基于运筹优化的大型航司航空发动机机队管理方法/Management method of large aviation engine fleet based on operation optimizat

基于运筹优化的大型航司航空发动机机队管理方法/Management method of large aviation engine fleet based on operation optimizat。

本文介绍了利用运筹优化方法对大型航司发动机机队进行辅助管理的方法和实践。通过运筹学的方法可以全局地考虑发动机机队管理中所需要考虑的多维度因素，包括发动机状态，备发数量，维修策略，成本预算控制等，从而达到在保证机队运营前提下降低运营成本，将发动机管理模式从被动式向主动式过渡。此方法中包括发动机状态预测、维修策略生成，全生命周期优化和维修计划生成四个主要模块。通过这四个模块的有机结合最终实现对机队发动机的中短周期以及长周期维修计划的输出。本文也介绍了此方法在某大型航司的应用实践，展示了此方法应用于实际后可能带来的价值以及潜在收益。

关键词：运筹优化；换发计划；全生命周期管理；动态规划；人工智能

1 研究背景与意义

国内大型航司航空发动机机队的显著特征是机队规模庞大、机型复杂。以国内某大型航司为例，发动机细分型号达到13种，整体数量超过1400台。航空发动机作为飞机最为核心的部件，不仅是因为其安全性和可靠性对飞机的运行影响重大，还包含了发动机的价格、运行成本、飞机保值以及其对航班正常运行影响等严重关乎航空公司的运营。因此，在日常运行中，航空公司对发动机有着严格的健康安全管理制度。航空发动机机队管理是一项“牵一发，动全身”的系统性工程，需要通盘考虑机队的正常运行并兼顾发动机精益成本的管控。通常来说，发动机机队管理主要包括备发保障管理、发动机送修管理、成本预算控制及分析、商务及索赔管理和项目管理等多项职责。在机队管理过程中，由于各阶段机队管理策略的不同，制定决策和方案时所需的资源和因素也会随之发生变化。现有发动机机队管理具有以下明显的难点。

1) 发动机维修成本数额巨大，一般占飞机维修成本的一半，其管理工作的决策质量直接影响机务整体成本考核；与此同时，发动机维修过程涵盖了工程、计划、商务、维修现场等业务环节，各环节之间信息孤立，通常采用被动式管理，主要依赖人工经验，缺乏一套科学系统的决策支持工具；

2) 机队规模大，机型种类多，发动机服役周期长，外部环境的不确定性等诸多因素导致机队及成本管理限制及约束繁多，通过传统人工管理的方式难以从全局角度进行最优决策；

3) 当前备发保障和发动机维修的相关决策基本以运营保障为主要导向，备用发动机的保障水平参差不齐，临时租发的使用和维修工作范围的制定尚未与成本核算建立起直接逻辑关系，缺乏整体量化的考量，给预算控制和精细化管理带来巨大的困难。

例如，以“可用备发控制”为核心的管控策略，其核心是在运行过程中随时保持一台备发可用，该策略的优点在于：

a. 运行得到保障，减少非计划下发对运行带来的影响；

b. 长期换发计划准确率较高；

c. 可控性和备发利用率较高；

而缺点在于：

a. 为了保证备发数量，会额外临时租发；

b. 有时为了减少租发费用，将一部分发动机大修改为小修，缩短送修周期，可能会导致发动机维修成本变化大，特别是对未来维修成本的影响；

再如，以“短期成本最低”为核心的管控策略，其核心是以公司下拨预算为控制上限，仅对当年维修成本进行控制，此策略的优点在于：

a. 保证当年维修成本在预算之内，完成公司下达的考核目标；

b. 充分使用发动机的剩余在翼时间；

但缺点在于：

a. 长期换发计划准确率较低；

b. 非计划换发率较高，发生AOG对正常运行带来影响；

c. 可控性和备发利用率较低；

d. 大修发动机搁置不送修，导致产生额外的租发费用；

由此可知，这些策略都存在影响长期维修成本的缺点，但具体影响程度如 何或者能否找到一个长短期兼顾的管理方式，仅靠目前传统的人工管理方式是很难实现的。因此在大数据时代，航空公司迫切需要通过数据和更加科学的管理方式提升发动机机队管理效率和准确性。对此，本文提出借助运筹学的理论与方法，从全局角度综合考虑发动机管理工作中的复杂输入数据与业务约束条件，将发动机管理模式从被动式向主动式过渡，综合优化长短期成本收益，实现成本预算控制和智能管理决策。

