基于直觉模糊贝叶斯网络的HUD系统多阶段任务可靠性分析

doi:10.7527IS1000-6893.2022.26853

Abstract

Abstract:

Insufficient bottom reliability data accumulation of some functional modules of the domestic Head Up Display （HUD） system poses difficulty in reliability analysis support. To solve this problem， a reliability analysis method for multi-phased mission of the HUD system based on the Intuitionistic Fuzzy Bayesian Network （IFBN） is proposed. The modeling method for multi-Phased Mission System （PMS） based on the Bayesian network is first studied， and meanwhile the possible Commom Cause Failure （CCF） effects are comprehensively considered. The fuzzy event failure data evaluation method based on the intuitionistic fuzzy theory is then explored， the fuzzy interval division method suitable for avionics equipment and the conversion algorithm between the intuitionistic fuzzy number and failure data proposed， and the intuitionistic fuzzy number aggregation algorithm based on the Tω operator adopted to reduce fuzzy accumulation. Finally， the multi-phased mission reliability is calculated with a HUD system as an example. The proposed method provides support for reliability analysis under the condition of fuzzy bottom failure data.

Key words: intuitionistic fuzzy number, Bayesian network, head up display system, multi-phased mission, reliability analysis

CLC Number:

Fan ZHANG, Zijing SUN, Guosong XIAO, Jiachen LIU, Peng WANG. Reliability analysis for multi-phased mission of HUD system based on intuitionistic fuzzy Bayesian network[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(4): 226853-226853.

Figures/Tables 27

Fig. 1

Table 1

Two TIFN operation rules based on Tω

运算	模糊表达式
加	$A ˜ ⊕ T ω B ˜ = b 1 + b 2 - m a x b 1 - a 1, b 2 - a 2, b 1 + b 2, b 1 + b 2 + m a x c 1 - b 1, c 2 - b 2;$ $b 1 + b 2 - m a x b 1 - a 1', b 2 - a 2', b 1 + b 2, b 1 + b 2 + m a x c 1' - b 1, c 2' - b 2$
减	$b 1 - b 2 - m a x b 1 - a 1', c 2' - b 2, b 1 - b 2, b 1 - b 2 + m a x c 1' - b 1, b 2 - a 2'$ $A ˜$ $T ω B ˜ = b 1 - b 2 - m a x b 1 - a 1, c 2 - b 2, b 1 - b 2, b 1 - b 2 + m a x c 1 - b 1, b 2 - a 2;$
乘	$λ ⊙ T ω A ˜ = λ a 1, λ b 1, λ c 1; λ a 1', λ b 1', λ c 1'$

Table 1

Fig. 2

Table 2

Probability distribution of CCE

共因事件CC _i 间关系	共因空间CCE _k 的概率P_CCE $k$
共因事件间相互独立或集合｛CC _i ｝中不存在互斥事件（i∈S）	$P C C E k = ∏ i ∈ S P C C i · ∏ i ∉ S 1 - P C C i$
集合｛CC _i ｝中存在至少两共因事件互斥（i∈S）	$P C C E k = 0$
所有共因事件中至少存在两共因事件CC _i 与CC _j 相关（i≠j）	$P C C E k = ∏ i ∈ S P C C i \| C C j · ∏ i ∉ S 1 - P C C i \| C C j ¯$

Table 2

Table 3

Table 4

Fig. 3

Table 5

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Table 6

Table 7

Fig. 8

Fig. 9

Table 8

Table 9

Table 10

Table 11

Polymerization of element X13 and its de-fuzzification calculation

指标	计算值	依据公式
EV（A $1$ ）	0.25	$E V A s ̃ = a j + a j' + 4 b j + c j + c j' 8$
EV（A $2$ ）	0.5
EV（A $3$ ）	0.25
S（A $1$ ，A $2$ ）	0.5	$S A s ̃, A k ̃ = E V A s ̃ / E V A k ̃, E V A s ̃ ≤ E V A k ̃ E V A k ̃ / E V A s ̃, E V A s ̃ ≥ E V A k ̃$
S（A $1$ ，A $3$ ）	1
S（A $2$ ，A $3$ ）	0.5
W（E $1$ ）	0.413 8	$W E i = ∑ j = 1 n x i j ∑ i = 1 m ∑ j = 1 n x i j$
W（E $2$ ）	0.344 8
W（E $3$ ）	0.241 4
AD（E $1$ ）	0.705 902 422	$A D E s = ∑ k = 1, k ≠ s m W E k · S A s ̃, A k ̃ ∑ k = 1, k ≠ s m W E k$
AD（E $2$ ）	0.5
AD（E $3$ ）	0.772 739 257
RA（E $1$ ）	0.585 372 754	$R A E s = A D E s ∑ s = 1 m A D E s$
RA（E $2$ ）	0.252 698 609
RA（E $3$ ）	0.390 540 271
AW（E $1$ ）	0.499 586 377	$A W E s = β W E s + 1 - β R A E s$
AW（E $2$ ）	0.298 749 305
AW（E $3$ ）	0.315 970 135
R（X13）	（0.293 3，0.353 3，0.413 2； 0.278 3，0.353 3，0.428 2）	$R ˜ = ∑ s = 1 m ⊕ T ω · A W E s A s ̃ = A W E 1 A 1 ̃ ⊕ A W E 2 A 2 ̃ ⊕ ⋯ ⊕ A W E m A m ̃$
IFFP	0.353 263 78	$I F F P = 13 c' - a' b - 2 c' - 2 a' + c - a a + b + c + 3 c' 2 - a' 2 c' - a' + c - a$
FR	6.580 96×10^-8	$F R = 1 10 K I F F P ≠ 0 0 I F F P = 0$ $K = - 2.182 7 l n I F F P + 4.974 1 0 ≤ I F F P < 0.25 - 8.05 I F F P 3 + 11.12 I F F P 2 - 12.16 I F F P + 10.6 0.25 ≤ I F F P ≤ 0.75 1 - I F F P / I F F P 0.630 9 × 8 0.75 < I F F P ≤ 1$

