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1. 中国民航大学 航空工程学院, 天津 300300;
2. 中国民航大学 中欧航空工程师学院, 天津 300300

Forecasting for aero-engine failure risk based on Monte Carlo simulation
ZHAO Hongli1, LIU Yuwen2
1. College of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China;
2. Sino-European Institute of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China
Abstract:In view of the fact that aero-engines have complicated structure and multiple failure modes, traditional methods are difficult to meet the requirements. A forecasting method for aero-engine failure risk based on Monte Carlo simulation is presented, which is used to evaluate the possibility of failure for each component of engine in the future. According to the characteristics of aero-engine failure data, the failure probability model is based on the Weibull distribution whose parameters are estimated by the method of rank regression. Combining multiplicative congruent generator with the inverse transform method, the random numbers are produced to satisfy Weibull distribution. The method used to forecast failure risk for engines with multi-failure modes is based on the one with single failure mode. The simulation procedures and algorithm, by comparing the simulation results with the forecasting datum from the engine manufacture are presented, it proves that the algorithm and Monte Carlo simulation are effective in aero-engine failure risk forecast.
Key words: aero-engine     multi-failure modes     scheduled maintenance     risk forecast     Monte Carlo simulation

1) 将故障时间数据T=[T1 T2Tn]T从小到大排列,并利用式(2)计算各个数据的中位秩,当故障时间数据中存在删失数据时,需利用式(3)调整数据排序值.

2) 计算故障时间的自然对数,记为Y=ln T,并令

3) 计算方程y=A+Bx的最小均方估计,满足式(5)和式(6).

4) 求解中位秩回归参数,为威布尔参数β，η的估计值.

2.2 随机变量的抽样方法

M(1)=2 146 058 219 a(1)=43 465 c(1)=1
M(2)=2 145 434 063 a(2)=45 271 c(2)=－1

2.3 蒙特卡罗模拟流程

 图 1 蒙特卡罗模拟流程Fig. 1 Monte Carlo simulation process

1) 输入机队的原始数据,包括机队总数,使用率,机队年龄分布;

2) 利用乘同余组合发生器构建[0,1]区间均匀随机数表;

3) 针对每台发动机,从随机数表中顺序选取随机数,利用式(13)计算各个故障模式的随机故障时间F1,F2,…,Fn,首次故障时间需大于发动机的已安全运行时间,否则需重新产生一组随机故障时间,直到均大于发动机已安全运行时间;

4) 判断min{F1,F2,…,Fn}是否小于定期检查时间T,若是,则记录该故障Fk,该故障模式发生次数累加1;

5) 针对k故障模式,重新抽样故障时间Fk;

6) 重复步骤4)和步骤5),直到min{F1,F2,…,Fn}超过发动机定期检查时间T,则一次模拟结束;

7) 遍历机队内所有发动机,每台发动机均进行N次模拟,并记录结果;

8) 计算发动机各个故障模式发生的概率;

9) 结合机队原始数据,计算机队未来一段时间内发动机各个故障模式可能发生的次数. 3 算例及结果分析 3.1 算例描述

 故障模式 η β F1 10 193 2.09 F2 2 336 4.57 F3 12 050 1.885 F4 3 149 4.03
 图 2 机队发动机运行时间分布Fig. 2 Operation time distribution of engine fleet
3.2 模拟流程

 图 3 模拟流程Fig. 3 Simulation process

1) 为4种模式生成随机故障时间.利用随机数表,顺序选取前4个[0,1]区间上的随机数:0.007,0.028,0.517,0.603.根据式(13),则有:F1=951 h,F2=1 072 h,F3=10 180 h,F4=3 088 h.

2) 4种故障模式中,最小的故障时间为951 h,并未达到定期检查时间1 000 h.

3) 最先发生的为F1故障,记录该故障发生时间为951 h,相当于在未来第38个月发生故障.从随机数表中选取下一个随机数0.442,为F1故障重新生成随机故障时间,F1=8 827 h.此时,min{F1,F2,F3,F4}已超过定期检查时间1 000 h.至此,一次模拟结束.

 月份 故障次数 F1 F2 F3 F4 1月 0 0 0 0 2月 0.203 815 0.461 832 0.240 431 0.221 532 3月 0.401 265 0.891 837 0.484 208 0.429 415 4月 0.609 607 1.382 214 0.730 675 0.666 959 5月 0.813 159 1.833 612 0.976 881 0.890 197 6月 1.036 660 2.343 870 1.235 160 1.136 468 7月 1.249 202 2.830 047 1.492 061 1.371 846 8月 1.475 197 3.382 893 1.755 327 1.635 703 9月 1.696 138 3.896 892 2.008 816 1.895 163 10月 1.927 382 4.476 445 2.270 442 2.178 049 11月 2.146 355 5.034 475 2.532 921 2.434 819 12月 2.376 549 5.657 666 2.801 109 2.729 058

 月份 故障次数 F1 F2 F3 F4 1月 0 0 0 0 2月 0.17 0.33 0.21 0.17 3月 0.38 0.67 0.47 0.34 4月 0.60 1.15 0.74 0.58 5月 0.78 1.47 0.95 0.74 6月 0.92 1.71 1.13 0.87 7月 1.22 2.27 1.49 1.15 8月 1.46 2.81 1.77 1.41 9月 1.66 3.16 2.02 1.60 10月 1.95 3.90 2.36 1.95 11月 2.07 4.03 2.51 2.03 12月 2.38 4.90 2.87 2.45
 图 4 12月份发动机故障次数收敛结果Fig. 4 Convergence results of engine failure number on December
3.3 结果分析

1) 在确定了失效分布规律后,利用蒙特卡罗模拟算法进行仿真,能够比较准确地估算出整个机队发动机在未来不同时间段内的故障风险水平,从而为发动机维修管理提供可靠性指标参考;

2) 蒙特卡罗模拟是多故障模式下风险预测的一个有效方法,并且在多故障模式下,该算法不但可以预测机队整体风险水平,而且还可确定何种故障模式最易发生,从而可以有针对性地对该故障制定相应的改进措施,降低机队的故障风险;

3) 当某个易发故障得到改进后,可重新进行仿真模拟来找到下一个易发故障,不断迭代,从而实现对机队内发动机的动态管理.

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#### 文章信息

ZHAO Hongli, LIU Yuwen

Forecasting for aero-engine failure risk based on Monte Carlo simulation

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 545-550.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0190