2 运筹学基本框架及其在发动机维修计划管理中的使用

运筹学是现代管理学中重要的技术手段，也是在大数据环境下提升决策质量的重要方法。运筹学解决的问题是在多维度目标和复杂约束条件下，在众多决策方案中选择符合约束且能最好达到目标的“最优”方案。如图1所示，运筹学解决问题的方法论主要分为两步。第一步是基于业务背景建立运筹优化模型，通过数据或业务经验决定模型中的重要参数，并定义优化目标与约束条件；第二步是求解优化模型，得到满足约束条件下能够最好达成目标的最优解。最终再通过人工的修正和调整将决策使用在业务之中。

在发动机全生命周期的管理中，核心目标在于综合优化长短期成本收益， 最终达到满足预算考核的目标。而这一优化目标的实现涉及了发动机送修、租赁、改装、包修、退租等一系列长短期决策工作。基于对现有发动机管理工作流程的梳理，在发动机维修管理中通常面临的核心决策包括：

a. 发动机换发计划；

b. 发动机维修工作范围；

c. 使用备发、临时租发、串发操作等管理策略；

d. 发动机拆解、置换等方案。

与此同时，以上相关决策的优化需要考虑以下4类约束条件：

1) 发动机硬件状态：包括发动机LLP和时控项目、孔探磁堵和油液分析结果；监控项目、性能、改装等相关数据结果所对应的业务约束；

2) 维修资源状态：维修厂维修资源及能力、维修周期、成本预算、拆解件和二手件的使用等约束；

3) 运行环境：包括与执管单位、环境、航线分布、减推等具体业务场景相关的约束；

4) 商务因素：包括诸如飞机退租、飞机处置、发动机包修等商务条款相关的业务约束等。

通过在综合考虑以上约束的条件下对核心决策进行优化，希望实现的最终效果是：

a. 制定更合理的长、短期发动机换发计划，减少非计划换发；

b. 减少临时租发比例，实现变化平缓、可预期、可控的备发保障水平；

c. 根据飞机退租和处置要求、发动机硬件状态及公司财务政策优化机队管理措施，如采取串发、阶梯使用、控制月使用循环数、控制推力等。在满足手册及局方要求前提下，降低给定计划周期内（如年度、全生命周期）发动机相关总成本（尤其是发动机送修和租赁成本）。

综上所述，航空发动机机队管理优化问题有着明确的决策、约束、目标的属性，属于较为典型的运筹学应用场景。

3 发动机维修优化解决方案

本节将具体描述利用运筹学和人工智能方法对发动机全生命周期进行计划 管理的方案，整体框架如图2所示，具 体主要包括4个核心模块。

3.1 发动机健康状态预测模块

这一模块首先对发动机部件损伤发展时间进行预测，主要利用历史数据和机器学习中的预测模型（如回归模型、树模型等）对发动机孔探中的部件损伤发展规律进行分析，如图3所示。具体而言，首先将发动机孔探历史数据进行清洗，采用回归和置信区间的方式对异常数据进行过滤，减少对于预测结果的影响。过滤后的数据使用基于随机森林（Random Forest）和自适应增强算法 （Adaboost）建立集成模型，预测发动机部件损伤发展时间，再使用交叉验证进行参数调整。除孔探模型之外，此模块也建立损伤区域与发动机运行参数的内在联系模型，预测损伤纳入重点监控和濒临损伤超标的时间。

其次，结合机队运行的因素对发动机健康状态进行预测，构建不同条件下的发动机在翼健康情况发展模型，建立发动机多级健康状态预测模型，优化发动机在翼管理。最终达到发动机在不同使用方式下对任意时间可以达到一个较为精准的状态预测。此部分的预测结果也将作为发动机维修计划优化模型的重要输入。

3.2 发动机维修策略生成模块

此部分首先根据发动机健康状态和修后目标生成发动机维修策略备选集合，并建立发动机修后健康性能评价方法。具体而言，基于发动机下发时的健康状态、维修工作手册，此模块将生成发动机各单元体基本工作范围的可选集合。再根据重要部件的剩余在翼时间和涉及的服务通告，更新发动机的维修工作范围。根据发动机不同的修后目标，做出发动机不同的工作范围，以及不同工作范围所对应的送修成本和修后的健康性能，综合输出发动机的维修策略集合。

与此同时，此模块还包括了发动机重点部件报废率的预测模型。具体是将发动机送修的历史数据进行清洗，运用聚类方法和联合集成模型，对部件报废率进行预测。另外，对历史数据中发动机维修后返回时间（TAT）进行分析，分解修后返回时间，建立特征工程，对返回时间的影响因素进行分解。最终使用机器学习的方法对每一个策略对应的返回时间进行估计。

