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COMPROMISE: AN EFFECTIVE APPROACH FOR CONDITION BASEDMAINTENANCE MANAGEMENT OF GAS TURBINESWei Chen a; Cyrus B. Meher-Homji b; Farrokh Mistree aaSystems Realization Laboratory, The George W. Woodruff School of Mechanical Engineering,Georgia Institute of Technology, Atlanta, Georgia, USA bBoyce Engineering International, Inc.,,Houston, Texas, USA

To cite this ArticleChen, Wei, Meher-Homji, Cyrus B. and Mistree, Farrokh(1994) 'COMPROMISE: AN EFFECTIVEAPPROACH FOR CONDITION-BASED MAINTENANCE MANAGEMENT OF GAS TURBINES', EngineeringOptimization, 22: 3, 185 201

To link to this Article: DOI: 10.1080/03052159408941333URL: http://dx.doi.org/10.1080/03052159408941333

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Eng Opt., 1994. Vol. 22, pp. 185-201 O 1994 G ordo n an d Breach S cience Publisllers S.A.Reprints available directly from the publisher Printed in MalaysiaPhotocopying permitted by license only

COMPROMISE: AN EFFECTIVE APPROACHFOR CONDITION BASED MAINTENANCEMANAGEMENT OF GAS TURBINESWE1 CHEN , CYRUS B. MEHER-HOMJ12and FARROKH MISTREE

System s Realization Laboratory, The George W Woodruff School ofMechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia30332-0405, USA.Boyce Engineering International, Inc., Houston, Texas 77099, USA.Received October 14. 1992; in Jinol form September 28, 1993)

decision-based appro ach t o condition-based maintenance m anagement of rotating m achinery is intro-duced and illustrated by formulating and solving a multiple objective maintenance management problemfor a 15 MW industrial pas turbine. The comoromise Decision Suo oo n Problem am roa ch is used becauseit provides a convenient way of incorporating both information from condition monitoring and con-siderations of factors such as machine degradation. ope rating cost fuel cost). production loss, main-tenance cost, environmental pro tection, m achine availability, etc. The focus in this paper is on explainingthe approach rather than on the results per seKEY WORDS: Cond ition monitoring , multiple objective maintenance management. gas turbine. com-promise Decision Support Problem.

NOTATIONBTPCATc cCiCitCoCTCEFdiDEEGTELi

bearing temperaturehourly overall cost for one overhaul cyclecumulative cost of fuelhourly interest chargetotal interest chargeinitial fuel costtotal cost during one overhaul cyclecompressor efficiencydeviation variables for the system goalsdeterioration rateelectricity profitexhaust gas temperatureelectricity profit loss during shutdownannual interest rate

I85


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W. HEN ET AL86O M CP M CToT,T

VIBVIS

overhaul maintenance costpreventive maintenance costtime between overhaulsoverhaul shutdown durationtime to pay off the maintenance costby savings in fuel costvibration levellubrication oil viscosity

hrsin/secSSU

FRAME OF RE FE RE NCEThe problem of maintenance management In recent years aero gas turbine tech-nology has been introduced in the design of heavy-duty industrial turbines. As aresult industrial gas turbines have become more sophisticated and demand rigor-ously controlled maintenance'. The problem of maintenance management is alsocomplicated because:

High fuel prices mandate that turbines operate at minimum degradation.Maintenance involves interdisciplinary work teams that must take into con-sideration factors such as machine d egradation, operating cost (fuel cost), produc-tion loss, maintenance cost, environmental protection, machine availability, etc.Amongst these factors, there are at least three major tradeoffs:The tradeoff between maintenance cost and machine performance.The tradeoff between the costs associated with preventive maintenance andfuel costs associated with operating the turbine when it is a less than efficient(degraded).The tradeoff between overhaul costs and increased turbine availability as wellas reduced production loss. Usually a fast overhaul, and hence a longer time forthe turbine operation and less production profit loss, is accompanied by anincrease in the cost of the overhaul.Mathematical modelling of maintenance management is essential to gain anunderstanding of the maintenance process. Ideally, maintenance considerationswill be introduced during turbine design, as has been proposed in ConcurrentEngineering '.

