NOMENCLATURE
- CFC
-
Component Fault Case
- EF/η
-
isentropic efficiency
- FC
-
Flow Capacity (kg/s)
- mf
-
fuel flow rate (kg/s)
- P
-
total pressure (atm)
- PCN
-
relative rotational speed (%)
- PR
-
compressor Pressure Ratio
- PSS
-
Power-Setting Sensor
- SF
-
health parameter Scaling Factor
- SFC
-
Sensor Fault Case
- T
-
total temperature (°K)
- TET
-
Turbine Entry Temperature (°K)
-
$\overset{\scriptscriptstyle\rightharpoonup}{x}$
-
health parameter vector
-
$\overset{\scriptscriptstyle\rightharpoonup}{y}$
-
ambient and power setting parameter vector
-
$\overset{\scriptscriptstyle\rightharpoonup}{z}$
-
measurement parameter vector
- ε
-
average prediction errors
Subscripts
- c
-
compressor
- deg
-
degraded
- B
-
burner
- DH
-
Enthalpy Drop
- FC
-
Flow Capacity
- LPC/HPC
-
Low-/High-Pressure Compressor
- LPT/HPT
-
Low-/High-Pressure Turbine
- PR
-
Pressure Ratio
- t
-
turbine
Superscripts
- →
-
vector
- ^
-
predicted
1.0 INTRODUCTION
Degradation and fault may happen to both gas path components and sensors alike in gas turbine engines. Engine gas path component degradation may result in poor engine performance and eventual failure of entire engines, which will have significant economic consequences for gas turbine users. Gas path sensors are installed for engine control and condition monitoring. If degradation happens to sensors installed for condition monitoring only, it may result in misleading engine fault signatures (i.e., the deviation of gas path measurements) and misleading diagnostic results. If degradation happens to sensors installed for engine control or power setting, such as those for the measurement of engine exhaust temperature, shaft rotational speed or shaft power output, it will result in shifted engine performance, shifted gas path measurements and therefore misleading fault signatures and even complete failure of gas path diagnostic analysis.
Different gas turbine gas path diagnostic techniques have been developed in the past and comprehensive reviews of the technology have been provided by Li,(Reference Li1) Singh(Reference Singh2) and Jaw(Reference Jaw3). Typical examples of gas path diagnostic techniques for gas turbines are gas path analysis and its derivatives,( Reference Urban 4 - Reference Li 9 ) neural network-based methods,(Reference Denney10–Reference Tan12) genetic algorithm-based methods,(Reference Zedda and Singh13–Reference Wallin and Grönstedt15) fuzzy logic-based methods,(Reference Ganguli16–Reference Eustace18) Bayesian belief network approaches,(Reference Romessis and Mathioudakis19) diagnostics using transient measurements,(Reference Li20–Reference Surender21) etc.
Most gas path sensors are used for condition monitoring purposes, some for safety control and one for engine control. The sensor used for engine control is one of the most important sensors and may be called the Power-Setting Sensor (PSS), and the corresponding parameter may be called the power-setting parameter. Gas path sensor fault diagnostics have been explored by many researchers using different methods, such as a Genetic Algorithm (GA) approach,(Reference Zedda and Singh13) Artificial Neural Networks (ANN),(Reference Ogaji, Singh and Probert22–Reference Palme, Fast and Thern24) GPA,(Reference Li and Singh8) pattern recognition,(Reference Aretakis, Mathioudakis and Stamatis25) Bayesian belief networks,(Reference Mehranbod, Soroush and Panjapornpon26) etc. These methods are able to detect gas path sensor faults, although they have different advantages and disadvantages. For example, the GA-based method is more robust than others but the computational load is higher; the ANN method is a computationally fast approach but needs a large number of training samples and long time for training; and the GPA methods use a moderate amount of computing time but may have convergence issues. However, the exploration of sensor fault diagnostics has been limited to gas path sensors except the power-setting sensor. In other words, it has been assumed implicitly so far that the power setting sensor has no fault. However, this sensor is so important that if it has a significant bias, it will result in a significant shift in engine performance and consequently may result in a complete failure of gas path diagnostic analysis. Initial investigation of this problem and a solution using artificial neural networks by the same research team was carried out and published in 2016(Reference Courdier and Li27).
