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sensors Article

Identification of Vibration Events in Rotating Blades Using a Fiber Optical Tip Timing Sensor Dechao Ye * , Fajie Duan, Jiajia Jiang, Guangyue Niu, Zhibo Liu and Fangyi Li State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China; [email protected] (F.D.); [email protected] (J.J.); [email protected] (G.N.); [email protected] (Z.L.); [email protected] (F.L.) * Correspondence: [email protected]; Tel.: +86-02227890261 Received: 16 February 2019; Accepted: 24 March 2019; Published: 27 March 2019







Abstract: The blade tip timing (BTT) technique has been widely used in rotation machinery for non-contact blade vibration measurements. As BTT data is under-sampled, it requires complicated algorithms to reconstruct vibration parameters. Before reconstructing the vibration parameters, the right data segment should first be extracted from the massive volumes of BTT data that include noise from blade vibration events. This step requires manual intervention, is highly dependent on the skill of the operator, and has also made it difficult to automate BTT technique applications. This article proposes an included angle distribution (IAD) correlation method between adjacent revolutions to identify blade vibration events automatically in real time. All included angles of the rotor between any two adjacent blades were accurately detected by only one fiber optical tip timing sensor. Three formulas for calculating IAD correlation were then proposed to identify three types of blade vibration events: the blades’ overall vibrations, vibration of the adjacent two blades, and vibration of a specific blade. Further, the IAD correlation method was optimized in the calculating process to reduce computation load when identifying every blade’s vibration events. The presented IAD correlation method could be used for embedded, real-time, and automatic processing applications. Experimental results showed that the proposed method could identify all vibration events in rotating blades, even small events which may be wrongly identified by skillful operators. Keywords: blade tip timing; blade vibration measurement; identification of vibration events; Pearson correlation coefficient; fiber optical tip timing sensor

1. Introduction It is important to measure the vibration amplitude of rotating blades in rotational machinery in real-time, which reflects the stress induced in the blades. Dynamic stress is crucial to assess machinery operation state and to predict blade failures. The blade tip timing (BTT) technique, using non-intrusive probes mounted on the engine casing to sense the “arrival time” of passing blades, has become one of the most widely used methods for non-contact blade vibration measurements [1–5]. The BTT technique has advantages over conventional strain gauge stress measuring methods, such as its non-intrusive nature and capability for being used for long-term monitoring. However, the main drawback of the BTT technique is under-sampling, which leads to frequency aliasing [6]. Different BTT data analysis methods for reconstructing vibration parameters have been provided over the past decades [7–15]. For synchronous blade vibrations, the least squares sine fitting method is described to predict resonance amplitude and frequency. The fast Fourier transform is often applied to analyze asynchronous blade vibrations. However, the identification of the occurrence of blade vibration events should be carried out before reconstructing vibration parameters, especially for long-term, real-time, and automatic

