Bayesian Estimation of Ammunition Dispersion Parameters Under Small-Sample Multi-Batch Growth Tests

Hu Cenyu; Shi Xianming; Wang Yabin; Chang Chao; Jiang Yu; Gong Yingguang

doi:10.12382/bgxb.2026.0384

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Bayesian Estimation of Ammunition Dispersion Parameters Under Small-Sample Multi-Batch Growth Tests

更新时间：2026-09-08

- Bayesian Estimation of Ammunition Dispersion Parameters Under Small-Sample Multi-Batch Growth Tests
- Acta Armamentarii (2026)
- 作者机构：
  
  陆军工程大学石家庄校区, 河北石家庄050004
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2026.0384
  CLC： TJ301
- Received：27 April 2026，
  
  Revised：2026-09-03，
  
  Accepted：10 June 2026，
- 稿件说明：
移动端阅览
Hu Cenyu, Shi Xianming, Wang Yabin, et al. Bayesian Estimation of Ammunition Dispersion Parameters Under Small-Sample Multi-Batch Growth Tests[J/OL]. Acta Armamentarii, 2026.
DOI：

Hu Cenyu, Shi Xianming, Wang Yabin, et al. Bayesian Estimation of Ammunition Dispersion Parameters Under Small-Sample Multi-Batch Growth Tests[J/OL]. Acta Armamentarii, 2026. DOI： 10.12382/bgxb.2026.0384.

摘要

针对弹药多批次迭代研发过程中小样本试验数据稀缺、历史信息利用不充分导致评估精度低的难题，提出一种融合多批次增长特性的贝叶斯评估方法。该方法基于弹着点二维正态散布规律构建多等级毁伤概率模型，引入弹药性能单调递增顺序约束，采用正态-逆伽马共轭先验推导多批次参数联合后验分布，设计带约束的Gibbs抽样算法实现多批次散布参数联合估计。示例分析表明，在每批次仅10发条件下，各批次参数估计均满足顺序约束，核心散布参数绝对误差最低为0.0080m。第3批轻度及以上累积毁伤概率达96.62%，各等级毁伤概率随批次递增，与性能提升规律一致，可为弹药研发迭代与作战毁伤概率评估提供可靠支撑。

Abstract

To address the challenge of low evaluation accuracy caused by scarce small-sample test data and insufficient utilization of historical information in the multi-batch iterative development of ammunition

a Bayesian evaluation method integrating multi-batch growth characteristics is proposed. Based on the two-dimensional normal dispersion law of impact points

a multi-level damage probability model is constructed

a monotonic increasing order constraint on ammunition performance is introduced

a normal-inverse gamma conjugate prior is adopted to derive the joint posterior distribution of multi-batch parameters

and a constrained Gibbs sampling algorithm is designed to realize the joint estimation of multi-batch dispersion parameters. Numerical examples show that

under the condition of only 10 rounds per batch

the parameter estimates of all batches satisfy the order constraints

with a minimum absolute error of 0.0080 m for the core dispersion parameters; the cumulative damage probability of mild or above for the third batch reaches 96.62%

and the damage probabilities at all levels increase monotonically with the batch number

consistent with the physical law of performance improvement. The proposed method can provide reliable support for the iterative development of ammunition and combat damage probability evaluation.

关键词

Keywords

references

刘彦 , 柳明 , 吕中杰 , 等 . 基于科学知识图谱的弹药毁伤评估技术发展现状与趋势研究 [J ] . 北京理工大学学报 , 2024 , 44 ( 3 ): 219 - 230 .

LIU Y , LIU M , LYU Z J , et al . Research on the Develop ment Status and Trend of Ammunition Damage Assess ment Technology Based on Mapping Knowledge Do mains [J ] . Transactions of Beijing Institute of Technology , 2024 , 44 ( 3 ): 219 - 230 .

徐豫新 , 蔡子雷 , 吴巍 , 等 . 弹药毁伤效能评估技术研究现状与发展趋势 [J ] . 北京理工大学学报 , 2021 , 41 ( 6 ): 569 - 578 .

XU Y X , CAI Z L , WU W , et al . Current Research and Development of Ammunition Damage Effect Assessment Technology [J ] . Transactions of Beijing Institute of Technology , 2021 , 41 ( 6 ): 569 - 578 .

王向民 , 王军 , 谢杰涛 , 等 . 基于射击误差状态方程的高炮毁伤概率建模 [J ] . 上海交通大学学报 , 2020 , 54 ( 9 ): 961 − 966 .

WANG X M , WANG J , XIE J T , et al . A damage probability calculation model based on state equation of firing error for anti−aircraft artillery [J ] . Journal of Shanghai Jiaotong University , 2020 , 54 ( 9 ): 961 − 966 .