这一部分生成的维修策略将形成每一台发动机在每一时间点可选策略集，以及生成每一个策略对应的维修成本、修后返回时间。这些对应关系成为在换发计划中算法选择的决策集合。最终算法再根据全局的优化选出最优的策略。

3.3 发动机全生命周期优化模块

全生命周期模型承接发动机健康状态预测、维修策略管理模型，对机队中发动机（包含自有、经营租赁等）进行全生命周期内的整体规划。全生命周期 内的整体规划将包含发动机从加入机队（或从当前时间点）开始到退出机队为止的大修计划。退出机队的时间将由发动机的产权类型（包括自有、经租）来决定：自有发动机将制定从进入机队起25年的计划；租赁发动机将制定与租赁合同相符的计划。在此时间范围内，全生命周期优化模型将在满足机队使用需求 的前提下合理安排发动机大修计划，尽可能最大化发动机全生命周期的使用效率，并在满足退租条件的前提下尽可能降低维修成本，实现“物尽其用”。

为了实现以上目标，全生命周期模型分为两个阶段。在第一阶段中，全生命周期优化模块将考虑不同发动机的当前健康状态、包修条件、退租条件，生成每台发动机可选择的维修策略集合。此模块以运筹学中的动态规划模型为工具（注：动态规划，即Dynamic Programming，是运筹学的一个分支，是求解最优动态决策的方法。如果一类决策过程可以分为若干个互相联系的阶段，在每一个阶段都 需做出决策，且一个阶段的决策会影响到下一个阶段的决策，则称它为多阶段动态规划问题），输出一类发动机最优的若干种修理模式（主要包括修理间隔和工作范围）。在动态规划模型中，每台发动机在每个时刻将具有一个状态变量s。此状态变量s将包含发动机寿命、租赁时长、发动机各个模块健康状态、上次维修记录、孔探等检查结果，以及发动机寿命件剩余使用寿命等刻画发动机状态的信息。在每个时间切片t，对应的模型决策为送修（维修的策略集由维修策略模型生成）或继续在翼。根据修理策略的不同（TAT、返回状态、返回后推力等），发动机状态变量s发生相应的转移。同时不同的修理策略也对应不同的维修费用成本。通过动态规划的策略迭代优化（注：策略迭代，即Policy Iteration，是一种求解动态规划的算法）方法，此模块将得到每台发动机在全生命周期内尽可能最多在翼的前提下，使得总维修折现价值最小的维修安排，通过合理安排多次维修决策，减少短视和不合理的维修，以实现发动机总费用的减少、效益的提高。图4中展示了动态规划的示意图。在实际测算问题中，以25年为发动机全生命时间，按月划切片为300个周期。发动机状态考虑模块和部件的细分维度超过60个维度。

在获得了每台或每类发动机的最优修理模式的集合之后，对机队整体的发动机进行全生命周期优化。在此过程中，每台发动机在其最优修理模式之中进行选择，使得全规划期内的下发水平尽量平稳，且满足不同推力飞机的发动机需求。整体求解框架如图5。

3.4 换发计划优化模块

本模块是发动机换发计划优化模型中的最后一步，也是最核心的一步。本模块将考虑全局优化发动机的换发计划。承接发动机健康预测、维修策略管理、全生命周期模块的输入，此模块对每台发动机的换发和送修时刻、送修时的维修策略进行优化。最终形成一个在一定时间跨度下的（如一年）最优换发计划。

具体而言，对每台发动机在任意时间窗口定义4个基础变量，将发动机状态刻画为在翼、备发、维修、不可用四种之一（在实际中还有一些其他状态刻画一些例外的情况，这里由于篇幅限制不加赘述）。当发动机在机队时，必为四种状态之一。当发动机不在机队时，通常为了提高效率不会生成相应状态变量。但对于可能续租的发动机，其是否继续在机队需要模型决策，故也会生成相应状态变量。其次，定义发动机在上述四种状态之间变化时的诱因变量，包括分为上发、下发、送修、返修（同样的在实际模型中还有一些例外的诱因变量，这里也不加赘述）。发动机状态随送修、返修操作而改变，而每一次状态的改变将通过变量之间的数学关系刻画。模型还将考虑临时租发变量、发动机送修策略变量等，刻画租发决策以及使用某种维修策略对发动机进行维修的行为。