Cond ition monitoring h as been proven to be essential for cost-efficient maintenancemanagement in ind ustrial, marine and aircraft applicationses. Using this techniquecan safely extend the interval between overhauls, minimize the number of open-inspect-and-repair cycles, and improve maintenance efficiency by directing repairand overhaul actions toward specific deficiencies, etc. However, maintenanceschedules based on condition monitoring alone cannot take into account the otherimportant factors mentioned earlier or the tradeoffs between them. Because of thecomplexity involved, maintenance planning is currently based on personal expe-rience and heuristic rules with the aid of condition monitoring. In order to meet


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G S TURBINE MAINTENANCE 87

the maintenance challenge an advanced maintenance strategy is required to achievemulti-level requirements.

Approach: decision-based perspective for the solution of maintenance manage-ment problems is proposed in this work. Decision Support Problems (DSPs) arebeing developed and implemented to provide a means for modeling decisionsencountered in design in a computer-assisted environment9. DSPs are categorizedas selection, compromise, hierarchical and conditional DSPsl . The integration ofcondition monitoring and the compromise DSP for maintenance management pro-posed by Meher-Homji, et al. . The efficacy of using Decision Support Problemsin maintenance management is reported in Chen . In this paper a method forusing a compromise DSP to solve a condition-based maintenance managementproblem is demonstrated. Here the method is emphasized rather than specificresults. Compromise DSPs refer to a class of constrained, multi-objective optimiza-tion problems which have a wide variety of engineering application^ ^. The com-promise DSP formulated in this paper addresses the decisions of when a gas turbineshould be overhauled, how long the overhaul should last and how much preventivemaintenance should be done during these overhauls. The model is based on acondition-based preventive maintenance policy which covers the following:

Periodic maintenance is performed during overhauls to keep components insatisfactory operating condition. This is achieved by means of systematic inspection,detection and prevention of incipient failure.

Condition monitoring is performed to discover the actual state of the systemand decide the preventive and overhaul maintenance actions.

The decision to overhaul the turbine is based on both information obtained byon-line monitoring and on an a priori model of the deterioration process.The importance of the integration of compromise DSP with condition monitoringlies in the fact that the DSP must be based on the actual running condition of aspecific gas turbine as well as on overall considerations such as costs. It is accom-plished as follows:

First, the performance degradation of the particular gas turbine is monitoredby collecting information about such factors as gas path analysis (e.g., gas pressureand temperature), mechanical performance (e.g., vibration level) and the accessories(e.g., lubrication analysis, ultrasonic monitoring and visual inspection).

Second, the data collected is validated, corrected and compressed to providereliable and simplified information for subsequent analysis.

Third, for data analysis, dominant health parameters are identified for therepresentation of turbine health and performance constraints/goals. The relation-ships between these parameters and the system variables are determined usingempirical or theoretical relationships, statistical analysis or other mathematicalapproaches. Also ihe constraint limits (or goal target values) are specified fordegradation limit checks.


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88 W HEN ET LFinally, the health and performance constraints/goals are incorporated withother constraints/goals into a comprom ise DSP. Solutions to the com promise DSPin terms of the system variables provide the most favorable operational and

maintenance requirements for the turbine.Focus: The approach is demonstrated by presenting the formulation, solution andvalidation of a compromise DSP for condition-based maintenance scheduling. A15 MW industrial power generation gas turbine is taken as the study case. Theformulation of the condition-based maintenance scheduling compromise DSP ispresented in Section 2. In Section 3 the validity and stability of the solutions areconfirmed. Conclusions, achievements and possible future work are presented inSection 4.

