Multi-objective optimization inspection decision-making method based on delay-time model
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摘要: 根据某航空公司货运机队的某型发动机HPTACC系统在某一周期内的预防性检查计划、检查发现的缺陷以及失效维修记录, 分析了系统在运行过程中将缺陷延迟发现时间作为安全性优化目标、将检修费用作为经济性优化目标的可行性。在预防性检查时刻发现缺陷的检修策略下, 推导了在各检查时刻基于时间延迟模型的缺陷数期望值和缺陷延迟发现时间期望值概率计算式。在缺陷退化为失效被及时发现并进行更换维修的检修策略下, 推导了在各检查间隔期内基于时间延迟模型的失效发生次数期望值概率计算式。基于2种检修策略下的概率公式, 建立了系统在给定寿命周期内的似然函数, 建立了检修费用和缺陷延迟发现时间的期望值双优化目标函数式, 运用了改进的非支配排序遗传算法优化得到双目标函数的Pareto最优解集。根据决策者的目标偏好及其分界值对应的检修费用及缺陷延迟发现时间的经验估计值, 分别确定了系统在寿命周期内的检修费用和缺陷延迟发现时间的目标偏好函数, 通过目标偏好函数划分区间确定Pareto最优解集中各最优解的偏好区间。基于收集的检修信息和提出的方法, 对决策者将缺陷延迟发现时间期望值目标偏好定为一般、将检修费用期望值目标偏好定为很好的偏好要求进行实例分析。分析结果表明: 最优检查间隔决策约为67、70或77次起降循环, 这些检查间隔为决策者进行多目标相对最优的精确决策提供细化和更精简的选择参考。Abstract: In accordance with the preventive check plans, the defects detected in the course of inspection, and the repairing and renewing records in a certain cycles for the HPTACC system of a type of aeroengine of an airline freight fleet, the feasibilities for regarding the delayed time for the defects detected and the inspection and repairing costs as safety and economy optimization objectives were analyzed respectively.Under the inspection and repairing strategy of defects detected at the moments of preventive inspection, the probability expressions of expected number of defects and the delayed time for defects detected based on the delay-time model at any inspection momentwere deduced.Under the inspection and repairing strategy of defects degrading into failure and then being found timely and renewed at once, the probability expression of expected number of failure occurring based on delay-time model in every inspection interval was deduced.Based on the probability expressions under 2inspection and repairing strategies, the likelihood function for the system in a given life cycle was build.The double optimization objective functions including inspection and repairing costs and expected delayed time for detected defects were formed.A Pareto optimal solution set of double objective functions were derived by using the improved nondominated sorting genetic algorithm.According to the deciders' objective preference options and the empirical estimates of inspection and repairing costs and the delayed time for detected defects corresponding to their boundary values, the objective preference functions of inspection and repairing costs and the delayed time for detected defects in certain life cycles were determined respectively.The preference interval for every value in the Pareto optimal solution set was determined by using the objective preference function.Based on the collected inspection and repairing data and the proposed methods, an example was analyzed, in which the objective preferences of the delayed time of detected defects and the inspection and repairing costs for deciders were general and good respectively.Analysis result shows that the optimal inspection intervals are 67, 70 or 77landing and take-off cycles, which could provide detailed and more accurate decision-making reference of multi-objective relative optimization for deciders.
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图 4 缺陷产生至失效发生的延时过程
Figure 4. Delay-time course from defect generation to failure occuring
图 6 Pareto最优解与最优检查间隔的关系
Figure 6. Relationship between Pareto optimal solution and optimal inspection interval
图 7 优化目标函数与目标偏好函数关系
Figure 7. Relationship between optimal objective function and target preference function
图 8 缺陷延迟发现期望时间目标偏好函数曲线
Figure 8. Target preference function curve of expected delayed time for defects detected
图 9 检修费用目标偏好函数曲线
Figure 9. Target preference function curve of inspection and repairing costs
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