In the lifespan of a gas turbine engine, abrupt faults and performance degradation of its gas-path components may happen; however the performance degradation is not easily foreseeable when the level of degradation is small. Gas path analysis (GPA) method has been widely applied to monitor gas turbine engine health status as it can easily obtain the magnitudes of the detected component faults. However, when the number of components within engine is large or/and the measurement noise level is high, the smearing effect may be strong and the degraded components may not be recognized. In order to improve diagnostic effect, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA) has been proposed in this study. The proposed approach has been tested in ten test cases where the degradation of a model three-shaft marine engine has been analyzed. These case studies have shown that the approach can accurately search and isolate the degraded components and further quantify the degradation for major gas-path components. Compared with the typical GPA method, the approach has shown better measurement noise immunity and diagnostic accuracy.
Gas turbine engines have been applied in a widespread manner in power plants, aviation industry, and navigation industry. In the lifespan of a gas turbine engine, various abrupt faults and performance degradation of its gas-path components may happen. And however the performance degradation is not easily foreseeable when the level of degradation is small [
Many gas-path analysis approaches have been proposed to estimate the performance and health status for gas turbine. From the linear GPA method developed by Urban in the late 1960s [
The common merit of artificial intelligence (AI) based GPA methods is no need of a complex engine thermodynamic performance model, and only the relation information between fault symptom and performance degradation is required. However, the accumulation of knowledge by experiments and experience is a costly and uneasy job and most case studies show that AI based GPA methods may effectively isolate the faulty components but not easily obtain the magnitudes of the detected faults.
The reason why model based GPA method has been widely applied to monitor gas turbine engine health status is that model based GPA can easily obtain the magnitudes of the detected component faults through the usage of a thermodynamic performance model which relates gas-path measurable parameters (e.g., temperatures, pressures, and shaft rotational speeds) to the fundamental component performance parameters (e.g., pressure ratio, mass flow rate, and isentropic efficiency) [
In this paper, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA) has been developed to detect performance degradation of engine components by the usage of gas-path measurements with the existence of measurement noise. The developed approach has been tested in ten Test Cases where the degradation of a model three-shaft marine engine has been analyzed. Analysis and conclusions were made accordingly compared with the typical GPA method.
Normally, gas turbine engine overall health status is represented by gas-path component health parameters (i.e., compressor and turbine flow capacity indices and efficiency indices and combustor efficiency index), which represent a shift of the characteristic curves on component maps due to degradation [
In the gas turbine operation, when some physical degraded problems of gas-path components happen, the component performance parameters (e.g., pressure ratio, mass flow rate, and isentropic efficiency) are changing and cause the deviation of gas-path measurable parameters, such as temperatures, pressures, and shaft rotational speeds [
Therefore, gas turbine health status estimation is a mathematical problem to obtain the deviation of engine component performance parameters
When an engine is healthy and operates at a specified operating condition, the performance status of the engine is denoted by subscript “0.” When the engine operates at slightly deviated conditions due to varying operating conditions or/and engine performance degradation, the engine performance expressed with (
Due to the nonlinearity of engine performance, an iterative process (a Newton-Raphson method) is used to obtain the deviation of engine component performance parameters
Simplified illustration of a typical GPA.
And then the deviation of gas-path component health parameters
When the level of degradation is small, it is always assumed that the characteristic maps of degraded components (i.e., compressors, combustors, and turbines) will keep more or less the same shape as their original maps based on the fact that the geometries of gas-path components do not change significantly after degradation. And then the degradation of gas-path components can be represented by the shift of the characteristic curves on the maps and such shift can be expressed by the component health parameters
For the previous GPA methods (e.g., approaches developed by authors [
Consider
Combustor degradation can be represented with the degradation of combustor combustion efficiency:
Consider
In order to isolate, detect, and quantify the component faults by PSO-GPA, a thermodynamic performance model which relates gas-path measurable parameters to component performance parameters for the target engine should be established.
