Turbine blade tip clearance determination using microwave measurement and k-nearest neighbour classifier

Journal Pre-proofs Turbine Blade Tip Clearance Determination Using Microwave Measurement and k-Nearest Neighbour Classifier Mehdi Aslinezhad, Maryam A. Hejazi PII: DOI: Reference:

S0263-2241(19)31008-5 https://doi.org/10.1016/j.measurement.2019.107142 MEASUR 107142

To appear in:

Measurement

Received Date: Revised Date: Accepted Date:

7 June 2019 12 September 2019 8 October 2019

Please cite this article as: M. Aslinezhad, M.A. Hejazi, Turbine Blade Tip Clearance Determination Using Microwave Measurement and k-Nearest Neighbour Classifier, Measurement (2019), doi: https://doi.org/10.1016/ j.measurement.2019.107142

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Elsevier Ltd. All rights reserved.

Turbine Blade Tip Clearance Determination Using Microwave Measurement and k-Nearest Neighbour Classifier Mehdi Aslinezhad 1, Maryam A.Hejazi 1 * 1 Electrical *

and Computer Engineering Department, University of Kashan, Kashan 8731753153, Iran [email protected]

Abstract: Turbine blade tip clearance and deformation can be monitored by measurement of scattering parameters. In this research, a k-band microwave sensor has been simulated, optimized and implemented in computer simulation technology software which can detect tip clearance variations by measurement of the scattering parameters using a network analyzer. The open-ended circular waveguide with the tip of the turbine blades forms a cavity resonator known as a microwave sensor. Scattering parameters can be used as fingerprints of the blade that are altered due to changes in tip clearance and deformation in accordance with the theory of small perturbations in cavity resonators. In this research, a new method for interpretation of the measured scattering parameters is presented that is based on measuring indices and the k-nearest neighbor classifier. It has been shown that the k-NN classifier provides acceptable accuracy for detection and determination of the blade tip clearance and deformation. 1. Introduction Enhancing the reliability of a gas turbine power plant can improve the availability of the power network [1,2]. The blade is an essential component of a gas turbine and a number of studies have reported that 42% of gas turbine defects are caused by turbine blade failure due to fatigue, extreme heat, centrifugal force, high vibration or collision of external objects with turbine blades [3]. There is an inverse relationship between tip clearance (distance between the tip of the blade and the shell) and turbine engine efficiency. It was found that a 0.0254 mm decrease in tip clearance can increase engine efficiency by 0.1%, because a wide tip clearance will allow high-pressure hot gas to escape from the main path and will eventually reduce engine efficiency. On the other hand, a large decrease in this distance will increase the risk of the tip of the blade rubbing on the shell, which will ultimately cause engine collapse. It is evident that this distance should be continuously monitored and controlled. The blade is a limiting element for gas turbines and it is necessary to develop methods for detection of turbine blade failure in order to increase the reliability of power systems. Online monitoring of turbine blades is an established method of improving reliability [4-7]. Deformation and the displacement of the blade tip toward the shell is shown in Fig. 1.

(a)

(b)

Fig. 1. Types of failures of turbine blade (a) decreased tip clearance, (b) Tip deformation

Operators are eager to know the state inside of a turbine, because monitoring of turbine blade health in operation mode can decrease the cost of overhaul and maintenance, increase the lifespan of the turbine, prompt quick and timely action to correct small defects that prevent them from spreading to other parts of the gas turbine. Efforts have been made to monitor and evaluate the health of blades by using optical, capacitive, inductive and microwave sensors. Optical sensors are small in size and provide good time accuracy, high resolution and sufficient bandwidth. However, the high operating temperature of the turbine and smoke particles and debris in the gas media make optical sensors unsuitable for many aero engines and gas turbines [1]. A capacitive sensor is an electric capacitor created in the air gap between the blade and the electrode mounted on the turbine shell. This sensor can withstand high temperatures, but their effects on the electrical properties of this sensor can invalidate the measurements. Inductive sensors are only able to sense ferromagnetic materials, which are not usually used in modern gas turbines [1, 8]. Microwave antennas are robust and reliable sensors for noncontact measurement of distance or velocity, even in harsh industrial environments. A microwave sensor is not sensitive to polluted media and has a sufficiently large bandwidth. This type of sensor is also resistant to high temperatures. Microwave sensor radar is part of a system which monitors the turbine blade through continuous wave transmission or by using pulsed waves. In the first approach, the microwave sensor can monitor the tip clearance and deformation by continuously transmitting waves toward the turbine blades. The type of sensor, its frequency and how it sends the waves depends on the position of the blade and sensor in relation to one another [9]. In this method, when the blades are short or the space between the two adjacent blades is high, the signal received by the sensor will be the reflection of a signal from the tip of the blade, the blade surface or the disc surface. The waves reflected from the

