Title:

Kind
Code:

A1

Abstract:

A process for optimizing maintenance work schedules for at least one engine includes the steps of retrieving at least one set of data for an engine from a computer readable storage medium; selecting at least one scheduling parameter for the engine; selecting a set of maintenance rules for the engine; selecting at least one maintenance work decision; selecting at least one objective for the engine; optimizing the at least one objective to generate at least one optimal maintenance work decision; and generating at least one optimal maintenance work schedule for the engine.

Inventors:

Costiner, Sorin (Somerville, MA, US)

Winston, Howard A. (Woodbury, CT, US)

Wang, Jihua (Unionville, CT, US)

Khibnik, Alexander I. (Glastonbury, CT, US)

Rajamani, Ravi (West Harford, CT, US)

Matthis, Thomas R. (Manchester, CT, US)

Benitez, Ricardo A. (Bolton, CT, US)

Ireland, Julie A. (East Hampton, CT, US)

Cohen, Robert M. (West Hartford, CT, US)

Cohen, Ellen (West Hartford, CT, US)

Winston, Howard A. (Woodbury, CT, US)

Wang, Jihua (Unionville, CT, US)

Khibnik, Alexander I. (Glastonbury, CT, US)

Rajamani, Ravi (West Harford, CT, US)

Matthis, Thomas R. (Manchester, CT, US)

Benitez, Ricardo A. (Bolton, CT, US)

Ireland, Julie A. (East Hampton, CT, US)

Cohen, Robert M. (West Hartford, CT, US)

Cohen, Ellen (West Hartford, CT, US)

Application Number:

11/725934

Publication Date:

09/25/2008

Filing Date:

03/19/2007

Export Citation:

Assignee:

United Technologies Corporation

Primary Class:

International Classes:

View Patent Images:

Related US Applications:

Other References:

Chang, C.S. et al. "Evolutionary Multi-Objective Optimization of Substation Maintenance using Markov Model." The 14th International Conference on Intelligent System Applications of Power Systems, Kaohsiung, Taiwan, 4-7 November 2007. pp. 77-82.

Greitzer, Frank L. et al . "Gas Turbine Engine Health Monitoring and Prognostics." International Society of Logistics (SOLE) 1999 Symposium, Las Vegas, Nevada, 30 August - 2 September 1999. pp. 1-7.

Meher, Cyrus B. et al. "An Approach for the Integration of Condition Monitoring and Multiobjective Optimization for Gas Turbine Maintenance Management." The 3rd Internation Monitoring and Diagnostic Conference, Las Vegas, Nevada 9-12 December 1991.

Nggada, Shawulu H. et al. "Dynamic Effect of Perfect Preventive Maintenance on System Reliability and Cost Using HiP-HOPS." 2010.

Greitzer, Frank L. et al . "Gas Turbine Engine Health Monitoring and Prognostics." International Society of Logistics (SOLE) 1999 Symposium, Las Vegas, Nevada, 30 August - 2 September 1999. pp. 1-7.

Meher, Cyrus B. et al. "An Approach for the Integration of Condition Monitoring and Multiobjective Optimization for Gas Turbine Maintenance Management." The 3rd Internation Monitoring and Diagnostic Conference, Las Vegas, Nevada 9-12 December 1991.

Nggada, Shawulu H. et al. "Dynamic Effect of Perfect Preventive Maintenance on System Reliability and Cost Using HiP-HOPS." 2010.

Primary Examiner:

NORTON, JENNIFER L

Attorney, Agent or Firm:

Bachman & LaPointe, P.C. (New Haven, CT, US)

Claims:

What is claimed is:

1. A process for optimizing maintenance work schedules for at least one engine, comprising: retrieving at least one set of data for an engine from a computer readable storage medium; selecting at least one scheduling parameter for said engine; selecting a set of maintenance rules for said engine; selecting at least one maintenance work decision; selecting at least one objective for said engine; optimizing said at least one objective to generate at least one optimal maintenance work decision; and generating at least one optimal maintenance work schedule for said engine.

2. The process of claim 1, wherein the optimization step comprises the steps of: evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; constructing a scheduled maintenance plan based upon the evaluation step; generating a projected cost of at least one maintenance work decision based upon the construction step; and selecting at least one cost effective maintenance work decision; and optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

3. The process of claim 2, wherein the evaluation step comprises using any one of the following approaches: deterministic approach and stochastic approach.

4. The process of claim 1, wherein the selection step of said at least one scheduling parameter comprises selecting said at least one scheduling parameter based upon said at least one set of data.

5. The process of claim 1, wherein the selection step of said set of maintenance rules comprises selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

6. The process of claim 1, wherein the selection step of said at least one maintenance work decision comprises the following steps: accepting said at least one scheduling parameter; incorporating said set of maintenance rules; and determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

7. The process of claim 6, wherein the determination step comprises processing said at least one scheduling parameter and said set of maintenance rules using any one of the following approaches: deterministic approach and stochastic approach.

