Using acoustic calculations to determine turbine inlet temperature

Abstract

A method of determining a turbine inlet temperature for a gas turbine engine, the method comprising measuring a pressure variation within a combustion section of the gas turbine engine during operation of the gas turbine engine to produce pressure versus time data, extracting a resonant frequency from the pressure versus time data, and calculating the turbine inlet temperature based only on the resonant frequency.

Description

BACKGROUND

[0001] Gas turbine engines operate at high temperatures to improve thermal efficiency and reduce undesirable emissions. One of the highest temperature regions in a gas turbine engine is the region near the turbine inlet. The typical temperatures in this region are high enough that most temperature measuring sensors cannot operate for long periods of time. SUMMARY

[0002] A method of determining a turbine inlet temperature for a gas turbine engine includes measuring pressure variations within a combustion section of the gas turbine engine during operation of the gas turbine engine to produce pressure versus time data, extracting a resonant frequency from the pressure versus time data, and calculating the turbine inlet temperature based only on the resonant frequency.

[0003] In another arrangement, a method of determining a turbine inlet temperature for a gas turbine engine includes positioning a dynamic pressure sensor in a combustion section, positioning a temperature sensor in a location suitable to measure the turbine inlet temperature, and measuring pressure variations using the dynamic pressure sensor to produce pressure versus time data. The method also includes measuring the turbine inlet temperature using the temperature sensor to produce temperature versus time data, determining a resonant frequency based on the pressure versus time data, determining a value of at least one constant in a polynomial equation using the resonant frequency and the temperature versus time data, and calculating the turbine inlet temperature using the polynomial equation and based only on the resonant frequency.

[0004] In another arrangement, a gas turbine engine includes a combustion section operable to combust a fuel to produce exhaust gases, a turbine section coupled to the combustion section and operable to receive the exhaust gases, the turbine section defining a turbine inlet having a turbine inlet temperature, and a dynamic pressure sensor positioned in the combustion section and operable to measure pressure fluctuations. The engine also includes a computer system coupled to the dynamic pressure sensor to receive pressure versus time data. The computer system includes a processor and a memory storing instructions that, when executed by the processor, cause the device to be configured to extract a resonant frequency from the pressure versus time data and calculate the turbine inlet temperature based only on the resonant frequency. BRIEF DESCRIPTION OF DRAWINGS

[0005] To easily identify the discussion of any particular element or act, one or more of the most significant digits in a drawing figure reference number are commonly used to identify the embodiment first introduced in the corresponding drawing figure.

[0006] Figure 1 is a cross-sectional longitudinal view of a gas turbine engine.

[0007] Figure 2 is a cross-sectional view of a combustor of a gas turbine engine. Figure 1

[0008] Figure 3 is a schematic diagram of a control system operable to control operation of a gas turbine engine of Figure 1

[0009] Figure 4 is a flowchart illustrating operation of a turbine inlet temperature calculation module operable using a control system of Figure 3 to determine a turbine inlet temperature of a gas turbine engine of Figure 1

[0010] Figure 5 is a series of plots illustrating a peak location step of a turbine inlet temperature calculation module.

[0011] Figure 6 includes two plots illustrating two results generated using two different spectral determination methods.

[0012] Figure 7 is a plot showing a trace of a resonant frequency calculated by a turbine inlet temperature calculation module over time.

[0013] Figure 8 is a plot comparing turbine inlet temperature results calculated by a turbine inlet temperature calculation module to actual measured turbine inlet temperatures.

[0014] Figure 9 is a plot of a selected region 900 of the plot of Figure 8 DETAILED DESCRIPTION

[0015] Before any embodiments of the application are explained in detail, it is to be understood that the application is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The application is capable of other embodiments and of being practiced or being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting.

[0016] Various techniques relating to systems and methods will now be described with reference to the drawings, wherein like reference numerals refer to like elements throughout. The drawings discussed below are included to provide a description of the principles of the disclosure and are not intended to limit the scope of the disclosure. One skilled in the art will understand that the principles of the disclosure can be implemented in any appropriate arrangement. ​​​​

[0017] It is to be understood that functions described as being performed by certain system elements can be performed by multiple elements. Similarly, for example, an element can be configured to perform functions described as being performed by multiple elements. Numerous innovative teachings are described throughout the present application, which will be described with reference to exemplary, non- limiting embodiments.