1

area between the blades are considered to be parasitic elements of the main signal and reduce the S/N value. In addition, environmental conditions will change the polarization and cause loss of power. In the pulsed method, when the pulse frequency is synchronous with the angular velocity of the blade, the electromagnetic wave will be able to detect the behavior of the tip. Outside of this mode, it will not be able to detect the blade, but will only produce a reference signal. Another radar method for turbine blade monitoring is microwave imaging. In this method, a scanned image is used to detect the existence and location of a defect. However, environmental pollution and the high speed of the blade will reduce the resolution and image quality [10]. Different types of microwave sensors have been designed and developed to measure tip clearance and tip timing [11-15]. The current study aimed to prevent unwanted reflections and noise caused by adjacent blades using a microwave sensor designed for the short range. The novelty of the proposed method is that it is based on the theory of small perturbations in a resonant chamber which is limited to microwave sensor from one end and turbine shell from the other end. In addition, the measurement indices based on the scattering parameters in the near field of the microwave sensor have been used as a blade failure detection index and the k-nearest neighbor (k-NN) classification algorithm for pattern recognition and machine learning to determine the amount of failure as a new method for monitoring the turbine blade. In this approach, monitoring is done by comparison of the phase and magnitude of the scattering parameters of the blades. The simulation and measurement results show that the measuring indices derived from the blade scattering parameters can be used as fingerprints to detect tip clearance and deformation. In the proposed method, the pattern recognition algorithm used is the k-NN, which can accurately determine the type and amount of turbine blade defection. The k-NN classification algorithm, as compared to other algorithms for pattern recognition and machine learning, offers conceptual simplicity and is broadly used in pattern recognition. The number of detection characteristics extracted by the sensor (amplitude and phase of scattering parameters) is limited, but the number of measurement samples (1001 for simulation mode and 3201 for measurement mode) is relatively high and these measurements are very close together. Because the class label for an unknown pattern is its closest neighbor and because this method is not sensitive to the number of identifying characteristics, it has been shown that the k-NN method provides acceptable accuracy when identifying and determining the amount of tip clearance and deformation of the blade. The error rate can fall below 1.8% using this method. In the first section, the design and construction of an open-ended circular waveguide is described. Placement of the tip of the blade in the near field allows it to act as a microwave resonator and is referred to as a short-range microwave sensor. The next section discusses extraction of the amplitude and phase of the scattering parameters from the sensor through simulation and measurement. Two indices are suggested for the detection of tip clearance displacement. The last section describes the types of failure

of the turbine blade and tip clearance displacement extent as determined by the k-NN classifier [16]. 2. Design and Implementation of Microwave Sensor This section discusses the design, simulation and fabrication of a circular microwave sensor at 24 GHz. The open-ended circular waveguide with the tip of the blades forms a cavity resonator, excited by coaxial cable in 𝑇𝐸11 mode which operates in the reactive near field region as a short-range sensor [17,18]. An antenna, denoted as the research sensor, has three regions of propagation with different characteristics [17]: the far-field region, radiating near-field region and reactive near-field region. The boundary of the reactive near-field of the antenna (R) is calculated as: 𝐷3 𝑅 < 0.62 (1) 𝜆 Where D is the largest sensor dimension and λ is the wavelength. Although the reactive near-field region is usually not considered to be an operational area, because the tip of the turbine blade is very close to the shell, this area can be used as a blade tip failure detector. To avoid undesired reflections, the sensor design must guarantee a minimum short range that does not much exceed the tip clearance (<5 mm); therefore, its diameter should be smaller than the distance between two neighboring blades and comparable to the thickness of the blade leaf [19]. The frequency range and resonance frequency of this sensor depend on the sensor diameter (Ds), length of the resonator (l), length of the feeding probe inside the sensor (Pl) and the distance to the short end of the resonator (Bd, denoted as the back-short distance) as shown in Fig. 2(a)) [20]. The circular sensor was designed and simulated in computer simulation technology (CST) software at 22 to 27 GHz. Numerical analysis of the circular cavity resonator in the dominant mode, determination of the resonance frequency (fr) and its cutoff frequency (fc) were initially performed by solving the Maxwell equations. Next, for feeding of the sensor through the coaxial cable from its lateral side for excitation in TE11 mode, the location of the cable and its optimal length (Ls) was determined. The transverse field components of the TEnm mode for +z-directed waves in a circular resonator is calculated as [21]: 𝑛𝜔𝜇 𝐸𝑟 = 𝑗𝐻0 2 𝑒 ―𝑗𝛽𝑧𝑗𝑛(𝐾𝑐𝑟)sin 𝑛∅ (2) 𝐾𝑐 𝑟 𝜔𝜇 ―𝑗𝛽𝑧 𝐸∅ = 𝑗𝐻0 𝑒 𝑗′𝑛(𝐾𝑐𝑟)cos 𝑛∅ (3) 𝐾𝑐𝑟 Where 𝐾𝑐 = 𝑞′𝑛𝑚 𝑎 , 𝛽2 = 𝜔2𝜇𝜀 ― 𝐾𝑐2 and 𝑞′𝑛𝑚 denotes the mth root of the Bessel function (𝑗𝑛′(𝑛) = 0). By choosing the dominant mode for the circular resonator (𝑇𝐸11), 𝑞′𝑛𝑚=1.8412. The resonance wavelengths should be lower than the cut-off wavelength during operation. The resonance wavelength is related to the dimension of the cavity and the filling materials. For a specific mode, it is calculated as: 1 1 2 𝑝 2 𝜆𝑟 = (4) 𝜆𝑐 + 2𝑙

() ()