8. The process of claim 1, wherein the selection step of said at least one objective comprises generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

9. The process of claim 1, wherein the generation step comprises generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

10. A system comprising a computer readable storage device readable by the system, tangibly embodying a program having a set of instructions executable by the system to perform the following steps for optimizing maintenance work schedules for at least one engine, the system comprising: means for retrieving at least one set of data for an engine from a computer readable storage device; means for selecting at least one scheduling parameter for said engine; means for selecting a set of maintenance rules for said engine; means for selecting at least one maintenance work decision; means for selecting at least one objective for said engine; means for optimizing said at least one objective to generate at least one optimal maintenance work decision; and means for generating at least one optimal maintenance work schedule for said at least one engine.

11. The system of claim 10, wherein the instruction to optimize comprises: means for evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; means for constructing a scheduled maintenance plan based upon the evaluation step; means for generating a projected cost of at least one maintenance work decision based upon the construction step; and means for selecting at least one cost effective maintenance work decision; and means for optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

12. The system of claim 11, wherein means for evaluating comprises means for using any one of the following approaches: deterministic approach and stochastic approach.

13. The system of claim 11, wherein means for selecting said at least one scheduling parameter comprises means for selecting said at least one scheduling parameter based upon said at least one set of data.

14. The system of claim 11, wherein means for selecting said set of maintenance rules comprises means for selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

15. The system of claim 11, wherein means for selecting said at least one maintenance work decision comprises: means for accepting said at least one scheduling parameter; means for incorporating said set of maintenance rules; and means for determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

16. The system of claim 15, wherein means for determining comprises means for processing said at least one scheduling parameter and said set of maintenance rules and to use any one of the following approaches: deterministic approach and stochastic approach.

17. The system of claim 11, wherein means for selecting said at least one objective comprises means for generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

18. The system of claim 11, wherein means for generating comprises means for generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

19. A process for optimizing maintenance work schedules for at least one industrial system, comprising: retrieving at least one set of data for at least one industrial system from a computer readable storage medium; selecting at least one scheduling parameter for said at least one industrial system; selecting a set of maintenance rules for said at least one industrial system; selecting at least one maintenance work decision for said at least one industrial system; selecting at least one objective for said at least one industrial system; optimizing said at least one objective to generate at least one optimal maintenance work decision for said at least one industrial system; and generating at least one optimal maintenance work schedule for said at least one industrial system.

20. The process of claim 19, wherein the optimization step comprises the steps of: evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; constructing a scheduled maintenance plan based upon the evaluation step; generating a projected cost of at least one maintenance work decision based upon the construction step; and selecting at least one cost effective maintenance work decision; and optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

21. The process of claim 20, wherein the evaluation step comprises using any one of the following approaches: deterministic approach and stochastic approach.

22. The process of claim 19, wherein the selection step of said at least one scheduling parameter comprises selecting said at least one scheduling parameter based upon said at least one set of data.

23. The process of claim 19, wherein the selection step of said set of maintenance rules comprises selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

24. The process of claim 19, wherein the selection step of said at least one maintenance work decision comprises the following steps: accepting said at least one scheduling parameter; incorporating said set of maintenance rules; and determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

25. The process of claim 24, wherein the determination step comprises processing said at least one scheduling parameter and said set of maintenance rules using any one of the following approaches: deterministic approach and stochastic approach.

26. The process of claim 19, wherein the selection step of said at least one objective comprises generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

27. The process of claim 19, wherein the generation step comprises generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

1. A process for optimizing maintenance work schedules for at least one engine, comprising: retrieving at least one set of data for an engine from a computer readable storage medium; selecting at least one scheduling parameter for said engine; selecting a set of maintenance rules for said engine; selecting at least one maintenance work decision; selecting at least one objective for said engine; optimizing said at least one objective to generate at least one optimal maintenance work decision; and generating at least one optimal maintenance work schedule for said engine.

2. The process of claim 1, wherein the optimization step comprises the steps of: evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; constructing a scheduled maintenance plan based upon the evaluation step; generating a projected cost of at least one maintenance work decision based upon the construction step; and selecting at least one cost effective maintenance work decision; and optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

3. The process of claim 2, wherein the evaluation step comprises using any one of the following approaches: deterministic approach and stochastic approach.

4. The process of claim 1, wherein the selection step of said at least one scheduling parameter comprises selecting said at least one scheduling parameter based upon said at least one set of data.

5. The process of claim 1, wherein the selection step of said set of maintenance rules comprises selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

6. The process of claim 1, wherein the selection step of said at least one maintenance work decision comprises the following steps: accepting said at least one scheduling parameter; incorporating said set of maintenance rules; and determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

7. The process of claim 6, wherein the determination step comprises processing said at least one scheduling parameter and said set of maintenance rules using any one of the following approaches: deterministic approach and stochastic approach.