This paper presents a novel GA-based gas path diagnostic approach for the diagnosis of engine power setting sensor fault with and without engine component and other gas path sensor degradations. The proposed new method was applied to a model aero turbofan engine to test the effectiveness of the method in several case studies. The results, discussions and conclusions are provided accordingly.
2.0 METHODOLOGY
2.1 Gas turbine performance and modelling
A gas turbine engine and its control system may be schematically shown in the upper part of Fig. 1. The thermodynamic behaviour of gas turbine engines may be mathematically represented by Equation (1)
$$\begin{equation}
\bm{\overset{\scriptscriptstyle\rightharpoonup}{z}} = \bm{h}\left( {\bm{\overset{\scriptscriptstyle\rightharpoonup}{x}},\ \bm{\overset{\scriptscriptstyle\rightharpoonup}{y}}} \right)
\end{equation}$$
where
$\overset{\scriptscriptstyle\rightharpoonup}{z} \in {R^N}$
is the gas path measurement parameter vector and N is the number of the parameters,
$\overset{\scriptscriptstyle\rightharpoonup}{x} \in {R^M}$
is the engine health parameter vector and M is the number of the parameters,
$\overset{\scriptscriptstyle\rightharpoonup}{y} \in {R^K}$
is the ambient and power-setting parameter vector and K is the number of the parameters, and h() represents a thermodynamic relationship among these parameters.
$\overset{\scriptscriptstyle\rightharpoonup}{y}$
may include
${\overset{\scriptscriptstyle\rightharpoonup}{y}_1}$
representing ambient condition parameters and
${\overset{\scriptscriptstyle\rightharpoonup}{y}_2}$
representing the power-setting parameter shown in Fig. 1.
Figure 1. Gas turbine and its control and diagnostic systems.
The engine operation may be instructed by a ‘power setting command’
${\widetilde {\overset{\scriptscriptstyle\rightharpoonup}{y}}_2}$
and controlled by an engine control system. The actual performance of the engine is indicated by the engine gas path measurements
$\ \overset{\scriptscriptstyle\rightharpoonup}{z}$
. The measured power setting parameter
${\overset{\scriptscriptstyle\rightharpoonup}{y}_2}\ $
has a direct impact on engine control and engine performance due to the fact that the control system always tries to keep the power-setting parameter to its target value based on its measurement. Therefore, any power-setting sensor (PSS) bias
$( {{{\overset{\scriptscriptstyle\rightharpoonup}{y}}_2} - {{\widetilde {\overset{\scriptscriptstyle\rightharpoonup}{y}}}_2}} )$
will result in a shifted power setting parameter and also engine performance. This phenomenon is schematically demonstrated in Fig. 2. Of course, the engine performance is also affected by ambient condition
$\ {\overset{\scriptscriptstyle\rightharpoonup}{y}_1}\ $
and engine degradation
$\ \overset{\scriptscriptstyle\rightharpoonup}{x}$
.
Figure 2. Engine controlled at constant power demand with PSS bias.
Gas turbine performance modelling is based on fundamental thermodynamics. Performance behaviour of major gas turbine components such as compressors, combustors and turbines are represented by empirical component characteristic maps that are normally obtained from component rig tests. Predictions of engine steady-state off-design and degraded performance are achieved by satisfying the continuity of mass flow and energy within engines using Newton Raphson iteration method. More details of gas turbine performance simulation can be found in Reference MacMillanRef. 28. PYTHIA computer software(Reference Li and Singh8) developed at Cranfield University for gas turbine performance simulation and gas path diagnostics is used in this study, where the diagnostic method introduced in this paper has been implemented.