在优化维修策略时，模型主要会考虑以下几类主要约束，每一个约束都会构成优化模型里的一个约束条件，即图6中的变量之间需要满足的一些数学不等式。

（1）机队运行因素约束：发动机时寿件、发动机月飞行小时、月飞行循环、 运行基地、所处推力、机队运力要求、突发适航指令等。

（2）发动机状态转移约束：发动机状态为在翼、备发、维修、不可用四种之一 ；发动机状态随上发、下发、维修、操作而改变。同一发动机在同一时刻只 能有一种状态。

（3）发动机换发约束：在固定时间窗（如每周、每月）内下发次数约束；强制下发约束；临时租发在真实租期（可能延长或提前）前需要下发；退租前不维修的发动机，租赁到期前拆下退租，退租前维修的发动机，租赁到期前维修后退租等约束。

（4）发动机返修约束：维修返回时间和上发时间的关系，发动机返修后需要一定准备时间才能上发；维修时间和返回时间的关系等约束。

（5）需求与备发约束：保证备发数量大于安全库存备发水平，不够时引入惩罚；保证在翼数量等于机队固定的在翼数量，不够时加入临时租发。

（6）临时租发约束：临时租发续租发动机，退租前最后时刻必须为在翼状态才可续租；续租发动机的最高时长约束；短租和长租数量约束。

（7）预算约束：修理+租发的费用上限不可超出预算。某一类型的费用也要满足对应的预算。

（8）其他约束：如AD时限约束、onwatch按顺序下发约束、二手件使用约束等。

以上部分约束为硬约束/硬时限，表示这些约束完全不能违反；另外一部分约束为软约束，表示这些约束最好不违反，若违反则会对策略的评估加以惩 罚。在软约束中，有些为强惩罚约束（若违反惩罚较大），还有些为弱惩罚约束 （若违反惩罚较小）。图7列举了一些各类约束的例子。图8中展示了一些由工程师和发动机管理团队可以在模型中调整的参数。

最后需要设定模型优化的目标。目标的设定会考虑多个方面，主要包括维修成本、超出预算的成本、临时新租租发成本、临时续租租发成本、退租成本、不足安全备发数量的惩罚、备发水平波动的惩罚、未执行全生命周期推荐策略的惩罚等。模型也会考虑到不同时期发动机增加的剩余价值。将以上数值进行加权计算之后得到优化模型的目标函数值。

在集合了以上的约束和目标之后，换发计划模型即定义完成。就模型属性而言，以上建立的换发计划模型是一种混合整数规划模型（Mixed-Integer Programming），通常问题有数万规模变量和约束。这类问题需要特定的软件，即优化求解器进行求解（注：优化求解器，也即Optimization Solver，为一类工业软件，用来高效求解优化模型）。在本次项目中使用了国产优化求解器对以上运筹优化问题进行高效求解，一般可在20～30分钟得到一版换发计划的结果。

4 应用结果

以上的发动机维修管理优化方法已经通过系统化的方式供南方航空的发动机维修计划团队使用。发动机维修优化系统通过对接基础信息系统获取历史发动机的维修情况，孔探数据、租发数据、退租数据等等，并进行建模和优化求解计算。同时，系统允许工程师配置不同参数获得全生命周期发动机维修计划及中短期维修计划的不同版本，并最终将希望使用的版本发布到发动机管理系统之中。

为了测算优化效果，将此模型应用到2021年5月至10月五个月时间段内V2500发动机机队真实换发场景，作为测试。整个测试问题中涉及发动机84台（实际机队中有300多台V2500发动机，测试问题选取84台可能发生状态变化的发动机，如即将下发、正在维修中待返回、正在备发准备上发等）进行对比。其余200余台发动机在此时间窗口内健康状态都为良好，事先判断在此时间窗口内都会在翼，不需要在换发计划中考虑）。在此测算中，首先利用全量孔探数据对孔探单损伤发展进行预测建模（具体见3.1中所述方法），通过机器学习模型获得对“下一次孔探时间测量值”的预测，可达到MAPE（Mean Absolute Percentage Error，也即平均绝对误差比例）约7%左右。同时建立孔探多损伤模型，结合发动机运行状况和下发数据进行剩余在翼时间预测，得到 “下一次下发时间”的预测MAPE在20%左右，并以此发动机健康状态发展模型作为优化问题的输入。

