Patent Description:
Swirl is the result of shifts in the exhaust pattern generated by a given combustor downstream of another combustor. Some combustors may emit relatively hot or cold streaks of gas when operating abnormally. Inordinately hot or cold streaks may be indicative of a problematic combustor. In order to efficiently repair or replace a combustor, the identification of the problematic combustor must occur. This may be aided by identification of the swirl pattern within the gas turbine.

The exhaust temperature from a gas turbine may be measured with a circumferential array of thermocouples positioned downstream from the turbine. These values provide information not only about the performance of the turbine as a whole, but deviations from one sensor to the next provide information about "health problems" in a hot or cold section. If one combustor is running incorrectly or damaged, its exhaust may be hotter or colder than average, resulting in a measurable temperature deviation in the exhaust. However, the flow rotates upon leaving the combustor and going through the turbine, thereby generating swirl. An apparatus and/or process which may identify the amount of swirl may assist in identifying the azimuthal location of the measured temperature, such that it can be associated with the combustor it originated from. Conventionally, swirl information may only be available from the gas turbine's manufacturer, and varies between engines and with engine operating conditions. Swirl information is used to identify which combustor is responsible for hot or cold exhaust paths, and is therefore useful for quick diagnosis and repair of faulty machines, and/or for health monitoring. This algorithm enables online identification of the swirl from gas turbine operational data, which is important if the swirl information is otherwise unavailable.

Access to swirl information may assist in relating measured temperature data back to a specific component of concern. Furthermore, the amount of swirl may change as a gas turbine ages.

A method for a gas turbine maintenance using a swirl evaluation is known from <CIT>.

The present subject matter relates to a non-transitory computer readable medium with instructions stored thereon, the instructions executable by one or more processors for: calculating base swirl in a gas turbine; and calculating relative swirl in the gas turbine.

The present subject matter also relates to a method for gas turbine maintenance, comprising: identifying a combustor in need of repair or replacement within a gas turbine; and repairing or replacing the combustor; wherein said identifying comprises calculating base swirl of the gas turbine and calculating relative swirl of the gas turbine in order to associate a gas path from a thermocouple to the combustor in need of repair or replacement.

The present subject matter provides swirl information by determining an up-to-date swirl number as a function of operating conditions, which enables one to determine swirl from standard data which is available from gas turbine systems and enables users to make health assessments from the data.

Embodiments of the subject matter are disclosed with reference to the accompanying drawings and are for illustrative purposes only. The subject matter is not limited in its application to the details of construction or the arrangement of the components illustrated in the drawings. As used herein, "at least one" means one or more than one, and "and/or" means items listed may be included exclusively or in combination. Like reference numerals are used to indicate like components, unless otherwise indicated.

<FIG> is a block diagram illustrating certain embodiments of the present subject matter.

Provided is a non-transitory computer readable medium with instructions stored thereon, the instructions executable by one or more processors for: calculating base swirl in a gas turbine; and calculating relative swirl in the gas turbine.

According to the invention, calculating base swirl comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and/or (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine.

Calculating unsteady pressure amplitude as a function of angular position within the gas turbine and/or calculating mean-subtracted exhaust temperature as a function of angular position within the gas turbine may be done by azimuthal decomposition. Azimuthal decomposition is an acoustic and/or exhaust temperature approach wherein sine waves are "fit" to a temperature pattern across angular position and/or an acoustics pattern across angular position. Any shift between the best fit sine waves is the swirl as determined by azimuthal decomposition. Azimuthal decomposition calculates the cross-correlation between the combustor unsteady pressure amplitude as a function of a predetermined can number within a combustor, the can number corresponding to a radial position, and the mean-subtracted exhaust temperature as a function of gas path radial position. With this data, the radial offset between can number and gas path number that maximizes a correlation coefficient is determined. This may be repeated for multiple data points as possible in a given power band. Next, for each power band, the method computes the average of the radial offsets that maximize the cross-correlation coefficient. The result is an average radial offset between can number (which corresponds to an angular location) and gas path number (which corresponds to an angular location) as a function of load, this is defined as the swirl. Azimuthal decomposition may be included in the calculation of base swirl. The determination of base swirl may consist of azimuthal decomposition.