田浩成 , 卢芳云 , 李志斌 , 等 . 基于改进毁伤矩阵的人员目标毁伤效能评估 [J ] . 兵器装备工程学报 , 2022 , 43 ( 7 ): 101 – 108 .

TIAN H C , LU F Y , LI Z B , et al . Evaluation of damage effectiveness of personnel target based on improved damage matrix [J ] . Journal of Ordnance Equipment Engineering , 2022 , 43 ( 7 ): 101 – 108 .

CHUSILP P , CHARUBHUN W , KOANANTACHAI P . Monte Carlo simulations of weapon effectiveness using Pk matrix and Carleton damage function [J ] . International Journal of Applied Physics and Mathematics , 2014 , 4 ( 4 ): 280 - 285 .

陈青华 , 姜月秋 , 艾宁 , 等 . 舰炮弹药对典型舰船目标毁伤效能研究 [J ] . 舰船科学技术 , 2022 , 44 ( 1 ): 169 - 173 .

CHEN Q H , JIANG Y Q , AI N , et al . Research on damage effectiveness of naval gun ammunition on typical ship target [J ] . Ship Science and Technology , 2022 , 44 ( 1 ): 169 - 173 .

王执权 , 魏继锋 , 王树山 , 等 . 一种双模战斗部毁伤效能评估研究 [J ] . 兵工学报 , 2016 , 37 ( S1 ): 24 - 29 .

WANG Z Q , WEI J F , WANG S S , et al . Research on damage effectiveness evaluation of a dual-mode warhead [J ] . Acta Armamentarii , 2016 , 37 ( S1 ): 24 - 29 .

李元温 , 玉全 . 定向战斗部毁伤效能评估 [J ] . 兵工学报 , 2021 , 42 ( S1 ): 1 - 10 .

LI Y W , YU Q . Evaluation of damage effectiveness of directional warhead [J ] . Acta Armamentarii , 2021 , 42 ( S1 ): 1 - 10 .

李伟 , 方洋旺 , 王晓云 , 等 . 空地导弹对飞机掩蔽库的毁伤效能评估 [J ] . 火力与指挥控制 , 2016 , 41 ( 5 ): 52 - 61 .

LI W , FANG Y W , WANG X Y , et al . Evaluation of the destructive effectiveness of air-to-ground missiles on aircraft shelters [J ] . Fire Control &Command Control , 2016 , 41 ( 5 ): 52 - 61 .

李康 , 史宪铭 , 李广宁 , 等 . 基于正态-逆伽马分布的反巡航导弹命中 [J ] . 系统工程与电子技术 , 2022 , 44 ( 8 ): 2621 − 2627 .

LI K , SHI X M , LI G N , et al . Estimation method of hit probability of anti-cruise missile based on normal-inverse Gamma distribution [J ] . Systems Engineering and Electronics , 2022 , 44 ( 8 ): 2621 - 2627 .

刘昊邦 , 史宪铭 , 赵美 , 等 . 基于正态-逆威沙特分布的地空导弹命中概率贝叶斯估计 [J ] . 兵工学报 , 2024 , 45 ( 1 ): 339 − 348 .

LIU H B , SHI X M , ZHAO M , et al . Bayesian estimation of surface-to-air missile hit probability based on normal-inverse Wishart distribution [J ] . Acta Armamentarii , 2024 , 45 ( 1 ): 339 - 348 .

LI H S , ZHANG X Q . ZHANG X W. Calculation Model and Method of Target Damage Efficiency Assessment Based on Warhead Fragment Dispersion [J ] . IEEE Trans. on Instrumentation and Measurement, 2020 , 70 : 1001308 .

LIU H B , SHI X M . Damage effectiveness calculation of hitting targetswith ammunition based on Bayesian multinomial distribution [J ] . Symmetry , 2022 , 14 ( 5 ): 892 .

SONG M C , LYU X , TAN S H , et al . The damage level assessment of equipment function based on Bayesian networks and transfer learning [J ] . AIP Advances , 2024 , 14 ( 1 ): 015158 .

ZHANG X W , LI H S , HU J . Research on target damage evaluation and optimization algorithm based on random incomplete information [J ] . AIP Advances , 2024 , 14 ( 2 ): 025330 .

LI H S , HAO Y , ZHANG X Q . Numerical calculation method of target damage effectiveness evaluation under uncertain information of warhead fragments [J ] . Mathematics , 2022 , 10 ( 10 ): 1688 .

XUE J Y , LI H S , ZHANG X Q . A damage effectiveness evaluation approach of warhead fragment group on missile target based on intuitionistic fuzzy neural network [J ] . Journal of Mechanical Science and Technology , 2024 , 38 ( 9 ): 4765 - 4780 .

赵汝东 , 史宪铭 , 姜广胜 , 等 . 基于先验信息的弹药消耗量统计推断方法 [J ] . 指挥控制与仿真 , 2019 , 41 ( 6 ): 59 - 62 .