另外还建立了维修策略模型。基于每一台发动机的当即状态（重要部件的剩余在翼时间、涉及的服务通告等）， 根据发动机不同的修后目标，计算出发动机不同的合理工作范围，以及不同工作范围对应的送修成本和修后的健康性能，并将所有合理工作范围作为备选方案，输入到优化问题中。同时利用TAT预测模型给出对维修时间的预估，利用叶片报废率模型修正送修成本中的更换叶片成本。在此项目中，最终将维修策略模块形成系统化工具，在系统中读取每台发动机的健康状态，BSI预测，维修定级手册等数据，自动生成几版合理的维修范围的结果。此系统支持用户进行维修范围的修改、删除和新增等操作。支持在新增或修改操作中，对关键信息的自动计算补充。图9中展示维修策略生成模块系统的示例。

在完成以上模块后，建立发动机换发优化模型。在此测试问题中，发动机 换发优化模型中涉及到决策变量大约有8万个（其中状态变量包含受影响发动机84台×时间窗个数158天×状态变量数4种=53424个；状态转移变量包括受影响发动机84台×备选变动时间窗个数30天×状态转移变量数4种=10080个；维修策略选择变量包括待选下发发动机67台×备选变动时间窗个数30天×平均策略3种=6030个；临时租发变量、辅助变量等总数10000左右）。约束大约有72000个（其中包括硬约束43000个，强惩罚约束13000个，软惩罚约束16000个）。在给定一组参数选择后（见图8），通过数学规划求解器计算换发计划大约用时1500秒（计算机使用cpu为2GHz四核Intel Core i5）。

在以上测算模型下，即可得到基于模型的最优换发策略，并可将模型策略和实际计划策略进行对比，如图10所示。图10中可以看到红色曲线为实际发生的备发水平，黑色曲线为按照模型规划的备发水平，绿色线为人工在时间窗口 初期制定的计划对应的备发水平曲线。需要注意的是，这里曲线中没有明显显示临时租发的情况，当出现备发短缺，即将出现负备发时往往需要通过临时租发解决，最终形成黑色和红色的曲线。从这些曲线可以看出，计划层面通常真实有效的计划周期在2个月左右，之后的计划曲线多为人力相对难以考量的，实际也会通过临时租发的情况进行紧急调整。

对比显示，测算的案例中通过模型的优化可节省临时租发天数30%，减少 零备发天数18天（真实零备发天数为19天，模型零备发天数为1天）。降低发动机库存天数70%（这里指超过一个备发的库存）。按模型测算可年节约成本期望可达千万元人民币以上。

另外，将此算法结果进行了系统化， 如图11所示供发动机维修团队使用的系统。当完成换发计划计算后，可以通过页面展示运行结果。在此结果中，工 程师和管理人员可以查看具体维修工作范围，如各module定级、总成本、TAT等信息。对于换发计划结果可以进行确认（如锁定某台发动机的计划）或者调整，或锁定后修改参数重新进行优化等，还可以通过甘特图展示换发状态，如图12所示。

5 总结

当前，航空发动机管理优化的相关研究集中在基于基础的统计模型和分析或采用模拟仿真的手段指导备发数量的规划。在实际业务中仍主要采取视情维修的管理模式，很多决策环节高度依赖人工经验，缺乏系统科学的方法论支持。本文提出的基于运筹学的维修管理模式系统性地设计了多模块，充分考虑机队、 发动机参数、部件可靠性、孔探结果、历史维修、租赁、财务等多维度数据，采用运筹优化、机器学习等前沿技术，建立起一套完整的智能决策系统，真正做到了数据驱动、全局优化、智能决策。具体特色如下：

（1）发动机状态预测

采用机器学习方法，给出发动机孔探恶化发展概率，减少非计划下发；

采用分层结构，输出发动机各单元体剩余在翼寿命，对下发决策提供科学 支持；

（2）发动机维修备选策略

以恢复在翼时间为核心，输出发动机送修的多种策略集合和成本；

引入发动机剩余健康状况，输出本次和下次的预估送修工作范围，避免出现维修不足和维修过度的情况；

建立决策树模型，预测送修TAT，合理规划换发计划；

（3）发动机全生命周期优化

科学合理安排发动机全生命周期中大修的修理时间和工作范围；

有效减少全生命内的大修次数，提高部件利用率，优化总体成本；

维修策略精确到重要部件修理深度，能够更准确地计算修后在翼时长、TAT、修理成本等指标，避免过度维修和维修不足；

对于单次维修提供多种维修策略集合，支持全生命周期与换发计划优化；

（4）发动机换发优化

引入智能备发管理水平，输出备发水平时间轴，减少备发波动影响；

将送修计划和换发计划综合考虑，将维修、租赁成本纳入额外优化目标， 产出不同预算下的换发维修方案；

使用混合整数规划模型，允许一系列定制化约束激活，提升模型应用的可 操作性。

综上所述，针对目前民航业对于发动机维修和换发方案的决策过程理论研究中存在的空白欠缺之处，本项目运用现代运筹学结合人工智能算法，通过对发动机健康状态预测、发动机维修策略生成、换发计划优化、全生命周期优化，建立一套基于运筹优化理论算法的智能发动机全生命周期管理闭环框架，并在实际业务场景下进行应用，形成了一套合理、有效、系统化的智能决策方法论。

Management method of large aviation engine fleet based on operation optimizat /Management method of large aviation engine fleet based on operation optimizat.