Sensors 2019, 19, 1482; doi:10.3390/s19071482

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processing applications. An effective method for the identification of blade vibration events without manual intervention will help the BTT technique gain broader applications in industrial automation. Current approaches to identify blade vibration events from BTT data are threshold value triggering or visual observation by skilled personnel. However, these may produce false identifications due to noise signals or DC drift of data. They also may overlook vibration events which are too small to observe. Rolls-Royce plc suggested an identification method in 2009 to calculate the correlation of the displacement of different probes between current and previous revolutions. Different tip timing probes observe the same “stack pattern” when there is no vibration event, while the “stack pattern” begins to spread as a vibration event commences [16]. For data applied in the calculation of the correlation from different probes, generally four or more, the identification will be more accurate with more probes. However, the inconsistency of different probes could possibly affect the effectiveness of identification. Besides this, the number of probes is strictly limited in actual applications, especially considering the possible failure of probes in long-term monitoring applications. This article proposes an included angle distribution (IAD) correlation method to identify blade vibration events in actual applications using data from only one fiber optical tip timing sensor. It could be very useful in cases with only one probe or not enough probes for long-term service. Inconsistencies of different probes could not be taken into consideration. The IAD correlation method was used to calculate the included angle distribution’s correlation between adjacent revolutions to identify blade vibration events automatically. Three improved formulas for calculating IAD correlation were suggested to identify three types of blade vibration events: the blades’ overall vibrations, vibration of the adjacent two blades, and vibration of a specific blade. This article also focuses on the aspect of computation load of the method when identifying every blade’s vibration events. The calculating process was optimized to make it suitable for embedded, real-time, and automatic processing applications. Once the vibration events were identified automatically, the following analysis of blade vibration amplitude and frequency through model fitting could be conducted in real time without manual intervention. 2. Methodology 2.1. BTT System Using Fiber Optical Tip Timing Sensor Typical BTT system for non-contact blade vibration measurement consists of five parts: tip timing sensors including a once-per-revolution (OPR) sensor, pre-amplifier, signal conditioning and triggering module, data acquisition unit, and data analysis software (Figure 1). In general, the tip timing sensor can use fiber optical, capacitance, microwave, or other types of sensors. The sensor senses the arriving signal of passing blades and the preamplifier amplifies and converts it into a voltage output signal. The voltage signal is conditioned and turned into a pulse at the moment of the “arrival time” in the conditioning and triggering module. The arrival time of passing blades can then be acquired by timing the rising edge of the pulse, as shown in Figure 2. However, the BTT data obtained from the data acquisition unit is under-sampled. The sample rate is equal to the rotor rotational speed. It is necessary to reconstruct the vibrations’ parameters using model fitting algorithms, which were carried out in the data analysis software. Many model fitting algorithms to reconstruct blade vibration information have been well established, though this paper will not discuss those algorithms. However, those algorithms require appropriate and correct input data—that is, they need to complete the identification of vibration events before model fitting. This paper proposes the use of one tip timing sensor, in particular a fiber optical tip timing sensor, to identify blade vibration events in a BTT system. The fiber optical sensor has advantages of higher resolution, lower noise level, and faster response capability. It can sense smaller blade tip vibration displacements than other types of sensors. The identification of blade events could be carried out in a computer-based software or data acquisition unit for embedded, real-time, and automatic processing applications.

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Figure 1. The block diagram of a blade tip timing (BTT) system. Figure 1. The block diagram of a blade tip timing (BTT) system. Figure 1. The block diagram of a blade tip timing (BTT) system.

Figure Figure2.2.Signal Signalprocessing processingof ofaaBTT BTTsystem. system.

Figure 2. Signal processing of a BTT system. The Theoptical opticalfiber fibertip tiptiming timingsensor sensorused usedin inthis thispaper paperconsists consistsof ofaatransmitting transmittingfiber fiberin inthe thecenter center of the probe head and six receiving fibers around, as shown in Figure 2. The probe head is mounted on of the probe head and six receiving fibers around, as shown in Figure 2. The probe head is mounted The optical fiber tip timing sensor used in this paper consists of a transmitting fiber in the center the engine casing and transmits a beam of light from the laser source, sensing the reflected light when engine casing andreceiving transmitsfibers a beam of light the source, the reflected light ofon thethe probe head and six around, as from shown inlaser Figure 2. Thesensing probe head is mounted the blade passes through. The fiber optical tip timing sensor’s sensing area on a blade is related to the the blade passes through. The fiber tip the timing areareflected on a blade onwhen the engine casing and transmits a beam of optical light from lasersensor’s source, sensing sensing the lightis core diameter and numerical aperture (NA) of the transmitting optical fiber. When the core diameter is related the core diameter and numerical aperturetip (NA) of the transmitting optical fiber. when thetoblade passes through. The fiber optical timing sensor’s sensing area on a When blade the is 62.5 µm and NA = 0.12, the diameter of the sensing area is smaller than 1.20 mm, meaning that the core diameter is 62.5 μm and = 0.12, aperture the diameter area isoptical smaller than 1.20 mm, related to the core diameter andNA numerical (NA)ofofthe thesensing transmitting fiber. When the sensing resolution is much better thaniseddy current, capacitive, or other types of probes [17–19]. meaning that the sensing resolution much better than eddy current, capacitive, or other types core diameter is 62.5 μm and NA = 0.12, the diameter of the sensing area is smaller than 1.20 mm,of probes [17–19]. meaning that the sensing much better than eddy current, capacitive, or other types of 2.2. IAD Correlation Methodresolution to IdentifyisBlade Vibration Events probes [17–19]. As shown in Section 2.1, tip timing sensors can sense the arrival time of all blades. The small changes of included angles between any two adjacent blades can be also sensed using one fiber optical