[0018] In addition, it should be understood that the words or phrases used herein in reference to particular embodiments are intended to be broad and inclusive rather than exclusive. For example, the terms "including" "has" and "having" and variations thereof as used herein are intended to be inclusive in a manner similar to the term "comprising." Unless specifically set forth herein, the terms "and," "or," and "but" are intended to be inclusive. The phrase "associated with" and variations thereof as used herein can mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, be proximate to, be bound to or with, have a property of, or the like. Furthermore, although numerous embodiments or configurations can be described herein, any feature, method, step, component, etc. described with respect to one embodiment or configuration can be incorporated into other embodiments or configurations, as appropriate, unless specifically stated otherwise.

[0019] Furthermore, although the terms "first," "second," "third," etc. can be used herein to refer to various elements, information, functions, or actions, such elements, information, functions, or actions should not be limited by these terms. Rather, these numeric adjectives are used to distinguish different elements, information, functions, or actions from each other. For example, a first element, a first information, a first function, or a first action can be termed a second element, a second information, a second function, or a second action, and similarly, a second element, a second information, a second function, or a second action can be termed a first element, a first information, a first function, or a first action, without departing from the scope of the present disclosure.

[0020] Additionally, unless otherwise indicated by context, the term "adjacent" can mean that an element is relatively close to another element but not in contact with the other element; or that an element is in contact with other portions. Additionally, unless otherwise clear from context, the phrase "based on" is intended to mean "based, at least in part, on." The term "about" or "approximately" or similar terms are intended to cover variations in values within a range that are normally industry standard for the size in question. If no industry standard is available, a variation of 20 percent will fall within the meaning of these terms unless otherwise indicated.

[0021] Figure 1 An example of a gas turbine engine 100 is shown that includes a compressor section 102, a combustion section 104, and a turbine section 106. The compressor section 102 includes a plurality of compressor stages 108, where each stage includes a set of rotating blades and a set of stationary or adjustable guide vanes. The compressor section 102 is in fluid communication with an inlet section 114 to allow the gas turbine engine 100 to draw atmospheric air into the compressor section 102. During operation of the gas turbine engine 100, the compressor section 102 draws atmospheric air and compresses the air for delivery to the combustion section 104.

[0022] In the illustrated configuration, the combustion section 104 includes a plurality of individual combustors 200 that each operate to mix a flow of fuel with compressed air from the compressor section 102 and to burn the air-fuel mixture to produce a high-temperature, high-pressure flow of combustion gases or exhaust gases 116. Of course, many other arrangements of the combustion section 104 are possible.

[0023] The turbine section 106 includes a plurality of turbine stages 110, where each stage includes a plurality of rotating blades and a plurality of stationary vanes or wheels. The turbine stages 110 are arranged to receive the exhaust gases 116 from the combustion section 104 at a turbine inlet 112 and expand the gases to convert thermal and pressure energy into rotational or mechanical work. The turbine section 106 is connected to the compressor section 102 to drive the compressor section 102. For a gas turbine engine used for power generation or as a prime mover, the turbine section 106 is also connected to an electrical generator, pump, or other device to be driven.

[0024] The control system 300 is coupled to the gas turbine engine 100 and operates to monitor various operating parameters and control various operations of the gas turbine engine 100. In the preferred arrangement, the control system 300 is typically microprocessor-based and includes memory devices and data storage devices for collecting, analyzing and storing data. In addition, the control system 300 provides output data to various devices including monitors, printers, indicators, etc. that allow a user to interact with the control system 300 to provide inputs or adjustments. In the example of a power generation system, a user can input a power output set point and the control system 300 adjusts various control inputs to achieve that power output in an efficient manner.

[0025] The control system 300 can control various operating parameters including, but not limited to, variable inlet guide vane position, fuel flow rate and pressure, engine speed, valve position and generator load. Of course, other applications can have fewer or more controllable devices. The control system 300 also monitors various parameters to ensure that the gas turbine engine 100 is operating properly. Some of the parameters monitored can include inlet air temperature, compressor outlet temperature and pressure, combustor outlet temperature, fuel flow rate, generator power output, etc. Many of these measurements are displayed to the user and recorded for later review if needed. It is also desirable to determine the turbine inlet temperature. However, as will be discussed in more detail, this temperature is difficult to measure directly.

