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摘要:
针对飞机电气线路互联系统(EWIS)差异性大、随时间退化严重、可靠性建模困难等问题,将通用生成函数(UGF)和GO法融合,提出了基于UGF-GO法的EWIS退化可靠性分析方法。首先,考虑EWIS各连接部件使用性能及环境的差异性,利用含随机参数的Wiener退化过程模型建立部件可靠性仿真模型,采用马尔可夫链蒙特卡罗(MCMC)算法对模型中的未知参数进行估计,并与传统二步法参数估计值进行对比,得到较为精确的系统部件退化可靠性曲线。其次,在分析系统退化可靠性时,利用UGF-GO法对某飞机EWIS结构可靠性进行建模及计算。最后,以某飞机电气线路互联系统为例,结合部件退化可靠性计算结果,评估系统在不同给定阈值下可靠性水平。结果表明:UGF-GO法可有效解决系统退化状态的可靠性分析问题。
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关键词:
- 电气线路互联系统(EWIS) /
- 系统可靠性 /
- Wiener过程 /
- 马尔可夫链蒙特卡罗(MCMC) /
- UGF-GO法
Abstract:In view of several problems of electrical wiring interconnection system (EWIS), such as condition difference, ageing phenomenon and modelling difficulty, a UGF-GO methodology based EWIS degradation reliability analysis method is proposed by combining traditional GO methodology and universal generating function (UGF). In this paper, based on the difference of performance and environment of system components, using Wiener degradation process model with random parameters, the component reliability simulation model has been built. Markov chain Monte Carlo (MCMC) algorithm is used to estimate parameters in the model. The simulation test show that MCMC algorithm improves the estimation accuracy compared to the parameter estimation values of traditional two-step method. In analyzing the reliability of a degenerate system, the UGF-GO methodology works for calculating the EWIS reliability. Finally, the EWIS of an aircraft is taken as an example, and combined with the reliability calculation result of components, the reliability level of EWIS is evaluated under different thresholds. The results show that UGF-GO methodology can effectively solve the reliability analysis problem of the deteriorating system.
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表 1 主设备汇流条可靠性模型参数估计
Table 1. Parameter estimate for reliability model of main equipment busbar
参数 期望 方差 置信区间(置信水平为0.95) μβ 0.447 0 0.017 7 [0.340 0,0.545 6] σβ2 0.005 0 0.009 6 [0.000 3,0.007 6] σ2 0.222 3 0.371 6 [0.129 0,0.301 0] 表 2 电子设备系统操作符数据
Table 2. Operator data of electronic equipment system
操作符编号 操作符类型 状态概率 pi, 0 pi, 1 1 5 0.01 0.99 2 1 0.05 0.95 3 1 0.10 0.90 4 1 0.05 0.95 5 1 0.10 0.90 表 3 电子设备系统可靠性结果对比
Table 3. Reliability result comparison of electronic equipment system
输出信号 概率公式算法 UGF-GO法 pi, 0 pi, 1 pi, 0 pi, 1 Po, 3 0.846 450 0.153 550 0.855 000 0.145 000 Po, 5 0.846 450 0.153 550 0.855 000 0.145 000 Po, 6(未修正) 0.976 422 0.023 577 0.978 975 0.021 025 Po, 6(修正后) 0.969 185 0.030 814 0.969 185 0.030 815 表 4 二步法与MCMC算法参数估计值对比
Table 4. Comparison of parameter estimate between two-step algorithm and MCMC algorithm
汇流条 二步法 MCMC算法 μβ σβ2 σ2 μβ σβ2 σ2 主设备 0.441 4 0.011 9 0.278 6 0.447 0 0.005 0 0.222 3 电子设备 0.431 1 0.014 1 0.319 7 0.421 9 0.005 1 0.221 7 非必需设备 0.473 9 0.005 5 0.207 0 0.464 1 0.004 5 0.201 0 蓄电池设备 0.499 8 0.005 1 0.224 8 0.479 3 0.005 0 0.218 9 表 5 某飞机电气线路互联系统操作符数据
Table 5. Operator data of an aircraft's EWIS
编号 类型 名称 状态概率 pi, 0 pi, 1 pi, 2 1 5 电源 0.999 984 - 0.000 016 2~6 1 导通控制 0.999 995 - 0.000 005 7 1 主设备汇流条 - R1(t) 1-R1(t) 8, 9 1 电子设备汇流条 - R2(t) 1-R2(t) 10 2 或门 - - - 11 1 非必需设备汇流条 - R3(t) 1-R3(t) 12 1 内部供电开关 0.999 995 - 0.000 005 13 1 外部供电开关 0.999 989 - 0.000 011 14 2 或门 - - - 15 1 蓄电池设备汇流条 - R4(t) 1-R4(t) 16 10 与门 - - - 表 6 不同阈值系统可靠性结果对比
Table 6. Comparison of system reliability results under different thresholds
时间/
(103h)失效阈值 5 mΩ 10 mΩ 15 mΩ 20 mΩ 0.5 0.999 869 23 0.999 869 23 0.999 911 11 0.999 952 99 1.0 0.983 131 70 0.983 201 29 0.991 532 16 0.999 933 62 1.5 0.807 300 25 0.814 910 50 0.900 868 99 0.995 894 56 2.0 0.410 376 10 0.455 760 56 0.650 608 32 0.928 757 82 2.5 0.111 053 74 0.161 576 30 0.328 864 11 0.669 353 15 3.0 0.017 385 46 0.037 127 48 0.107 027 91 0.308 530 88 3.5 0.001 890 51 0.005 873 75 0.022 638 82 0.087 255 26 -
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