As shown in Section 2.1, tip timing sensors can sense the arrival time of all blades. The small changes of included angles between any two adjacent blades can be also sensed using one fiber optical tip timing sensor. The sensor obtains the arrival time (

tk

) of all blades and the OPR sensor

θ obtains the rotation period (T) (Figure 3). The included angle ( k ) between blade k# and k+1# of the

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rotor can then be obtained from Equation (1). In a BTT system, the included angle between two adjacent blades can be measured at the same time. So, the IAD correlation method was proposed to tip timing sensor. The sensor obtains the arrival time (tk ) of all blades and the OPR sensor obtains identify blade vibration events: the rotation period (T) (Figure 3). The included angle (θk ) between blade k# and k+1# of the rotor can tk ] 2π [t k +the then be obtained from Equation (1). In a BTT system, angle between two adjacent blades 1 − included θk = (1) can be measured at the same time. So, the IAD correlation method was proposed to identify blade T . vibration events: 2π [angle tk+1 −distribution tk ] It is assumed that the rotor’s included of the previous revolution is θk = . (1) T φ p = (θ 0 p , θ1 p , ⋅⋅⋅, θ kp , ⋅⋅⋅, θ np ) θ kp , where refers to the included angle between blade k# and k+1# It is assumed that the rotor’s included angle distribution of the previous revolution is of the previous revolution and n is the last number of blades. Besides this, φ p = (θ0p , θ1p , · · · , θkp , · · · , θnp ), where θkp refers to the included angle between blade k# and k+1# of φc previous = (θ 0 c , θ1revolution , θnncis) the c , ⋅⋅⋅, θ kc , ⋅⋅⋅ the and last to number of blades. Besides this, φc =of(θthe , · · · , θkc , · · · , θnc ) 0c , θ1c refers the included angle distribution current revolution. refers to the included angle distribution of the current revolution. When any blade is vibrating, φc will φp φc . When any is vibrating, change andblade be different from φ p . will change and be different from

Figure 3. Measurement of the included angle distribution. Figure 3. Measurement of the included angle distribution.

The IAD correlation method calculates the Pearson correlation coefficient between included angle The IAD correlation method calculates the Pearson correlation coefficient between included distributions of previous and current revolutions (r pc ) to identify blade vibration events, as seen in r Equation (2). In Equation (2), θ p and average values respectively. c are therevolutions p and φc ,blade vibration events, as angle distributions of previous and θcurrent ( pc )oftoφidentify

seen in Equation (2). In Equation (2),

θp

and

φp n φ θ c are and c , respectively. [θip average − θ p ][θicvalues − θc ] of ∑ the

r pc = corr (φ p , φc ) = s

rpc = corr (φ p , φc ) =

i =0 n

[θip[θ− θ−p ]θ ∑ n

ip

2

s

i =0 i = 0 n



p

2 ][∑ θn ic[θ−icθ− c ]θ c ] i =0 n



(2)

(2)

[θipof−the θ p ]r pc value, [θic where − θ c ] a1 is a scaling factor, as This could be improved to amplify the changes = = i i 0 0 seen in Equation (3). In a normal non-vibrating state, r pc is equal to 1. The value of r pc will decrease while some blades are vibrating. r a This could be improved to amplify the changes of the pc value, where 1 is a scaling factor, r pc = 1 − (1 − corr (φ p , φc )) (3) r × a1 r as seen in Equation (3). In a normal non-vibrating state, pc is equal to 1. The value of pc will decrease while bladesworking are vibrating. Changes insome the rotor’s environment, such as changes of airflow or rotational speed, may 2

2

also lead to a variation of r pc . These variations are much slower than those caused by blade vibrations. If φ p is obtained on the adjacent revolution or adjacent several revolutions before the current revolution, the variation of r pc is small due to the changes in the rotor’s working environment. As the change of the included angle between the adjacent revolution or adjacent several revolutions is very small, the tip timing sensor requires high resolution capability. A fiber optical tip timing sensor meets this requirement. Equation (3) shows that the rotor is suffering blade vibrations when r pc < Th1 . Th1 is the threshold value. As the vibrations of any blade or several blades would lead to the decrement of the r pc value, Equation (3) can be used to identify the rotor’s overall vibration event.