[0026] Figure 2 is Figure 1An enlarged cross-sectional view of one of the burners in the burner 200 of a gas turbine engine 100. Each burner 200 includes a top cap section 202, at least one flame tube 208, a burner cylinder 204, and a transition member 212. The top cap section 202 is attached to the gas turbine engine 100 and supports any pipes and valves required to direct fuel into the burner 200. The burner cylinder 204 extends from the top cap section 202 toward the turbine section 106 and defines a long axis 206 arranged at an oblique angle relative to the central axis 118 of the gas turbine engine 100. The burner cylinder 204 operates as a bushing to separate the combustion zone of the burner 200 from the outer wall of the engine 100. At least one flame tube 208, and in many cases, multiple flame tubes 208, are disposed within the burner cylinder 204. The flame tube 208 discharges a fuel and air stream, which is ignited to form one or more flames 210 within the burner cylinder 204. The combustor casing 204 includes a plurality of orifices (not shown) that allow additional air to enter the combustion zone to ensure complete combustion and to cool the combustion gases before they are discharged to the turbine section 106. A transition member 212 is positioned adjacent to the combustor casing 204 to receive the combustion gases and to effectively guide them to the turbine inlet 112.

[0027] Continue to refer to Figure 2 A first dynamic pressure sensor 214 is positioned at the outlet end of the burner canister 204, and a second dynamic pressure sensor 216 is positioned downstream of the first dynamic pressure sensor 214 in the transition member 212. The dynamic pressure sensors 214 and 216 are operable to detect small and rapid pressure changes within the burner 200 that are associated with audible variations. Although two sensors 214 and 216 are illustrated, only one sensor is needed to detect the desired pressure fluctuations. In other configurations, these sensors 214 and 216 may be positioned in the top cap section 202 or in other areas of the burner 200. Because small design variations can have a significant impact on the acoustic environment, the actual location and number of sensors required can vary depending on the burner design.

[0028] Other sensors 222, such as acoustic sensors alone or in some combination, low-frequency pressure sensors, temperature sensors 218, optical sensors, or ionization sensors, can be configured to detect physical phenomena in at least a portion of the gas flow. In some embodiments, multiple actuators or sensors, or both, are collectively referred to as transducers.

[0029] Dynamic pressure sensors 214, 216 receive the acoustic oscillations generated within combustor can 204 and convert these oscillations into signals that can be analyzed by control system 300 or other systems. In other embodiments, different acoustic transducers sensitive to acoustic phenomena in the same or different location or locations are used in combustor can 204. In some configurations, pressure sensors 214, 216 are positioned upstream of flame 210. This location is cooler than the sensor locations shown in Figure 2

[0030] Dynamic pressure sensors 214, 216 are installed on each combustor can 204 in a can-annular combustor system, or several dynamic pressure sensors are installed in an annular system in the case of an annular chamber. These sensors 214, 216 are sensitive enough to obtain the sound generated in gas turbine engine 100 by many events and operational changes, according to the results obtained by the advanced data acquisition system.

[0031] It should be noted that first dynamic pressure sensor 214 and second dynamic pressure sensor 216 are typically positioned as shown in Figure 2 However, other locations sensors or additional sensors can be employed depending on what is being analyzed. These sensors 214, 216 are typically installed to monitor operational characteristics that are not necessarily related to turbine inlet temperature.

[0032] Figure 2 A temperature sensor 220 is also illustrated positioned adjacent to turbine inlet 112. Although temperature sensor 220 is capable of directly measuring turbine inlet temperature, the temperature in this region, typically 1600°C or higher, rapidly destroys and damages temperature sensor 220 during operation. Thus, it is typically not possible or cost effective to use this temperature sensor 220 to measure turbine inlet temperature over the long term.

[0033] Figure 3 A portion of control system 300 is illustrated that is operable to control operation of gas turbine engine 100, as well as determine, estimate or calculate turbine inlet temperature. As is typically included in current gas turbine engines 100, Figure 3 First dynamic pressure sensor 214, second dynamic pressure sensor 216, engine controller 310 and engine operating data storage unit 312 or other storage device suitable for storing operating data are illustrated.