8. The process of claim 1, wherein the selection step of said at least one objective comprises generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

9. The process of claim 1, wherein the generation step comprises generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

10. A system comprising a computer readable storage device readable by the system, tangibly embodying a program having a set of instructions executable by the system to perform the following steps for optimizing maintenance work schedules for at least one engine, the system comprising: means for retrieving at least one set of data for an engine from a computer readable storage device; means for selecting at least one scheduling parameter for said engine; means for selecting a set of maintenance rules for said engine; means for selecting at least one maintenance work decision; means for selecting at least one objective for said engine; means for optimizing said at least one objective to generate at least one optimal maintenance work decision; and means for generating at least one optimal maintenance work schedule for said at least one engine.

11. The system of claim 10, wherein the instruction to optimize comprises: means for evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; means for constructing a scheduled maintenance plan based upon the evaluation step; means for generating a projected cost of at least one maintenance work decision based upon the construction step; and means for selecting at least one cost effective maintenance work decision; and means for optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

12. The system of claim 11, wherein means for evaluating comprises means for using any one of the following approaches: deterministic approach and stochastic approach.

13. The system of claim 11, wherein means for selecting said at least one scheduling parameter comprises means for selecting said at least one scheduling parameter based upon said at least one set of data.

14. The system of claim 11, wherein means for selecting said set of maintenance rules comprises means for selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

15. The system of claim 11, wherein means for selecting said at least one maintenance work decision comprises: means for accepting said at least one scheduling parameter; means for incorporating said set of maintenance rules; and means for determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

16. The system of claim 15, wherein means for determining comprises means for processing said at least one scheduling parameter and said set of maintenance rules and to use any one of the following approaches: deterministic approach and stochastic approach.

17. The system of claim 11, wherein means for selecting said at least one objective comprises means for generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

18. The system of claim 11, wherein means for generating comprises means for generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

19. A process for optimizing maintenance work schedules for at least one industrial system, comprising: retrieving at least one set of data for at least one industrial system from a computer readable storage medium; selecting at least one scheduling parameter for said at least one industrial system; selecting a set of maintenance rules for said at least one industrial system; selecting at least one maintenance work decision for said at least one industrial system; selecting at least one objective for said at least one industrial system; optimizing said at least one objective to generate at least one optimal maintenance work decision for said at least one industrial system; and generating at least one optimal maintenance work schedule for said at least one industrial system.

20. The process of claim 19, wherein the optimization step comprises the steps of: evaluating said at least one objective, said at least one data and said at least one simulated maintenance work decision based upon a set of engine life realizations; constructing a scheduled maintenance plan based upon the evaluation step; generating a projected cost of at least one maintenance work decision based upon the construction step; and selecting at least one cost effective maintenance work decision; and optimizing said at least one objective based upon said at least one cost effective maintenance work decision.

21. The process of claim 20, wherein the evaluation step comprises using any one of the following approaches: deterministic approach and stochastic approach.

22. The process of claim 19, wherein the selection step of said at least one scheduling parameter comprises selecting said at least one scheduling parameter based upon said at least one set of data.

23. The process of claim 19, wherein the selection step of said set of maintenance rules comprises selecting said set of maintenance rules based upon the selection of said at least one scheduling parameter.

24. The process of claim 19, wherein the selection step of said at least one maintenance work decision comprises the following steps: accepting said at least one scheduling parameter; incorporating said set of maintenance rules; and determining said at least one maintenance work decision based upon said at least one scheduling parameter and said set of maintenance rules.

25. The process of claim 24, wherein the determination step comprises processing said at least one scheduling parameter and said set of maintenance rules using any one of the following approaches: deterministic approach and stochastic approach.

26. The process of claim 19, wherein the selection step of said at least one objective comprises generating said at least one objective based upon said at least one data and said at least one simulated maintenance work decision.

27. The process of claim 19, wherein the generation step comprises generating at least one optimal maintenance work schedule based upon said at least one optimal maintenance work decision.

Description:

The invention relates to maintenance schedules and costs. More particularly, the invention relates to a system and process for determining schedules that minimize maintenance costs of fleet management programs.

An important aspect of cost-effectively executing a Fleet Management Program (hereinafter “FMP”) is determining maintenance schedules (MS) that minimize maintenance costs such as the cost of maintenance work and of parts of an engine over a longer time interval. Maintenance schedules depend upon a number of parameters such as maintenance time intervals, thresholds for changing or upgrading engine components, etc. The challenge lies in determining which parameter values minimize the resultant maintenance costs of an engine during an interval of the lifetime of the engine.