Performance characteristics of compressors are usually described by compressor maps with nondimensional groups of corrected parameters and a general relation between these corrected parameters can be presented as follows:
When some physical degraded problems of compressors happen, the compressor performance parameters are changing which can be represented by the shift of the characteristic curves on the compressor characteristic maps and such shift can be expressed by the compressor health parameters as described in (
Therefore the performance characteristics of actual compressor can be presented as follows:
Compared with compressor and turbine, the performance characteristics of combustor are relatively simple and usually described by only pressure recovery coefficient and combustion efficiency. At large part-load operating range, combustor keeps high combustion efficiency for a clean or healthy combustion chamber. Introducing the combustor health parameter as described in (
Like compressor, performance characteristics of turbines are usually described by turbine maps with nondimensional groups of corrected parameters and a general relation between these corrected parameters is the same as compressor.
When some physical degraded problems of turbines happen, the turbine performance parameters are changing which can be represented by the shift of the characteristic curves on the turbine characteristic maps and such shift can be expressed by the turbine health parameters as described in (
Therefore the performance characteristics of actual turbine can be presented as follows:
After the thermodynamic performance model of the target engine has been established, the on-design and off-design steady-state performance of the target engine together with detailed measureable parameters at each gas-path station can be calculated. More detailed information about gas turbine performance modeling is described in [
Particle swarm optimization (PSO) is a biologically inspired technique derived from the collective behavior of bird flocks, developed by Eberhart and Kennedy [
The flow chart of PSO searching process.
In searching process, the position and velocity of each particle are updated by tracking two extreme values, that is,
By continually updating positions, particles fly towards the position of the optimal solution in the solution space and then the searching process is finished with the final output global best solution
Compared with genetic algorithm (GA) [
For the previous GPA method, due to the gas-path component performance parameters
And the diagnostic procedure of the approach for the estimation of gas turbine health status is shown in Figure
Diagnostic procedure of PSO-GPA.
In the procedure of the approach for the estimation of gas turbine health status, an accurate nonlinear steady-state thermodynamic performance model as described in Section
Here,
An optimization objective is defined in
The target engine chosen for demonstration of effectiveness of the proposed diagnostic approach is a model three-shaft marine gas turbine and its configuration is shown in Figure
The schematic diagram of the three-shaft marine engine.
This three-shaft gas turbine includes a low-pressure compressor (LC), a high-pressure compressor (HC), a combustor (B), a high-pressure turbine (HT), a low-pressure turbine (LT), and a power turbine (PT), and the propeller is connected to the power turbine (PT) by a reduction gear box. The power output of LT is consumed by LC over a low-pressure shaft to condense air from intake duct and the power output of HT is consumed by HC over a high-pressure shaft to condense air from the outlet of LC. Then the high-pressure enters total air flow rate: 82.11 kg/s, LC pressure ratio: 4.57, HC pressure ratio: 4.53, PT output power: 24265.1 kW, total thermal efficiency: 34.94%.
The engine performance model for the target engine is created based on the simulation platform of MATLAB software. The input for engine performance model is ambient conditions (e.g., environmental temperature, pressure, and relative humidity), fuel supply flow rate as operating condition, fuel composition, and fuel lower heating value, and the deviation of gas-path component health parameters
To test the effectiveness of the approach for health status estimation, it is assumed that the compressors, the combustor, and the turbines of the model engine may be degraded and single, dual, or triple components may be degraded in the meantime due to the fact that single component fault is most common in practical engine operation. The degradation of the engine is simulated by changing the deviation of gas-path component health parameters
Implanted degradation of major gas-path components.
