Rama S.R. Gorla

Cleveland State University, Cleveland, Ohio

Shantaram S. Pai and Jeffrey J. Rusick

Glenn Research Center, Cleveland, Ohio

Probabilistic Analysis of Gas

Turbine Field Performance

NASA/TM—2002-211699

November 2002

TED–AJ03–649
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Rama S.R. Gorla

Cleveland State University, Cleveland, Ohio

Shantaram S. Pai and Jeffrey J. Rusick

Glenn Research Center, Cleveland, Ohio

Probabilistic Analysis of Gas

Turbine Field Performance

NASA/TM—2002-211699

November 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Sixth Thermal Engineering Joint Conference

cosponsored by the Japan Society of Mechanical Engineers, Thermal Engineering Division,

and the American Society of Mechanical Engineers, Heat Transfer Division

Hawaii Island, Hawaii, March 16–20, 2003

TED–AJ03–649
Acknowledgments

Rama S.R. Gorla is grateful to NASA Glenn Research Center, for supporting this work through

Grant NAG3–2745.

Available from

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7121 Standard Drive

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National Technical Information Service

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This report is a preprint of a paper intended for presentation at a conference. Because

of changes that may be made before formal publication, this preprint is made

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Available electronically at http://gltrs.grc.nasa.gov
NASA/TMó2002-211699 1 

PROBABILISTIC ANALYSIS OF GAS TURBINE FIELD PERFORMANCE 

Rama S.R. Gorla* 

Professor of Mechanical Engineering 

Cleveland State University 

Cleveland, Ohio 44115, USA 

Shantaram S. Pai* and Jeffrey Rusick 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135, USA 

ABSTRACT 

 A gas turbine thermodynamic cycle was computationally simulated and probabilistically evaluated in view of 

the several uncertainties in the performance parameters, 

which are indices of gas turbine health. Cumulative distribution functions and sensitivity factors were computed for 

the overall thermal efficiency and net specific power output due to the thermodynamic random variables. These 

results can be used to quickly identify the most critical 

design variables in order to optimize the design, enhance 

performance, increase system availability and make it cost 

effective. The analysis leads to the selection of the appropriate measurements to be used in the gas turbine health 

determination and to the identification of both the most 

critical measurements and parameters. Probabilistic analysis aims at unifying and improving the control and health 

monitoring of gas turbine aero-engines by increasing the 

quality and quantity of information available about the 

engineís health and performance. 

 Conventional engineering design methods are deterministic. The components of a machine are considered as 

ideal systems and parameter optimizations provide single 

point estimates of the system response. In reality, many 

engineering systems are stochastic where a probability 

assessment of the results is required. Probabilistic engineering design analysis assumes probability distributions 

of design parameters, instead of mean values only. This 

enables the designer to design for a specific reliability and 

hence maximize safety, quality and cost. The approaches 

for incorporating probabilistic effects in design include 

the use of factors of safety, the use of the worst case 

design and the use of probabilistic design. Utilizing the 

uncertainties in the estimations, deterministic engineering 

design uses factors of safety to assure that the nominal 

operational condition does not come too close to the point 

where the system will fail. The approximation of minimum properties and maximum loads known as the absolute worst case gives information about this critical point. 

This approach limits the optimization capability of a system and fails to provide important information about the 

system lifetime. 

 The design procedures of the advanced aerospace vehicles must account for uncertainties calculating the risk 

or reliability. These calculations will involve probabilistic 

analysis. When compared with traditional factor of safety 

methods, probabilistic methods require additional inputs 

but provide higher quality outputs. The uncertain or random variables are assumed to have a probability density 

function. The output will be a probability density function 

for the response quantities. 

 A robust design is one that has been created with a 

system of design tools that reduce product or process variability while guiding the performance toward an optimal 

setting. Robustness means achieving excellent performance under a wide range of operating conditions. All engineering systems function reasonably well under ideal 

conditions, but robust designs continue to function well 

when the conditions are non-ideal. Analytical robust design attempts to determine the values of design parameters 

which maximize the reliability of the product without 

tightening the material or environmental tolerances. Probabilistic design and robust design go hand in hand. In order to determine the domains of stability, the system has 

to be analyzed probabilistically. 