This determination is generally characterized as a multi-objective global optimization problem, where the objectives are the mentioned costs. For improved cost predictions it may be useful to take into account not only the current state of an engine to be serviced but to consider also an estimated cost incurred at future shop visits during the lifetime of the engine. Moreover, the cost predictions may be further improved by taking into account future probabilities of failure during the service life of the engine. These aspects are usually handled by simulations of the service life of the engine taking into account stochastic events. Thus, the multi objective global optimization problem of optimizing a maintenance schedule has in addition both a time dependent characteristic and a stochastic characteristic. Moreover, a maintenance schedule by itself may be a quite complex and long running program that considers different combinations of parts to be replaced and different types of work that may be implemented and that takes into account the usage of the parts and other aspects of maintenance to propose a current best set of maintenance decisions. Such maintenance decisions may include what parts have to be replaced and what maintenance work has to be performed. The optimization problem is nonlinear and has constraints.

Generally, the multi-objective global optimization problem is a mixed integer problem since some optimization parameters may be integer variables, such as decisions to be taken or not taken, or continuous variables such as time limits. All these aspects of the multi-objective global optimization problem usually make the optimization problem hard to solve. Difficulties with classical optimization approaches when facing such problems are known to one of ordinary skill in the art. For example, classical exhaustive optimization techniques can provide high confidence that the best solutions are found, such as by enumerations; grid searches, or graph searches; however, these techniques require too large computational time especially when considering a larger number of parameters. In contrast, branch and bound techniques are known to have difficulties handling multiple objectives. Stochastic approaches, such as evolutionary algorithms, simulated annealing, genetic algorithms, tend to find local optima and may provide limited confidence that global optima are found, while gradient based or pattern search approaches tend to find a local optimum, etc.

Therefore, for the optimization of maintenance schedules of aircraft engines, there exists a need for a multi objective optimization procedure that takes into account the time dependent and stochastic nature of the problem and that is designed to overcome the above mentioned difficulties.

In accordance with one aspect of the present disclosure, a process for optimizing maintenance work schedules for at least one engine broadly comprises retrieving at least one set of data for an engine from a computer readable storage medium; selecting at least one scheduling parameter for the engine; selecting a set of maintenance rules for the engine; selecting at least one maintenance work decision; selecting at least one objective for said engine; optimizing the at least one objective to generate at least one optimal maintenance work decision; and generating at least one optimal maintenance work schedule for the engine.

In accordance with another aspect of the present disclosure, a system comprising a computer readable storage device readable by the system, tangibly embodying a program having a set of instructions executable by the system to perform the following steps for optimizing maintenance work schedules for at least one engine, the system broadly comprising means for retrieving at least one set of data for an engine from a computer readable storage device; means for selecting at least one scheduling parameter for the engine; means for selecting a set of maintenance rules for the engine; means for selecting at least one maintenance work decision; means for selecting at least one objective for the engine; means for optimizing the at least one objective to generate at least one optimal maintenance work decision; and means for generating at least one optimal maintenance work schedule for the at least one engine.

In accordance with yet another aspect of the present disclosure, a process for optimizing maintenance work schedules for at least one industrial system broadly comprises retrieving at least one set of data for at least one industrial system from a computer readable storage medium; selecting at least one scheduling parameter for the at least one industrial system; selecting a set of maintenance rules for the at least one industrial system; selecting at least one maintenance work decision for the at least one industrial system; selecting at least one objective for the at least one industrial system; optimizing the at least one objective to generate at least one optimal maintenance work decision for the at least one industrial system; and generating at least one optimal maintenance work schedule for the at least one industrial system.

The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

FIG. 1 is a representation of a system embodying the multi-objective global maintenance schedule optimizer described herein;

FIG. 2 is a representation of a schematic for a single level maintenance schedule optimizer;

FIG. 3 is a representation of a hierarchical maintenance schedule optimizer with one schedule optimizer per level;

FIG. 4A is a representation of a two level hierarchical maintenance schedule optimizer with two schedule optimizers on the second level;

FIG. 4B is a representation of a hierarchical maintenance schedule optimizer with multiple schedule optimizers per level;

FIG. 5 is a representation of an optimization module utilizing searches and elimination criteria;

FIG. 6 is a representation of a graphical plot of a multi-objective optimization Pareto surface; and

FIG. 7 is a representation of multi-objective global optimization scheme.

Like reference numbers and designations in the various drawings indicate like elements.

Maintenance schedules for industrial systems of parts, such as engines, are plans or programs for repairing or replacing system parts at given time intervals or when certain events (e.g., failures) happen. The MS module decides what parts may be replaced and what maintenance work may be performed on an engine, at a specified shop visit. Generally, a MS receives as input a system or engine in a given state, defined by measures of the life of the engine parts, by engine measurements, and by a maintenance history of the engine. Based on MS parameters X, the MS produces as output another state of the engine, providing parts to be upgraded or changed, and maintenance work to be performed on the engine. In addition, MS returns a scheduled maintenance date for the output engine, and other information such as costs of parts and work performed.

