基于特小子样下弹药命中概率的贝叶斯改进算法

doi:10.12305/j.issn.1001-506X.2026.04.20

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (4): 1322-1330.doi: 10.12305/j.issn.1001-506X.2026.04.20

• 系统工程 • 上一篇

基于特小子样下弹药命中概率的贝叶斯改进算法

王亚龙¹(), 史宪铭¹^,*, 刘昭¹, 刘昊邦², 夏伟³

1. 陆军工程大学石家庄校区，河北石家庄 050003
2. 海军工程大学管理工程与装备经济系，湖北武汉 430033
3. 陆军步兵学院石家庄校区，河北石家庄 050003

收稿日期:2024-10-18 修回日期:2025-04-10 接受日期:2026-03-23 出版日期:2025-06-11 发布日期:2025-06-11
通讯作者: 史宪铭 E-mail:jsydb@qq.com
作者简介:王亚龙（1989—），男，助理工程师，硕士，主要研究方向为系统工程、消耗预测
刘　昭（1991—），男，讲师，硕士，主要研究方向为管理科学与工程
刘昊邦（1998—），男，博士研究生，主要研究方向为系统工程、装备管理与保障
夏　伟（1984—），女，教授，博士，主要研究方向为装备供应保障理论
基金资助:
河北省重点科研项目；河北省研究生资助课题项目资助课题

Bayesian improved algorithm for estimating ammunition hit probability under ultra-small subsample

Yalong WANG¹(), Xianming SHI¹^,*, Zhao LIU¹, Haobang LIU², Wei XIA³

1. Shijiazhuang Campus of Army Engineering University, Shijiazhuang 050003, China
2. Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan 430033，China
3. Shijiazhuang Campus of Army Infantry College, Shijiazhuang 050003, China

Received:2024-10-18 Revised:2025-04-10 Accepted:2026-03-23 Online:2025-06-11 Published:2025-06-11
Contact: Xianming SHI E-mail:jsydb@qq.com

摘要/Abstract

摘要：

针对传统方法在特小子样下对高性能弹药命中概率的计算存在精度不高的问题，提出了一种基于贝叶斯假设检验的改进算法。在弹药分布落点为圆散布假设的前提下，通过分析弹药脱靶量的边缘分布列出命中概率的计算公式，并采取贝叶斯假设检验的方法，在充分利用先验信息的同时，采用间接、直接两种算法计算出假设检验参数的累积分布函数，在满足指定检验水平所要求的置信区间的前提下，估计出弹药落点密集度。仿真结果表明，所提算法与传统方法相比极大地简化了计算步骤、提升了计算结果的准确性，为计算特小子样下的弹药命中概率提供了参考依据。

关键词: 特小子样, 贝叶斯推断, 弹药命中概率, 落点密集度, 假设检验

Abstract:

Addressing the issue of low accuracy in calculating the hit probability of high-performance ammunition in ultra-small subsample using traditional methods, an improved algorithm based on Bayesian hypothesis testing is proposed. Under the assumption that the distribution of ammunition impact points follows a circular dispersion, the calculation formula for the hit probability is derived by analyzing the marginal distribution of the ammunition miss distance. By utilizing Bayesian hypothesis testing, the cumulative distribution function of the hypothesis testing parameters is calculated using both indirect and direct algorithms while fully utilizing prior information. The ammunition impact point density is estimated under the premise of satisfying the confidence interval required by the specified testing level. Simulation results show that the proposed algorithm significantly simplifies the calculation steps and improves the accuracy of the calculation results compared to traditional methods, providing a reference for calculating the hit probability of ammunition under ultra-small subsample.

Key words: ultra-small subsample, Bayesian inference, ammunition hit probability, dispersion density, hypothesis testing

中图分类号:

TJ 413

王亚龙, 史宪铭, 刘昭, 刘昊邦, 夏伟. 基于特小子样下弹药命中概率的贝叶斯改进算法[J]. 系统工程与电子技术, 2026, 48(4): 1322-1330.

Yalong WANG, Xianming SHI, Zhao LIU, Haobang LIU, Wei XIA. Bayesian improved algorithm for estimating ammunition hit probability under ultra-small subsample[J]. Systems Engineering and Electronics, 2026, 48(4): 1322-1330.

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序号	脱靶量r_i/m
Y₁	5.732
Y₂	4.683
Y₃	5.421

序号	脱靶量r_i/m
X₁₁	4.589
X₁₂	4.432
X₁₃	5.514
X₁₄	6.023
X₁₅	5.061

组别	$ {\sigma }_{i}{}^{2} $	组别	$ {\sigma }_{i}{}^{2} $
X₁	0.341	X₁₁	0.827
X₂	0.878	X₁₂	0.286
X₃	0.539	X₁₃	0.730
X₄	1.259	X₁₄	1.319
X₅	0.580	X₁₅	0.528
X₆	0.538	X₁₆	1.062
X₇	0.613	X₁₇	0.569
X₈	0.891	X₁₈	2.645
X₉	0.354	X₁₉	0.639
X₁₀	6.280	X₂₀	1.421

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基于特小子样下弹药命中概率的贝叶斯改进算法

Bayesian improved algorithm for estimating ammunition hit probability under ultra-small subsample

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