*ASME Member. 
NASA/TMó2002-211699 2 

INTRODUCTION 

 Gas turbine aero-engines are used in all the new commercial aircraft and most business aircraft. Due to their 

capital cost and numbers installed, notably in the fleets of 

aircraft operated by the armed services and commercial 

airlines, there is considerable pressure to reduce the cost 

of ownership incurred by the operator. In the civil sector, 

this pressure is currently increasing with the rising popularity of the concept of ìpower by the hourî engine sales 

contract in which the operator is sold a fleet of engines but 

no spares. The operator pays the engine supplier a predetermined engine-operating rate for maintenance. Both 

owner and supplier share a common interest in minimizing 

repair and overhaul cost. Effective engine health monitoring techniques can reduce the cost of ownership by setting 

appropriate levels of routine maintenance and by locating 

and assessing the significance of specific problems with 

an engine. The emphasis in the gas turbine engine industry today is reduced cost in procurement and operation. 

Any unscheduled maintenance or outages will cause additional costs and lost revenues. In many critical applications, standby gas turbines are used for emergency 

conditions, thus resulting in a more cost intensive operation. The optimum use of machine availability, management and maintenance can reduce financial losses due to 

gas turbine outages. Madej et al. [1] discussed the monitoring of service delivery system and diagnostics of gas 

turbine engines. An updated schedule of gas turbine operating state will be required to diagnose the causes of performance degradation. 

 The gas path analysis can be used to determine the gas 

turbine operating state. This method uses field measurements to estimate the characteristic performance parameters by means of thermodynamic cycle analysis [2ñ5]. 

Measurements are taken of pressures and temperatures at 

various stations along the gas flow paths, together with 

other engine parameters such as the spool speeds. These 

measurements are used in conjunction with physical laws 

and the known characteristics of the engineís components 

such as the efficiencies of turbines and compressors. The 

determination of the operating state using this approach 

may include uncertainties in the accuracy of thermodynamic measurements and a priori selection of the geometric and performance characteristic parameters. The main 

benefit of such schemes to the owner/operator would be 

that any sudden deterioration in the engineís health parameters could be flagged almost immediately and corrective action taken before significant financial loss was 

incurred. 

 With the increase in gas turbine engine complexity and 

performance over the past 50 years, structural engineers 

have created an array of safety nets to ensure against 

component failures in turbine engines. In order to reduce 

what is now considered to be excessive conservatism and 

yet maintain the same adequate margins of safety, there is 

a pressing need to explore methods of incorporating probabilistic design procedures into engine development. 

Probabilistic methods combine and prioritize the 

statistical distributions of each design variable, generate 

an interactive distribution and offer the designer a quantified relationship between robustness, endurance and performance. 

 Conventional engineering design methods are deterministic. Machines and their components are considered 

as ideal systems and parameter optimizations provide single point estimates of the system behavior or response. 

Probabilistic engineering design uses probability distributions of design parameters instead of mean or nominal 

values only. This will enable a designer for a specific reliability and hence maximize safety, quality and economy. 

A probabilistic design system was developed by Fox [6] at 

Pratt & Whitney for the purpose of integrating deterministic design methods with probabilistic design techniques. 

Here, two different approaches were used for estimating 

uncertainty. A Monte Carlo approach was used on design 

codes that were judged to run relatively quickly. For more 

computationally intensive design codes, a second order 

response surface model in conjunction with Box-Behnken 

design experiments was used and then a Monte Carlo 

simulation was executed. Several researchers at NASA 

Glenn Research Center have applied the probabilistic design approaches to turbine engines and related systems. 

Chamis [7] developed a Probabilistic Structural Analysis 

Method (PSAM) using different distributions such as the 

Weibull, normal, log-normal, etc. to describe the uncertainties in the structural and load parameters or primitive 

variables. Nagpal, Rubinstein and Chamis [8] presented a 

probabilistic study of turbopump blades of the Space 

Shuttle Main Engine (SSME). They found that random 

variations or uncertainties in geometry have statistically 

significant influence on the response variable and random 

variations in material properties have statistically insignificant effects. Chamis [9] summarized the usefulness 

and importance of the probabilistic approach, especially 

for turbopumps. Gorla et al. [10] computationally simulated and probabilistically evaluated a combustor liner in 

view of several uncertainties in the aerodynamic, structural, material and thermal variables that govern the combustor liner. 

 To cost effectively accomplish the design task, we 

need to formally quantify the effect of uncertainties (variables) in the design. Probabilistic design is one effective 

method to formally quantify the effect of uncertainties. In 

the present paper, a probabilistic analysis is presented for 

the influence of measurement accuracy and a priori fixed 

parameter variations on the random variables for gas turbine system health determination. 