2

Where 𝑝 is the number of half-wave field variations in the z direction, 𝑙 is the length of the resonator and 𝜆𝑐 is the cut-off wavelength in which the circular resonator is proportional to its diameter and equal to: 𝜆𝑐 = 𝑘𝑛𝑚.𝐷 (5) 𝜋 ′ 𝑞 𝑘 𝑇𝐸 = where 𝑛𝑚 11 is 1.706 [21]. 𝑛𝑚 in which By choosing a diameter of 10.2 mm for the resonator diameter, which is proportional to the thickness of the blade, and with applying to Eq. (5), the cut-off wavelength will become 𝜆𝑐 = 17.4 mm. In accordance with the mode chart for an air-filled cavity resonator [21] and using Eq. (4), its length will be 𝑙 = 17.9 mm. In this research, a highly sensitive sensor has been designed using a circular resonator which is fed by a coaxial cable with a SMA connector on its lateral side. Due to the presence of a feeding probe inside the resonator, the length of the sensor was increased. The length of the probe (𝑃𝑙) and its distance from short end of sensor (𝐵𝑑) was set to 𝜆𝑔 4 to provide the best match between the resonator and coaxial line [20, 22, 23, 24]. Here, 𝜆𝑔 is the guide wavelength and equals: 𝜆 𝑓𝑐 2 𝜆𝑔 = (6) 1+ 𝑓

circuit. Thus, the tip of the blade and the open-ended waveguide creates a short-circuit resonator. As the blade crosses in front of the sensor field, the circuit will reset. In this research, monitoring was based on analysis of changes in the scattering parameters and resonance frequency in the reactive near-field of the sensor. For the sensor to be able to detect the tip clearance of the blade accurately, it must be sensitive to very small faults. Given that, in the reactive near field, the tip of the blade is part of the sensor resonance circuit, sensitivity analysis was performed by sweeping the diameter and length of sensor parameters so that the sensitivity of these parameters relative to the resonant frequency could be determined. It was observed that a decrease of 60μm in the sensor length increased the resonance frequency about 15 kHz. The effect of sensor length on variation of 𝑆11(dB) vs. frequency (GHz) is shown in Fig.3.

()

Knowing that 𝑓𝑐 = 17.24 GHz and 𝑓 = 24 GHz, the guide wavelength will be 𝜆𝑔 = 17.9 mm and the distance of the probe from the short end of the sensor will be 𝐵𝑑 = 4.49 mm; thus, the sensor length can be deduced as follows: 𝐿𝑠 = 𝐵𝑑 +𝑙 (7) where 𝑙 is the resonator length. Using Eqs. (4), (6) and (7), the sensor length was calculated as being 22.46 mm. The sensor length can be optimized by sweeping its length at a frequency range of 22 to 27 GHz in CST. Sweeping continues until a minimum 𝑆11 is obtained at resonance frequency (24 GHz). In these simulations, the optimum length of the sensor is 𝐿𝑠 = 22.4 mm and 𝑆11 is 70 dB. Thus, optimization will decrease of its length about 0.06 mm. Fig. 2 shows the designed and implemented sensor. The sensor material is aluminum and it is fed by a 23SMA5003 connector.

Fig. 3. 𝑆11(𝑑𝐵) vs. frequency(GHz) considering the effect of sensor length Section 3 explains the use of the theory of small perturbations and simulation to demonstrate the effects of blade displacement on the scattering parameters and resonance frequency. 3.

Blade Monitoring Using Scattering Parameters 3.1. Theory of Small Perturbations for the Detection of Tip Clearance Fig. 4 shows the placement of N microwave sensors on the body of the turbine, which allows it to be modeled as an N-port microwave network. The sensor power can be injected into the turbine and absorbed from the blade tip reflection [25].

(a)

(b)

Fig. 2. (a) Schematic of sensor; (b) fabricated sensor. Given that the tip of the blade is less than λ/2 from the sensor, the blade becomes part of the sensor resonance

Fig. 4. Turbine model as an n port network 3

As shown, 𝑉𝑛 + is the amplitude of the incident waves on port n, and 𝑉𝑛 ― is the amplitude of the waves reflected from the blades in port n. These occurrences and the reflected voltage waves can be used to define the scattering matrix as:  V  V  .  .   .  V 



1

  2          n



  S 11   S 21   .   .   .   S  n1

S 12 S 22

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

S n2

.

.

.

S 1 n  V 1     S 2 n  V 2     .   .   S nn 

.

  .    .      .    V n   

(8)

In Eq. (8), the S-parameters matrix presents the behavior of the turbine case as an N-port network. The system designed in this paper has one sensor for both input and output, so the scattering matrix consists of only one element, which can be represented as: 𝑉1 ― 𝑆11 = + (9) 𝑉1 In the proposed method, the amplitude and phase of the scattering parameters as measured by the k-band sensor are compared. In this method, the scattering parameters are compared based on time as measured by the sensor with the latest measurements for undamaged blades. Here, a decrease in the time interval between measurements will increased the amount of information collected from the same blade and time-based comparison can be used for accurate online monitoring. If the turbine chamber is a cavity resonator, the sensitivity of the scattering parameters to displacement of the tip of the turbine blades can be explained by the theory of small perturbation in a cavity resonator. A cavity resonator is any enclosed space that is surrounded by a metal surface with high conductivity. Maxwell's equations must be solved for the boundary conditions of the cavity in order to analyze its electromagnetic fields and the resonance frequency. Fig. 5(a) shows a cavity resonator formed by a conductor covering S with loss-free area 𝜏 located inside it. Fig. 5(b) shows the original cavity deformation for which the conductor covers 𝑆′ = 𝑆 ― ∆𝑆 and encloses 𝜏′ = 𝜏 ― ∆𝜏.