Calculating unsteady pressure amplitude as a function of angular position within the gas turbine and/or calculating mean-subtracted exhaust temperature as a function of angular position within the gas turbine may be done by cross correlation. Cross correlation projects the combustor pressure amplitude pattern onto the following expression: A *e^(i * Θd), where A is a constant coefficient, i is the square root of -<NUM>, e is Euler's number (approximately <NUM>), and Θd is the angular phase of the pressure amplitude pattern. Similarly, the mean-subtracted gas path temperature pattern is projected onto the function: B* e^(i * Θt), where B is a constant coefficient, i and e are number constants as described above, and Ot is the angular phase of the temperature pattern. This method then defines the swirl to be the phase difference between the pressure amplitude pattern and the gas path temperature pattern. In degrees, this is equal to <NUM>*π*(Θt - Θd). The shift with the highest correlation to the observed temperature and pressure patterns represents the swirl. According to certain embodiments, this highest correlation to the observed temperature and pressure patterns may be represented as a single coefficient. Cross correlation may be included in the calculation of base swirl. The determination of base swirl may consist of cross correlation.

The determination of base swirl may consist of azimuthal decomposition and cross correlation. Azimuthal decomposition and cross correlation may both be included in the calculation of base swirl, and may be provided as a check on one another. In certain embodiments, both azimuthal decomposition and cross correlation are included in the determination of base swirl, and the determination of swirl in each is compared with one another to ensure a high confidence base swirl. The determination of base swirl may consist of azimuthal decomposition, cross correlation, and comparing the azimuthal decomposition swirl and cross correlation swirl.

Calculating relative swirl within a gas turbine may include auto correlation. The relative swirl is the difference between the swirl at any given operating condition and the known swirl (reference swirl) at a reference condition. The reference swirl may be known from experience with the gas turbine. The reference swirl may be determined by manually comparing pressure dynamics data to gas path temperature data. First, the auto correlation may average the mean-subtracted exhaust temperature pattern for many samples at the reference condition, thereby defining the reference pattern. Next, auto correlation may average the mean-subtracted gas path temperature pattern over many samples at the operating condition of interest, thereby defining the test sample. Thus, auto correlation correlates the reference pattern with the test pattern. Finally, auto correlation determines that the relative swirl is equal to the correlation shift that gives the highest correlation coefficient. The shift with the highest correlation to the observed temperature and pressure patterns represents the swirl. According to certain embodiments, this highest correlation to the observed temperature and pressure patterns may be represented as a single coefficient. Auto correlation may be included in the determination of relative swirl. The determination of relative swirl may consist of auto correlation.

In some embodiments, the temperature cross correlation may be evaluated according to Equation <NUM>: <MAT>.

T can be a vector of temperatures from each of the thermocouples, N can be the number of thermocouples, c can be the index for a given thermocouple, and Δc can be the index shift of which the correlation is a function. The thermocouple indices represented by c can range from <NUM> to N and can be periodic.

In certain embodiments, the pressure cross correlation may be evaluated according to Equation <NUM>: <MAT>.

p can be a vector of pressures from each of the pressure probes, N can be the number of combustors, c can be the index for a given pressure probe, and Δc can be the index shift, of which the correlation is a function. The pressure indices represented by c can range from <NUM> to N and can be periodic.

In certain embodiments, calculating base swirl comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine.

Calculating base swirl may comprise determining the average angular offset between the unsteady pressure amplitude as a function of angular position within the gas turbine and mean-subtracted exhaust temperature as a function of angular position within the gas turbine. In some embodiments, the average angular offset is a function of gas turbine load.

According to certain embodiments, calculating base swirl comprises measuring pressure amplitude within the gas turbine and fitting the pressure amplitude to the expression A *e^(i * Θd), wherein A is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θd is the angular phase of the measured pressure amplitude. In some embodiments, the fitting may be performed by taking a plurality of pressure measurements, given by N, which may be equal to the number of combustors within the gas turbine. pn(θ) may represent the Nth pressure amplitude as a function of angular position θ. From these measurements, A and Â may be determined by the formulas: <MAT> <MAT> <MAT>.