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However, Equation (3) cannot be used to identify which blades are vibrating. As the vibration of blade k# and k+1# will both affect the value of θkc , an improved calculating formula of IAD correlation method to identify vibration events of the adjacent two blades is proposed in Equation (4). Assuming φck = (θ0p , θ1p , · · · , θkc , · · · , θnp ), r kpc will be equal to 1 in a normal non-vibrating state. a2 is a scaling factor. r kpc = 1 − (1 − corr (φ p , φck )) × a2 (4) Assuming Th2 and Th3 are threshold values, if r kpc < Th2 , then blades k# and k+1# may be vibrating. Equation (5) is a further improved formula for calculating IAD correlation to identify the vibration events of the specific blade k#. Equation (5) could eliminate the effect of blade k+1# because the vibration of blade k+1# would not affect the r kpc−1 value. The vibration of blade k# can lead to decrements of r kpc and r kpc−1 at same time. This indicates that blade k# is vibrating when ik >Th3 . a3 is a scaling factor. ( (1 − r kpc ) × (1 − r kpc−1 ) × a3 , i f (r kpc < Th2 ) ik = (5) 0, i f (r kpc ≥ Th2 ) A practical method to determine the values of Th1 , Th2 , and Th3 is proposed in the following steps: 1.

2.

3.

Calculate the values of r pc , r kpc , and ik during a period of time when there is no vibration event in the rotating blades, and find their values when the blade deflection’s noise achieves its maximum. Record the values of φ p and φc simultaneously. According to the signal to noise ratio of BTT data and the radius of the blade tip, set the minimum vibration amplitude to be detected, and then calculate the changes of the included angle between the adjacent two blades caused by that vibration. Refresh the values of φc . It is noteworthy that if the minimum vibration amplitude is set too small, a blade event may be incorrectly identified. Recalculate the values of r pc , r kpc , and ik with the updated values of φc , which can be used as the values of Th1 , Th2 , and Th3 respectively.

It is noteworthy that in Equation (5), if blade k−1# and k+1# are both vibrating but at the same time blade k# does not have any vibration, the ik value will increase. In this case, a incorrect identification of a blade event may occur, though the probability of this occurrence is relatively low in practical applications. Other factors could be taken into consideration to assist in identifying vibration events of blade k#, such as amplitude threshold triggering. 2.3. Optimized Calculation Process In order to be used in the health monitoring of industrial machinery the IAD correlation method should have the capability of fast and real-time processing. The calculating process of the IAD correlation method could be expanded into an iterative procedure with less computation. From the definition of the Pearson correlation coefficient formula, five components (∑ xi , ∑ xi 2 , ∑ xi yi , ∑ yi , and ∑ yi 2 ) are involved in the calculation, shown as Equation (6). Assuming that H1 , H2 , H3 , H4 , and H5 refer to ∑ xi , ∑ xi 2 , ∑ xi yi , ∑ yi , and ∑ yi 2 of blade 0#, respectively, only three components need additional calculation when identifying vibration events of blade k#. Thus, the calculation of blade k# using Equation (4) or Equation (5) could be derived from blade 0#, shown as Table 1. corr ( x, y) = q

N ∑ xi yi − ∑ xi ∑ yi q N ∑ x i 2 − ( ∑ x i )2 N ∑ y i 2 − ( ∑ y i )2

(6)

The optimized calculation process means that the IAD correlation method proposed in this paper is suitable for identifying vibration events of every blade with less computation, meeting the requirements of real-time, embedded, and automatic processing applications.