ZHAO R D , SHI X M , JIANG G S , et al . A statistical inference method of ammunition consumption based on a priori information [J ] . Command Control and Simulation , 2019 , 41 ( 6 ): 59 - 62 .

ZHAO R D , SHI X M , WANG Q , et al . Bayesian inference for ammunition demand based on the Gompertz distribution [J ] . Journal of Systems Engineering and Electronics , 2020 , 31 ( 3 ): 567 - 577 .

LIU H B , SHI X M , CHEN X J , et al . Bayesian inference of ammunition consumption based on normal-inverse gamma distribution [J ] . Discrete Dynamics in Nature and Society , 2022 , 14 ( 2 ): 56 - 67 .

LI Y , ZHAO R D , SHI X M , et al . Simulation of ammunition consumption conversion factor considering damage degree [J ] . Journal of Physics: Conference Series , 2020 , 1533 ( 2 ): 022127 .

ANDRADE J , RATHIE P . Exact posterior distribution for nonconjugate Pareto models [J ] . Advances in Computational Mathematics , 2023 , 49 ( 3 ): 35 .

DAS R , PRADHAN B . Bayesian reliability acceptance sampling plan with optional warranty under hybrid censoring [J ] . Quality and Reliability Engineering International , 2024 , 41 ( 2 ): 872 - 896 . DOI: 10.1002/qre.3684 http://dx.doi.org/10.1002/qre.3684 .

WANG H Y , MOTEN C , DRIELS M , et al . Explicit exact solution of damage probability for multiple weapons against a unitary target [J ] . American Journal of Operations Research , 2016 , 6 ( 6 ): 450 – 467 .

刘昊邦 , 陈童 , 胡涛 , 等 . 基于多批次增长试验的舰空导弹命中概率贝叶斯估计 [J ] . 系统工程与电子技术 , 2025 , 47 ( 3 ): 871 - 882 .

LIU H B , CHEN T , HU T , et al . Bayesian estimation of ship-to-air missile hit probability based on multi-batch growth tests [J ] . Systems Engineering and Electronics , 2025 , 47 ( 3 ): 871 - 882 .

胡岑语 , 史宪铭 . 面向多批次改进的防空弹药期望消耗优化 [J/OL ] . 北京航空航天大学学报 , 1 - 19 [ 2026-04-27 ] .

Hu C Y , Shi X M . Optimization of Expected Consumption of Air Defense Ammunition for Multi-Batch Improvement [J/OL ] . Journal of Beijing University of Aeronautics and Astronautics , 1 - 19 [ 2026-04-27 ] .

闫志强 , 蒋英杰 , 谢红卫 . 基于顺序约束的命中概率多批次试验统计评定方法 [J ] . 宇航学报 , 2010 , 31 ( 4 ): 1206 - 1211 .

YAN Z Q , JIANG Y J , XIE H W . Statistical evaluation method of hit probability for multi-batch tests based on sequence constraints [J ] . Journal of Astronautics , 2010 , 31 ( 4 ): 1206 - 1211 .

CAI M Y , VAN B S , VINK G . Joint distribution properties of fully conditional specification under the normal linear model with normal inverse-Gamma priors [J ] . Scientific Reports , 2023 , 13 ( 1 ): 33 - 46 .

JUN K , SHINTARO H . Approximate Gibbs sampler for Bayesian Huberized lasso [J ] . Journal of Statistical Computation and Simulation , 2023 , 93 ( 1 ): 55 - 63 .

CIVEK B C , ERTIN E . Bayesian sparse blind deconvolution using MCMC methods based on normal-inverse-gamma prior [J ] . IEEE Transactions on Signal Processing , 2022 , 70 ( 6 ): 1256 - 1269 .

刘昊邦 , 胡涛 , 陈童 , 等 . Dirichlet分布的导弹命中精度贝叶斯估计 [J ] . 国防科技大学学报 , 2025 , 47 ( 3 ): 119 - 127 .

LIU H B , HU T , CHEN T , et al . Bayesian estimation o missile hit accurary for Dirichlet distribution [J ] . Joumal of National University of Defense Technology , 2025 , 47 ( 3 ): 119 - 127 .

尹鹏 , 黄风雷 , 石科仁 , 等 . 基于改进粒子群优化算法的多弹打击面目标瞄准点优化方法 [J ] . 兵工学报 , 2025 , 46 ( 09 ): 40 - 50 .

Yin P , Huang F L , Shi K R , et al . An Optimization Method for Aiming Points of Multiple Projectiles Attacking Area Target Based on Improved Particle Swarm Optimization Algorithm [J ] . Acta Armamentarii , 2025 , 46 ( 09 ): 40 - 50 .

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