2.2 Engine and sensor degradation
Gas turbine gas path component degradation results in changes of component characteristic maps, and such phenomena can be mathematically represented by scaled component maps. Take a compressor, for example; as shown in Fig. 3, the solid lines represent a clean compressor map while the dotted lines represent a degraded compressor map. It is assumed that the degraded maps of compressors, combustors and turbines keep the same shape as those of the original maps based on the fact that their geometries do not change significantly.
Figure 3. Compressor characteristic map [Reference Li9].
The scaling of the map as shown by example in Fig. 3, is represented by three degradation indices: flow capacity, isentropic efficiency and pressure ratio indices for compressors; a combustion efficiency index for burners; and flow capacity, isentropic efficiency and enthalpy-drop indices for turbines, respectively. They are defined by the ratio between the values of corresponding points on the degraded curves (dotted lines, XB ) and the original ones (solid lines, XA )(Reference Li9) in Equation (2).
$$\begin{equation}
{\bm{SF}} = \frac{{\bm{X}}_{\bm{B}}}{{\bm{X}}_{\bm{A}}}.
\end{equation}$$
To simplify the representation of compressor degradation, it is assumed that the compressor flow capacity index is equal to that of the compressor pressure ratio index in Equation (3), based on the observation that the degradation of both pressure ratio and flow capacity result in the speed lines shifting toward the left-hand side of their original position and therefore has a similar effect on engine performance(Reference Li9).
$$\begin{equation}
\bm{S}{\bm{F}_{\bm{c},\bm{FC}}} = \bm{S}{\bm{F}_{\bm{c},\bm{PR}}}
\end{equation}$$
A similar assumption is applied to turbines, where it is assumed that the flow capacity degradation is equal but with an opposite sign to the enthalpy drop degradation as represented by Equation (4).
$$\begin{equation}
\bm{S}{\bm{F}_{\bm{t},\bm{FC}}} = - \bm{S}{\bm{F}_{\bm{t},\bm{DH}}}
\end{equation}$$
Based on these assumptions, only two degradation indices are used to describe compressor and turbine degradations: flow capacity index (SFFC) and isentropic efficiency index (SFEFF.).
Combustor degradation is represented by one index only, which is the combustion efficiency index.
Sensor degradation can be represented by bias of measurements relative to the true values of the corresponding parameters. When a sensor has a fault, it produces a significant bias that is much larger than its measurement noise.
Gas turbine gas path component degradation will have a negative impact on engine performance, such as a drop in thrust or shaft power output, an increase in turbine entry temperature, a drop in specific fuel consumption or thermal efficiency, etc. Gas path sensor degradation normally does not have an impact on engine performance if it is only used for condition monitoring. However, if the measurements are used for engine control such as those for exhaust temperature, shaft rotation speeds, shaft power output (for industrial gas turbines only), etc., any bias of the power setting measurement may change the engine operating condition and consequently change engine performance and other gas path measurements.
Engine degradation may result in a deviation of engine performance. Such deviation may be indicated by so-called fault signature represented by the deviation of gas path measurements defined by Equation (5)
$$\begin{equation}
\frac{{\Delta {z_i}}}{{{z_i}}} = \frac{{{{\hat{z}}_i} - {z_i}}}{{{z_i}}}
\end{equation}$$
where zi
is a measurement of a clean engine and
${\hat{z}_i}\ $
is the measurement of the degraded engine. Different engine degradation may result in different fault signatures; such information is used by gas path diagnostic system to detect the degradations.