In some embodiments, calculating base swirl comprises measuring mean-subtracted gas path temperature within the gas turbine and fitting the mean-subtracted gas path temperature to the expression B *e^(i * Ot), wherein B is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θt is the angular phase of the measured mean-subtracted gas path temperature. In some embodiments, the fitting may be performed by taking a plurality of temperature measurements, given by M, which may be equal to the number of combustors within the gas turbine. TM(θ) may represent the Mth exhaust temperature measurement as a function of angular position θ. From these measurements, B and B̂ may be determined by the following formulas: <MAT> <MAT> <MAT>.

In some embodiments, calculating base swirl comprises: measuring pressure amplitude within the gas turbine and fitting the pressure amplitude to the expression A *e^(i * Θd), wherein A is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θd is the angular phase of the measured pressure amplitude; and measuring mean-subtracted gas path temperature within the gas turbine and fitting the mean-subtracted gas path temperature to the expression B *e^(i * Ot), wherein B is a constant coefficient, i is the square root of negative one, e is Euler's number, and Ot is the angular phase of the measured mean-subtracted gas path temperature. In some embodiments, calculating base swirl consists of: measuring pressure amplitude within the gas turbine and fitting the pressure amplitude to the expression A *e^(i * Θd), wherein A is a constant coefficient, i is the square root of negative one, e is Euler's number, and Oa is the angular phase of the measured pressure amplitude; and measuring mean-subtracted gas path temperature within the gas turbine and fitting the mean-subtracted gas path temperature to the expression B *e^(i * Ot), wherein B is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θt is the angular phase of the measured mean-subtracted gas path temperature.

According to certain embodiments, calculating base swirl comprises calculating a second swirl, wherein said second swirl is <NUM> * π * (Θt - Θd).

Calculating base swirl may comprise determining the average angular offset between the unsteady pressure amplitude as a function of angular position within the gas turbine and mean-subtracted exhaust temperature as a function of angular position within the gas turbine, and wherein the average angular offset is compared with the second swirl. An example of MATLAB® code which may be included on the non-transitory computer readable medium for the sake of this comparison may be seen in Example <NUM>, which is provided only by way of example and not limitation. Initially, temperature and pressure amplitude patterns are determined at the maximum load of the gas turbine. A variable may be assigned to the maximum load in megawatts, and as well as an array assigned to all of the data points at lower loads, wherein the load is measured as its difference from the maximum load. Then, data points are gathered for a plurality of temperature and pressure measurement devices at the loads within the array, and corresponded to the given load by taking the arithmetic average of the temperature and pressure measurements at given loads. The difference between the temperature and pressure measurements in terms of angular difference may be the swirl.

The non-transitory computer readable medium comprises instructions for updating a reference database with base swirl data as a function of gas turbine load. According to the invention, the reference database is updated in real time. The reference database may be included on the same non-transitory computer readable medium or on a separate non-transitory computer readable medium.

Calculating relative swirl comprises calculating the difference between the base swirl and a reference swirl. This reference swirl is obtained from a database of known swirls corresponding to a given gas turbine load. The reference swirl is retrieved from a reference database, and the reference swirl is selected on the basis of turbine load. According to certain embodiments, the reference swirl comprises the mean-subtracted exhaust temperature pattern for a plurality of samples.

The relative swirl is equal to a cross-correlation shift, wherein the cross-correlation shift is a phase shift that gives the highest correlation coefficient between the base swirl and reference swirl. Provided by way of example and not limitation, an example of MATLAB® code which may be included on the non-transitory computer readable medium for the sake of this comparison may be seen in Example <NUM>. Initially, a calibration may be performed, wherein a temperature pattern at the maximum load of the gas turbine is calculated. Then, at separate time intervals, an array may be populated with data points for a plurality of temperature and pressure measurement devices at the loads within the array, and corresponded to the given load by taking the arithmetic average of the temperature and pressure measurements at given loads. This data may then be compared with data from similar gas turbine loads. After that, the collection of temperature measurements across a given time may be averaged to produce a pattern that is no longer a function of time, but a function of azimuth or angle only. The pattern may then be subtracted from the average, and it may be doubled to simulate two paths around the gas turbine. The mean-subtracted temperature pattern may then be cross correlated against the temperature pattern of the gas turbine as maximum load, and the cross correlation parameter is then a shift corresponding to angular position. This may produce a correlation coefficient as a function of angular shift, thereby indicating the magnitude of angular shift required for the mean-subtracted temperature field at maximum load. The angular shift with the maximum correlation coefficient may be the relative swirl, indicating the amount of swirl at the current load relative to the swirl at maximum load.