Referring to FIG. 1 as an example, a multi-objective global maintenance schedule optimizer system and process described herein may be embodied tangibly in a computer readable medium **101**, loaded within a computer **100** as discussed later in greater detail, and/or stored in a computer readable storage medium **102** and executed using the computer **100**. Generally, the exemplary system and process may receive as input **108**, **112** an engine **106** or industrial system **104**, respectively, in the aforementioned given states. Based on MS parameters X, the exemplary system and method produces as output **110**, **114**, another state of the engine **118** or industrial system **116**, respectively, as described above. In addition, the exemplary system and process returns a scheduled maintenance date for the output engine **118** or industrial system **116** and the aforementioned information.

To achieve these results an MS may use different algorithms such as stochastic optimization, combinatorial searches, exhaustive searches, heuristic decision rules, or other optimization approaches known to one of ordinary skill in the art. The particular ways by which an MS obtains its decisions are not particularly relevant. The decision parameters X may be discrete or continuous such as: given time thresholds for future shop visits, engine operation variables or thresholds, part life thresholds, part upgrade thresholds, or parameters of decision rules used for maintenance.

A main purpose of the optimization of the MS described herein is to find the values of the parameters X that will produce an MS such that the total expected engine maintenance cost, including part costs and work costs incurred in a given time interval such as a contract interval, should be minimal. For fixed values of X, such costs may be computed in an average way, for example using Monte Carlo techniques to simulate a set of engine life realizations and averaging the costs of said realizations. The averaging may take into account the probabilities that a given life realization will happen, for example, taking into account the probabilities of failure associated with events that happened in a particular life realization of the engine. Such formulations are known to one of ordinary skill in the art, for example, multiplying the costs incurred at a given shop visit by the probability by which said shop visit happened.

The simulation of the engine life realizations may be performed by an engine life simulator. More particularly, the engine life simulator module may simulate time sequences of shop visits in the life of an engine. Such shop visits may be either scheduled by the MS or may be random, for example, determined by failure probabilities. The estimation of the different costs may be performed by the cost evaluator. Hence, the cost evaluator may estimate one objective or several objectives O_{1}(X), . . . , O_{n}(X) for the given parameters X, using the costs and probabilities obtained from a set of engine life simulations. The set of objectives O_{1}(X), . . . , O_{n}(X) may represent, for example, the cost(s) of part(s), and the cost(s) of work performed over a time interval of the life of an engine and associated costs, contract related costs, and the like. The optimization module may incorporate a multi-objective optimizer described herein that finds values of parameters X that minimize the objectives O_{1}(X), . . . , O_{n}(X).

An exemplary single-level multi-objective global optimization module described herein may construct a set of parameter values X; and for each X the optimization module may evaluate an MS(X) on a set of engine life realizations generated by the engine life simulator. The single-level multi-objective global optimization module may obtain the values of the objectives O_{1}(X), . . . , O_{n}(X), and then select the best X based on these objectives.

A multi-level or hierarchical MS optimizer described herein may be a process comprising a sequence of single level MS optimizers, the levels going from low to high fidelity. A lower fidelity module may be a faster, coarser, simpler representation of a higher level module. Lower fidelity models may be approximations of high fidelity models, often being reduced order models, surrogate models, or lumped models. For example, a low fidelity MS may lump together subsets of parts and use pre-computed solutions or heuristic rules for faster decisions. Lower fidelity simulators may use larger time steps, coarser probability steps, or smaller numbers of simulation steps.

Coarse level optimizers may use larger search steps, a smaller number of optimization parameters, and find approximate solutions indicating the regions of the finer level solutions. The types of optimizers may differ on different levels, for example a coarse level optimizer may be a robust global search, while a fine level optimizer may be a gradient based optimization acting only locally close to the best solutions found by the coarse level optimizer.

The multi-objective global optimization process and system and variations thereof described herein may be implemented using any one of a number of exemplary embodiments, some of which will now be discussed.

Referring now to FIG. 2, a representation of a top level scheme of the multi-objective global optimization system utilizing the exemplary multi-objective global optimization module and employing the process described herein is shown. An exemplary single level schedule optimizer **10** may comprise an optimization module **12**, a simulation and MS module **14** having a maintenance scheduler module **16** and an engine life simulator module **18**, and a cost evaluator module **20**.

The optimization module **12** generally ascertains at least one scheduling parameter X **26** that may optimize a set of Objectives O_{1}(X), . . . , O_{n}(X). The decision parameters X may be discrete or continuous such as: given time thresholds for future shop visits, engine operation thresholds, part life thresholds, part upgrade thresholds, or parameters of decision rules used for maintenance, and the like. The set of Objectives O_{1}(X), . . . , O_{n}(X) may represent, for example, the cost(s) of part(s), cost(s) of work over a time interval of the life of an engine and associated costs, contract related costs, and the like.