Component | Mark number | Symbols | Implanted degradation (%) | Case 8 | Case 9 | Case 10 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | Case 6 | Case 7 | ||||||
LC | 1 |
|
−2 | 0 | 0 | 0 | 0 | −2 | 0 | 0 | 0 | −2 |
2 |
|
−2 | 0 | 0 | 0 | 0 | −2 | 0 | 0 | 0 | −2 | |
|
||||||||||||
HC | 3 |
|
0 | −2 | 0 | 0 | 0 | 0 | −2 | −2 | −2 | 0 |
4 |
|
0 | −2 | 0 | 0 | 0 | 0 | −2 | −2 | −2 | 0 | |
|
||||||||||||
B | 5 |
|
0 | 0 | −2 | 0 | 0 | 0 | 0 | 0 | −2 | −2 |
|
||||||||||||
HT | 6 |
|
0 | 0 | 0 | −2 | 0 | −2 | 0 | −2 | −2 | 0 |
7 |
|
0 | 0 | 0 | 2 | 0 | 2 | 0 | 2 | 2 | 0 | |
|
||||||||||||
LT | 8 |
|
0 | 0 | 0 | 0 | 0 | 0 | −2 | 0 | 0 | 0 |
9 |
|
0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | |
|
||||||||||||
PT | 10 |
|
0 | 0 | 0 | 0 | −2 | 0 | 0 | −2 | 0 | −2 |
11 |
|
0 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 0 | 2 |
Here case 1 to 5 has single component degradation only and case 6 to 10 has multiple components degraded meanwhile. The first five cases are used to test the ability of the approach of isolating a degraded component and further quantifying the degradation when only one component is degraded, while case 6 to 10 is used to test whether the approach can accurately estimate the engine degradation when multiple components are degraded simultaneously. Once the simulated gas-path measurements are collected, it is assumed that the implanted gas-path component degradation is unknown and the simulated gas-path measurements are used as the input to the developed diagnostic system described in Section
The engine gas-path instrumentation set for the analysis of the model engine is shown in Table
Engine gas-path instrumentation set.
Symbols | Parameters |
---|---|
|
Ambient pressure |
|
Ambient temperature |
|
Relative humidity |
|
LC inlet pressure |
|
LC inlet temperature |
|
Fuel flow rate |
|
LC outlet pressure |
|
LC outlet temperature |
|
HC outlet pressure |
|
HC outlet temperature |
|
HT outlet pressure |
|
HT outlet temperature |
|
LT outlet pressure |
|
LT outlet temperature |
|
PT outlet temperature |
|
LT shaft rotational speed |
|
HT shaft rotational speed |
By implanting the various component degradations shown in Table
Measurement deviations (i.e., fault signatures) in ten Test Cases (
Symbols | Measurement deviations (%) (relative to the measurements when the engine is healthy) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Test Case 1 | Test Case 2 | Test Case 3 | Test Case 4 | Test Case 5 | Test Case 6 | Test Case 7 | Test Case 8 | Test Case 9 | Test Case 10 | |
|
1.634 | −0.839 | 1.047 | −1.468 | −2.660 | 0.188 | 5.528 | −5.075 | −1.223 | 0.053 |
|
−0.254 | −0.256 | 0.322 | −0.448 | −0.807 | −0.709 | 1.730 | −1.527 | −0.373 | −0.751 |
|
0.935 | 0.946 | 1.437 | 3.792 | −1.254 | 4.700 | 2.0579 | 3.443 | 6.048 | 1.132 |
|
−0.444 | −0.449 | 0.417 | 1.113 | −0.360 | 0.670 | −0.141 | 0.318 | 1.098 | −0.392 |
|
0.913 | 0.923 | 1.421 | 1.490 | −1.023 | 2.398 | 3.816 | 1.338 | 3.763 | 1.312 |
|
−0.832 | −0.841 | 0.640 | −1.492 | 0.592 | −2.349 | −0.916 | −1.680 | −1.666 | 0.407 |
|
0.801 | 0.810 | 1.265 | 1.320 | 0.846 | 2.118 | 1.578 | 2.896 | 3.340 | 2.886 |
|
−0.8749 | −0.885 | 0.604 | −1.499 | 1.001 | −2.400 | −1.767 | −1.307 | −1.753 | 0.741 |
|
−1.111 | −1.124 | 0.325 | −1.867 | 0.205 | −3.021 | −2.234 | −2.713 | −2.657 | −0.571 |
|
−0.315 | 0.863 | 0.802 | 1.386 | −0.950 | 1.068 | 2.016 | 1.035 | 2.877 | −0.586 |
|
−0.530 | 0.255 | 0.410 | 2.709 | 0.306 | 2.285 | −2.703 | 2.907 | 3.156 | 0.192 |
It shows that different engine degradations induce various engine performance deviations shown by different gas-path measurement deviations. To test the effectiveness of the approach, these sets of the gas-path measurements are input into the developed diagnostic system, respectively, assuming that the degradation of the compressors, the turbines, and the combustor is unknown.