PROBABILITY THEORY 

 Let X1, X2, Ö., Xn be a set of random variables defined on a (discrete) probability space Ω . The probability 

that the events X1= x1 X1, X2= x2, ..., and Xn= Xn happen 

concurrently, is denoted by 

) 1 2 n 1 1 2 2 n n f(x , x ,...., x ) = P(X = x , X = x ,...., X = x for 

the set of desired solutions A⊆Ω. If the function 
NASA/TMó2002-211699 3 

),....,,( 21 n xxxf is discrete, it is called the joint probability mass function of X1, X2,..., Xn and has the following properties. 

0 ≤ f(x1, x2, .Ö, xn) ≤ 1 

 

∑ ∑

Ω∈

=

),...,,(

21

21

1),...,,(

nxxx

nxxxf (1) 

P[(X1,X2,Ö,Xn) ∈A] 

∑ ∑ Ω⊆==

Ω∈

A xxxf

nxxx

n ,1),...,,(

),...,,(

21

21

If f(x1, x2, .Ö, xn) is continuous it is called joint probability density function of X1, X2,..., Xn and has the following 

properties: 

0 ≤ f(x1, x2, Ö, xn) 

 

1,, 2121 = ∫ ∫

Ω

nn ...dxdx)dxx...x,f(x... (2) 

P ),..,,[( 21 XXX n ∈A] 

∫ ∫ Ω⊆=

A

nn ,,,.. A...dxdx)dxx...x,f(x 2121 

If the lower bound of A, the set of desired solutions, is 

equal to the infimum of Ω for all Xi, i.e., if A = [infi (Ω), 

ai], for all i = 1,2,Ö, n, a function F(a1,a2,Ö,an)can be 

defined, such that: 

F(a1,a2,Ö.,an) = ])[( 21 n ∈ AX,..,X,XP

∑∑

∈

=

A

n

nxxx

xxxf ),...,,(... 21

),...,,( 21

, 

A Ω⊆ (f is discrete) (3) 

F(a1,a2,Ö.,an) = ])[( 21 n ∈ AX,..,X,XP

 = ∫ ∫ Ω⊆

A

nn ,...),...,,(.. Adxdxdxxxxf 2121

 (f is continuous) (4) 

F is called the joint cumulative probability distribution 

function. For Ω = R

n and a continuous function f : 

F(a1,a2,Ö.,an) = 21 n )[ X,...,X,(XP ∈((-∞,-∞,Ö,-∞), 

(a1,a2,Ö.,an))] = ∫ ∫

− ∞ ∞ −

na a

nn dxdxdxxxxf

1

...),...,,(.. 2121 (5) 

The common notation F(a1,a2,...,an) 

= 2211 ≤≤≤ nn )( aX,...,aX,aXP will be used subsequently also. 

 The univariate probability function fXi for each criterion Xi, obtained from the traditional probabilistic design 

process, can also be generated with the joint probability 

function f. fxi is called marginal probability mass or density function of Xi and is defined by: 

1 fx = ∑ ∑

),...,( ∈

2

2

),...,(...

n x R x

n xxf (f is discrete) (6) 

 

1 fx = ∫∫ nn

R

...),...,(... dxdxxxf 22 (f is continuous) (7) 

The joint probability function, fXY (x, y), creates the surface of a probability ëhumpí in the x-y-f-space, characterized by rings of constant probabilities. The distribution 

curves over the x- and y-axis are the aforementioned marginal probability functions fX(x) and fy(y), respectively. 

The last necessary concept to mention here for the development of a joint probabilistic formulation is the concept 

dependence of criteria. Two random variables X and Y are 

said to be independent, if fXY(x, y) = fX(x). fY(y) otherwise 

X and Y are said to be dependent. This dependence is a 

mathematical notion and should not be confused with 

ëcasual dependenceí. For here on, mathematical dependence will be referred to as correlation. Correlation is 

measured by the covariance of two criteria, X and Y, defined by 

Cov(X,Y) = E[X,Y] ñ E[X]E[Y]. (8) 

It is more convenient, however, to use a covariance normalized by the standard deviations, σX and σY, for both 

criteria, called correlation coefficient. 

ρ = YX

YX,

σ σ

Cov )(

 (9) 

The correlation coefficient is defined over the interval 

[ñ1,1], indicating strongly positively correlated criteria at 

values close to 1 and strongly negatively correlated criteria at values close to ñ1. The criteria are independent, if 

ρ = 0. In aerospace systems design ρ can be quite difficult 

to calculate by Eq. (9). It is much more effective to view 

the correlation coefficient differently for calculation purposes. Jointly collected data from a probabilistic or any 

other analysis can be thought of as vectors of numbers. 