The exemplary global optimization module **12** may be implemented by any one of a number of classic optimization techniques such as mixed integer optimization algorithms (e.g., branch and bound) when only one objective is present, e.g., when a single compound objective is chosen as a weighted sum of the n objectives as: O(X)=O_{1}(X)w**1**+ . . . +O_{n}(X)wn. Here w**1**, . . . , wn are weights that multiply the objectives O_{1}(X), . . . , O_{n}(X). A multi-objective optimization may be used when more than one objective is present. Any of the multi-objective optimizations techniques described in literature or implemented in commercial optimization software such as in Matlab or iSIGHT may be used. Deterministic approaches (e.g., mesh searches, graph searches, and the like) or stochastic techniques (Monte Carlo, genetic/evolutionary algorithms, simulated annealing, and the like) may also be utilized.

The simulation and MS module **14** may include a maintenance schedule module **16** and an engine life simulator module **18**. The maintenance scheduler module **16** is a decision tool that may be used to decide what maintenance work may be performed on a given engine, at a given shop visit. Generally, the maintenance schedule module **16** may be a program that incorporates sets of maintenance rules as known to one of ordinary skill in the art and accepts as parameters the aforementioned scheduling parameters X. The MS may encompass different levels of fidelity and may incorporate optimizations by itself to determine the best maintenance decision for each particular shop visit of a given engine. For example, the MS may incorporate combinatorial or stochastic algorithms in order to carry out the determination(s).

The engine life simulator module **18** may simulate sequences of shop visits in the life of a part. Such shop visits may be scheduled by the maintenance scheduler **16** or may be unscheduled, e.g., a shop visit may occur randomly due to different causes with certain probability distributions. Generally, the engine life simulator module **18** may, for example, generate sequences of deterministic and random time events in the life of an engine, take decisions using the maintenance scheduler **16** with at least one parameter X, update engine states as a result of the maintenance performed, generate data for use by the cost evaluator module **20**, and the like. In addition, the engine life simulator module **18** may send engine and event data **22** to the maintenance scheduler **16** and receive maintenance decisions and costs **24** from the maintenance scheduler **16**.

The cost evaluator module **20** may utilize data generated by the engine life simulator module **18** to compute the aforementioned set of objectives O_{1}(X), . . . , O_{n}(X) for the given values of at least one parameter X. Such data may include different costs and probabilities of events incurred during a set of life realizations of a given part.

Referring now to FIG. 3, the multi-objective global optimization system and process described herein may be exemplified in another embodiment. The exemplary multi-objective optimization system and process may be embodied in a hierarchical MS optimizer **30** having at least one MS optimizer per each level **32**, **33**, **36**, each of which is an MS optimizer **10** as described in FIG. 2.

In the hierarchy, as each level progress higher (Level k, . . . , Level 1), the fidelity of the optimization, simulation and decision modules also becomes higher, Level 1 being the highest fidelity level **32**. Higher level modules **32** (e.g., Level 1 MS Optimizer) may send information **34** such as engine data, failure probabilities, maintenance data, and the like, to lower level modules **36**. The lower level MS optimizers **36** (e.g., Level k Optimizer) may provide information **38** on optimal solutions such as approximate solutions, ranges of solutions, and the like, to the higher level modules. For example, where k=2 and a two level hierarchical optimizer is being utilized, the lower level simulation and MS module **16** may use larger time simulation steps and/or a smaller number of simulations for each given parameter X.

In this exemplary embodiment, a level k=2 maintenance scheduler **16** may be a simplified maintenance scheduler, e.g., utilizing fewer look ahead steps, larger steps; using combinations of parts; utilizing heuristic decision rules; or using databases of previous solutions for approximating decisions. Likewise, on level k=2, the maintenance scheduler **16** may also comprise a different optimization technique than the optimization techniques used by the level k=1 MS. Similarly, the two MS optimizers **12** used on levels 1 and 2 may be different. For example, the different optimization techniques may include a combinatorial optimization, an exhaustive search, a stochastic decision optimization, and the like. The lower level MS optimizer, e.g., a Level 2 MS Optimizer **33**, may send a set of optimal solutions to the higher level MS optimizer, e.g., Level 1 MS Optimizer. The high level MS optimizer may begin with these solutions and improve upon them by further optimization using higher fidelity models. In this manner, a sequence of levels may be employed in the alternative. The lower level MS optimizers would hierarchically reduce the vast search space of all possible solutions and indicate the regions where the best solutions may be found. The higher level optimizers may then further refine the regions of the good solutions, working locally in the regions discovered by the lower level optimizers. For example, the lower level optimizer may constitute the exemplary multi-objective global optimizer described herein while the higher level optimizer may be a local optimizer such as a gradient based optimizer or a pattern search optimizer.