In this study, the simulated engine performance with implanted different engine component degradations is called “actual performance” and the predicted engine performance by using the developed diagnostic system based on gas-path measurements is called “predicted performance.”
Due to the fact that measurement noise is inevitable in practical gas-path measurements and can cause a negative effect on health status estimation results, measurement noise is introduced in the simulated gas-path measurements to make the analysis more realistic. The maximum measurement noise for various gas-path measurement parameters is based on the information provided by Dyson and Doel [
Maximum measurement noise.
Measurement | Range | Typical error |
---|---|---|
|
3~45 psia | ±0.5% |
8~460 psia | ±0.5% or 0.125 psia | |
whichever is greater | ||
|
||
|
−65~290°C | ±3.3°C |
290~1000°C |
| |
1000~1300°C |
|
To reduce the negative effect of measurement noise on diagnostic analysis, multiple gas-path measurement samples are obtained in the simulation and a 10-point rolling average [
The PSO parameters chosen for this paper are shown in Table
PSO parameters.
Parameters | Value |
---|---|
Population size | 60 |
Number of generations | 80 |
From Figures
Diagnostic results for Test Case 1.
Diagnostic results for Test Case 2.
Diagnostic results for Test Case 3.
Diagnostic results for Test Case 4.
Diagnostic results for Test Case 5.
Due to the fact that there are many combination types of dual and triple component fault pattern, here only two Test Cases among dual component fault pattern and three Test Cases among triple component fault pattern are used to test the effectiveness of the PSO-GPA method. From Figures
Diagnostic results for Test Case 6.
Diagnostic results for Test Case 7.
Diagnostic results for Test Case 8.
Diagnostic results for Test Case 9.
Diagnostic results for Test Case 10.
PSO fitness versus PSO generations.
In this study, a PSO-GPA method has been developed to effectively isolate degraded components and accurately quantify the magnitude of the detected faults by the usage of gas-path measurements. The effectiveness of the proposed approach has been verified by case studies compared with the typical GPA method for a model three-shaft marine gas turbine where the number of components within engine is large which enlarges the dimension of fault coefficient matrix. Some conclusions have been obtained as follows. The smearing effect which is commonly observed by typical GPA method can be effectively eliminated by the proposed approach, and the degraded components are successfully isolated due to the fact that the nature of the typical GPA method is a local optimum searching method while PSO-GPA is a global optimum searching method. The proposed approach can be used for diagnosis for single and multiple fault patterns of major gas-path components, and the fault degradation rate predicted is almost the same as that of implanted fault patterns. Although the verification of the effectiveness is based on the case studies with pseudo “actual” gas-path measurements which are simulated by engine performance model implanted with various fault patterns and are added on random measurement noise, it shows a great potential for application for complex gas turbine engine in which the number of gas-path components is large. The time cost by the approach for one Test Case is within 40 seconds involving generation number of 80 and population size of 60 by using a laptop computer with a 2.0 GHz dual processor, which is longer than the typical GPA methods with only few seconds. Thus the proposed approach is suitable for the application of off-line health monitoring.
Gas-path analysis
Component health parameter vector
Gas-path measurement parameter vector
Component performance parameter vector
Ambient and operating condition vector
Transducer measurement noise vector
Compressor flow capacity index
Compressor isentropic efficiency index
Combustion efficiency index
Turbine flow capacity index
Turbine isentropic efficiency index
Low-pressure compressor
High-pressure compressor
Combustor
High-pressure turbine
Low-pressure turbine
Power turbine.
Compressor
Flow capacity
Degraded condition
Combustor
Isentropic efficiency
Turbine
High-pressure
Low-pressure
Low-pressure compressor
High-pressure compressor
High-pressure turbine
Lower-pressure turbine
Power turbine
Fuel flow.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by the Fundamental Research Funds for the Central Universities (HEUCFZ1005).