This paper introduces the method and practice of auxiliary management of large aviation engine fleet by means of operation research optimization. Through the method of operations research, the multi-dimensional factors that need to be considered in the engine fleet management can be considered globally, including the engine state, the number of backup, maintenance strategy, cost budget control, etc., so as to achieve the reduction of operating costs under the premise of ensuring the fleet operation, and the engine management mode will transition from passive to active. This method includes four main modules: engine condition prediction, maintenance strategy generation, life cycle optimization and maintenance plan generation. Through the organic combination of these four modules, the output of medium and short cycle and long cycle maintenance plans for fleet engines is finally realized. This paper also introduces the application practice of this method in a large airline, and shows the value and potential benefits that this method may bring after being applied in practice.

Key words: operational research optimization; Replacement plan; Full life cycle management; Dynamic programming; Artificial intelligence

1. Research background and significance

The significant characteristics of the domestic large aviation engine fleet are the large fleet size and complex models. Taking a large domestic airline as an example, there are 13 types of engine subdivisions, and the overall number exceeds 1,400 units. As the most core component of aircraft, aviation engine is not only because its safety and reliability have a significant impact on the operation of the aircraft, but also includes the price of the engine, operating costs, aircraft preservation and its impact on the normal operation of the flight, which are seriously related to the operation of the airline. Therefore, in daily operation, the airline has a strict health and safety management system for the engine. Aero engine fleet management is a systematic project of "taking one step and moving the whole body", which needs to consider the normal operation of the fleet and the control of engine lean cost. Generally speaking, engine fleet management mainly includes provisioning support management, engine repair management, cost budget control and analysis, business and claims management and project management. In the process of fleet management, due to different fleet management strategies at different stages, the resources and factors required to make decisions and programs will also change. The existing engine fleet management has the following obvious difficulties.

1) The engine maintenance cost is huge, generally accounting for half of the aircraft maintenance cost, and the quality of its management decision-making directly affects the overall maintenance cost assessment; At the same time, the engine maintenance process covers engineering, planning, business, maintenance site and other business links, with isolated information among each link, usually adopt passive management, mainly rely on manual experience, and lack of a set of scientific and systematic decision support tools.

2) The large fleet size, various types of models, long engine service cycle, uncertainty of external environment and many other factors lead to numerous restrictions and constraints on fleet and cost management, and it is difficult to make optimal decisions from a global perspective through traditional manual management;

3) At present, the relevant decisions of backup support and engine maintenance are mainly oriented to operation support, and the support level of backup engine is uneven. The use of temporary lease and the formulation of maintenance work scope have not established a direct logical relationship with cost accounting, and lack of overall quantitative consideration, which brings great difficulties to budget control and fine management.

For example, the management and control policy based on Availability Backup control is to keep a backup server available at any time during operation. The advantages of this policy are as follows:

a. Operation is guaranteed to reduce the impact of unplanned delivery on operation;

b. The long-term replacement plan has high accuracy;

c. High controllability and backup utilization;

The downside is that:

a. In order to ensure the supply quantity, additional temporary leasing will be provided;

b. Sometimes, in order to reduce leasing costs, some engine overhaul is changed to minor repair and the repair cycle is shortened, which may lead to large changes in engine maintenance costs, especially the impact on future maintenance costs;

Another example is the control strategy with the "lowest short-term cost" as the core, the core of which is the company's allocated budget as the control ceiling, and only the maintenance cost of the current year is controlled. The advantages of this strategy are as follows:

a. Ensure that the maintenance cost is within the budget and complete the assessment objectives assigned by the company;

b. Make full use of the remaining wing time of the engine;

But here's the downside:

a. The accuracy of long-term replacement plan is low;

b. The unplanned turnover rate is high, and the occurrence of AOG has an impact on normal operation;

c. Low controllability and backup utilization;

d. Overhauling engine shelving without sending for repair, resulting in additional rental costs;

It can be seen that these strategies all have shortcomings that affect long-term maintenance costs. However, it is difficult to realize the specific impact degree or whether a management method that takes into account both the long and short term can be found by relying only on the current traditional manual management method. Therefore, in the era of big data, airlines urgently need to improve the efficiency and accuracy of engine fleet management through data and more scientific management methods. In this regard, this paper puts forward the theory and method of operations research to comprehensively consider the complex input data and business constraints in engine management from a global perspective, transition the engine management mode from passive to active, comprehensively optimize the long-term and short-term cost benefits, and realize cost budget control and intelligent management decisions.