2.3 GA-based gas path diagnostics
Gas path diagnostics for gas turbine engines may be regarded as an optimisation problem where a best possible solution of engine degradation is searched among all feasible solutions. Different searching or optimisation methods are available, but a genetic algorithm is used in this study due to many of its advantages described in the following. Compared with conventional optimisation methods, GAs have several distinctive features. For example, no derivatives are needed, so any non-smooth functions can be optimised; constraints can be dealt with in a very different way, such as by means of penalty functions or design of special operations; global search is used to avoid getting stuck at a local minimum; and probabilistic rather than deterministic transition rules are used to create the next generation of strings from the current one. Four operators are typically used in GAs to generate strings from one generation to the next during searching processes. More details of GAs may be found in Reference MichalewiczRef. 29. The GA operators used in this study according to ‘survival of the fittest‘ criteria are as follows:
-
• Selection – select better strings from current population and keep them only as the base strings for the next generation.
-
• Crossover – randomly pick up pairs of strings based on crossover probabilities. It allows information exchange between the pairs of strings in the form of swapping of parts of the strings in an attempt to produce better pairs of new strings.
-
• Mutation – randomly pick up strings from the current population based on mutation probabilities. Random changes are introduced to part of the selected strings in an attempt to produce better new strings.
-
• Alienation – randomly introduce new strings into the current population.
The basic idea of such a diagnostic method for engine and sensor fault diagnostics is proposed in this paper and shown in the lower part of Fig. 1. In the approach, a gas turbine performance model representing the ‘real’ engine should be set up first. Then performance adaptation(Reference Li, Pilidis and Newby30,Reference Li, Abdul Ghafir, Wang, Singh, Huang, Feng and Zhang31) may be used to make the model accurate by using available test data of the clean engine.
The engine model receives the same ambient condition
$\ {\overset{\scriptscriptstyle\rightharpoonup}{y}_1}$
and measured power setting parameter
${\overset{\scriptscriptstyle\rightharpoonup}{y}_2}$
as that of the ‘real’ engine and also the predicted engine degradations to produce an initial predicted performance
$\ \widehat {\overset{\scriptscriptstyle\rightharpoonup}{z}}$
. The prediction error ε shown in Equation (6) represents the difference between the actual measurements and the predicted measurements
$$\begin{equation}
\varepsilon = \sum\limits_{i = 1}^N {\frac{1}{N}\left| {\frac{{{{\hat{z}}_i} - {z_i}}}{{{z_i}}}} \right|}
\end{equation}$$
where zi
is the actual measurements from the “real” engine and
${\hat{z}_i}$
the predicted measurements from the engine model. A GA fitness defined by Equation (7) represents the quality of the GA solutions. The prediction error
$\overset{\scriptscriptstyle\rightharpoonup}{\varepsilon }$
is used as the feedback to the GA algorithm in order to search for better estimation of sensor and engine degradations
$\ \widehat {\overset{\scriptscriptstyle\rightharpoonup}{x}}$
. In a genetic algorithm searching process, the GA fitness is maximised in order to search for the optimal estimate of engine component degradation, gas path sensor degradation and power setting sensor fault.
$$\begin{equation}
{\rm{Fitness}} = \frac{1}{{1 + \varepsilon }}
\end{equation}$$
GA-based gas path diagnostic approach normally has a significant smearing effect in the predicted degradations if all degradations are searched simultaneously, i.e. predicted degradations may be distributed on all searched gas path components even when only few of the components or sensors are actually degraded. Such smearing effect may results in misleading diagnostic results. Therefore a component fault case (CFC) concept and sensor fault case (SFC) concept introduced in(Reference Zedda and Singh13) are adopted in this study in order to isolate degraded components and sensors and reduce the smearing effect. In addition, a power setting sensor (PSS) fault case is introduced in this study to take into account the PSS fault. In other words, all potential fault cases, i.e., the combination of all potentially degraded gas path components and/or sensors, will be searched by the GA algorithm and those with high values of GA fitness would indicate most likely degraded components and/or sensors.
During the GA diagnostic searching process, CFCs, SFCs and PSS fault may be searched individually or in combinations. From practical point of view, the following considerations are recommended:
-
• Power setting sensor (PSS) faults should always be included in GA searching processes.
-
• Gas path sensor faults should be searched before gas path component faults are searched.