The non-transitory computer readable medium is included in a computer system comprising at least one processor coupled to memory. A gas turbine system comprising at least one gas turbine provides data to the computer system comprising the non-transitory computer readable medium. The computer system is configured to receive data input from at least one thermocouple within the gas turbine, and the data input may be performed in real time. The computer system may be configured to receive data input from at least one pressure sensor, and the data input may be performed in real time.

Also provided is a method for gas turbine maintenance, comprising: identifying a combustor in need of repair or replacement within a gas turbine; and repairing or replacing the combustor; wherein said identifying comprises calculating base swirl of the gas turbine and calculating relative swirl of the gas turbine in order to associate a gas path from a thermocouple to the combustor in need of repair or replacement.

Calculating unsteady pressure amplitude as a function of angular position within the gas turbine and/or calculating mean-subtracted exhaust temperature as a function of angular position within the gas turbine may be done by azimuthal decomposition. Azimuthal decomposition is an acoustic and/or exhaust temperature approach wherein sine waves are "fit" to a temperature pattern across angular position and/or an acoustics pattern across angular position. Any shift between the best fit sine waves is the swirl as determined by azimuthal decomposition. Azimuthal decomposition calculates the cross-correlation between the combustor unsteady pressure amplitude as a function of a predetermined can number within a combustor, which corresponds to a radial position, and the mean-subtracted exhaust temperature as a function of gas path radial position. With this data, the radial offset between can number and gas path number that maximizes a correlation coefficient is determined. This may be repeated for multiple data points as possible in a given power band. Next, for each power band, the method computes the average of the radial offsets that maximize the cross-correlation coefficient. The result is an average radial offset between can number (which corresponds to an angular location) and gas path number (which corresponds to an angular location) as a function of load, this is defined as the swirl. Azimuthal decomposition may be included in the calculation of base swirl. The determination of base swirl may consist of azimuthal decomposition.

Calculating unsteady pressure amplitude as a function of angular position within the gas turbine and/or calculating mean-subtracted exhaust temperature as a function of angular position within the gas turbine may be done by cross correlation. Cross correlation projects the combustor pressure amplitude pattern onto the following expression: A *e^(i * Θd), where A is a constant coefficient, i is the square root of-<NUM>, e is Euler's number, and Θd is the angular phase of the pressure amplitude pattern. Similarly, the mean-subtracted gas path temperature pattern is projected onto the function: B* e^(i * Ot), where B is a constant coefficient, e and i are as defined above, and Ot is the angular phase of the temperature pattern. This method then defines the swirl to be the phase difference between the pressure amplitude pattern and the gas path temperature pattern. In degrees, this is equal to <NUM>*π*(Θt - Θd). The shift with the highest correlation to the observed temperature and pressure patterns represents the swirl. According to certain embodiments, this highest correlation to the observed temperature and pressure patterns may be represented as a single coefficient. Cross correlation may be included in the calculation of base swirl. The determination of base swirl may consist of cross correlation.

Calculating relative swirl within a gas turbine may include auto correlation. The relative swirl is the difference between the swirl at any given operating condition and the known swirl (reference swirl) at a reference condition. The reference swirl may be known from experience with the gas turbine. The reference swirl may be determined by manually comparing pressure dynamics data to gas path temperature data. First, the auto correlation may average the mean-subtracted exhaust temperature pattern for many samples at the reference condition, thereby defining the reference pattern. Next, auto correlation may average the mean-subtracted gas path temperature pattern over many samples at the operating condition of interest, thereby defining the test sample. Thus, auto correlation correlates the reference pattern with the test pattern. Finally, auto correlation determines that the relative swirl is equal to the correlation shift that gives the highest correlation coefficient. Auto correlation may be included in the determination of relative swirl. The determination of relative swirl may consist of auto correlation.