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Table 1. Optimized calculation of r kpc . r kpc

∑ xi

∑ xi 2

r0pc

H1

H2

∑ xi yi

H3 H3 +θ0p (θ0p −θ0c ) H1 H2 −θ1p (θ1p −θ1c ) ... ... ... ... H +θ (θ0p −θ0c ) 3 0p r kpc H1 H2 −θkp (θkp −θkc ) Sensors 2019,. .19, . x FOR . . . PEER . . .REVIEW ... r1pc

∑ yi

∑ yi 2

H4

H5 H5 +(θ0p −θ0c )(θ0p +θ0c ) −(θ1p −θ1c )(θ1p +θ1c ) ... H5 +(θ0p −θ0c )(θ0p +θ0c ) −(θkp −θkc )(θkp +θkc ) ...

H4 + (θ0p −θ0c )−(θ1p −θ1c ) ... H4 + (θ0p −θ0c )−(θkp −θkc ) ...

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3. Experimental Results and Discussion 3.1. High-Speed Bench Bench Test Test 3.1. High-Speed In In order order to to verify verify the the effectiveness effectiveness of of the the IAD IAD correlation correlation method, method, five five fiber fiber optical optical sensors sensors numbered as P0 to P4 were mounted on a high-speed test rig for a blade vibration numbered as P0 to P4 were mounted on a high-speed test rig for a blade vibration measuring measuring experiment. Theinstallation installation sensors is shown in Figure 4. rotor The has rotor has aoftotal eight experiment. The ofof thethe sensors is shown in Figure 4. The a total eightofblades, blades, and the radius of each blade tip is 60 mm. The thickness of the blades is 2 mm. Blades were and the radius of each blade tip is 60 mm. The thickness of the blades is 2 mm. Blades were excited excited by nitrogen with high pressure during the experiment. Synchronous vibration will occur when by nitrogen with high pressure during the experiment. Synchronous vibration will occur when blade frequency is multiple of of rotational rotational frequency. blade natural natural frequency is an an integral integral multiple frequency. This This integral integral number number is is often often called the engine order (EO). Besides this, the blade will also be bended slightly due to air force. called the engine order (EO). Besides this, the blade will also be bended slightly due to air force.

Figure of fiber fiber optical optical tip tip timing timing sensors. sensors. Figure 4. 4. Test Test rig rig and and installation installation of

thispaper, paper, P0 is sensor used to identify blade vibration events. The In this thethe datadata of theofP0the sensor used toisidentify blade vibration events. The displacements displacements of blade 6#, the blade 7#, and speed the rotational ranging 5000rpm rpmare to shown 8500 rpm of blade 6#, blade 7#, and rotational rangingspeed from 5000 rpmfrom to 8500 in are shown in Figure 5. Both blades experienced several first-order synchronous vibrations under Figure 5. Both blades experienced several first-order synchronous vibrations under the excitation of the excitation of blades nitrogen. two blades have differentand vibration amplitudeswith andnoises natural nitrogen. The two haveThe different vibration amplitudes natural frequencies in frequencies with noises in thecertain waveforms. is likely certain using vibration events will be the waveforms. Thus, it is likely vibrationThus, eventsitwill be misjudged methods of threshold misjudged usingor methods of thresholdby value triggering or visual observation by skilled personnel. value triggering visual observation skilled personnel.

In this paper, the data of the P0 sensor is used to identify blade vibration events. The displacements of blade 6#, blade 7#, and the rotational speed ranging from 5000 rpm to 8500 rpm are shown in Figure 5. Both blades experienced several first-order synchronous vibrations under the excitation of nitrogen. The two blades have different vibration amplitudes and natural frequencies Sensors 2019, 19,with 1482 noises in the waveforms. Thus, it is likely certain vibration events will 7 ofbe 12 misjudged using methods of threshold value triggering or visual observation by skilled personnel.