Fig. 5. Perturbation of cavity walls: (a) original; (b) perturbed cavity. The change in resonance frequency due to a change in the cavity wall can be determined. If 𝐸0, 𝐻0 and 𝑤0 represent the field and the resonance frequency of the original cavity and if E, H and 𝑤 denote the same quantities of a perturbed cavity, in both cases, the field equations must be satisfied as: ―∇ × 𝐸0 = 𝑗𝜔0𝜇𝐻0 ―∇ × 𝐸 = 𝑗𝜔𝜇𝐻 (10) ∇ × 𝐻 = 𝑗𝜔𝜀𝐸 ∇ × 𝐻0 = 𝑗𝜔0𝜀𝐸0 ,

A series of mathematical calculations produces the following equation [25]: 𝜔 ― 𝜔0 ≈ (11) 𝜔0 If ∆𝜏 is small, then the relation can be approximated as [26]: (𝜔𝑚 ― 𝜔𝑒)∆𝜏 𝜔 ― 𝜔0 ∆𝜏 ≈ =𝐶 (12) 𝜔𝜏 𝜏 𝜔0 Where 𝜔𝑚 and 𝜔𝑒, respectively, are the time-average electric and magnetic energies originally contained in ∆𝜏 and 𝜔 is the total energy stored in the original cavity. C depends only on the cavity geometry and the perturbation details [27]. Eq. (12) shows that a shift in resonance frequency is a function of 𝛥𝜏/𝜏. This indicates that a further change in blade position relative to the sensor will have a greater effect on changes in the resonance frequency and the scattering parameters. Changes in the tip defect clearance were simulated. A change in the amount of 𝛥𝜏/𝜏 changed the scattering parameters and resonance frequency in the near field of the sensor, which was stored in a database denoting undamaged and defective states of the blade. These deformations were simulated in CST. To simulate the blade and sensor, a computer system with 256 gigabytes of RAM, an 18-core processor and a processing frequency of 3.6 GHz was used. Each simulation required five hours to complete. 3.2. Simulation of Tip Clearance variations and Measurement The scattering parameters in the normal condition with a tip clearance of 2 mm was used as the base case to distinguish the turbine blade fingerprint. The scattering parameters were simulated at the determined intervals and compared with the normal condition. The tip clearance, type of defect and extent of defect were determined with an expert system. In this research, the tip clearance values were simulated and measured at 0.2 to 5 mm in increments of 0.1 mm (49 modes). In each of these modes, the amplitudes and phases of the scattering parameters were extracted. A constant blade was simulated and the scattering parameters at the different tip clearances were measured by the k-band sensor (Fig. 6).

Fig. 6. Simulation of turbine blade tip clearance Fig. 7 shows the measurement set-up for determining the tip clearance. This includes the designed and constructed k-band sensor, engine with aluminum blades, motor driver and a network analyzer.

4

200

S11 Phase(degree)

150

Tip Tip Tip Tip Tip

100 50 0

clearance=1mm clearance=2mm clearance=3mm clearance=4mm clearance=5mm

-50 -100 -150 -200 22

23

24

25

26

27

Frequency(GHz)

(a) 40 20 0

S11 Phase(degree)

Fig. 7. Measurement set-up and network analyzer Figs. 8(a) and 8(b) show only in 5 of 49 modes, for simplicity. The blades are failure-less and five tip clearance values (1, 2, 3, 4 and 5 mm) are shown in the simulated and measured amplitudes and phases of the scattering parameters at the desired frequency.

-20 -40 -60

Tip clearance=1mm Tip clearance=2mm Tip clearance=3mm Tip clearance=4mm Tip clearance=5mm

-80 -100

5 -120

S11 Magnitude(dB)

0

-140 -160 23.5

-5

Frequency(GHz)

Tip Tip Tip Tip Tip

-15 -20 -25

clearance=1mm clearance=2mm clearance=3mm clearance=4mm clearance=5mm

-30 -35 22

23

24

25

26

27

Frequency(GHz)

(a) 0 -5

S11 Magnitude(dB)

-10 -15

Tip clearance=1mm Tip clearance=2mm Tip clearance=3mm Tip clearance=4mm Tip clearance=5mm

-20 -25 -30

(b)

Fig. 9. Phase of scattering parameters: (a) simulated; (b) measured vs. change in tip clearance. It can be seen that an increase in the space between the blade and microwave sensor increased the resonance frequency and the amplitude of the scattering parameters at that frequency. However, because the blade is positioned inside the boundary of the near-field region (4 mm) and the tip of the blade in the standard state is 2 mm from the sensor, the phase change rate was not symmetric in the different tip clearance modes, but decreased and increased. It should be noted that the Network Analyzer is capable of sampling the scattering parameters of a rotating blade at different speeds. We have performed measurements at speeds that laboratory conditions allow us. Fig.10 shows an example of a scattering parameter measured from a blade at a speed of 500 rpm. For this measurement, the sampling time is set to 12 millisecond and 801 sampled are recorded. -5

-10

24

24.5

25

25.5

Frequency(GHz)

(b)

Fig. 8. Amplitude of scattering parameters: (a) simulated; (b) measured vs change in tip clearance. The results show that, when the blade tip is 2 mm from the sensor at a frequency of 24 GHz, good adaptation between the sensor and the blade tip exists. Figs. 9(a) and 9(b) show the phases of the scattering parameters at the desired frequency in the simulation and measurement modes. Because of blade dimensional difference between the measurement and simulation modes, as well as the loss of the measurement environment, the difference between two above curves is quite predictable.