-
• The measurements of faulty gas path sensor(s) should be excluded from the measurement set for engine component fault diagnosis.
The following criteria may be used to terminate GA searching process:
-
(1) Maximum GA Fitness of the population exceeds 0.95
-
(2) Generation number exceeds 50
3.0 APPLICATION, RESULTS AND DISCUSSION
3.1 Model gas turbine engine and measurements
A model aero gas turbine engine is used in this study. It is a two-shaft turbofan engine consisting of an intake, a fan or low-pressure compressor (LPC) driven by a low-pressure turbine (LPT), a high-pressure compressor (HPC) driven by a high-pressure turbine (HPT), a combustor, a bypass nozzle and a core nozzle. The configuration of the model engine is schematically shown in Fig. 4 and its performance specification is shown in Table 1.
Figure 4. Model engine configuration.
Table 1 Model engine performance specification at cruise condition (Altitude 11km and Mach number 0.8 at standard ISA condition)
A performance model for the model engine was created by using Cranfield's gas turbine performance and diagnostics software PYTHIA(Reference Li and Singh8) and the model configuration is graphically shown in Fig. 5.
Figure 5. Gas turbine performance model in PYTHIA.
It is assumed that the model engine operates at cruise condition, i.e. at altitude of 11 km and flight Mach number 0.8 at standard ISA condition, which is regarded as a nominal operating condition.
The gas path measurements of the model engine are shown in Table 2 where the gas path station numbers are shown in Fig. 4. The engine operating condition is indicated by its turbine entry temperature (TET) that is also used as the power setting parameter of the model engine. As TET cannot be directly measured due to the hostile environment, it is normally induced from engine exhaust temperature, so estimation errors or sensor bias of TET may exist.
Table 2 Gas path measurements
3.2 Model engine component and sensor degradation
Although multiple gas path components and sensors may degrade simultaneously in gas turbine engines, it is assumed in this study that a power-setting sensor (PSS) fault, a gas path sensor fault and a gas path component fault may exist individually or simultaneously as typical scenarios. The assumed sensor and engine component faults are shown in Table 3 for the purpose of demonstration of the introduced diagnostic approach. The values of the sensor faults are chosen randomly with the consideration that they should be much larger than measurement noise but not so large so the fault cannot be easily spotted. These degradations are implemented into the model engine either individually or simultaneously, and the corresponding performance change and measurement samples can be simulated.
Table 3 Sensor and engine degradation
3.3 Simulation of fault signatures
The samples of gas path measurements (Table 2) of a clean (i.e., un-degraded) and degraded engine are simulated by running the engine performance model with and without component degradations (Table 3) at cruise condition. Measurement noise is not included in the simulated measurement samples for simplicity. However, the impact of the measurement noise on the accuracy of diagnostic results is discussed later in this paper.
Referring to the engine and its control system shown in Fig. 1, the ‘power setting command’ requests the engine to operate at TET of 1,480°K and such a command is passed to the model engine via the control system. When a –10°K bias happens to the TET measurement, the engine control system still keeps the engine operating at measured TET of 1,480°K based on the PSS signal while the engine is actually operating at 1,490°K. Such a shift in power setting, together with HPT and P5 sensor degradation, will generate fault signatures of the engine. The fault signatures for the three fault scenarios shown in Table 4 are simulated and shown in Fig. 6. These fault signatures are crucial input for the GA-based engine and sensor fault diagnostics.
Table 4 Implanted degradations in case studies
Figure 6. Fault signatures of three degradation scenarios.
3.4 PSS fault case, CFCs and SFCs
The power-setting sensor fault has a special impact on engine performance and the diagnosis of PSS fault is also the focus of this study. Therefore it is treated as a separate type of fault case.