Referring now to FIGS. 4A and 4B, the multi-objective global optimization system and process described herein may be exemplified in yet another embodiment. The exemplary multi-objective optimization system and process may be embodied in a hierarchical schedule optimizer **40** having two levels where the lower level optimizer **42** (e.g., Level 2 Optimizer) may comprise two coupled single level MS optimizers **44**, **46** (See FIG. 3A). The hierarchical schedule optimizer **40** of FIG. 3A may comprise any number of MS optimizers on level 2 coupled in any desired input-output structure.

The embodiment of optimizer **40** shown in FIG. 4B may be expanded to encompass any number of levels larger or equal to 2. On each level, the hierarchical optimizer may have any number of MS optimizers coupled in any proper input-output structure, such as optimizers **43** and **45**, and optimizers **44**, **46**, **49** and **51**. The Level 2 Optimizer **45** may contain a single MS optimizer or may contain two or more MS optimizers as the MS Optimizer **42** of FIG. 4A, where MS optimizer **42** contains optimizers **44** and **46** coupled together. The same structure may be applicable to Level 2 Optimizer **43** of FIG. 4B. For example, if three levels are present, i.e., k=3, then FIG. 4B may illustrate an embodiment where the structure of three optimizers **45** and **44**, **46** may be similar to the structure of three optimizers **48** and **44**, **46** of FIG. 4A. Likewise, the structure of three optimizers **43** and **49**, **51** of FIG. 4B may be similar to the structure of three optimizers **48** and **44**, **46** of FIG. 4A.

For example, FIG. 4B illustrates that subsets of MS optimizers may be grouped together and coupled by input-outputs on any of the levels, for example, optimizers **44**, **46**, **49** and **51** may all be coupled, respectively, on level k. Each of the MS optimizers on any of the levels may use a different set of optimization parameters Y that are subsets of the parameters X. For example, when considering FIG. 4A, the optimizers **44** and **46** may use the subsets of parameters X_{1 }and X_{2}, respectively, that are subsets of X of the higher level optimizer **48**. The set of optimization parameters X_{1 }and X_{2 }may or may not share some common parameters, e.g., if X={x, y, z}, then one embodiment may have two MS optimizers, **44** and **46**, with common variables y such as X_{1}={x, y}, X_{2}={y, z}; or the sets of variables of the 2 MS optimizers may not have common variables, such as X_{1}={x, y}, X_{2}={z}.

The single level optimizers **44**, **46** may communicate with each other and share optimal solution information with one another. For example, when X_{1}={x, y}, X_{2}={y, z}, the optimizer **44** may execute first, identify an optimal solution {x_{1},y_{1}}, send the solution y_{1 }to optimizer **46** who may execute to find the solution {y_{2},z_{2}}, then **46** would send the output Y_{2 }to the optimizer **44** which would continue in the same way. This example may be used to illustrate possible interactions between optimizers. Also, the single level optimizers **44**, **46** may operate sequentially, as described in the previous example, or simultaneously, e.g., both MS optimizers may act simultaneously.

One example to illustrate the simultaneous operation of the optimizers may have X_{1}={x, y}, X_{2}={z}, i.e., the optimizers **44** and **46** act without direct interactions on level 2. The solution {x, y, z} found on level 2 may be sent to the level 1 MS optimizer which may perform an optimization iteration to generate {x_{2}, Y_{2}, Z_{2}} on level 1, then send these solutions to level 2 where the optimizers **44** and **46** would continue the optimization from {x_{2}, Y_{2}, Z_{2}} and so forth. This is a generic way by which a higher level optimizer may couple lower level optimizers. In this case, the lower level MS optimizers may contain a smaller number of variables. This example may also suggest one reason why a hierarchical MS optimizer may be more efficient than the single level 1 MS optimizer, by reducing an expensive high level 1 optimization work to work performed by lower dimensional optimizers on levels k>1.

Referring now to FIG. 5, the single and multi-objective optimization techniques and approaches described herein, for example, an optimization module **60** for use with the multi-objective global optimization process and system described herein, may be executed using at least one search **62** coupled with at least one elimination criteria **64** and at least one constraint **66** as illustrated in FIG. 4. The searches **62** may be deterministic approaches such as grid, mesh, and the like, or may be stochastic approaches such as Monte Carlo, evolutionary algorithms, genetic algorithms, and the like. The constraints **66** may be any one of a number of types as known to one of ordinary skill in the art, for example, bounds of variables, or logical constraints imposed by the rules of the maintenance scheduler. In addition, the constraints **66** may be included as penalties in the objectives or treated as additional objectives to be minimized.