S11 Magnitude(dB)

-35 -40 23.5

25.5

25

24.5

24

-10

-15

-20

-25

-30

Tip clearance=2mm Tip clearance=3mm

-35

-40 23.5

23.6

23.7

23.8

23.9

24

24.1

24.2

24.3

24.4

24.5

Frequency(GHz)

Fig. 10. Scattering parameters for a rotating blade It should be noted that decreasing the number of sampled frequency by Network Analyzer increases the sampling speed and reduces noise. The speed of gas turbine in power plants with operating frequency of 60Hz in north America is 3600 rpm and for power plants in Europe with frequency of 50Hz is 5

3000rpm [28]. In this research, due to the limitations of the laboratory environment, we have used a constructed blade smaller in size than an actual blade, which its speed can vary between 1 to 2000rpm. It should be noted that in order to measure the scattering parameter of a moving blade, the sweep time and the distance between the two sweeps (sweep interval) must be adjusted in a Network Analyzer so that scattering parameters of a specific blade can be sampled. If the Network Analyzer wants to be used for measuring the scattering parameters of a real turbine, the sweep time should be set to 1.6 milliseconds. That is, if a blade moves at a speed of 3600 rpm we can sample a specific blade of it 3.3. Sensitivity of the Sensor to Blade tip Deformation It should be noted that the constructed sensor is capable of detecting deformation of blade tip in addition to detection of the blade tip clearance which have been investigated by simulation. Fig. 11 shows a simulated chipping of the turbine blade tip that may be caused by various factors:

Fig. 11: Simulated turbine blade tip deformation In Table 1, 5 types of fracture formed at the tip of the blade are listed:

4. Failure Detection Using Measuring Indices Comparison of the measuring indices was based on a simulated electromagnetic model of the turbine blades, microwave sensor and measuring set-up which could estimate the tip clearance and mode of blade defect from the undamaged state. Continuous monitoring of the turbine blade using the scattering parameter data received from the microwave sensor provided the necessary data for comparison. The basis of detection with the measurement of indices is a change in the resonance frequency and scattering parameters at a frequency of 22 to 27 GHz in the simulation. These values were 23.5 to 25.5 GHz for measurement because of the change in the length of the microwave cavity resonator (sensor) necessitated by a change in the shape of the blade tip and the tip clearance. The index of mean absolute magnitude difference (MAMD) and mean absolute phase difference (MAPD) for state x with respect to the reference state are: 𝑁 ∑𝑖 = 0||𝑆𝑖(𝑥)| ― |𝑆𝑖(0)|| (13) 𝑀𝐴𝑀𝐷(𝑥) = 𝑁 𝑁 ∑𝑖 = 0|∠𝑆𝑖(𝑥) ― ∠𝑆𝑖(0)| 𝑀𝐴𝑃𝐷(𝑥) = (14) 𝑁 Where |Si(x)| and |Si(0)| are the amplitudes of the scattering parameter in the ith frequency and ∠Si(x) and ∠Si (0) are the phases of the scattering parameter in the ith frequency in state x and the reference state, respectively. 4.1. Estimation of Tip Clearance Extent Figs. 13(a) and 13(b) show the MAMD and MAPD, respectively, versus tip clearance displacement from 1 to 5 mm for 1001 frequency points in the simulation and for 3201 frequency points for measurement (22 to 27 GHz). 2.5

Table 1 Deformation of blade NO.1 1 2 2 4

NO.2 2 2 2 8

NO.3 4 2 2 16

NO.4 6 2 2 24

NO.5 8 2 2 32

MAMD

Deformation type a(mm) b(mm) C(mm) Deformation volume(mm3)

Measurement Simulation

2 1.5 1 0.5

Fig. 12 shows the amplitude of the scattering parameter in these 5 deformation types. In these simulations the tip clearance is not changed and is equal to 2mm.

0

0

1

2

4

5

(a)

5

100

0

Measurement Simulation

80

-5 -10 -15

MAPD

S11 Magnitude(dB)

3

Tip Clearance(mm)

Undamaged deformation.1 deformation.2 deformation.3 deformation.4 deformation.5

-20 -25

60 40 20

-30 -35 22

0 22.5

23

23.5

24

24.5

25

25.5

26

26.5

27

Frequency(GHz)

Fig. 12: S parameter magnitude vs. blade tip deformation and fracture

0

1

2

3

4

5

Tip Clearance(mm)

(b) Fig. 13. (a) MAMD; (b) MAPD for measured and simulated tip clearance change. 6