2 FORMULATION OF A COMPROMISE DSP FOR G AS TURBINEMAINTENANCE2.1 Problem sta temen t for maintenance schedulingIn order t o ma ke decisions involving m aintenance, it is desired t o find the a ppro -priate values for time between overhauls, overhaul shutdown duration, and dete-rioration rate. The gas turbine studied is a 15 MW industrial power generationturbin e with 27% initial thermal efficiency. Its hourly fuel consu mp tion is estimatedas 4.6 10' m3. Th e initial fuel cost is 870/hr. It is known that- the loss in profitis about 1,00O/hr if the gas turbine is shut down fo r overhaul. The current interestrate is 15% per annum. Based on historical data, preventive maintenance cost(PMC) during gas turbine operation is formulated as the function of deteriorationrate D, and overhaul m aintenance cost (OMC) is formulated a s a function of over-haul shutdown Time T,. In addition to the health condition of the gas turbinewhich is an essential consideration for maintenance scheduling, it is also necessaryto minimize the overall cost (consisting of operation cost, preventive maintenance,overhaul maintenance cost, downtime production profit loss and interest loss).Ideally, the overall costs should be no more than 900/hr. A performanc e effec-tiveness (overall thermal efficiency) of 22% is expected. The pollution caused byNOx emission must be minimized below 40 ppm . 92 % availability of the gas turbineis expected.

2.2 Descriptions of system variables constraints goals and deviation functionfor maintenance scheduling

System variables, constraints and goals a re identified for the c ompro mise DSP for-mulation on the basis of the problem statement given in Section 2.1.Description of the system variables: The system variables for the maintenancescheduling compromise DSP are, 1) time between overhau ls (To), (2) ove rhau l


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GAS TURBINE MAINTENANCE 189shutdown duration (T,) and 3) deterioration rate (D). Time between overhaulsTo) s the time between two overhauls. The timeline for the whole overhaul cycleof the gas turbine is shown in Figure 1. Overhaul shutdown duration TJ s theduration of overhaul maintenance actions or the time between stopping and restart-ing the turbine. Here the shutdown time is taken as a system variable that can becontrolledn based on the change in electricity production loss and availabilityrequirements. The overhaul duration can be shortened by assigning more labor o rexecuting replacement to replace repair. The tradeoff must be made between theshortened duration and the increased overhaul cost.Deterioration rare D ) is the degree of accumulated deterioration over a specifictime. Engine deterioration is measured by an increase in specific fuel consumption.The performance deterioration may not be fully recoverable with preventive main-tenance, e.g. loss of tip clearance, erosion effects and seal leakage, etc. In Figure2 the influence of preventive maintenance on the deterioration rate is illustratedschematically. The thinner line represents the change of functional effectiveness ofthe turbine with a greater amount of preventive maintenance while the thicker line

Start StartOne overhaul cycle

Running timestr L1ime Between OverhaulsOverhaulShutdownDurationFigure Gas turbine overhaul cycle.

Larger Preventive Maintenancevolume

Degradation limitSmaller Preventive Maintenance Volumel \-Reduced Time Between Overhauls

Operating HoursFigure Influence of preventive maintenance volume on deterioration rate.


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19 W HEN T AL

represents a smaller amount of preventive maintenance. It is obvious that thedeterioration rate D) is reduced if more preventive maintenance, such as com-pressor washing, is undertaken and the time between overhauls is extended. There-fore the selection of D, the deterioration rate, can be used to determine theappropriate amount of preventive maintenance.Des cription and derivation of the system constraints: The machine health con-straints are taken as system constraints to ensure that the degradation of a gasturbine is within certain limits before overhaul. Either measurable parameters orperformance characteristics can be factored into the health constraint equations. Itis recommended that the factors chosen should reflect the most frequently occurringproblems with gas turbines. Here six health parameters have been selected to repre-sent the dominant health constraints.

Vibration level constraint VI B ): Vibration measurement is a well-establishedtechnique for the condition monitoring of rotating equipmentl6I6. It can be usedto identify the source of the vibration, e.g., unbalance misalignment, inappropriateblade passing frequencies or surging and combustion pulsation problems. Theallowable maximum overall vibration level is 0.42 in/sec.