Table 11

Table 12

Table 13

Probability table of CCE

子空间	子空间组成	$P C C E k$
CCE₀	$C C E 0 = C C 1 ¯ ⋂ C C 2 ¯$	$P C C E 0 = 1 - P C C 1 1 - P C C 2 = 0.999 913 9$
CCE₁	$C C E 1 = C C 1 ⋂ C C 2 ¯$	$P C C E 1 = P C C 1 1 - P C C 2 = 1.269 9 × 10 - 5$
CCE₂	$C C E 2 = C C 1 ¯ ⋂ C C 2$	$P C C E 2 = 1 - P C C 1 P C C 2 = 7.339 9 × 10 - 5$
CCE₃	$C C E 3 = C C 1 ⋂ C C 2$	$P C C E 3 = P C C 1 P C C 2 = 9.321 8 × 10 - 10$

Table 13

Fig. 10

Table 14

Fuzzy event aggregation results without Tω

模糊事件	$R ˜$
X13	（0.210 6，0.353 3，0.495 9；0.171 2，0.353 3，0.535 3）
X14	（0.473 5，0.629 0，0.784 6；0.424 8，0.629 0，0.833 2）
CC₁	（0.500 9，0.650 1，0.799 4；0.455 4，0.650 1，0.844 8）
CC₂	（0.600 7，0.736 7，0.872 7；0.563 4，0.736 7，0.910 0）

Table 14

Table 15

Fig. 11

Fig. 12

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定性概率术语	定量概率指标（每飞行小时）	描述
可能的	1×10^-3~1×10^-5	预见到在每架飞机整个寿命期间会发生一次或更多次
微小的	1×10^-5~1×10^-7	每架飞机总的寿命期间不太可能会发生，但该类型飞机的许多飞机总的运行寿命中可能发生几次
极微小的	1×10^-7~1×10^-9	每架飞机总的寿命期间没有预见到会发生，但该型所有飞机总的运行寿命中可能发生几次
极不可能的	<1×10^-9	某型飞机的所有飞机的整个运行寿命期间不太可能发生

分级编号	分级	指标（每飞行小时失效概率）
1	有可能失效	>1×10^-3
2	失效可能较小	1×10^-5~1×10^-3
3	失效可能微小	1×10^-7~1×10^-5
4	失效可能极微小	1×10^-9~1×10^-7
5	极不可能失效	<1×10^-9

失效可能性	IFFN
可能失效	（0.82，0.91，1；0.8，0.91，1）
失效可能较小	（0.63，0.75，0.87；0.6；0.75；0.9）
失效可能微小	（0.35，0.5，0.65；0.3，0.5，0.7）
失效可能极微小	（0.13，0.25，0.37；0.1，0.25，0.4）
极不可能失效	（0，0.09，0.18；0，0.09，0.2）

模块	编号	模块	编号	模块	编号	子系统	编号
数据接口模块1	X1	符号画面生成模块	X6	畸变校正模块	X11	平显计算机	S1
数据接口模块2	X2	符号画面确认模块	X7	像源模块	X12	投影成像装置	S2
导引能力确认模块	X3	符号画面记录模块	X8	光学结构	X13	折转显示仪	S3
数据处理模块	X4	A818（HDC）	X9	折转组件	X14
数据处理确认模块	X5	A818（HID）	X10	显示面板	X15

模块	失效率	模块	失效率	模块	失效率
X1	2.97×10^-6	X6	4.63×10^-6	X11	2.15×10^-6
X2	2.97×10^-6	X7	5×10^-7	X12	6.7×10^-6
X3	5×10^-7	X8	5×10^-7	X13
X4	4.63×10^-6	X9	2.48×10^-6	X14
X5	5×10^-7	X10	2.48×10^-6	X15	2.5×10^-6

Reliability analysis for multi-phased mission of HUD system based on intuitionistic fuzzy Bayesian network

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专家	专家评价结果
E₁	（0.13，0.25，0.37； 0.1，0.25，0.4）
E₂	（0.35，0.5，0.65； 0.3，0.5，0.7）
E₃	（0.13，0.25，0.37； 0.1，0.25，0.4）

模糊事件	IFFP	FR
X13	0.353 263 78	6.58×10^-8
X14	0.629 036 515	8.50×10^-6
CC1	0.650 129 123	1.27×10^-5
CC2	0.736 707 056	7.34×10^-5

模糊事件	IFFP	FR
X13	0.452 295 296	3.71×10^-7
X14	0.807 576 594	5.80×10^-4
CC₁	0.834 115 118	0.001 295
CC₂	0.943 063 008	0.043 540

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