	0	1	3w₁
$Θ$	1/5w₁	1/3w₁	1

表4

表5

专家2认知判断矩阵

专家2	$P 1$	$P 2$	$Θ$
$P 1$	1	0	6w₂
$P 2$	0	1	2w₂
$Θ$	1/6w₂	1/2w₂	1

表5

表6

专家3认知判断矩阵

专家3	$P 1$	$P 2$	$Θ$
$P 1$	1	0	5w₃
$P 2$	0	1	3w₃
$Θ$	1/5w₃	1/3w₃	1

表6

表7

表8

约束条件

编号	约束
1	$P (S = 0 \| C = 0) > P (S = 1 \| C = 0)$
2	$P (S = 0 \| C = 1) > P (S = 1 \| C = 1)$
3	$P (R = 0 \| C = 0) > P (R = 1 \| C = 0)$
4	$P (R = 0 \| C = 1) > P (R = 1 \| C = 1)$
5	$P (W = 0 \| S = 0, R = 0) > P (W = 1 \| S = 0, R = 0)$
6	$P (W = 0 \| S = 0, R = 1) > P (W = 1 \| S = 0, R = 1)$
7	$P (W = 0 \| S = 1, R = 0) > P (W = 1 \| S = 1, R = 0)$
8	$P (W = 0 \| S = 1, R = 1) > P (W = 1 \| S = 1, R = 1)$

表8

图3

图4

图5

图6

图7

表9

表10

专家1认知判断矩阵

专家1	${F 1, F 2}$	$F 3$	$Θ$
${F 1, F 2}$	1	0	5w₁
$F 3$	0	1	3w₁
$Θ$	1/5w₁	1/3w₁	1

表10

表11

专家2认知判断矩阵

专家2	$F 1$	$F 2$	$Θ$
$F 1$	1	0	4w₂
$F 2$	0	1	2w₂
$Θ$	1/4w₂	1/2w₂	1

表11

表12

专家3认知判断矩阵

专家3	$F 1$	${F 2, F 3}$	$Θ$
$F 1$	1	0	4w₃
${F 2, F 3}$	0	1	6w₃
$Θ$	1/4w₃	1/6w₃	1

表12

表13

专家4认知判断矩阵

专家4	$F 1$	$F 3$	$Θ$
$F 1$	1	0	5w₄
$F 3$	0	1	2w₄
$Θ$	1/5w₄	1/2w₄	1

表13

表14

专家综合先验知识

编号	约束	编号	约束
1	$P T H T \| T A I (1 \| 1) ≈ 0.593 3$	12	$P T P T \| T A I (3 \| 2) ≈ 0.201 6$
2	$P T H T \| T A I (2 \| 1) ≈ 0.117 9$	13	$P O D \| T A I (1 \| 1) ≈ 0.746 6$
3	$P T H T \| T A I (3 \| 1) ≈ 0.288 8$	14	$P O D \| T A I (2 \| 1) ≈ 0.151 3$
4	$P T H T \| T A I (1 \| 2) ≈ 0.189 4$	15	$P O D \| T A I (3 \| 1) ≈ 0.102 2$
5	$P T H T \| T A I (2 \| 2) ≈ 0.692 5$	16	$P O D \| T A I (1 \| 2) ≈ 0.097 8$
6	$P T H T \| T A I (3 \| 2) ≈ 0.118 1$	17	$P O D \| T A I (2 \| 2) ≈ 0.266 8$
7	$P T P T \| T A I (1 \| 1) ≈ 0.591 4$	18	$P O D \| T A I (3 \| 2) ≈ 0.635 4$
8	$P T P T \| T A I (2 \| 1) ≈ 0.302 6$	19	$P F C C \| T A I (1 \| 1) ≈ 0.903 7$
9	$P T P T \| T A I (3 \| 1) ≈ 0.106 1$	20	$P F C C \| T A I (2 \| 1) ≈ 0.096 3$
10	$P T P T \| T A I (1 \| 2) ≈ 0.417 5$	21	$P F C C \| T A I (1 \| 2) ≈ 0.209 8$
11	$P T P T \| T A I (2 \| 2) ≈ 0.380 9$	22	$P F C C \| T A I (2 \| 2) ≈ 0.790 2$

表14

表15

参数约束集合

编号	约束
1	$P (T H T = 1 \| T H I = 1) > P (T H T = 3 \| T A I = 1) > P (T H T = 2 \| T A I = 1)$
2	$P (T H T = 2 \| T H I = 2) > P (T H T = 1 \| T A I = 2) > P (T H T = 3 \| T A I = 2)$
3	$P (T P T = 1 \| T H I = 1) > P (T P T = 2 \| T A I = 1) > P (T P T = 3 \| T A I = 1)$
4	$P (T P T = 1 \| T H I = 2) > P (T P T = 2 \| T A I = 2) > P (T P T = 3 \| T A I = 2)$
5	$P (O D = 1 \| T A I = 1) > P (O D = 2 \| T A I = 1) > P (O D = 3 \| T A I = 1)$
6	$P (O D = 3 \| T A I = 2) > P (O D = 2 \| T A I = 2) > P (O D = 1 \| T A I = 2)$
7	$P (F C C = 1 \| T A I = 1) > P (F C C = 2 \| T A I = 1)$
8	$P (F C C = 2 \| T A I = 2) > P (F C C = 1 \| T A I = 2)$
9	$P (T F S = 1 \| T P T = 1) > P (T F S = 2 \| T A I = 1)$
10	$P (T F S = 1 \| T P T = 2) > P (T F S = 2 \| T A I = 2)$
11	$P (T F S = 2 \| T P T = 3) > P (T F S = 1 \| T A I = 3)$