Exhaust gas temperature constraint EG T) : Measurement of the EGT is essen-tial regardless of the type of analysis. High EGT indicates either an excessively highturbine inlet temperature or a faulty turbine; perhaps there is combustion of fuelnozzle plugging, compressor fouling or other problems. EGT must be limited at aselected baseload. EGT cannot exceed 1,020F.Compress or efficiency constra int C E F) : Compressor efficiency itself is notdirectly measured, but is computed from the overall pressure ratio (combus-tion shell pressure divided by the ambient pressure or preferably the inlet and dis-charge compressor temperature). The compressor efficiency reflects deterioration

in the compressor section and is especially sensitive to compressor fouling1 . Thelower limit of compressor efficiency is 84 .Lubrication oil viscosity constraint VIS ): Monitoring the viscosity of the lubri-cation oil is another important method of investigating turbine malfunctions bydetecting oil c~nt am in at io n ~-~ ~.change in viscosity is caused by a change in lubeoil properties or by a change in the condition of the machine. Considering the longterm trend of debris collection, the minimum acceptable viscosity is 100 ssu.Bearing temperature constraint BT P) : When a bearing is subjected to strongradial loads or excessive bearing loading due an increase in bearing shell temper-ature, there is an increase in bearing metal temperature. Bearing temperatureprovides corroboratory evidence on bearing condition and should be used in con-junction with vibration monitoring16. The maximum acceptable bearing temper-

ature is 95C.Nozzle crack constraint: In some aero engines, a correlation has been foundbetween deterioration and cracks1 . This constraint has been introduced t o showconceptually how additional health constraints are added. The nozzle crack con-


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GAS TUR INE MAINTENANCE 9

straint is formulated using discriminant analysis which is a technique for the descrip-tion and testing of between-group differences . For this maintenance problem,sample published data has been collected and two groups (requiring overhaul notrequiring overhaul) have been identified.Among the above health constraints, except the vibration, exhaust gas temperatureconstraints are based on the on-line monitorine, data and nozzle crack constraintis obtained by discriminant analysis, the other health constraints are formulatedusing historical data obtained from condition monitoring. Regression a n a l y s i ~ ~ ' - ~is used to provide statistical information about the multidimensional parameters.The solutions are summarized in Section 2 3 Detailed analysis and formulationscan be found in Chen .Description and derivation of the system goals: The description and deriva-tion of the overall hourly cost, efficiency, availability and emission control goalsare:Goal I-Overall hourly cost goal: 0;erall cost within one overhaul cycle consistsof three parts: the operating cost, the maintenance cost and the interest charge. Eachcomponent of the overall cost is described as follows:Operating cost: Deterioration in specific fuel consumption will greatly increase theoperation cost of a turbine. As it is assumed that the engine is returned to the asnew condition after every overhaul and the engine deteriorates linearly at a rateD the calculated cost of fuel consumed during one overhaul cycle is

Maintenance cost: This consists of overhaul maintenance cost (OMC), preventivemaintenance cost (PMC) and downtime electricity profit loss (EL). EL is relatedto the loss of electricity profit during overhaul, it is assumed that EL is linearlyrelated to the shutdown time (T,):

Interest charge: If the turbine is unused, interest payments on the cost of overhaulwill accumulate without compensating saving in the cost of fuel. This is simulatedby crediting the saving of fuel cost against the cost of overhaul and production lossuntil it is paid off, and charging simple interest against the outstanding balance.The derivation of the total interest cost C over one overhaul cycle is given inChenI2, it is omitted here.The Overall cost C is calculated by adding. the different costs:

Considering the average hourly cost CAT ver one overhaul cycle To T,, the totalcost is expressed for two cases and summarized as follows:


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W CHEN ET AL92

Case A: When

Case B: When

PMC OMC EL o T,CODTOCo(To 0.5D T,)' (PMC OMC EL)CAT= To T, To T,

i(PMC OMC EL)2x 8766 CODTO(o T,)

c0 T ~ 0.5D (PMC OMC EL)C A ~ To Ts To Ts

i[2(PMC OMC EL) Ca To (T o T,) ]2 x 8766 7)

The overall cost goal is

where CAT s actual average overhaul cost, and d;, d are under- and over-achievement deviation variables.

