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摘要:
针对民用飞机部件具有多重失效的特点，提出一种面向多重耗损失效模式的运行风险评估方法。以机队运行失效数据为样本，构建基于混合威布尔分布的多重失效模型，提出基于期望最大（EM）算法的混合威布尔分布参数估计方法，并利用粒子群优化（PSO）算法对EM算法进行优化，提高了参数估计精度；以基于混合威布尔分布的多重失效模型为基础，利用蒙特卡罗仿真的方法提出多重失效模式影响下的机队缺陷飞机数量（DA）预测算法；构建贝叶斯网络模型以分析初因事件发生条件下的不安全后果发生概率（CP），并结合由历史运营经验得到的死亡率（IR）和未检出率（ND），计算总体未纠正机队风险（
R T）。实例表明：所提风险评估方法可以直接应用于多重失效模式导致的机队风险评估，所提模型参数估计方法相比极大似然估计和最小二乘估计方法，均方根误差分别降低了80.6%和85.7%。Abstract:An operation risk assessment method is proposed for aircraft components with multiple wear-out failure modes. A multiple failure model is constructed using the fleet operating failure data samples and the mixed Weibull distribution. And the parameter estimation method of the mixed Weibull distribution is proposed based on the expectation maximization (EM) algorithm, which has been optimized by using the particle swarm optimization (PSO) algorithm to improve the accuracy of the parameter estimation. In terms of the mixed Weibull distribution-based reliability model, the calculating method for the number of defect airplanes (DA), which is caused by the multiple failure modes, is given via the Monte Carlo simulation method. To determine the Conditional Probability (CP) of dangerous consequences emerging from a certain initial situation, the Bayesian network (BN) is designed. Finally, the total uncorrected fleet risk (
R T) is calculated in terms of the injury ratio (IR), the Not Detected probability (ND), the DA value, and the CP value. A case study shows that the proposed risk assessment method can be directly applied in the evaluation of fleet risks caused by multiple failure modes.Furthermore, the root mean squared error of the suggested parameter estimation approach has been decreased by 85.7% and 80.6%, respectively, when compared to the maximum likelihood estimation (MLE) and the least-squares estimation (LSE). -
图 1 基于PSO-EM算法的混合威布尔分布参数估计方法
Figure 1. Parameter estimation method of mixed Weibull distribution based on PSO-EM algorithm
图 5 机队裂纹失效概率密度函数拟合结果
Figure 5. Fitting results of probability density function for fleet crack failure
表 1 机队运行寿命数据
Table 1. Fleet operational failure data
序号 时间/
飞行循环序号 时间/
飞行循环序号 时间/
飞行循环序号 时间/
飞行循环1 1410 6 6202 11 10978 16 18196 2 2786 7 6750 12 14660 17 18558 3 5145 8 7253 13 15110 18 19636 4 5877 9 9753 14 15559 19 23603 5 6086 10 9944 15 17527 20 23924 
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表 2 模型参数初值及边界值
Table 2. Initial values and boundary values of model parameters
模型参数 ${ \pi _1}$ ${ \pi _2}$ $ {\alpha _1} $ $ {\alpha _2} $ 初值 0.35 0.65 5876.1 17526.4 边界下限 0.1 0.5 5288 15773 边界上限 0.5 0.8 6464 19279
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表 3 多重失效模型参数估计结果
Table 3. Parameters’ estimation results of multiple failure model
估计方法 ${ \pi_1}$ ${ \pi_2}$ $ {\alpha _1} $ $ {\alpha _2} $ δRMSE 本文方法 0.29 0.71 5412.7 17468.1 0.0024 基于PSO
的LSE0.26 0.74 5384.5 16991.7 0.0126 基于PSO
的MLE0.26 0.74 5339.9 16645.8 0.0168
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表 4 BN节点信息
Table 4. Node information in BN
节点 事件 状态 A 翼肋裂纹 1 0 B 桁条/腹板失效 1 0 C 蒙皮失效 1 0 D 失压 1 完全失去控制 2 部分失去控制 3 无影响 4 E 空中解体 1 坠毁 2 人员死亡 3 跑道偏离 4 无影响 5
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表 5 节点D条件概率
Table 5. Conditional probability of node D
C $P\left( {D = 1\left| C \right.} \right)$ $P\left( {D = 2\left| C \right.} \right)$ $P\left( {D = 3\left| C \right.} \right)$ $P\left( {D = 4\left| C \right.} \right)$ 1 0.5 0.001 0.05 0.449 0 0 0 0 1
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表 6 节点E条件概率
Table 6. Conditional probability of node E
D $P\left( {E = 1\left| D \right.} \right)$ $P\left( {E = 2\left| D \right.} \right)$ $P\left( {E = 3\left| D \right.} \right)$ $P\left( {E = 4\left| D \right.} \right)$ $P\left( {E = 5\left| D \right.} \right)$ 1 0.001 0.005 0.01 0 0.984 2 0.5 0.5 0 0 0 3 0.001 0.01 0 0.1 0.889 4 0 0 0 0 1
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表 7 四种不安全后果的死亡率
Table 7. The injury ratio of four unsafe outcomes
不安全后果 死亡率 人员死亡 0.001 跑道偏离 0.03 坠毁 0.98 空中解体 1
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