To isolate degraded component(s) in different degradation scenarios, it is assumed that the five major gas path components – i.e. the low- and high- pressure compressors (LPC and HPC), the burner, and the high- and low-pressure turbines (LPT and HPT) – are potentially degraded components and only one of the components may degrade significantly at a time. Therefore, there are five component fault cases in total and they are shown in Table 5 where the health parameters and the GA searching domains for the parameters are also included. In the GA diagnostic process, each of the CFCs is searched and the CFCs with high values of GA fitness are most likely to be true.
Table 5 Component fault cases (CFCs)
Similarly, sensor fault cases are identified in order to isolate and detect gas path sensor faults. It is assumed that only one gas path sensor may fail at a time. Therefore each SFC includes all sensors listed on Table 2 except one; these SFCs and the excluded sensors in individual SFCs are listed on Table 6.
Table 6 Sensor fault cases (SFCs)
3.5 GA parameters
To carry out the GA diagnostic searching process based on Fig. 1, the most important GA parameters and their values are identified and shown in Table 7. The selection of the values of the GA parameters is a compromise between the searching accuracy and the speed of GA calculations. Trial and error may be used to find the best values for the parameters.
Table 7 GA parameters
3.6 Case study 1: Diagnosis of PSS degradation
In this case study, it is assumed that only the PSS bias of –10°K happens and no other gas path sensor and engine component faults exist.
If no sensor faults are considered, the diagnostic analysis may only focus on engine gas path components. In other words, all CFCs defined in Table 5 may be searched and the results are shown in Fig. 7 marked as ‘Exclude PSS fault’. It can be seen that the GA Fitness for all component fault cases are very low, between 0.4 and 0.6. This indicates that the obtained CFC results are not correct and the searching for degradation fails.
Figure 7. GA fitness of CFCs with and without inclusion of PSS fault in case study 1.
If the PSS fault is included, the above searching process is repeated and the results are also shown on Fig. 7 marked as ‘Include PSS fault’. It can be seen that the obtained GA fitness are much higher (around 0.9 for all CFCs), indicating that the actual degradation may very likely have been found in the obtained results. By comparing the predicted degradation with the implanted degradation in Fig. 8, it can be seen that the PSS fault has been predicted quite satisfactorily with a small smearing effect on the LP turbine.
Figure 8. Predicted engine component and PSS faults in case study 1.
Based on the results shown in Fig. 8, it can be concluded that the PSS has a fault and the PSS bias may be between –9°K and –13°K and there is a possibility of LP turbine degradation. Based on such analysis, –10°K PSS bias is corrected and all the CFCs are searched again. The corresponding results are shown on Figs 7 and 9 marked as ‘With PSS fault correction’. It is obvious at this time that the GA fitness for all CFCs is close to 1.0, and the predicted component degradations are very small and can be ignored. It clearly indicates that the true degradation happens at PSS only and no engine components degrade.
Figure 9. Predicted engine component degradation with PSS fault correction included in case study 1.
3.7 Case study 2: Diagnosis of PSS and P5 sensor degradation
In this case study, it is assumed that PSS has a bias of –10K and P5 has a bias of –5 times of its maximum measurement noise level. Both faults are implemented into the engine model and the fault signature is shown on Fig. 6 marked as ‘PSS (–10°K) +P5 (-5 · Max noise) fault’.
Sensor fault detection is normally done before engine gas path component diagnostics. If it is assumed that the PSS has no fault, all eight single SFCs shown in Table 6 may be searched and the results are shown in Fig. 10. It can be seen that GA fitness for all SFCs are around 0.35 and 0.45, regarded as low values. This indicates that the search for sensor faults has failed.
Figure 10. GA fitness of case study 2.
By including the PSS fault in the GA search, all SFCs have been searched again and the corresponding GA fitness for all SFCs is shown on Fig. 10. It can be seen that the GA fitness for most of the SFCs is around 0.4 and SFC3 shows exceptionally high value of GA Fitness, around 0.9. Such results indicate that the true gas path sensor fault may very likely happen on P5. Further results of the predicted PSS biases for all SFCs as seen in Fig. 11 show that the predicted PSS bias of SFC3 is around –12.2°K, quite close to the true value of the PSS bias of –10°K. The predicted PSS biases of other SFCs are regarded as not true due to corresponding low GA fitness.
