Design of Bayesian acceptance scheme for missile hit accuracy based on multinomial distribution
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摘要:
导弹命中精度验收试验是检验导弹命中性能的重要环节。针对现有GJB3400—1998中的二项分布命中精度验收试验方法难以细致描述导弹精度性能问题，考虑点目标区域对其作战效能影响，将命中精度内涵由将目标看作毁伤效果具有同一性的整体，拓展为导弹命中不同区域会产生不同等级毁伤效果的多区域目标，并将导弹命中精度试验采用多项分布表示。同时在验收试验中采用贝叶斯方法并结合Dempster-Shafer(D-S)证据理论可融合多源先验信息，提出一种基于多项分布的导弹命中精度贝叶斯验收方案设计方法。示例结果表明：所提方法相比GJB3400—1998中的方法能够从命中不同重要区域的多个标准检验导弹精度性能，有利于帮助使用方得到命中精度更为可靠的导弹，并充分利用命中精度先验信息，有效降低验收双方风险，为导弹命中精度鉴定和验收设计提供借鉴。
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关键词:
- 导弹命中精度 /
- 验收方案 /
- 多项分布 /
- 贝叶斯 /
- Dempster-Shafer证据理论
Abstract:The acceptance test of missile hit accuracy is an important step in verifying missile hit performance. Since the existing binomial distribution hit accuracy acceptance test method in GJB3400—1998 makes it difficult to describe the precision performance of the missile, the impact of the point target regions on its combat effectiveness was considered, and the hit accuracy was redefined as follows: The target was not regarded as the whole with the same damage effect but the multi-area target with different damage effects in different areas hit by the missile. In addition, the missile hit accuracy test was represented by a multinomial distribution. At the same time, the Bayesian method and the Dempster-Shafer (D-S) evidence theory could be used in the acceptance test to integrate multi-source prior information, and the Bayesian acceptance scheme design method of missile hit accuracy based on multinomial distribution was proposed. The example results show that compared with the method in GJB3400—1998, this method can test the accuracy performance of missiles from multiple criteria of hitting different important areas, which is beneficial to help users obtain missiles with more reliable hit accuracy and make full use of the prior information of hit accuracy, thus effectively reducing the risk of both sides involving in the acceptance. This study can provide a reference for the identification and acceptance design of missile hit accuracy.
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图 1 $ n{\text{ = }}15 $时双方风险随$ {m_j} $的变化情况
Figure 1. Variation of risk of both sides with $ {m_j} $ when $ n{\text{ = }}15 $
图 2 $ m_j^ * $给定时双方风险随$ n $的变化情况
Figure 2. Variation of risk of both sides with $ n $ when $ m_j^ * $ is given
表 1 点目标重要性区域划分
Table 1. Point target importance area division
区域划分 区域概况 无影响区域 区域距离目标较远，当导弹命中这些区域时，未能对目标作战效能产生影响 轻度影响区域 使目标作战效能受到轻度影响的区域，当导弹命中这些区域时，对点目标产生轻度毁伤 中度影响区域 使目标作战效能受到中度影响的区域，当导弹命中这些区域时，对点目标产生中度毁伤 重度影响区域 使目标作战效能受到重度影响的区域，当导弹命中这些区域时，能够对点目标产生摧毁 
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表 2 先验信息概率赋值
Table 2. Probability assignment of prior information
辨识框架 专家知识信息$ m({B_i}) $ 仿真试验信息$ m({C_i}) $ $ {A_1} $ $ m({B_1}) $ $ m({C_1}) $ $ {A_2} $ $ m({B_2}) $ $ m({C_2}) $ $ \vdots $ $ \vdots $ $ \vdots $ $ {A_N} $ $ m({B_N}) $ $ m({C_N}) $
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表 3 $ n{\text{ = 15}} $时验收方案设计
Table 3. Acceptance scheme design when $ n{\text{ = 15}} $
区域标准 $ m_j^ * $的取值范围 $ m_j^ * $的最优值 $ n - m_j^ * $ 轻度区域标准 1,2 1 14 中度区域标准 4,5,6 5 10 重度区域标准 7,8,9,10 9 6
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表 4 $ m_j^ * $给定时验收方案设计
Table 4. Design of acceptance scheme when $ m_j^ * $ is given
区域标准 $ m_j^ * $ $ n $的取值范围 $ n $的最优值 轻度区域标准 2 19,20,21,22,23,24,25 21 中度区域标准 5 13,14,15,16,17,18,19 16 重度区域标准 9 15,16,17 16
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