[0034] ​As discussed, each of the first dynamic pressure sensor 214 and the second dynamic pressure sensor 216 is located in the combustion section 104 and arranged to measure rapid pressure changes, specifically acoustic pressure changes. The first dynamic pressure sensor 214 measures the pressure change during operation and generates a signal indicating the measured pressure change. This signal is then directed to an amplifier 304 or other conditioning loop, which adjusts the signal to suit its use. Figure 3 In this case, the signal is amplified to produce an amplified signal. The amplified signal is then directed to isolator 306, which operates to isolate the sensitive amplifier 304 and the first dynamic pressure sensor 214 from stray voltages or currents that could cause damage. A suitable isolator 306 is an electrical separator. In other configurations, transformers, opto-isolators, capacitors, Hall effect devices, etc., can be suitable as isolators 306.

[0035] After passing through isolator 306, the signal is transmitted to sensor monitor 308 for further analysis, storage, or transfer to engine controller 310. The second dynamic pressure sensor 216 generates a signal that follows a path through similar components, as described just with respect to the first dynamic pressure sensor 214.

[0036] The engine controller 310 collects operational data, including pressure, temperature, speed, fuel flow, etc., to allow for accurate and efficient control and operation of the gas turbine engine 100. Some or all of the collected operational data is directed to the operational data storage unit 312, where some or all of the collected operational data can be stored for later use, access by other systems, archiving, transmission, or other purposes.

[0037] On this point Figure 3 The described components are included in most operating gas turbine engines. Of course, additional sensors, controllers, or other devices may also be included, and often are also included. For example... Figure 3 The diagram also illustrates a turbine inlet temperature calculation system 314, including a computer system 302. The computer system 302 includes components capable of operating in pairs. Figure 1 An interface 320, a computing server 318, and a data storage 316 are provided for calculating the turbine inlet temperature of the gas turbine engine 100.

[0038] To calculate the turbine inlet temperature, a signal from each isolator 306 is provided to a computer system 302. Preferably, the signal is sampled at a rate of at least 5 kHz to ensure the required accuracy, while some structures are sampled at a rate exceeding 20 kHz.

[0039] Figure 4 A turbine inlet temperature calculation module 400 is illustrated that includes various steps executed by the computer system 302 to calculate turbine inlet temperature using only data provided by one or both of the dynamic pressure sensors 214, 216. These steps include a resonant frequency extraction step 402, a tracking step 404, and a frequency to temperature mapping step 406. Sensor data 408 from one or more of the dynamic pressure sensors 214, 216 is fed to the resonant frequency extraction step 402, and turbine inlet temperature results 410 are output from the frequency to temperature mapping step 406. In a preferred construction, the turbine inlet temperature results 410 are in the form of a trace of temperature over time, or can include only a reading of the current turbine inlet temperature.

[0040] In some constructions, an operational check step 412 can be performed prior to starting the turbine inlet temperature calculation module 400. The operational check step 412 can determine whether the gas turbine engine 100 is operating, whether it is at or above a certain load, whether it is operating at a certain speed, or the operational check step 412 can check any other parameter prior to starting the turbine inlet temperature calculation module 400. In some modes of operation, the accuracy of the turbine inlet temperature results 410 can not be as high as desired. The operational check step 412 can be used to disable the turbine inlet temperature calculation module 400 when operating in these modes.

[0041] The resonant frequency extraction step 402 includes a frequency determination step 600, a peak location step 500, and a peak density analysis step 414. In the frequency determination step 600, the turbine inlet temperature calculation module 400 receives sensor data 408 in the form of amplitude over time data. The amplitude over time data is converted to the frequency domain so that frequency over amplitude data can be used for analysis. A preferred system employs an autoregressive power spectral density analysis in the frequency determination step 600 that converts the sensor data 408 to the frequency domain and produces an autoregressive PSD result 602 as shown in Figure 6 Other systems can use other techniques or methods, including a fast Fourier transform (FFT), among others. As illustrated in Figure 6 The autoregressive PSD result 602 is superior to an FFT result 604 produced using a standard FFT as illustrated in

[0042] Figure 5 The peak location step 500 and the tracking step 404 operate to identify and track frequencies in any resonant frequencies contained in the frequency over amplitude data 508. In Figure 5In the first plot 502, the peak localization step 500 utilizes an unsupervised learning method to localize the resonant frequencies within the data 508 of frequency versus amplitude and define a cylinder 510 around each resonant frequency. A kernel density estimator uses the defined cylinders 510 as input to calculate the location of these resonant frequencies. Figure 5 Each peak 512 in the second plot 504 represents the results from the kernel density estimator, where the width of each peak 512 represents the assignment or spread of values around the center of the peak 512.

