Research on aircraft engine maintenance strategy considering mixture distribution of random failures under special operating conditions
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摘要:
鉴于航空涡轮风扇发动机在恶劣气象条件、鸟击碰撞、异物损伤等特殊工况下存在耦合失效风险，构建了集成退化失效与突发失效的混合分布维护优化模型。在构建模型层面，运用Weibull分布刻画突发失效特征，并基于共享的潜在风险因子混合Gamma过程与Clayton Copula函数建立多元退化失效的联合概率分布框架，建立了以维护成本最小化、退化失效可靠度最大化、突发失效可靠度最大化为目标的多目标优化模型，采用NSGA-Ⅲ算法求解帕累托最优解集。基于NASA涡轮风扇发动机退化仿真数据集的验证结果表明：最优维护策略下，维护总期望成本为15 749.6元，系统综合可靠度达到
0.9506 ；NSGA-Ⅲ算法的IGD指标为5.8×10−4，相比NSGA-Ⅱ算法性能提升13.4%，收敛性能提升29.3%；LS-SVM预测模型的平均相对误差为6.676%。混合分布模型能够准确量化复合失效风险，在确保系统可靠性的前提下实现维护成本的最优控制，为航空发动机智能维护决策提供了理论支撑。Abstract:Given the coupled failure risks of aero-turbofan engines under special operating conditions such as adverse meteorological conditions, bird strike impacts, and foreign object damage (FOD), a hybrid distribution maintenance optimization model integrating degradation failure and sudden failure was constructed. At the model construction level, the Weibull distribution was employed to characterize sudden failure characteristics, and a joint probability distribution framework for multivariate degradation failure was established by integrating the Gamma process with the clayton copula function based on shared latent risk factors. A multi-objective optimization model was formulated with objectives of minimizing maintenance cost, maximizing degradation failure reliability, and maximizing sudden failure reliability, and the NSGA-Ⅲ algorithm was adopted to solve for the Pareto optimal solution set. Validation results based on the NASA turbofan engine degradation simulation dataset demonstrated that under the optimal maintenance strategy, the total expected maintenance cost was 15 749.6 yuan, and the overall system reliability reached 0.950 6. The IGD (inverted generational distance) metric of the NSGA-Ⅲ algorithm was 5.8×10−4, representing a 13.4% performance improvement and a 29.3% convergence performance enhancement compared to the NSGA-Ⅱ algorithm. The LS-SVM (least squares support vector machine) prediction model achieved a mean relative error of 6.676%. The hybrid distribution model can accurately quantify composite failure risks and achieve optimal control of maintenance costs while ensuring system reliability, thereby providing theoretical support for intelligent maintenance decision-making of aero-engines.
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Key words:
- aviation turbofan engine /
- sudden failure /
- degradation failure /
- hybrid distribution /
- NSGA-Ⅲ algorithm
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图 10 决策变量敏感性分析散点图
Figure 10. Sensitivity analysis scatter plot of decision variables and objective functions
表 1 模型基础参数取值
Table 1. Basic model parameter settings
参数 p/
（个/天）d/
（个/天）Co/
（元/次）Ci/
（元/次）H/
（元/个/天）Cs/
（元/个）Cp/
（元/次）Cf/
（元/次）数值 300 250 800 200 1.2 50 2000 5000 
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表 2 模型参数优化与性能提升取值表
Table 2. Model parameter optimization and performance improvement value table
参数名称 种群规模 最大迭代次数 交叉概率 变异概率 最优值 80 60 0.5 0.02 性能提升/% 29.3 37.0 19.4 22.7
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表 3 混合模型关键参数设置
Table 3. Key parameter settings of hybrid model
失效类型 参数名称 数值 退化失效 形状参数$ \alpha $ 0.5 尺度参数$ \beta /\mathrm{h} （\text{%}） $ 0.1 退化失效阈值$ {D}_{\text{th}}/\text{%} $ 1.0 非线性特征系数b 1.2 多指标数量p 3 突发失效 分散性模量m 10 气象回归系数βi 待估计 Weibull形状参数$ k $ 0.5 Weibull尺度参数σu/MPa 600 极端天气权重$ {p}_{1} $ 0.4 鸟击权重$ {p}_{2} $ 0.4 异物损伤权重$ {p}_{3} $ 0.2 预期疲劳寿命tf/次 104 衰减系数ki 0.5 维护策略 最低可靠性标准Rmin 0.95 预防性维护成本$ {C}_{\mathrm{p}} $/（元/h） 500 突发失效维修成本$ {C}_{\mathrm{s}} $/（元/h） 1500 退化失效维护成本$ {C}_{\mathrm{d}} $/（元/h） 1000 最优维护时机topt/h 400
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表 4 不同分布类型的AD值
Table 4. AD values for different distribution types
性能指标 指数分布 正态分布 对数正态分布 Weibull分布 EGTM 1.670 0.210 0.160 0.159 AVB2R 1.245 0.321 0.239 0.223
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表 5 算法收敛性能分析对比
Table 5. Algorithm performance comparison （IGD metric）
算法 平均值/10−4 标准差/10−4 IGD最佳值/10−4 IGD最差值/10−4 HV Δ 排名 NSGA-Ⅲ 5.8 1.2 4.9 7.1 0.8924 ±0.0120.387±0.021 1 NSGA-Ⅱ 6.7 1.8 5.8 9.2 0.8756 ±0.0180.432±0.028 2 MOPSO 8.3 2.1 7.1 11.0 0.8456 ±0.0310.534±0.038 3 MODE 9.7 2.6 8.2 13.0 0.8234 ±0.0240.578±0.032 4 MOSA 12 3.4 9.8 16.0 0.8013 ±0.0410.629±0.045 5
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表 6 成本参数敏感性分析结果
Table 6. Cost parameter sensitivity analysis results
参数 变化范围/% 最优经济生产批量Q* 预防维修阈值Dp1 预防维修阈值Dp2 平均生产成本Ca $ {C}_{0} $ −20 3357 13.2672 8.3456 465.8109 −10 3401 13.5678 8.6230 480.5403 0 3467 14.0000 9.0000 518.1397 10 3589 14.6899 9.2354 536.6673 20 3752 15.7459 9.5572 557.4597 $ {C}_{\mathrm{i}} $ −20 3415 13.7892 8.8324 493.8216 −10 3418 13.9210 8.9532 502.1355 0 3467 14.0000 9.0000 518.1397 10 3493 14.1254 9.2345 523.0953 20 3526 14.2543 9.3415 537.5327 H −20 3523 13.9959 8.9546 487.9834 −10 3487 13.9845 8.9765 498.3549 0 3467 14.0000 9.0000 518.1397 10 3453 14.0123 9.0012 527.9107 20 3436 14.0227 9.0037 538.7243 $ {C}_{\mathrm{s}} $ −20 3512 14.0453 9.0210 458.1140 −10 3497 14.0254 9.0147 469.6609 0 3467 14.0000 9.0000 518.1397 10 3356 13.9876 8.9978 530.1132 20 3312 13.9723 8.9921 537.2354 $ {C}_{\mathrm{p}} $ −20 3323 13.1245 7.3453 481.8146 −10 3485 13.5634 8.2354 490.6563 0 3467 14.0000 9.0000 518.1397 10 3745 14.5673 9.4567 526.8745 20 3803 15.1307 9.8976 543.8248 $ {C}_{\mathrm{r}} $ −20 3162 14.5323 9.3421 432.4056 −10 3470 14.2345 9.1243 506.3092 0 3467 14.0000 9.0000 519.1397 10 3585 13.8734 8.8775 543.3124 20 3682 13.7812 8.6789 557.2031
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