The correlation coefficient measures the orthogonality, 

i.e., independence, of both vectors. ρ is simply the cosine 

of the angle between the two criterion vectors, indicating 

their alignment. For ρ = 1, vectors are parallel and point 

in same direction, for ρ = ñ1, vectors are parallel and 

point in opposite direction. For ρ = 0, vectors are
NASA/TMó2002-211699 4 

orthogonal and the criteria are independent. The correlation coefficient plays a significant role in the formulation 

of joint probability distribution models as described in the 

next section. 

Probability Functions 

 Attention is now directed to the implementation of this 

probabilistic formulation in the design process. The necessary transition from the mathematical formulation above 

to a probabilistic model that yields the information relevant for multi-variate decision making is described in this 

section. There are two alternatives for this task. 

Joint Probability Model 

 The first joint probability density function introduced 

here is an analytical probability model for criteria whose 

univariate distributions and their corresponding means and 

standard deviations are known. All necessary information 

for the model can be generated by the traditional probabilistic design process, using its output of univariate criterion 

distributions. A particular model for two criteria with 

normal distributions, represented by Eq. (10), has been 

introduced by Garvey and Tuab. Garvey further generated 

models for two criteria with combinations of normal and 

lognormal distributions, which are summarized in 

Ref. [11]. 

2 ( )( ) ( ) ]} (10)

[( )

2 2

1 exp{

2 1

1 ( , )

2

2

2 2

Y

Y

Y

Y

X

X

X

x

X Y

x y y

x μ f x y XY

σ

μ

σ

μ

σ

μ ρ

ρ σ π σ σ ρ

− + − − −

−

− − =

Note that the only information needed for the Joint Probability Model consists of the means μX and μY, the standard deviations σX and σY, and the correlation coefficient 

ρ for the criteria X and Y. The model variables, x and y, 

are defined over the interval of all possible criterion values. The advantage of this model is the limited information needed, which makes it very flexible for use and 

application. For example, if only expert knowledge and no 

simulation/modeling is available in the early stages of 

design, educated guesses for the means, standard deviations, and the correlation coefficient can be used to execute the joint probability model. It also lends itself to use 

in combination with increasingly important fast probability integration (FPI) techniques. 

Implementation of Probabilistic Procedure Using FPI 

 FPI is a probabilistic analysis tool that implements a 

variety of methods for probabilistic analysis. The procedure follows the steps given below: 

1. Identify the independent and uncorrelated design 

variables with uncertainties. 

2. Quantify the uncertainties of these design variables with probability distributions based on 

expert opinion elicitation, historical data or 

benchmark testing. 

3. It is required that there is a response function that 

defines the relationship between the response and 

the independent variables. 

4. The FPI uses the responses generated to compute 

the cumulative distribution functions (CDF)/ 

probability density functions (PDF) and the corresponding sensitivities of the response. 

 Several methods are available in the FPI to compute a 

probabilistic distribution. In addition to obtaining the 

CDF/PDF of the response, the FPI provides additional 

information regarding the sensitivity of the response with 

respect to the primitive variables. They provide valuable 

information in controlling the scatter of the response variable. The random primitive variable with the highest sensitivity factor will yield the biggest payoff in controlling 

the scatter in that particular response variable. Such information is very useful to the test/design engineer in designing or interpreting the measured data. 

DISCUSSION OF RESULTS 

 The probabilistic analysis of gas turbine field performance due to the uncertainties was applied to a 10 MW two 

shaft heavy duty industrial gas turbine with variable power 

turbine nozzle. Figure 1 shows the layout of the gas turbine system. The thermodynamic random variables and 

their respective values used in this analysis are shown in 

Table 1. The random variables are labeled in Table 2. All 

the random variables were assumed to be independent. A 

scatter of ± 10% was specified for all the variables. 

Normal distribution was assumed for all random variable 

scatters. 

 The overall thermal efficiency of the gas turbine system was determined from a control volume analysis using 

the first and second laws of thermodynamics. The cumulative distribution functions (CDF) and the sensitivity factors were evaluated for the overall thermal efficiency 

response. CDF for the overall thermal efficiency are 

Figure 1 Layout of the gas turbine system.