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3.2. Identification of Blades’ Overall Vibration Events As shown in Equation (3), the overall vibration events of blades during the test can be identified, and the results are shown in Figure 6. All eight blades experienced first-order bending vibrations due to the excitation of nitrogen, when blade natural frequency is an integral multiple of rotational frequency. The displacements of all eight blades are also shown in Figure 6, separated 0.1 mm apart from each other. The displacements varied thespeed blades were experiencing vibration Figure Blade vibrationdeflection deflection andwhen rotation speed waveforms. Figure 5.5.Blade vibration and rotation waveforms. 3.2. Identification of Blades’ Overall Vibration events, and the vibration amplitudes wereEvents different from each other. Setting

r

Th1

= 0.98 indicates

Th

pc 1 . The As shown in (3), the overall vibration of identification blades during results the testwere can be identified, < events then set at a the occurrence of Equation a blade vibration event if and the results are shown in Figure 6. All eight blades experienced first-order bending vibrations high level, including the previous 50 revolutions and subsequent 50 revolutions, providing due to thedata excitation of nitrogen, when frequency isresults an integral multiple rotational adequate for model fitting. In this blade paper,natural the identification were all set as of dashed lines frequency. The displacements of all eight blades are also shown in Figure 6, separated 0.1 mm apart to highlight the vibration events in the displacement waveforms. from As each other. in The displacements variedvibration when theevents bladesof were experiencing vibration events, and shown Figure 6, the overall blades were correctly identified. The the vibration amplitudes were different from each other. Setting Th1 = 0.98 indicates the occurrence of rpc variation of of anyevent bladeif or blades led to a decrement of then the set avibrations blade vibration r pc several < Th1 . The identification results were atvalue. a highThe level, including displacements at around 1750 revolutions may not truly be a blade vibration event, which can be the previous 50 revolutions and subsequent 50 revolutions, providing adequate data for model fitting. eliminated using Equation (4) or Equation In addition, blade vibration eventsevents ranging In this paper, the identification results were(5). all set as dashedsome linestiny to highlight the vibration in from 2000 to 2500waveforms. revolutions were not identified. the displacement

Figure 6. Identification results of blades’ blades’ overall overall vibration vibration events events using using Equation Equation (3). (3).

As shown in of Figure 6, the overall vibration events of blades were correctly identified. The vibrations 3.3. Identification Adjacent Two Blades’ and a Specific Blade’s Events of any blade or several blades led to a decrement of the r pc value. The variation of displacements According to Equation (4), the identification results of adjacent two blades’ events are shown at around 1750 revolutions may not truly be a blade vibration event, which can be eliminated using 6 r Th pc 2 Equation (4)where or Equationwas (5).set Inequal addition, some events rangingwhen fromblade 2000 to to 0.98. Thetiny blade valuevibration decreased significantly 6# in Figure 7, 2500 revolutions were not identified. or blade 7# was vibrating. The tiny blade vibration events between 2000 and 2500 revolutions were

successfully identified.

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3.3. Identification of Adjacent Two Blades’ and a Specific Blade’s Events According to Equation (4), the identification results of adjacent two blades’ events are shown in Figure 7, where Th2 was set equal to 0.98. The r6pc value decreased significantly when blade 6# Sensors 2019, 19, x FOR PEER REVIEW 9 of 13 or blade 7# was vibrating. The tiny blade vibration events between 2000 and 2500 revolutions were successfully Sensors 2019, 19,identified. x FOR PEER REVIEW 9 of 13

Figure 7. Identification results of blade 6# and 7# using Equation (4). Figure 7. Identification results of blade 6# and 7# using Equation (4). Figure 7. Identification results of blade 6# and 7# using Equation (4).