Elimination criteria **64** may be constructed while the searches **62** are being executed. Regions of poor solutions may be identified and eliminated from the searches **62**, that is, the elimination criteria may act as new constraints that may prevent the searches from evaluating solutions in poor regions.

Elimination criteria may then increase the efficiency of the optimization by reducing the search space. This may be especially effective if the elimination of the poor regions is performed on a coarse level using faster simulations and simplified maintenance schedules. Moreover, the low level optimizers may use exhaustive techniques to search the whole domain of solutions and identify the regions of possible good solutions. Good solutions may be sought in these regions by the higher fidelity optimizers. Such hierarchical optimizers may provide both the confidence provided by exhaustive searches and the accuracy of the local optimizers. Other types of optimizations may be used as well and each MS optimizer on each level may use a different type of optimization.

FIG. 6 illustrates the Pareto surface of optimal solutions for a case that uses two objectives O_{1}(X) and O_{2}(X) The two objectives may be, for example, the cost of parts and the cost of work cumulated during the life of a given engine. The parameters X of the solutions on the Pareto surface are optimal or best in the sense that there is no other set of parameters Y for which both objectives O_{1}(Y) and O_{2}(Y) are smaller, that is, there is no Y better than X, i.e., such that O_{1}(Y)<O_{1}(X) and O_{2}(Y)<O_{2}(X). The Pareto surface for any number of objectives O_{n}(X) may be defined in the same way as for 2 objectives, that is, X is optimal if there is no Y such that (O_{1}(Y), O_{2}(Y), . . . , O_{n}(Y))<(O_{1}(X), O_{2}(X), . . . , O_{n}(X)). In a hierarchical optimization approach, the poor regions, i.e., regions away from the Pareto surface, may be eliminated hierarchically, and the searches may focus on the good regions near the Pareto surface, as described above in the discussion on elimination criteria. The hierarchical optimizer finds the Pareto surface hierarchically. A broad search may be performed using low fidelity models, for example, the simulator and MS may be simplified and used in a search to approximate the region containing the Pareto surface. This region may be further refined at higher levels using higher fidelity models. This approach suggests an efficient hierarchical multi-objective optimization technique.

Referring again to FIG. 5 and the exemplary embodiment illustrated, the effectiveness of the searches may come close to the results of exhaustive searches by providing high confidence that the best global solutions have been found. However, searches utilizing elimination criteria are far more effective than exhaustive searches since the largest part of the poor solutions may be eliminated using the elimination criteria (See FIG. 5). In addition, local optimizations, for example, gradient based or pattern searches, may be added locally during highest level optimizations.

Referring now to FIG. 7, the multi-objective global optimization process and system may be utilized for tuning at least one parameter X of a maintenance scheduler. Tuning the maintenance scheduler will assist maintenance personnel to determine whether or not an engine requires a shop visit, whether or not any component(s) of the engine should be repaired, replaced or scrapped, and the like. The multi-objective global optimization system and process described herein may comprise an executable program, that is, a set of instructions, embodied tangibly in a computer readable medium **101** and/or stored in a computer readable storage device **102** and executed using a computer **100** (See FIG. 1). The illustrated computer **100** may represent a server, desktop, laptop, personal digital assistant, and the like, and may be networked using a WLAN, Ethernet, and the like, and may also be part of a distributed computing system as known to one of ordinary skill in the art. The various modules, and all their alternative embodiments, may all be embodied tangibly in the same aforementioned computer readable mediums, storage devices, and the like, as known to one of ordinary skill in the art. Another embodiment generalizes the above description to distributed computing systems, as may be understood by the skilled in the art, i.e., multiple connected computers may store different parts of the data and may run any of the mentioned modules, such as the MS, optimizers, engine life simulators, etc.

For example, a multi-objective global optimization system **70** may execute the multi-objective global optimization process described herein to tune the aforementioned at least one parameter X of a maintenance scheduler for a fleet management program. A hierarchical schedule optimizer **72** may comprise any one of the exemplary multi-objective global optimization embodiments described herein, along with any and all permutations as recognized by one of ordinary skill in the art. The hierarchical schedule optimizer receives at least one data from a database **74** such as part history data in general, component and systems data specifically, maintenance data, maintenance history, engine performance parameter(s), failure probabilities for the parts and engine, costs associated with the maintenance of the engine, and the like.

The hierarchical schedule optimizer **72** receives the data from the database **74** and by utilizing the exemplary multi-objective global optimization process(es) described herein, for example in FIGS. 2-4B, determines those scheduling parameters X **78** that may optimize the objectives O_{1}(X), . . . , O_{n}(X). The scheduling parameters X that are identified become at least one optimal scheduling parameter X **78**. An optimized maintenance schedule **76** that uses the optimal X is obtained, and it may be used to determine what maintenance work is required for the given engine at the current and future shop visits.

One or more embodiments of the present invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.