The results show that a change in tip clearance led to a linear increase in the indices from the reference point. These can be used as an indicator to detect tip clearance and estimate its extent. It should be noted that MAMD and MAPD are functions of displacement and cannot discriminate between a decrease or increase in tip clearance. 5. Tip Clearance Extent Determination Using k-NN The conceptual simplicity of the k-NN classification means it is broadly used in pattern recognition [29]. Here, the k-NN classifier is used to define the type and amount of turbine blade failure in which the class label for an unknown pattern is its closest neighbor [30]. Pattern recognition systems that are designed with data, generally use separate data types. The training data set is the largest collection and is used to obtain the model parameters for classification. The testing data is used to adjust the design parameters and determine the accuracy of classification, which demonstrates the performance of the classifier [29]. The training samples are defined as having ndimensional numeric properties. The k-NN classification algorithm looks for k training samples that are closest to the unknown sample. This proximity is expressed in terms of the Euclidean distance (ED) and can be calculated for ndimension data Z and Y as follows: 𝑛

𝐸𝐷(𝑥,𝑦) =

∑(𝑧 ― 𝑦 ) 𝑖

𝑖

2

(15)

𝑖=1

The unknown sample classification is that of the most frequently occurring class among k-NNs. For instance, at k=1, the unknown sample categorized to its nearest neighbor. In order to avoid tie votes, an odd number of k values must be selected [31]. The choice of k is very important; if the value of k increases, then the noise of classification will decrease, but the boundaries between the classes will be ambiguous [32]. For a fixed training sample, the k-NN error is dependent on the value of k. Thus, the accuracy of the whole system will improve if multiple kNNs with different k values are combined. In this research, results were analyzed using the k-NN classification algorithm and its accuracy in determination of failure, which can be two types of tip clearance variations and tip deformation are analyzed and presented in Table 2. Table 2 k-NN Accuracy Classification k-NN Method k=3 k=5 accuracy 88% 88%

k=7 87%

0.2 0.6 1.3 1.6 2.1 3.1 3.6 4.2 4.5 4.8

0.27417 0.6 1.3 1.6 2.1 3.18075 3.66104 4.20407 4.56082 4.71991

3.70891 0 0 0 0 4.03795 3.05208 0.20390 3.04134 4.00432

{

}

{𝑊1 ,𝑊2,…,𝑊𝑘}

=

(16) F: Compute the class label of the query pattern as: 𝑘 ∑𝑗 = 0𝑊𝑗𝑙(𝑆𝑥𝑗) 𝑙(𝑠𝑞) = (17) 𝑘 ∑𝑗 = 1𝑊𝑗 The query pattern class label l(sq) is not necessarily finite for the database class labels and, based on the weighting matrix, can be changed continuously. As a result, this procedure can provide an online estimation of tip clearance. The scattering parameters of different tip clearances are divided to the training data and test data. The test data of the unknown tip clearance for the blade tip were calculated using the k-NN regression procedure and compared with the unchanged tip clearance. The k-NN regression test results of the unknown clearance are listed in Table 3. The percentage of error becomes Absolute Error Error(%) = Clearance Length × 100 (18) For different values of k in this method, the percentage of average error is presented in Table 4. The minimum detectable tip clearance is very important, because the errors more than 5% can cause severe damage to the blades. The minimum error of detectable tip clearance displacement using the S-parameters fingerprint was 0.31%. Table 4 Comparison of Average Error of k-NN Method k-NN Method k=3 k=5 k=7

The estimation of the tip clearance, as a continuous parameter, should be considered as a regression procedure. In this research, for the estimation of tip clearance, a k-NN regression procedure that averages the values of the k-NNs Table 3 k-NN Regression Results Actual tip Predicted tip Error% for clearance clearance for k=3 k=3

is used. This can be effective for weighting the contributions of neighbors such that closer neighbors will contribute more to the average than the more distant ones. If the tip clearance changes, the most variation in the scattering parameters will occur at 23.5 to 24.5 GHz. At other frequencies in the range, the data overlap is so great that they can be omitted from the pattern recognition data. The suggested method can be summarized as follows [33]: A: Set the magnitude of scattering parameters 𝑆𝑥 (1 ≤ 𝑥 ≤ 𝑛) with l(𝑆𝑥) class label into the training database, where 𝑛 is the number of training tests. B: Classify the unknown tip clearance and provide a query pattern of its scattering parameter magnitude (𝑆𝑞). C: Compute the Euclidean distance ED (Sq, Sx) of Sq and each pattern Sx is stored in the training database. D: For ED, select the k-NN {𝑆𝑥1 ,𝑆𝑥2,…,𝑆𝑥𝑘} and its class label matrix as 𝑙(𝑆𝑥) = {𝑙(𝑆𝑥1),𝑙(𝑆𝑥2),…,𝑙(𝑆𝑥𝑘)}. E: Computing the weighting matrix by Eq. (16) 1 1 1 𝑊 = 𝐸𝐷(𝑆𝑞 ,𝑆𝑥1),𝐸𝐷(𝑆𝑞 ,𝑆𝑥2),…,𝐸𝐷(𝑆𝑞 ,𝑆𝑥𝑘)

Average error%

(1.8%)

(2.1%)

(2.24%)

By comparing the performed method in this paper with the other references [11-15], we have listed the results in Table 5.