The disclosed method provides that calculating base swirl comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and/or (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine. In some embodiments, the method may provide that calculating base swirl comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine. According to certain embodiments, calculating base swirl comprises determining the average angular offset between the unsteady pressure amplitude as a function of angular position within the gas turbine and mean-subtracted exhaust temperature as a function of angular position within the gas turbine. The average angular offset may be a function of gas turbine load, or may be a function of gas turbine load only. In some embodiments, the average angular offset is independent of time.

The method of the disclosed embodiments may provide that calculating base swirl comprises: measuring pressure amplitude within the gas turbine; and fitting the pressure amplitude to the expression A *e^(i * Θd), wherein A is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θd is the angular phase of the measured pressure amplitude. In some embodiments, the fitting may be performed by taking a plurality of pressure measurements, given by N, which may be equal to the number of combustors within the gas turbine. pn(θ) may represent the Nth pressure amplitude as a function of angular position θ. From these measurements, A and Â may be determined by the formulas: <MAT> <MAT> <MAT>.

According to certain embodiments, calculating base swirl comprises: measuring mean-subtracted gas path temperature within the gas turbine; and fitting the mean-subtracted gas path temperature to the expression B *e^(i * Ot), wherein B is a constant coefficient, i is the square root of negative one, e is Euler's number, and Θt is the angular phase of the measured mean-subtracted gas path temperature. In some embodiments, the fitting may be performed by taking a plurality of temperature measurements, given by M, which may be equal to the number of combustors within the gas turbine. TM(θ) may represent the Mth exhaust temperature measurement as a function of angular position θ. From these measurements, B and B̂ may be determined by the following formulas: <MAT> <MAT> <MAT>.

In some embodiments, the method provides that calculating base swirl comprises measuring pressure amplitude within the gas turbine and fitting the pressure amplitude to the expression A *e^(i * Θd), wherein A is a constant coefficient, i is the square root of negative one, e is Euler's number, and Oa is the angular phase of the measured pressure amplitude. In certain embodiments, calculating base swirl comprises calculating a second swirl, wherein said second swirl is <NUM> * π * (Θt-Θd).

The method further provides that a reference database is updated with base swirl data as a function of gas turbine load. A non-transitory computer readable medium comprises instructions for updating a reference database with base swirl data as a function of gas turbine load. The reference database is updated in real time. The reference database may be included on the same non-transitory computer readable medium or on a separate non-transitory computer readable medium. In some embodiments, the base swirl may be calibrated only once from the reference database. According to certain embodiments, the reference database is configured to be updated with new data as directed by the user.

According to the invention, calculating relative swirl comprises calculating the difference between the base swirl and a reference swirl. The method may further provide that the reference swirl is retrieved from a reference database, and wherein the reference swirl is selected on the basis of turbine load. In some embodiments, the method may provide that the reference swirl comprises the mean-subtracted exhaust temperature pattern for a plurality of samples.

According to the invention, the relative swirl is equal to a cross-correlation shift, wherein the cross-correlation shift is a phase shift that gives the highest correlation coefficient between the base swirl and reference swirl. Initially, a calibration may be performed, wherein a temperature pattern at the maximum load of the gas turbine is calculated. Then, at separate time intervals, an array may be populated with data points for a plurality of temperature and pressure measurement devices at the loads within the array, and corresponded to the given load by taking the arithmetic average of the temperature and pressure measurements at given loads. This data may then be compared with data from similar gas turbine loads. After that, the collection of temperature measurements across a given time may be averaged to produce a pattern that is no longer a function of time, but a function of azimuth or angle only. The pattern may then be subtracted from the average, and it may be doubled to simulate two paths around the gas turbine. The mean-subtracted temperature pattern may then be cross correlated against the temperature pattern of the gas turbine as maximum load, and the cross correlation parameter is then a shift corresponding to angular position. This may produce a correlation coefficient as a function of angular shift, thereby indicating the magnitude of angular shift required for the mean-subtracted temperature field at maximum load. The angular shift with the maximum correlation coefficient may be the relative swirl, indicating the amount of swirl at the current load relative to the swirl at maximum load.