Figure 11. Predicted PSS bias in case study 2.
3.8 Case study 3: Diagnostics of PSS, P5 and HPT degradation
A more complicated degradation case is demonstrated here where PSS, P5 and the HPT are degraded simultaneously, and the fault signature of this case is shown in Fig. 6.
To include all three types of degradations in the diagnostic analysis, the following should be considered:
-
• PSS fault case should be included in all GA diagnostic searches.
-
• Gas path SFCs should be searched first to detect and exclude a faulty gas path sensor.
-
• During the SFC search, a CFC has to be chosen randomly and searched simultaneously with SFCs.
Based on the above, the randomly chosen CFC may refer to an un-degraded component (such as HPC in CFC2) or the degraded component (such as HPT in CFC4) as the actually degraded engine component is unknown.
To demonstrate the difference between choosing an un-degraded component and the degraded component for sensor fault detection, two examples of the search results of all SFCs are shown in Fig. 12 where one refers to choosing CFC2 (HPC) and the other refers to choosing CFC4 (HPT). It can be seen in the first example that the GA fitness for all SFCs has low values of around 0.4 except SFC3, which has a GA fitness of around 0.9 referring to the P5 sensor. When the degraded component HPT (CFC4) is chosen in the second example, the GA fitness for most of the SFCs increase to around 0.65, except SFC3 (P5) and SFC4 (T5) have a GA fitness close to 1.0. The increase of the average GA fitness is expected as the actually degraded component HPT is included in the GA search. The faulty P5 sensor is correctly picked up in SFC3, while unfortunately the high GA fitness for SFC4 is unexpected, as T5 is not faulty. To understand the reasons for the high value of GA fitness for SFC4, further analysis was carried out and the details are given in the following.
Figure 12. Predicted GA fitness in case study 3.
By looking at the details of the predicted degradations in the two examples and a comparison with the implanted degradation shown in Table 8, the predictions from CFC4 + SFC3 are very satisfactory, but the predicted degradations from CFC4 + SFC4 are very different compared with those of the implanted fault. Further analysis reveals that when T5 is excluded in SFC4, a combination of PSS (TET) bias of 1.45°K and a HPT degradation (−0.87% degradation in efficiency index and 1.32% degradation in flow capacity index) produce almost an identical fault signature to that of the implanted degradation as shown in Fig. 13. This indicates that T5 is so important in the diagnostic analysis that if the T5 sensor is excluded, misleading diagnostic results may be predicted. In other words, the T5 sensor and HPT degradation can be misdiagnosed in such a complicated degradation scenario, which may be inevitable.
Table 8 Predicted degradation in case study 3
Figure 13. Comparison of PSS and HPT fault signatures.
3.9 Case study 4: Prediction uncertainties
There are two major factors that may result in reduced accuracy of the GA diagnostic predictions; one is the GA approach itself due to its stochastic nature, and the other is the impact of measurement noise.
The prediction uncertainties are investigated by running 10 repeated GA searches of CFC4 + SFC3 in Case Study 3 and comparing the results marked as 1–10 in Fig. 14. The range of prediction uncertainties due to GA stochastics are shown in Table 9 where the variations of the efficiency (EF) index and the flow capacity (FC) index are within 0.04% and 0.54% respectively, and the variation of the TET bias is within 1.83°K, which is quite small.
Figure 14. Predicted degradation from repeated GA search of CFC4 + SFC3 with and without measurement noise in case study 3.
Table 9 Range of prediction uncertainties
Measurement noise is inevitable in real life and will have a negative impact on diagnostic results. To analyse the impact of measurement noise on diagnostic errors, a measurement noise model with the maximum levels of measurement noise shown in Table 10 is implemented into measurement simulations. The measurement noise is randomly generated following Gaussian-type distribution and is imposed on the true values of the simulated gas path measurements to generate multiple samples. In this study, 10 sets of random samples are generated and the corresponding fault signatures are shown in Fig. 15 showing that the fault signatures are slightly different.