Predicted tip clearance for k=5

Error% for k=5

Predicted tip clearance for k=7

Error% for k=7

0.25901 0.61081 1.3 1.6 2.11940 3.18540 3.67284 4.24904 4.53881 4.71529

2.95068 0.54082 0 0 0.97022 4.27031 3.64219 2.45198 1.94076 4.23507

0.25839 0.61589 1.3 1.60633 2.12286 3.18766 3.66376 4.25081 4.55968 4.71610

2.91951 0.79457 0 0.31669 1.14318 4.38336 3.18825 2.54094 2.98421 4.19490

7

Table 5 Comparison of Methods Monitoring research Method Small perturbation(open ended resonator) Current paper [11] [12] [13] [14] [15]

Phase modulation Phase difference Open ended resonator PIFA antenna Open ended resonator

The superiority of the proposed method is in simultaneous detection of tip clearance and blade deformation. However, the accuracy of the proposed method can be improved and is not limited to 0.1mm. The measurements in this paper have been carried out at room temperature and the temperature changes in the turbine environment which are between 800 up to 1300 degrees Celsius have been ignored. In the next step, the sensor should be placed on a real turbine. In that case, the effect of high ambient temperatures can be counteracted by placing a ceramic cap on the openings of the microwave sensor. As proposed method is based on comparison, measurements can be accomplished in fixed temperature to minimize the effect of it. 6. Conclusion The turbine blade tip clearance displacement and deformation are major faults that can affect the reliability of the power plant. Online monitoring of the blade is proposed using k-band microwave sensors which are utilized in the near field. Scattering parameters are sensitive to the slightest changes in turbine blade tip clearance because the blade is part of the cavity resonator for which the resonance frequency varies with the slightest change in the walls in accordance with the theory of small perturbations. The k-band sensor was simulated using CST and fabricated. Model turbine blades and a motor controlled by a drive was used for the test set-up. The fault can be detected by measuring the indices calculated from the simulated and measured scattering parameters. For the determination of the extent of tip clearance, a weighted kNN regression method was used. The results show that the proposed k-NN method can accurately determine the amount of clearance. 7. References [1] Jilong Zhang, Fajie Duan, Guangyue Niu, Jiajia Jiang and Jie, Li.: 'A blade tip timing method based on a microwave sensor', MDPI Physical Sensors, 11 May 2017, vol. 17. [2] Fernando Jesus Guevara Carazas, Gilberto Francisco Martha de. Souza: 'Availability analysis of gas turbines used in power plants', International Journal of Thermodynamics, March 2009, 12, ( 1), pp. 28-37. [3] V. Naga Bhushana Rao, IN. Niranjan Kumar and K. Bala Prasad: 'Failure analysis of gas turbine blades in a gas turbine engine used for marine applications', International journal of Engineering, Science and Technology, 2014, 6, (1) , pp. 43-48. [4] Rajni Dewangan, Jaishri Patel, Jaishri Dubey, Prakash Kumar Sen and Shailendra Kumar Bohidar: 'Gas turbines blades a critical review of failure on first and second stages', International Journal of Mechanical

Resolution

Detection type

0.1mm

Tip clearance Tip deformation Amount of tip clearance using k-NN algorithm Tip clearance Tip clearance Blade tip timing Tip clearance Tip clearance

0.0127mm 0.05mm Not declared 0.0125mm Not declared

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

Engineering and Robotics Research, January 2015, 4, (1). Woike, M. R., Roeder, J. W., Hughes, C. E. and Bencic, T. J. : 'Testing of a microwave blade tip clearance sensor at the NASA Glenn research center'. 47th AIAA Aerospace Sciences Meeting, Orlando, Florida 5-8 January, 2009. Goel, N. , Kumar, A. , Narasimhan, V., Nayak, A. and Srivastava, A. : 'Health risk assessment and prognosis of gas turbine blades by simulation and statistical methods'. Proc. Int. Conf. Electrical and Computer engineering, Niagara Falls on Canada, May 2008, pp. 1087–1091. Anwesha Dutta, Shivangi, Valarmathi, J.: 'Blade tip clearance measurement using microwave sensing system', International Journal of Recent advances in Mechanical Engineering (IJMECH) , May 2015,4, (2). Thomas Arthur Holst: 'Analysis of spatial filtering in phase-based microwave measurements of turbine Blade Tips'. MS thesis, Academic Faculty by Georgia Institute of Technology, August 2005. Andreas Schicht, Klaus Huber, Andreas Ziroff, Michael Willsch, and Lorenz-Peter Schmidt: 'Absolute phase-based distance measurement for industrial monitoring systems', IEEE Sensor Journal, September 2009, 9, (9). Zhen Li, Constantinos Soutis, Arthur Haigh, Robin Sloan, Andrew Gibson and Noushin Karimian, “Microwave imaging for delamination detection in Tjoints of wind turbine composite blades, ” in 46th European Microwave IEEE Conference, pp.1235 – 1238, 2016. Geisheimer, J., Billington, S., Holst, T. and Burgess, D.: 'Performance testing of a microwave tip clearance sensor'. Proc. Int. Conf. AIAA Joint Propulsion, Tucson, AZ, USA, 10–13 July 2005. Alexander, Mikhail, M., and Maksim, B.: 'Microwave blade tip clearance measurements principles, current practices and future opportunities'. Proc. Int. Conf. ASME Turbo Expo 2012, Copenhagen, Denmark, 11– 15 June 2012. Violetti, M., Xu, Q., Hochreutiner, O. and Skrivervik, A.K.: 'New microwave sensor for on-line blade tip timing in gas and steam turbines'.Proc. Int. Conf. IEEE sensor, Taiwan, 28-31 Oct. 2012. Maddalena Violetti, Jean Francois Zurcher, Jonathan Geisheimer and Skrivervik, Anja K.: 'Design of antenna based sensors for blade tip clearance measurement in gas turbines'. Proc. Int. Conf. IEEE Publications, Barcelona, , Spain , 2010,pp.1-4. Violetti, M. , Skrivervik, A.K. , Xu, Q and Hafner, M.: New microwave sensing system for blade tip 8