<FIG> is a block diagram illustrating certain embodiments of the present subject matter. The instructions <NUM> include calculating base swirl <NUM> and calculating relative swirl <NUM>. The calculation of base swirl <NUM> includes azimuthal decomposition <NUM>, cross correlation <NUM>, or both azimuthal decomposition <NUM> and cross correlation <NUM>. Azimuthal decomposition <NUM> outputs a swirl <NUM>, and cross correlation outputs a second swirl <NUM> independently. The swirl <NUM> and second swirl <NUM> may be compared <NUM> to ensure substantial agreement in the determination of base swirl <NUM>. The base swirl <NUM> provides an output of the swirl at base load <NUM>, which is passed to the determination of relative swirl <NUM>. Utilizing the swirl at base load <NUM> determined by the calculation of base swirl <NUM>, the determination of relative swirl <NUM> utilizes auto correlation <NUM> to determine the relative swirl <NUM>. The output of relative swirl <NUM> is a degree of swirl <NUM>.

The following examples are set forth merely to further illustrate the subject gas turbine swirl detection. The illustrative examples should not be construed as limiting the subject matter in any manner.

Initially, temperature and pressure amplitude patterns are determined at the maximum load of the gas turbine. A variable may be assigned to the maximum load in megawatts, and as well as an array assigned to all of the data points at lower loads, wherein the load is measured as its difference from the maximum load. Then, data points are gathered for a plurality of temperature and pressure measurement devices at the loads within the array, and corresponded to the given load by taking the arithmetic average of the temperature and pressure measurements at given loads. The difference between the temperature and pressure measurements in terms of angular difference may be the swirl, and in this particular example, the reference swirl at maximum load. Averages can be subtracted from the arrays based on the computation of the arithmetic averages to obtain the mean-subtracted array. A mean-subtracted array can be cross-correlated to obtain the reference swirl at maximum load.

Initially, a calibration may be performed, wherein a temperature pattern at the maximum load of the gas turbine is calculated. Then, at separate time intervals, an array may be populated with data points for a plurality of temperature and pressure measurement devices at the loads within the array, and corresponded to the given load by taking the arithmetic average of the temperature and pressure measurements at given loads. This data may then be compared with data from similar gas turbine loads. After that, the collection of temperature measurements across a given time may be averaged to produce a pattern that is no longer a function of time, but a function of azimuth / angle only. The pattern may then be subtracted from the average, and it may be doubled to simulate two paths around the gas turbine. The mean-subtracted temperature pattern may then be cross correlated against the temperature pattern of the gas turbine as maximum load, and the cross correlation parameter is then a shift corresponding to angular position. This may produce a correlation coefficient as a function of angular shift, thereby indicating the magnitude of angular shift required for the mean-subtracted temperature field at maximum load. The angular shift with the maximum correlation coefficient may be the relative swirl, indicating the amount of swirl at the current load relative to the swirl at maximum load. <IMG>
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Claim 1:
A computer implemented method for gas turbine maintenance, comprising:
identifying a combustor in need of repair or replacement within a gas turbine; and
repairing or replacing the combustor;
wherein said identifying comprises calculating base swirl (<NUM>) of the gas turbine and calculating relative swirl (<NUM>) of the gas turbine in order to associate a gas path from a thermocouple to the combustor in need of repair or replacement, wherein calculating relative swirl (<NUM>) comprises calculating the difference between the base swirl (<NUM>) and a reference swirl retrieved from a reference database
characterized in that
the reference swirl is retrieved from a reference database, and wherein the reference swirl is selected on the basis of turbine load, wherein the reference swirl comprises the mean-subtracted exhaust temperature pattern for a plurality of samples;
wherein the relative swirl (<NUM>) is equal to a cross-correlation shift, wherein the cross-correlation shift is a phase shift that gives the highest correlation coefficient between the base swirl (<NUM>) and reference swirl;
wherein calculating base swirl (<NUM>) comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and/or (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine; preferably
wherein calculating base swirl (<NUM>) comprises calculating (a) unsteady pressure amplitude as a function of angular position within the gas turbine and (b) mean-subtracted exhaust temperature as a function of angular position within the gas turbine; and
wherein a reference database is updated in real time with base swirl (<NUM>) data as a function of gas turbine load.