2 The basic framework of operations research and its use in engine maintenance program management

Operations research is an important technical means in modern management, and it is also an important method to improve the quality of decision making in the environment of big data. The problem of operations research is to select the "optimal" solution that meets the constraints and can best achieve the goal among many decision schemes under the conditions of multi-dimensional objectives and complex constraints. As shown in Figure 1, the problem solving methodology of operations research is mainly divided into two steps. The first step is to establish an operational research optimization model based on the business background, determine the important parameters of the model through data or business experience, and define the optimization objectives and constraints; The second step is to solve the optimization model to obtain the optimal solution that can best achieve the goal under the constraint conditions. The decision is then applied to the business through manual corrections and adjustments.

In the whole life cycle management of the engine, the core goal is to comprehensively optimize the long-term and short-term cost benefits, and finally achieve the goal of meeting the budget assessment. The realization of this optimization goal involves a series of long and short term decisions, such as engine repair, lease, modification, contract repair and lease cancellation. Based on the review of the existing engine management workflow, the core decisions usually faced in engine maintenance management include:

a. Engine replacement plan;

b. Scope of engine maintenance work;

c. Use management strategies such as standby, temporary lease and serial delivery;

d. Engine disassembly, replacement and other programs.

At the same time, the optimization of the above related decisions needs to consider the following four types of constraints:

1) Engine hardware status: including engine LLP and time control items, hole detection magnetic plug and oil analysis results; Monitor the corresponding business constraints of project, performance, modification and other related data results;

2) Status of maintenance resources: constraints on maintenance resources and capabilities, maintenance cycle, cost budget, use of disassembled parts and second-hand parts;

3) Operation environment: including constraints related to specific business scenarios such as management unit, environment, route distribution, and reduction of push;

4) Business factors: including business constraints related to commercial terms such as aircraft rentals, aircraft disposal, engine repair, etc.

By optimizing the core decision under the conditions of comprehensive consideration of the above constraints, the desired final effect is:

a. Develop more reasonable long - and short-term engine replacement plans to reduce unplanned replacement;

b. Reduce the proportion of temporary leasing to achieve a smooth, predictable and controllable level of backup protection;

c. Optimize fleet management measures according to aircraft rent-out and disposal requirements, engine hardware status and company financial policies, such as serial delivery, tiered use, monthly cycle control, thrust control, etc. Reduce the total engine related costs (especially engine repair and lease costs) within a given planned period (e.g., annual, full life cycle), subject to the requirements of the manual and the bureau.

To sum up, the aero-engine fleet management optimization problem has clear attributes of decision, constraint and goal, and belongs to a typical operational research application scenario.

3 Engine maintenance optimization solutions

This section will specifically describe the plan for planning management of the whole life cycle of the engine by using operations research and artificial intelligence methods. The overall framework is shown in Figure 2, which mainly includes four core modules.

3.1 Engine health state prediction module

This module first predicts the damage development time of engine components, and mainly uses historical data and predictive models in machine learning (such as regression model, tree model, etc.) to analyze the damage development law of components in engine borehole exploration, as shown in Figure 3. Specifically, the historical data of engine borehole exploration is cleaned first, and the abnormal data is filtered by regression and confidence interval to reduce the impact on the prediction results. Based on the filtered data, an integrated model based on Random Forest and adaptive enhancement algorithm (Adaboost) was established to predict the damage development time of engine components, and then parameters were adjusted by cross-validation. In addition to the borehole model, this module also establishes the internal relationship model between the damage area and the engine operating parameters, and predicts the time when the damage is included in the key monitoring and is on the verge of exceeding the damage limit.

Secondly, combined with the factors of fleet operation, the engine health status was predicted, and the development model of engine health status under different conditions was built, and the multi-stage health status prediction model of engine was established to optimize engine management in wing. Finally, the engine can achieve a more accurate state prediction at any time under different modes of use. The forecast results of this part will also be an important input to the optimization model of engine maintenance plan.