The compromise DSP formulation must be established for both cases A and BEqs. (4) and (6) provide system constraints in each case, solutions with smallervalues of the deviation function will be chosen.Goal 11-Overall turbine efficiency goal: The overall turbine efficiency q ismeasure of output power compared with input energy. From the designer s view-point, it is important to meet power demands and limit fuel expenses. Regressionanalysis of simulated historical data gives a relationship between the overall turbineefficiency and the system variables

In this problem, an efficiency of at least 22 is specified. The overall turbine effi-ciency goal is therefore given by the following equation:

(5.084/(T0&) 0.001)/22 d; d = 1.0 (10)Goal 111-NOx emission control goal: Given the current level of environmentalconcern, the limit on the emission level (EMS) s of great importance. In fact, inthe near future, maintenance may be driven by NOx and efficiency considera-t i o n ~ ~ ~ .iolation of emission level limits results in penalty costs which woulddecrease profits. Regression analysis on simulated historical data shows that rela-tionship between the emission level and the system variables can be expressed as

48000.85DEMS = 2.197901.692 .O7 To 0.24 T:


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GAS TURBINE MAINTENANCE 93

It is expected that the gas turbine NOx emission level will be less than 42 ppm.The emission level goal is given by the following equation:

Goal IV-Availability goal: Gas turbine overall availability (AVB) is a measure ofthe amount of time the unit is actually available to produce power in any givenperiod. In terms of the system variables, the theoretical overall availability becomes

As it is assumed that the shutdown time for preventive maintenance is neglected,the AVB value obtained from Eq. (13) must be larger than the actual value, anapproximate correction factor of 0.94 is used. Then Eq. (13) becomesAVB 0.94- x 100To Ts

It is expected that the availability must be at least 92 . The availability goal is givenby the following equation:

The deviation function: The solution of a compromise DSP minimizes the deviationfunction which consists of undesirable deviations from the system goals. There arevarious methods of measuring the effectiveness of the minimization of these devia-tions. In the authors' opinion, the lexicographic minimum concept is the mostsuitable approachz6. As an example, consider two solutions, f and f , wheref (0, 10, 400, 56) andf (0, 11, 12, 20). In this example, f is preferred tof . The value 10 in f s smaller that the value 11 in f . Once a preference isestablished, then all higher order elements are assumed to be equivalent. Hence, thedeviation function, Z, for the preemptive formulation is written as V, d- , d+) ,. .,f,(d-, d + ) ] . In the present model, the first priority level is assigned to mini-mizing the overall cost and emission level and maximizing the efficiency and avail-ability. As the overall cost is always the most important factor, engine performance(efficiency) is the next most important, and emission control and availability arethe least important, weights of 0.4, 0.3, 0.15, 0.15, respectively, are given for eachgoal. In priority level 11, the overall efficiency and emission level are expectedto attain the target values. These are less important goals as compared with thosein level 1. Therefore the deviation function is

Minimize Z [ (0.4d: 0.3d; 0.15 d l 0.15 d;),(0.5d: 0.5d;) (16)


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94 W HEN T AL

2.3 Mathem atical formulation of the compromise DSPBased on the description of the constraints and goals in Section 2.2, the mathe-matical formulation of the compromise DSP is as follows:Find

Independent system variables To, T,, DDeviation variables d t d ;

SatisfySystem constraints

Health constraintsVIB: 0.069 0.007T0 0.001T; 5 0.42EGT: 901.18 4.887, 0.096T: 1020CEF: 0.914 0.002T0 1.6 104T; 0.0560 84VIS: 149.76 2.512T0 0.1 Ti 50.080 100BTP: 66.13 0.138T; 50DZ 4.1 ToD 5 95Nozzle crack: D 0.05To5

Constraints due to cost derivationCase A PMC OMC EL 5 To T,CODTO

PMC OMC EL, To TsCase B CODTO(either A or B is used for each possibility)System goalsOverall cost: C,,/900 d ; d : = 1.0 8)Overall thermal efficiency: ( 5 . 0 8 4 / ( ~ , a ) -0.001)/22 d; d: = 1.0 (10)Emission level: 48000.850901 .692 11.07 To 0.24 T: 2.1971 142

1 0Availability: 0.94 100 /0.92 d; d: = 1.0To T,Bounds on the system variables

10 5 To5 250.5 5 T, 5 10 s .3


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GAS TURBINE MAINTE NANC E 195Minimize

The preceding DSP provides a specific mathematical model for maintenancescheduling. Deviation variables are associated with various goals. The objectivethen is to minimize the sum of these deviations. System and deviation variables(generally represented by d; and d;) in a compromise DSP are always non-negative. To effect solution, one of the following three conditions must hold,namely; [(d; 0) and ( d l O)] or [(d; 0) and ( d l > 0) or [(d; > 0) and(d: O)]. This requirement is modeled by: [ d;. d l O)]. Details are provided inMistree et aL9