[0043] Once the frequencies are determined, the tracking step 404 tracks the location of each peak 512 as shown in the third plot 506. The output of the tracking step 404 can be a trace 700 of resonant frequency versus time for each peak 512 determined in the peak localization step 500. To track each peak 512 and complete the desired trace 700 of resonant frequency versus time, a filter 416 is applied. In the illustrated configuration, a Kalman filter 416 is used as the filter. The Kalman filter 416 has the advantage of always providing a value so that the filter 416 can fill in missing data or remove bad data where there are interruptions or other issues that can create gaps in the data. Of course, other filters and filtering methods can be employed to obtain the desired results.

[0044] Using the now available trace 700 of resonant frequency versus time as illustrated in Figure 7 the computer system 302 can perform the frequency to temperature mapping step 406. The following equation is used to calculate the turbine inlet temperature at each time step using only one of the resonant frequencies 702.

[0045] T = af + bf + c 2

[0046] In the above equation, T is the turbine inlet temperature, f is the resonant frequency, and a, b, and c are constants that must be determined prior to implementing the turbine inlet temperature calculation module 400. One method suitable for determining the constants involves using a temperature sensor 220 positioned near the turbine inlet 112. The temperature sensor 220 measures the actual turbine inlet temperature during operation while the first dynamic pressure sensor 214 measures the pressure values. With the temperature and resonant frequency known, one can solve the above equation to determine the best values for a, b, and c. Not all gas turbine engines 100 include a temperature sensor 220 near the turbine inlet 112, and those that do often experience failure of the temperature sensor 220 after a short period of operation due to the high temperatures in that location. Therefore, the process is used to determine the values of a, b, and c when a temperature sensor 220 is available.​

[0047] It should be noted that each gas turbine engine is different, such that values for one turbine can not be appropriate for another gas turbine engine. Further, many gas turbine engines include multiple combustors 200, and each of the combustors 200 has slight differences that can require different values of a, b, and c for each of the combustors 200. Further, in some applications, different equations including higher order polynomials or in other forms can be more appropriate for a particular gas turbine engine or one or more of the combustors 200.

[0048] For gas turbine engines 100 that do not have a suitable temperature sensor 220 near the turbine inlet 112, a heat balance can be used to determine the values of the constants a, b, and c. A heat balance makes predictions of expected turbine inlet temperature values at various operating conditions. Thus, one would operate the gas turbine engine 100 at these conditions and use the first dynamic pressure sensor 214 to measure pressure data. One would then have enough data to solve the equation for a, b, and c. Although not as accurate as using actual turbine inlet temperature data, using a heat balance to calculate the constants is accurate enough to provide useful turbine inlet temperature results 410.

[0049] As will be appreciated by those of ordinary skill in the art, other methods and systems can be used to determine the values of the constants a, b, and c, and combinations of the two methods can also be used if desired. As noted above, some gas turbine engines can be more accurately represented by different equations including higher order polynomials or in other forms.

[0050] It should also be noted that although the computing system 314 has been described as using only one of the resonant frequencies to determine the turbine inlet temperature, other configurations can employ multiple resonant frequencies. In these systems, a single equation can use two or more resonant frequencies, or each resonant frequency 702 can be used in its own equation, with the results being combined (e.g., averaged) to arrive at a single temperature value.

[0051] Figure 8 is a plot comparing the turbine inlet temperature results 410 to the actual measured turbine inlet temperature 802. As can be seen, the error between the actual measured turbine inlet temperature 802 and the turbine inlet temperature results 410 produced by the computing system 314 is significant at lower temperature values. Typically, this lower temperature value corresponds to lower loads. The operational check step 412 can be used to disable the turbine inlet temperature calculation module 400 at these lower loads to ensure that the turbine inlet temperature calculation module 400 only reports accurate turbine inlet temperature results 410.

[0052] With continued reference to Figure 8 , one can see that as temperature and load increase, the accuracy of the calculated turbine inlet temperature results 410 become more accurate. For example, in one configuration, the operational check step 412 verifies that the gas turbine engine 100 is operating at 80% or greater temperature prior to starting the turbine inlet temperature calculation module 400. Because operation at these higher temperatures is more critical, the restrictive operation of the turbine inlet temperature calculation module 400 at only these higher temperatures and loads is acceptable.