表15

表16

BN参数学习结果

节点	状态	参数学习结果
$T A I$	$T A I = 1$	$T H T 123 = (0.561 0, 0.061 0, 0.378 0)$
		$T P T 123 = (0.581 3, 0.313 0, 0.105 7)$
		$O D 123 = (0.723 6, 0.162 6, 0.113 8)$
		$F C C 12 = (0.894 3, 0.105 7)$
	$T A I = 2$	$T H T 123 = (0.232 3, 0.622 0, 0.145 7)$
		$T P T 123 = (0.409 4, 0.421 3, 0.169 3)$
		$O D 123 = (0.133 9, 0.259 8, 0.606 3)$
		$F C C 12 = (0.228 3, 0.771 7)$
$T P T$	$T P T = 1$	$T F S 12 = (0.866 4, 0.133 6)$
	$T P T = 2$	$T F S 12 = (0.608 7, 0.391 3)$
	$T P T = 3$	$T F S 12 = (0.449 3, 0.550 7)$

表16

图8

图9

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认知程度	数值比率
极重要	6
极重要-重要	5
重要	4
重要-较重要	3
较重要	2

编号	约束
1	$P (S = 0 \| C = 0) > P (S = 1 \| C = 0)$
2	$P (S = 0 \| C = 1) > P (S = 1 \| C = 1)$
3	$P (R = 0 \| C = 0) > P (R = 1 \| C = 0)$
4	$P (R = 0 \| C = 1) > P (R = 1 \| C = 1)$
5	$P (W = 0 \| S = 0, R = 0) > P (W = 1 \| S = 0, R = 0)$
6	$P (W = 0 \| S = 0, R = 1) > P (W = 1 \| S = 0, R = 1)$
7	$P (W = 0 \| S = 1, R = 0) > P (W = 1 \| S = 1, R = 0)$
8	$P (W = 0 \| S = 1, R = 1) > P (W = 1 \| S = 1, R = 1)$

编号	TAI	THT	TPT	OD	FCC	TFS
1	2	1	1	2	2	1
2	1	1	1	1	1	1
3	2	3	3	3	2	1
4	1	1	2	2	1	2
5	2	3	1	1	1	1
6	2	1	1	1	2	1
7	1	1	2	1	1	2
8	1	2	1	1	1	1
9	2	3	2	3	2	2
10	1	1	1	2	1	1

编号	约束	编号	约束
1	$P T H T \| T A I (1 \| 1) ≈ 0.593 3$	12	$P T P T \| T A I (3 \| 2) ≈ 0.201 6$
2	$P T H T \| T A I (2 \| 1) ≈ 0.117 9$	13	$P O D \| T A I (1 \| 1) ≈ 0.746 6$
3	$P T H T \| T A I (3 \| 1) ≈ 0.288 8$	14	$P O D \| T A I (2 \| 1) ≈ 0.151 3$
4	$P T H T \| T A I (1 \| 2) ≈ 0.189 4$	15	$P O D \| T A I (3 \| 1) ≈ 0.102 2$
5	$P T H T \| T A I (2 \| 2) ≈ 0.692 5$	16	$P O D \| T A I (1 \| 2) ≈ 0.097 8$
6	$P T H T \| T A I (3 \| 2) ≈ 0.118 1$	17	$P O D \| T A I (2 \| 2) ≈ 0.266 8$
7	$P T P T \| T A I (1 \| 1) ≈ 0.591 4$	18	$P O D \| T A I (3 \| 2) ≈ 0.635 4$
8	$P T P T \| T A I (2 \| 1) ≈ 0.302 6$	19	$P F C C \| T A I (1 \| 1) ≈ 0.903 7$
9	$P T P T \| T A I (3 \| 1) ≈ 0.106 1$	20	$P F C C \| T A I (2 \| 1) ≈ 0.096 3$
10	$P T P T \| T A I (1 \| 2) ≈ 0.417 5$	21	$P F C C \| T A I (1 \| 2) ≈ 0.209 8$
11	$P T P T \| T A I (2 \| 2) ≈ 0.380 9$	22	$P F C C \| T A I (2 \| 2) ≈ 0.790 2$

编号	约束
1	$P (T H T = 1 \| T H I = 1) > P (T H T = 3 \| T A I = 1) > P (T H T = 2 \| T A I = 1)$
2	$P (T H T = 2 \| T H I = 2) > P (T H T = 1 \| T A I = 2) > P (T H T = 3 \| T A I = 2)$
3	$P (T P T = 1 \| T H I = 1) > P (T P T = 2 \| T A I = 1) > P (T P T = 3 \| T A I = 1)$
4	$P (T P T = 1 \| T H I = 2) > P (T P T = 2 \| T A I = 2) > P (T P T = 3 \| T A I = 2)$
5	$P (O D = 1 \| T A I = 1) > P (O D = 2 \| T A I = 1) > P (O D = 3 \| T A I = 1)$
6	$P (O D = 3 \| T A I = 2) > P (O D = 2 \| T A I = 2) > P (O D = 1 \| T A I = 2)$
7	$P (F C C = 1 \| T A I = 1) > P (F C C = 2 \| T A I = 1)$
8	$P (F C C = 2 \| T A I = 2) > P (F C C = 1 \| T A I = 2)$
9	$P (T F S = 1 \| T P T = 1) > P (T F S = 2 \| T A I = 1)$
10	$P (T F S = 1 \| T P T = 2) > P (T F S = 2 \| T A I = 2)$
11	$P (T F S = 2 \| T P T = 3) > P (T F S = 1 \| T A I = 3)$