基于多项分布的弹药多批次试验命中概率估计

doi:10.12382/bgxb.2022.0490

摘要/Abstract

摘要：

弹药命中概率试验通常分多个批次进行,某一批次试验结束后会对弹药物理性能进行改进,各批次试验命中概率呈现动态变化特点。每批次试验前会获取到该批次弹药命中概率仿真实验信息,充分利用各批次射击试验信息与仿真实验信息是弹药命中概率估计的重点。考虑到弹药命中目标不同区域造成的毁伤程度不同,对原有二项分布命中概率试验进行改进,改用多项分布进行描述。引入体系贡献度衡量各批次试验对弹药命中概率估计的影响程度,并结合贝叶斯方法对各批次试验信息进行融合,通过构建顺序约束关系鉴定弹药命中性能改进效果,并提出基于多项分布的弹药多批次试验命中概率估计方法。研究结果表明,该方法相比二项分布方法能够细致描述弹药命中性能,并科学融合各批次射击试验信息与仿真实验信息,为弹药命中概率估计提供借鉴。

关键词: 弹药, 命中概率, 多批次试验, 多项分布, 贝叶斯推断, 体系贡献度

Abstract:

Ammunition hit probability tests are usually carried out in multiple batches. With each test batch, the physical properties of ammunition evolve, influencing hit probabilities dynamically. Before each batch, simulated ammunition hit probability information is obtained. Effectively utilizing the shooting tests information and simulation data of each batch is key to hit probability estimation. In addition, considering the different degrees of damage caused by ammunition hitting different areas of the target, the original binomial distribution hit probability test is improved and described by multinomial distribution. System contribution is introduced to measure the impact of each batch of tests on the estimation of the ammunition hit probability, and the Bayesian method is used to fuse the test data of each batch. The ammunition hit property improvement is identified by constructing sequence constraint relation. Finally, the estimation of ammunition hit probability in multiple batch tests based on multinomial distribution is proposed. The example shows that the method can describe the hit properties of ammunition in detail compared with the binomial distribution method. It can also scientifically integrate the information of each batch shooting tests and simulation tests, providing reference for the estimation of the hit probability.

Key words: ammunition, hit probability, multiple batches tests, multinomial distribution, Bayesian inference, system contribution

中图分类号:

E917

刘昊邦, 史宪铭, 郝冰, 姜永超. 基于多项分布的弹药多批次试验命中概率估计[J]. 兵工学报, 2023, 44(10): 3156-3164.

LIU Haobang, SHI Xianming, HAO Bing, JIANG Yongchao. Estimation of Ammunition Hit Probability in Multiple-Batch Tests Using Multinomial Distribution[J]. Acta Armamentarii, 2023, 44(10): 3156-3164.

图/表 8

图1 多批次命中概率试验信息融合过程

Fig.1 Information fusion process of multiple batches hit probability trials

表1 多批次试验弹药命中概率信息

Table 1 Ammunition hit probabilities in multiple-batch tests

批次	x⁽ⁱ⁾	α⁽ⁱ⁾
初始批次	( $3322$ )	( $1.2 1 0.8 0.75$ )
第2批次	( $2422$ )	( $1.5 2.8 2 1.8$ )
第3批次	( $1243$ )	( $1 2.4 3.5 2.8$ )

表1 多批次试验弹药命中概率信息

Table 1 Ammunition hit probabilities in multiple-batch tests

批次	x⁽ⁱ⁾	α⁽ⁱ⁾
初始批次	( $3322$ )	( $1.2 1 0.8 0.75$ )
第2批次	( $2422$ )	( $1.5 2.8 2 1.8$ )
第3批次	( $1243$ )	( $1 2.4 3.5 2.8$ )

表2 先验信息专家隶属度打分

Table 2 Prior information membership score in expert interview

专家序号	$ω δ 1 d$	$υ δ 1 d$	$ω δ 2 d$	$υ δ 2 d$
1	0.5	0.3	0.4	0.3
2	0.6	0.3	0.7	0.2
3	0.8	0.2	0.5	0.4
4	0.4	0.4	0.5	0.3
5	0.6	0.4	0.6	0.3
6	0.7	0.3	0.6	0.4

表2 先验信息专家隶属度打分

Table 2 Prior information membership score in expert interview

专家序号	$ω δ 1 d$	$υ δ 1 d$	$ω δ 2 d$	$υ δ 2 d$
1	0.5	0.3	0.4	0.3
2	0.6	0.3	0.7	0.2
3	0.8	0.2	0.5	0.4
4	0.4	0.4	0.5	0.3
5	0.6	0.4	0.6	0.3
6	0.7	0.3	0.6	0.4

图2 初始批次命中概率参数迭代迹图

Fig.2 Iteration trace graph of initial batch hit probability parameters

图3 第2批次命中概率参数迭代迹图

Fig.3 Iteration trace graph of the second-batch hit probability parameters

图4 第3批次命中概率参数迭代迹图

Fig.4 Iteration trace graph of the third-batch hit probability parameters

图5 各批次弹药命中概率参数概率密度函数图

Fig.5 Probability density function diagram of ammunition hit probability parameters of each batch

表3 各批次弹药命中概率参数贝叶斯统计分析

Table 3 Bayesian statistical analysis of ammunition hit probability parameters for each batch

P⁽ⁱ⁾	初始批次试验贝叶斯估计		第2批次试验贝叶斯估计		第3批次试验贝叶斯估计
P⁽ⁱ⁾	均值	方差	均值	方差	均值	方差
$P 1 (i)$	0.305	0.2256	0.231	0.1832	0.124	0.0847
$P 2 (i)$	0.291	0.2197	0.344	0.2447	0.251	0.1993
$P 3 (i)$	0.204	0.1556	0.218	0.1646	0.343	0.2443
$P 4 (i)$	0.20	0.1544	0.207	0.1573	0.282	0.2123

表3 各批次弹药命中概率参数贝叶斯统计分析

Table 3 Bayesian statistical analysis of ammunition hit probability parameters for each batch

P⁽ⁱ⁾	初始批次试验贝叶斯估计		第2批次试验贝叶斯估计		第3批次试验贝叶斯估计
P⁽ⁱ⁾	均值	方差	均值	方差	均值	方差
$P 1 (i)$	0.305	0.2256	0.231	0.1832	0.124	0.0847
$P 2 (i)$	0.291	0.2197	0.344	0.2447	0.251	0.1993
$P 3 (i)$	0.204	0.1556	0.218	0.1646	0.343	0.2443
$P 4 (i)$	0.20	0.1544	0.207	0.1573	0.282	0.2123

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