[0053] Figure 9 is a plot of a selected region 900 of the graph of Figure 8 and better illustrates the accuracy of the computing system 314. As can be seen, the calculated turbine inlet temperature results 410 are generally within a few degrees of the actual measured turbine inlet temperature 802. In fact, even during transient operation, such as sudden load changes, the calculated turbine inlet temperature results 410 remain within a few degrees of the actual measured turbine inlet temperature 802. Figure 9 illustrates a sudden load decrease from about time 1.625 to time 1.7, followed by a sudden increase until about time 1.75. As can be seen, the calculated turbine inlet temperature results 410 remain within a few degrees of the actual measured turbine inlet temperature 802 (e.g., within 5 degrees C or one percent of the actual value).

[0054] In operation, a gas turbine engine 100 is operated using a working temperature sensor 220 in the turbine inlet 112 for each combustor 200. Operational data, including frequency data and actual measured turbine inlet temperature 802, is collected. The frequency data is directed to the computer system 314 and analyzed by the turbine inlet temperature calculation module 400. The values of the constants a, b, and c are adjusted until the calculated turbine inlet temperature data 410 matches or closely matches the actual measured turbine inlet temperature 802. Once a, b, and c are determined for each combustor 200, the turbine inlet temperature calculation module 400 can be used.

[0055] During operation without the use of temperature sensors 220, the operational check step 412 determines whether the gas turbine engine 100 is operating in a mode where the turbine inlet temperature should be calculated. If so, the turbine inlet temperature calculation module 400 is used to analyze the pressure data received from the isolators 306 to determine the turbine inlet temperature. As discussed, each combustor 200 can have its own equation, such that the turbine inlet temperature is determined for each combustor.

[0056] While example embodiments of the disclosure have been described herein, those skilled in the art will understand that various modifications, substitutions, changes, and improvements can be made to what is disclosed herein without departing from the spirit and scope of the broadest form of the disclosure.

[0057] No description herein is to be interpreted under any aspect as implying any particular element, step, act or function is an essential element of the patentable subject matter claimed: the scope of the patent subject matter is defined only by the allowed claims. Moreover, these claims are not intended to be interpreted under the doctrine of equivalents to the extent that the foregoing description might allow such doctrine.

Claims

1. A method for determining the turbine inlet temperature for a gas turbine engine having a computer system, the method comprising: Pressure changes within the combustion section of the gas turbine engine are measured during operation to generate data on pressure changes over time. The resonant frequency is extracted based on the pressure change over time data. as well as The turbine inlet temperature is calculated solely based on the resonant frequency and at least one constant, wherein, prior to this calculation step, the computer system performs at least one step of solving for at least one constant in an equation using the turbine inlet temperature, the equation using the resonant frequency and the turbine inlet temperature to solve for at least one constant. The calculation steps include using the resonant frequency in the polynomial equation to calculate the turbine inlet temperature, and Wherein, the polynomial equation is in the form of The equation is a second-order polynomial equation of the form T, where T is the turbine inlet temperature, f is the resonant frequency, and a, b, and c are constants.

2. The method according to claim 1, wherein, The extraction step includes converting the pressure-time variation data to the frequency domain to generate frequency and amplitude data.

3. The method according to claim 2, wherein, The conversion step includes calculating the autoregressive power spectral density based on the pressure change over time data.

4. The method according to claim 2, wherein, The extraction step includes identifying multiple resonant frequencies in the data containing the frequency and amplitude, and tracking the multiple resonant frequencies over time to generate a trace of the resonant frequencies changing over time.

5. The method according to claim 4, wherein, The trace of the resonant frequency changing over time is generated using a Kalman filter, which operates to fill in missing data and remove bad data.

6. The method of claim 1, further comprising measuring the actual turbine inlet temperature during operation of the gas turbine engine to generate data on the actual turbine inlet temperature changing over time, and determining the values ​​of a, b, and c by comparing the turbine inlet temperature calculated by the polynomial equation with the data on the actual turbine inlet temperature changing over time.

7. The method of claim 1, further comprising using turbine thermal balance to calculate the actual turbine inlet temperature to generate data on the actual turbine inlet temperature over time, and determining the values ​​of a, b, and c by comparing the turbine inlet temperature calculated by the polynomial equation with the data on the actual turbine inlet temperature over time.

8. The method according to claim 1, wherein, The gas turbine engine includes a plurality of combustors, and wherein the turbine inlet temperature is calculated individually for each of the plurality of combustors.

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