基于GSPN的导弹多层级测试性需求建模与指标评估

doi:10.12305/j.issn.1001-506X.2021.04.14

摘要/Abstract

摘要：

针对目前导弹测试性需求建模尚未成熟, 开展测试性需求分析难度较高的问题, 提出一种基于广义随机Petri网(generalized stochastic Petri net, GSPN)的测试性需求建模方法。在分析导弹结构的基础上对导弹测试性需求问题进行了建模, 给出导弹两级GSPN模型, 深入分析其导弹系统的故障检测及维修过程。根据GSPN模型同构于嵌入马尔可夫链(embedded Markov chain, EMC), 以实存状态集和消失状态集表征库所变迁, 采用同构法对测试性指标进行求解。将多层级GSPN模型分解化简, 减少状态空间数量的求解。对导弹的GSPN模型进行定性和定量分析, 求解不同层级测试性指标最后通过仿真计算, 与系统要求可用度误差不超过0.7%, 验证了多层GSPN模型的可行性和分析结果的可信性。

关键词: 测试性需求建模, 测试性, 嵌入马尔可夫链, 同构法, 测试性指标, 可用度

Abstract:

Aiming at the problem that the test requirement modeling of missiles is not yet mature and it is difficult to conduct test requirement analysis, a test requirement modeling method based on generalized stochastic Petri net (GSPN) is proposed. Based on the analysis of the missile structure, the testability requirements of the missile are modeled, and a two-stage GSPN model of the missile is given to analyze the fault detection and maintenance process of the missile system. According to the GSPN model, it is isomorphic to the embedded Markov chain. The existing state set and disappearing state set are used to represent the change of the place, and the test index is solved by using the isomorphism method. The multi-level GSPN model is decomposed into multiple subnets from top to bottom, which greatly reduces the number of state spaces. The equivalent transition rule solves the compressed subnet. Finally, a combination of qualitative analysis and quantitative calculation is used to determine the test index requirements of missiles at all levels. Through simulation calculation, the availability error with the system requirements does not exceed 0.7%, which verifies the feasibility of the multi-layer GSPN model and the credibility of the analysis results.

Key words: testability requirements modeling, testability, embedded Markov chain (EMC), isomorphism, testability index, availability

中图分类号:

TP206

翟禹尧, 史贤俊, 吕佳朋, 韩露. 基于GSPN的导弹多层级测试性需求建模与指标评估[J]. 系统工程与电子技术, 2021, 43(4): 970-979.

Yuyao ZHAI, Xianjun SHI, Jiapeng LYU, Lu HAN. Modeling and index evaluation of multi-level testability of missiles based on GSPN[J]. Systems Engineering and Electronics, 2021, 43(4): 970-979.

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元素	符号	基本含义
库所		系统的状态
瞬时变迁		事件发生的概率
延时变迁		事件发生的速率
令牌		库所出现令牌, 表示该状态发生
有项弧		令牌流动的方向
禁止弧		当禁止弧出现时, 库所满足变迁条件会被禁止

库所	含义	变迁	含义	速率或概率
p₁	导弹系统正常	t₀	出现虚警	γ_FA
p₂	导弹出现故障	t₁	故障发生	λ
p₃	检测到故障	t₂	故障检测率	γ_FD
p₄	故障不能被检测	t₃	故障不可检测的概率	1-γ_FD
p₅	发生故障的LRU	t₄	人工测试	λ_t
p₆	维修后的LRU	t₅	拆卸LRU	λ_r
p₇ⁱ	LRU_i故障	t₆	安装LRU	μ_o
p₈ⁱ	LRU_i故障检测完成	t₇ⁱ	LRU_i故障发生概率	γ_i
p₉ⁱ	LRU_i故障无法检测	t₈ⁱ	LRU_i故障检测	η_i
p₁₀ⁱ	LRU_i检测出故障	t₉ⁱ	LRU_i故障检测率	γ_{FD_i}
p₁₁	修复好的LRU	t₁₀ⁱ	LRU_i故障不可检测率	1-γ_{FD_i}
		t₁₁ⁱ	LRU_i人工测试	μ_i
		t₁₂ⁱ	故障维修	λ_s
		t₁₃	运送LRU	λ_ti

参数	λ	λ₁	λ₂	μ₀/h^-1	λ_r/h^-1	λ_t1/h^-1	λ_t2/h^-1
取值	0.003 4	0.001 4	0.002 0	1	1	0.1	0.2

M	p₁	p₂	p₃	p₄	p_5L	p₆
M₀	1
M₁		1
M₂			1
M₃				1
M₄					1
M₅						1

参数	γ_FD	γ_FI	1/λ_t	γ_FA/%	t_FDL/h	γ_FD1	γ_FD2
指标	0.92	0.90	6.67	0.9	0.94	0.91	0.93