3 IMPLEMENTATION AND VALIDATION3.1 Solution of the compromise DSP fo r maintenance schedulingThe DSP was solved on a SUN 4/110 and 4/260 series computer using the DSIDESsoftware9. Tests are run using different starting points for Cases A and to checkthe convergence of the solutions. These are reported in Chen . Solution conver-gence indicates that the model is well formulated and the algori thm used is feasible.Numerical solutions for Cases A and are presented in Table 1.Observations: The solutions for both cases provide meaningful results. As thedeviation function of level I in Case is smaller than that in Case A, the solutionof Case is selected to be the solution. Comparing the values of system variablesand goals in both cases, we find the time between overhauls, To for Case(22.24 x 10' hrs) is slightly larger than that for Case A (21.97 x I d hrs). Deterio-ration rate, D, .for Case (0.7024 %/4000hrs) is smaller than for Case A (0.9017%/4000hrs). It is also noted that for Case the goals are better satisfied than forCase A. This indicates that extending the time between overhauls by taking moreTable Solution o f the compromise DSP in Case A and Case B.

ase ueSYST M VARIABLESTime Between Overhaul To ( l d h r s )Shutdown Time T l d h r s )Deterioration Rate (Vd4.000hrs)DEPENDENT VARIABLESCost (target value 9 /hr)Efficiency (target value 22%)Emission Level (target value 40ppm)Availability (target value 92%)Deviation FunctionsPriority level IPrioritv level I1


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1 W . CHEN ET ALpreventive maintenance work is beneficial for minimizing the deviation function(maximizing goal achievement). In both cases, Sh utdow n time, T attains its lowerbou nd, i.e. 500 hrs. This means th at, in this formulation, to achieve the availabilitygoal and reduce profit loss the smaller the T, the better.3 2 Parametric studies of the maintenance templateParametric studies were performed to demonstrate that the solution is close toreality and to give confidence in the results. Param etric studies help verify tha t themodel obeys the laws of physics, and that its behavior is intuitively correct. Thesestudies are also useful for investigating the sensitivity of the maintenance decisionsto chang es in parameters. Th e effect of change in electricity profit, com pressor effi-ciency constraint limit and goal target values are shown as examples here.Effect of change in electricity profit One reason why the overhaul shutdown time(T,) in both cases reaches the lower bound is because the goals of reducing theelectricity profit loss and achieving availability are more imp ortan t than the savingsin overhaul cost by extending the overhaul cycle. Therefore, the change in electricityprofit as well as the electricity profit loss may affect the solutions. The effects ofelectricity profit on the deviation function, overhaul shutdown time, overall costand availability change over the range of (500-1,40O)/hr of electricity profit a replotted in Figure 3 at five sample points.Observations It is noted that the deviation function at level I of,Ca se is quiteclose to that of Case B at lower electricity profit values. However, within the range

4 800 1200 1600Electricity Profit ( h)

920910

90400 800 1200 1600 4 800 1200 1600Elecaicity Profit ( fir) Electricity Profit 6hrFigure Effect of the electricity profit.


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GAS TURBINE MAINTENANCE 197of study , the solutions to Case B are always preferred. T his phenomenon indicatestha t extending the time between overhauls by taking m ore preventive maintenanceisalways beneficial. While the time between overhauls and deterioration rate arequite stable, the change in electricity prof it within the (500-850)/hr range indicatesits strong impact on the overhaul shutdown time, T . As the overall cost goal andavailability goal are strongly related t o the recomm ended T changing them causesthe changes in the two goals. The graphical solutions match very well with ou r intui-tion and the mathematical analysis of the formulation.Effect of compressor efficiency constraint limit The compressor efficiency con-straint limit must be chosen by a m aintenance engineer. In o ur exam ple, 84 hasbeen selected. It is necessary t o examine the response of the SP to either reducedor expanded constraint limits. Four tests are run for both Cases and B withinthe range of 82 to 87 of co mpress or efficiency. As ll of the deviation function sat priority level I of Case B are all smaller than those of Case A solutions to CaseB are preferred in all the tests. T he solutions are provided in Table 2. The effectson the To and overall cost goal are illustrated in Figure 4.Observations From Table 2, t is seen that the shutdo wn tim e is quite stable. How-ever, time between overhauls and deterioration rate are all affected by changes inthe compressor efficiency constraint limit. By increasing the compressor efficiencyconstraint limit, values of time between overhauls and deterioration rate all decreasewhile the overall cost increases. This is in keeping with reality. Increasing the com-pressor efficiency constraint limit is more conservative, hence more conservativedecisions are required for time between overhauls and deterioration rate. Theincrease in overhaul cost also reflects the trade-off between the technical and eco-nomic factors.Effects of changes in goal target values Target values could chang e with the con-dition of the company, outside regulations or other management considerations.Table 2 Effect of compressor efficiency constraint limit.