C GGT PT

2

1

3

4 5

Mf

CC
NASA/TMó2002-211699 5 

 Table 1.Random Variables

Random Variable Mean 

Value 

Compressor inlet pressure (P1) 101.3 kPa 

Compressor inlet temperature (T1) 288 K 

Compressor exit (P2) 1439.9 kPa 

Mass flow rate of fuel (Mf) 0.645 kg/s 

Compressor turbine (CGT) exit pressure (P4) 306.0 kPa 

Adiabatic efficiency of compressor 0.85 

Adiabatic efficiency of compressor turbine 0.90 

Adiabatic efficiency of power turbine 0.86 

Table 2.Random Variable Labels 

Label Description 

P1 Compressor inlet pressure 

T1 Compressor inlet temperature 

P2 Compressor exit 

T3 Inlet temperature to the compressor turbine 

P4 Compressor turbine (CGT) exit pressure 

COMPEFF Adiabatic efficiency of compressor 

TURB1EFF Adiabatic efficiency of compressor turbine 

TURB2EFF Adiabatic efficiency of power turbine 

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.1 0.3 0.5

Figure 2 Cumulative probability of overall thermal efficiency.

Efficiency

Cumulative probability

shown in Fig. 2. The sensitivity factors for the overall 

thermal efficiency are plotted in Figs. 3ñ5. From these 

figures, we observe that the inlet pressure and temperature 

of the compressor, exit pressure of the compressor, inlet 

temperature to the compressor gas turbine and adiabatic 

efficiencies of the compressor turbine and power turbine 

have a lot of influence on the overall thermal efficiency. 

These thermodynamic random variables represent the 

most important indices for the gas turbine health determination. The adiabatic efficiencies of the compressor and 

turbines in the system are measures of irreversibilities or 

increase of entropy. The sensitivity factor for the compressor adiabatic efficiency is much smaller than those for 

the compressor turbine and power turbine. The sensitivity 

factors due to the adiabatic efficiencies of the compressor 

turbine and power turbine influence the most in the determination of the overall thermal efficiency of the system. 

Figure 3 Sensitivity factors versus random variables.

P1

T1

P2

T3

COMPEFF

TURB1EFF

TURB2EFF

–0.8

–0.6

–0.4

–0.2

0.0

0.2

Random variables

Sensitivity factors

Probability = 0.001

Figure 4 Sensitivity factors versus random variables.

–0.8

–0.6

–0.4

–0.2

0.0

0.2

Random variables

Sensitivity factors

Probability = 0.01

P1

T1

P2

T3

COMPEFF

TURB1EFF

TURB2EFF

Figure 5 Sensitivity factors versus random variables.

–0.6

–0.4

–0.2

0.0

0.2

0.4

Random variables

Sensitivity factors

Probability = 0.999

P1

T1

P1

P2

T3

COMPEFF

TURB1EFF

TURB2EFF

T3

 Figure 6 shows the CDF for the net specific output of 

the gas turbine system. The sensitivity factors for the net 

specific output are plotted in Figs. 7ñ9. The sensitivity 

factor due to the compressor turbine inlet temperature 

influences the most in the evaluation of the net specific 

power output in the cycle. 

 These results can be used to further optimize the design for cost effectiveness and also to assist in the health 

determination of the system. The prediction of degradation of system performance can be achieved from the results obtained. 
NASA/TMó2002-211699 6 

Figure 6 Cumulative probability of net specific power output.

Specific power

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100 150 200 250 300 350 400 450

Cumulative Probability

Figure 7 Sensitivity factors versus random variables.

Random variables

Sensitivity factors

Probability = 0.001

P1

T1

P2

T3 COMPEFF

TURB1EFF

TURB2EFF

–0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

Figure 8 Sensitivity factors versus random variables.

Random variables

Sensitivity factors –0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

P1

T1

P2

T3

COMPEFF

TURB1EFF

TURB2EFF

Probability = 0.01

CONCLUDING REMARKS 

 In this paper, a non-deterministic, non-traditional 

method has been developed to support reliability-based 

aerospace design. The revolutionary part of the proposed 

work is the probabilistic evaluation of the thermodynamic 

analysis. The nontraditional part of the proposed work is 

the identification of criteria for using computational 

accuracy. Probabilistic methods were applied to the 

Figure 9 Sensitivity factors versus random variables.