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

clearance measurement in gas turbines'. Proc. Int. Conf. IEEE Publications, Taipei, Taiwan, Oct 2012. Liying Jiang, Chengan Xue, Jianguo Cui, Mingyue Yu, Xueping Pu, Jianqiang Shi.: 'Research Recognition of aircraft engine abnormal state'. Proc. Int. Conf. IEEE Control and Decision, China, , Tsinghua Univ., May 2015. Aline Katharina Zimmer.: 'Investigation of the impact of turbine blade geometry on near-field microwave blade tip time of arrival measurements'. M.S dissertation, Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, December 2008. M. Violetti, A. K. Skrivervik, Q. Xu, J. Geisheimer, and G. Egger: Device and method for monitoring rotor blades of a turbine, European Patent Application No. 11181622’, https://www.epo.org/, accessed 16, Sept 2011. Ryszard Szczepanik, Radoslaw Przysowa, Jaroslaw Spychala, Edward Rokicki, Krzysztof Kamierczak and Pawel Majewski: 'Application of blade tip sensors to blade vibration monitoring in gas turbines'. Proc. Int. conf. Thermal Power Plants, Poland Air Force Institute of Technology, 2012, pp.145-175. Paul Wade.: ' W1GHZ Online Microwave Antenna Book[Online]'.http://www.w1ghz.org/antbook/content s.htm/Understanding Circular Waveguide— Experimentally press, 2001, Jan/Feb. Peter Rizzi, A.: 'Microwave resonator and filters in Microwave engineering passive circuits', 2004, Latest. (Ed), pp. 427-438. Justin Pollock, G.: 'Analysis and Design of A New Class of Miniaturized Circular Waveguides Containing Anisotropic Metamaterial Liners'. Doctor of Philosophy thesis, Department of electrical and computer engineering university of Alberta, Justin G. Pollock, 2016. Wilson W. S. Lee and Edward Yung, K. N.: 'The Input Impedance of a Coaxial Line Fed Probe in a Cylindrical Waveguide', IEEE Transactions on Microwave Theory and Techniques, August 1994, 42,(8).

[24]

[25] [26] [27]

[28]

[29]

[30]

[31]

[32]

[33]

Yan Jiang, Xiang Li.: 'Design of a Cylindrical Cavity Resonator for Measurements of Electrical Properties of Dielectric Materials'. Master thesis, University of Gavle, Department of Technology, September 2010. Pozar, D. M.: 'Microwave network analysis' (in microwave engineering, Wesley, 2005, 3rd edn). Roger F. Harrington.: 'Time–Harmonic Electromagnetic Fields' (Mc Graw Hill, 1961). Maier, C. Leonard.: 'Field Strength Measurements in Resonant Cavities' (Research Laboratory of Electronics, Massachusetts Institute of Technology, November 2, 1949), No.143. A.W.James, S.Rajagopalan.: 'Gas turbines: operating conditions, components and material requirements', Operational Challenges and High-Temperature Materials ,Woodhead Publishing Series in Energy, Pages 3-21, 2014. Cover, T. M., Hart, P. E.: 'Nearest neighbor pattern classification', IEEE Trans. Inf. Theory, 1967, 13, pp. 21–27. L.J. Wang, X.L. Wang and Chen, Q.C.: 'GA-based feature subset clustering for combination of multiple nearest neighbors classifiers' Proc. Int. Conf. Machine Learning and Cybernetics, Guangzhou, China, August 2005, pp. 2982–2987, see also pp. 18–21. Panigrahi, B. K., Pandi, V. R.: 'Optimal feature selection for classification of power quality disturbances using wavelet packet-based fuzzy knearest neighbour algorithm', IET Gener. Transm & Distribution, 2009,3, pp. 296–306. Parveen, P., Thuraisingham, B.: 'Face recognition using multiple classifiers'. Proc. Int. Conf. 18th IEEE Tools with Artificial Intelligence, Arlington, Virginia, 2006, pp. 179-186. Hejazi, M.A., Gharehpetian, G.B., Moradi, G., Alehosseini1, H.A. and Mohammadi, M.: 'Online monitoring of transformer winding axial displacement and its extent using scattering parameters and knearest neighbour method', IET Gen. Trans& Distribution, 5, August 2011, pp. 824 - 832.

1- Turbine blade tip clearance is monitored with scattering parameters measurement 2- S parameters are measured through an open ended circular waveguide 3- Scattering parameters are measured in the reactive near-field by Network Analayzer 4- The change of resonance frequency is the basis of detection by measuring indices 5- Amount of blade tip clearance is determined with k-NN classifier

9