LIMIT LIMIT I LIMIT II LIMIT 11184 82 85Yo 87

SYSTEM VARIABLESo Idhrs) 22.2410 22.5500 21.4023 19.6656Shutdown Time Ts Idhrs ) 0.5000 0.5000 0.5000 0.5000Deterioration Rate D 0.7023 0.7547 0.6034 0.4642

DEPENDENT VARIABLESCost S/hr) T 9 918.77 918.77 919.70 924.30Efficiency ( ) T = 22 24.50 23.30 27.48 34.12Emission Level @pm) 7 4 34.95 37.39 30.35 23.90Availability 70)T 92 91.93 91.96 91.85 91.33DEVIATION FUNCTIONSLevel 0.0084 0.0084 0.0090 0.0122Level 11 0.1199 0.0623 0.2451 0.4767


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G A S N R B I N E MA I NT E NA N C E 1 99

Observations: From the solutions provided in Table 3, it can be seen that, for thechanges of th e cost target value Scenarios I and 11), values of system variablesremain stable. This is due to the restricted design space formed by health con-straints. Within that space no better solution can be achieved. The use of morerestricted regulations fo r emission control has an impact on the solutions Scenario111); time between overh auls and deterio ration rate ar e reduced as they were for theconservative design. T he solutions of Scenario IV shows that there is no change inthe values of system variables when greater availability is expected. This is also du eto the restricted design space formed by health constraints.Th e parametric studies on targ et values show that, generally, th e effects are quitelimited. However, the solution will be affected if the change is not small, as is thecase in Scenario 111 Th e effects of chan ging th e fuel cost, coefficient of preventivemaintenance cost, interest rate, u nit incremental overhaul maintenance cost an d thegoal priority levels were also studied in this work. These are described in detail byChen12.

CLOSUREThis condition-based preventive maintenance approach shows great potential foruse by gas turbine operators. Accuracy in degradation detection, da ta managementand pattern recognition is enhanced by using a compromise D SP based o n on-linecondition monitoring, borescope inspection and the mathematics of discriminantanalysis and regression analysis. The compromise DSP is an effective tool formodeling and solving multiobjective maintenance management problems. The vali-dation of the maintenance template gives a deeper insight into the problem of gasturbine maintenance and makes it possible to predict the responses of the solutionsto th e changes of m ainten ance parameters. It is recognized that a gr eat deal of workis still required to refine this model. Much more accurate information on the para-meters representing health must be collected to establish accurate relationshipsbetween mechanical and aerothermal parameters. The use of on-line conditionmo nitorin g systems can facilitate this. Th e parametric study could also be improvedby studying the combined effects of several parameters. In the longer term, under-standing of main tenan ce processes an d their effect on designing is necessary for fur-thering Concurrent Engineering Design.AcknowledgmentsThis work was completed while the first and third authors were at the University of Hous ton. We grate-fully acknowledae the financial contribution made by our coroorate soonsor. The BE Goodrich Com-pany, for the further development of the Decision ~ u b ~ o r trob lem ~ e c h n i ~ u e .grant from the TexasAdvanced Technology Program Grant No . 3652-227) and the NSF equipment Grant 880681 are botharatefullv acknowledaed. The cost o f comDuter time w s underwritten bv The Svstems Desinn Labora-tory of The ~ n i v e r s c ~f Houston.


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200 W. CHE N E T A L .References

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