–0.8

–0.6

–0.4

–0.2

0.0

0.2

0.4

0.6

Probability = 0.999

P1

T1

P2

T3

COMPEFF

TURB1EFF

TURB2EFF

Random variables

Versus random variables

thermodynamic analysis of a gas turbine system. The interconnection between the thermodynamic analysis and 

NESTEM codes was necessary to compute the probabilistic evaluation of a gas turbine field performance. Overall 

thermal efficiency and net specific power output of the gas 

turbine plant was evaluated using the thermodynamic random variables. Cumulative distribution functions and sensitivity factors were computed for the overall thermal 

efficiency and net specific power output due to the thermodynamic random variables. Evaluating probability of 

risk and sensitivity factors will enable the identification of 

the most critical design variables in order to optimize the 

design, make it cost effective and assist in the health determination of the system. 

REFERENCES 

 [1] Madej, J., Longtin K., and Smith, D.P., 1996, ìMonitoring Service Delivery System and Diagnostics,î 

Proceedings, 39th GE Turbine State-of-the-Art Technology Seminar, General Electric Company, 

Schenectady, New York, GERñ3956. 

 [2] Stamatis, A., Mathioudakis, K., and Papailiou, K.D., 

1990, ìAdaptive Simulation of Gas Turbine Performance,î ASME J. Eng. Gas Turbine Power, 112, 

pp. 168ñ175. 

 [3] Doel, D.L., 1994, ìTEMPER-A Gas-Path Analysis 

Tool for Commercial Jet Engines,î ASME J. Eng. 

Gas Turbines Power, 116, pp. 82ñ89. 

 [4] Doel, D.L., 1994, ìAn Assessment of Weightedñ

Least-Squares based Gas Path Analysis,î ASME J. 

Eng. Gas Turbine Power, 116, pp. 366ñ373. 

 [5] Pinelle, M., and Spina, P.R., 2002, ìGas Turbine 

Field Performance Determination: Sources of Uncertainties,î 124, pp. 155ñ160. 

 [6] Fox, E.P., 1994, ìThe Pratt & Whitney Probabilistic 

Design System,î AIAAñ94ñ1442ñCP. 

 [7] Chamis, C.C., 1986, ìProbabilistic Structural Analysis Methods for Space Components,î Space Systems 

Technology Conference, San Diego, California, June 

9ñ12, 1986. 

 
NASA/TMó2002-211699 7 

[8] Nagpal, V.K., Rubinstein, R., and Chamis, C.C., 

1987,î Probabilistic Structural Analysis to Quantify 

Uncertainties Associated with Turbopump Blades,î 

AIAAñ87ñ0766. 

 [9] Chamis, C.C., 1986, ìProbabilistic Structural Analysis Methods for Critical SSME Propulsion 

Components,î Third Space Systems Technology 

Conference, AIAA, pp. 133ñ144. 

[10] Gorla, R.S.R., Pai, S.S., and Rusick, J.J., 2002, 

ìProbabilistic Study of Fluid Structure Interaction,î 

International Journal of Engineering Science (in 

print). 

[11] Sundararajan, R., 1995, ìProbabilistic Structural Mechanics Handbook,î Chapman and Hall, New York, 

NewYork.
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

November 2002

NASA TM—2002-211699

TED–AJ03–649

E–13440

WU–704–04–13–00

13

Probabilistic Analysis of Gas Turbine Field Performance

Rama S.R. Gorla, Shantaram S. Pai, and Jeffrey J. Rusick

Thermodynamic cycle; Probabilistic analysis; Gas turbines; Health monitoring

Unclassified -Unlimited

Subject Category: 02 Distribution: Nonstandard

Prepared for the Sixth Thermal Engineering Joint Conference cosponsored by the Japan Society of Mechanical

Engineers, Thermal Engineering Division, and the American Society of Mechanical Engineers, Heat Transfer Division,

Hawaii Island, Hawaii, March 16–20, 2003. Rama S.R. Gorla, Cleveland State University, Cleveland, Ohio 44115;

Shantaram S. Pai and Jeffrey J. Rusick, NASA Glenn Research Center. Responsible person, Jeffrey J. Rusick, organization

code 0510, 216–433–5375.

A gas turbine thermodynamic cycle was computationally simulated and probabilistically evaluated in view of the

several uncertainties in the performance parameters, which are indices of gas turbine health. Cumulative distribution

functions and sensitivity factors were computed for the overall thermal efficiency and net specific power output due to

the thermodynamic random variables. These results can be used to quickly identify the most critical design variables in

order to optimize the design, enhance performance, increase system availability and make it cost effective. The analysis

leads to the selection of the appropriate measurements to be used in the gas turbine health determination and to the

identification of both the most critical measurements and parameters. Probabilistic analysis aims at unifying and

improving the control and health monitoring of gas turbine aero-engines by increasing the quality and quantity of

information available about the engine’s health and performance.