3.2 Engine maintenance strategy generation module

In this part, the alternative set of engine maintenance strategy is generated according to the engine health state and repair objectives, and the evaluation method of engine health performance after repair is established. Specifically, based on the health status of the engine at the time of delivery, the maintenance workbook, this module will generate an optional collection of the basic operating ranges of the engine units. Then update the scope of engine maintenance work according to the remaining wing time of important components and the service announcements involved. According to the different repair objectives of the engine, the different working ranges of the engine, the corresponding repair cost and repair health performance of the different working ranges are made, and the maintenance strategy set of the engine is synthesized.

At the same time, the module also includes a prediction model of the obsolescence rate of key engine components. Specifically, the historical data of the engine sent for repair are cleaned, and the clustering method and the joint integrated model are used to predict the scrap rate of the parts. In addition, the engine return time after maintenance (TAT) in the historical data is analyzed, the return time after repair is decomposed, the feature project is established, and the influencing factors of the return time are decomposed. Finally, the machine learning method is used to estimate the corresponding return time of each strategy.

The maintenance strategy generated in this part will form a set of optional strategies for each engine at each time point, and generate the corresponding maintenance cost and repair return time for each strategy. These correspondences become the set of decisions for algorithm selection in the exchange plan. Finally, the algorithm selects the optimal strategy according to the global optimization.

3.3 Engine life cycle optimization module

The whole life cycle model carries on the engine health state prediction and maintenance strategy management model, and makes the overall planning for the whole life cycle of the engine in the fleet (including own, operating lease, etc.). The overall life cycle planning will include an overhaul plan for the engine from the time it joins the fleet (or from the current point in time) to the time it leaves the fleet. The timing of fleet exit will be determined by the type of engine ownership (both owned and leased) : owned engines will have a 25-year plan from the time they enter the fleet; The lease engine will develop a plan in accordance with the lease contract. Within this time range, the whole life cycle optimization model will reasonably arrange the engine overhaul plan on the premise of meeting the needs of the fleet, maximize the use efficiency of the whole life cycle of the engine as much as possible, and reduce the maintenance cost as much as possible on the premise of meeting the conditions of leasing, so as to achieve the "best use".

To achieve these goals, the lifecycle model is divided into two phases. In the first phase, the full life cycle optimization module will take into account the current health status of different engines, repair conditions, lease conditions, and generate a collection of service strategies for each engine. This module uses the Dynamic Programming model in operations research as a tool (Note: Dynamic Programming, also known as dynamic programming, is a branch of operations research and a method for solving optimal dynamic decisions). If a class of decision-making process can be divided into several interrelated stages, each stage needs to make a decision, and the decision of one stage will affect the decision of the next stage, it is called a multi-stage dynamic programming problem), output a class of engine optimal repair mode (mainly including repair interval and working range). In the dynamic programming model, each engine will have a state variable s at each moment. This state variable s will contain information that characterizes the state of the engine, such as engine life, lease duration, health status of each module of the engine, last maintenance record, inspection results such as hole exploration, and remaining service life of the engine life parts. At each time slice t, the corresponding model decision is to send repair (the maintenance policy set is generated by the maintenance policy model) or continue on the wing. According to the different repair strategy (TAT, return state, thrust after return, etc.), the engine state variable s will be transferred accordingly. At the same time, different repair strategies also correspond to different maintenance costs. Iterative optimization of strategies through dynamic programming (note: Policy Iteration, also known as policy Iteration, is an algorithm for solving dynamic programming. This module will obtain the maintenance arrangement that minimizes the total maintenance discount value under the premise of wing as much as possible in the whole life cycle of each engine, and reduce short-sighted and unreasonable maintenance by rationally arranging multiple maintenance decisions. In order to reduce the total cost of the engine and improve the efficiency. A schematic of dynamic programming is shown in Figure 4. In the actual calculation problem, 25 years is taken as the whole life time of the engine, and 300 cycles are divided by month. Engine status considers more than 60 dimensions of subdivision of modules and components.

After obtaining a set of optimal repair modes for each engine or class of engines, the whole engine life cycle optimization of the fleet is carried out. In this process, each engine is selected among its optimal repair modes, so that the delivery level is as smooth as possible throughout the planning period and meets the engine needs of different thrust aircraft. The overall solution framework is shown in Figure 5.

3.4 Exchange plan optimization module

This module is the last step in the optimization model of engine replacement plan, and also the most core step. This module will consider the global optimization of the engine replacement plan. To undertake the input of engine health prediction, maintenance strategy management, and the whole life cycle module, this module optimizes the maintenance strategy of each engine when it is replaced and sent for repair. Finally, an optimal replacement plan is formed over a certain time span (for example, one year).

Specifically, for each engine in any time window, define 4 base variables that will change the engine