Table 10 Maximum measurement noise [Reference Dyson and Doel32]
Figure 15. Fault signatures inclusive of measurement noise.
The GA diagnostic searching process (Fig. 1) is applied to the search of CFC4 + SFC3 using the 10 fault signatures shown in Fig. 15 with the inclusion of PSS fault case. Consequently, the obtained GA fitness values of the 10 results are shown on Fig. 16 (points 11–20) and the predicted HPT degradation and the PSS bias are shown in Fig. 14 (numbered from 11–20). Compared with similar results shown in Fig. 16 where no measurement noise is considered, it can be seen that the average GA fitness drops from around 0.94–0.99 to around 0.64–0.87, i.e., becoming lower and having greater scattering. The prediction uncertainties of the health parameters also become larger as shown in Fig. 14 and Table 9. In other words, the prediction uncertainties increase from 0.04% to 0.25% for HPT FC index, from 0.54% to 2.02% for HPT FC index, and from 1.8°K to 8.4°K for TET bias.
Figure 16. GA fitness from repeated GA search inclusive of measurement noise: CFC4 + SFC3 in case study 3.
3.10 Speed of calculations
A typical convergence process is shown in Fig. 17 where the maximum Fitness of the population varies with the GA generation number. It takes about 18 seconds for a generation and about 15 minutes to get a solution based on the GA setting shown on Table 7 using a typical desktop computer with a duo Intel Core i7-3770 processor and 3.4 GHz CPU. Such a calculation is relatively slow compared with other gas path diagnostic methods and is only suggested for off-line diagnostic analysis.
Figure 17. GA searching process – fitness vs number of generations.
3.11 Applicability of diagnostic approach
Although gas turbine engines may have slightly different configurations, they all have similar components, work following a similar principle, have similar gas path measurements and are controlled in a similar way by using a power setting parameter. Therefore, the gas path diagnostic method introduced in this paper for gas turbine power setting sensor, gas path sensors and gas path components has no limitations in theory to be applied to any other gas turbine engines.
4.0 CONCLUSIONS
In this paper, a GA-based gas path diagnostic approach for gas turbine power-setting sensor faults with or without the existence of gas path component degradation and a gas path sensor fault has been proposed. The developed diagnostic approach has been applied to the diagnostic analysis of a model aero turbofan engine where the degradation of the power-setting sensor, the high-pressure turbine and total pressure sensor at the exit of the high-pressure compressor is assumed to have happened. The diagnostic results of three case studies for the model engine show that:
-
• The PSS fault will shift the whole gas turbine performance. Without the inclusion of the PSS fault case, the GA diagnostic approach is not able to perform properly when the PSS fault happens.
-
• The introduced GA diagnostic method is able to detect power setting sensor fault successfully with and without the existence of single component fault (such as HPT degradation) and single gas path sensor fault (such as a P5 fault).
-
• The PSS fault may result in a fault signature similar to that of component degradation in exceptional situations, which may cause difficulties in identifying the true degradation
-
• Both GA stochastics and measurement noise have a negative impact on diagnostic accuracy. Case studies show that there are up to 0.04%, 0.54% and 1.83°K prediction uncertainties for HPT EF index, HPT FC index and TET bias respectively due to GA stochastics, and up to 0.25%, 2.02% and 8.4°K prediction uncertainties for the same health parameters respectively due to both GA stochastics and measurement noise.
-
• The computing speed of the GA-based diagnostic approach is relatively low compared to other gas path diagnostic methods. It takes about 15 minutes of computing time to get a solution using a typical desktop computer, which may only be suitable for off-line diagnostic applications.
-
• In theory, such diagnostic method can be applied to different gas turbine engines.