Equation (5) was used to identify a specific blade’s vibration events. The identification results Equation (5) was used to identify a specific vibration events. The identification results of Th3blade’s Equation (5)shown was used to identify a specific blade’s vibration events. The results = 0.04. 8 indicates thatidentification the IAD correlation of blade 6# are in Figure 8, where blade 6# are shown in Figure 8, where Th3 = 0.04. Figure 8Figure indicates that the IAD correlation method Th method using Equation (5) can accurately identify all of events the vibration events the andinterference eliminate the using Equation can accurately and eliminate of = vibration 0.04. Figure 8 indicates that the IAD correlation of blade 6# are(5) shown in Figure identify 8, whereall of 3the interference of adjacent blades. Even skilled personnel maywhen maketrying mistakes when trying tobetween identify adjacent blades. Even skilled personnel may make mistakes to identify signals method using Equation (5) can accurately identify all of the vibration events and eliminate the signals 1500 andThe 2500 revolutions. The1700 large signal around 1700 revolutions was not 1500 and between 2500ofrevolutions. large around revolutions was not actually a realtovibration interference adjacent blades. Evensignal skilled personnel may make mistakes when trying identify actually a real vibration event. It might have been caused by the rotating shaft or the OPR sensor, event. It might have been caused by the rotating shaft or the OPR sensor, which cannot affect signals between 1500 and 2500 revolutions. The large signal around 1700 revolutions was the not which cannot affect the included angle of rotor.inThe method proposed in this eliminate paper can included distribution of rotor. Thedistribution method proposed this paper can successfully actually aangle real vibration event. It might have been caused by the rotating shaft or the OPR sensor, successfully eliminate such interferences. such interferences. which cannot affect the included angle distribution of rotor. The method proposed in this paper can successfully eliminate such interferences.

Figure 8. Identification results of blade 6# using Equation (5). Figure 8. Identification results of blade 6# using Equation (5).

Figure 9 shows the identification results of blade 7# 6# using Equation Figure 8. Identification results of blade using Equation (5). (5). The vibration events Figure 9 shows the identification results of blade 7# using Equation (5). Theatvibration events of just blade 7# itself were identified as well as the coupled vibration events 2600, 3300, andof just blade 7# itself were identified as well as the coupled vibration events at 2600, 3300, and 4000 4000 revolutions. These vibration events by the large of theevents adjacent Figure 9 shows thecoupled identification results of were bladeintroduced 7# using Equation (5).vibration The vibration of revolutions. These coupled vibration events were introduced by the large vibration of the adjacent blade 6#. Such tiny coupled vibration also be identified just blade 7# itself were identified assignals well ascould the coupled vibration using eventsEquation at 2600, (5). 3300, and 4000 blade 6#. Such tiny coupled vibration signals could also be identified using Equation (5). revolutions. These coupled vibration events were introduced by the large vibration of the adjacent blade 6#. Such tiny coupled vibration signals could also be identified using Equation (5).

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Equation (5). (5). Figure 9. Identification results of blade 7# using Equation Figure 9. Identification results of blade 7# using Equation (5).

Once the blade vibration events were correctly identified in real time, time, BTT BTT data data analysis analysis could could Once the blade vibration events were correctly identified in real time, BTT data analysis could be conducted to reconstruct the vibration amplitude and frequency. In this paper, a least squares frequency. squares be conducted to reconstruct the vibration amplitude and frequency. In this paper, a least squares fitting method model thethe fit of data. data. The model fitting fitting result of bladeof6#blade around methodwas wasused usedtoto model fitthe of BTT the BTT The model result 6# fitting method was used to model the fit of the BTT data. The model fitting result of blade 6# 4000 revolutions is shown in Figure 10. The amplitude a maximum 0.07 mm atof 8201 around 4000 revolutions is shown in Figure 10. The reached amplitude reached aofmaximum 0.07rpm, mmthe at around 4000 revolutions is shown in Figure 10. The amplitude reached a maximum of 0.07 mm at engine order (EO) was 13, and the first-order vibration frequency was 1777.02 Hz. All other vibration 8201 rpm, the engine order (EO) was 13, and the first-order vibration frequency was 1777.02 Hz. All 8201 rpm, the engine order (EO) was 13, and the first-order vibration frequency was 1777.02 Hz. All events of Figure 8events were extracted BTT data using leastanalysis squaresusing fittingthe method. other vibration of Figureto8 carry wereout extracted to analysis carry out BTTthe data least other vibration events of Figure 8 were extracted to carry out BTT data analysis using the least The results are shown in Table 2. squares fitting method. The results are shown in Table 2. squares fitting method. The results are shown in Table 2.

Figure Figure 10. 10. Model Model fitting fitting result result of of blade blade 6# 6# at at 8200 8200 rpm, rpm, engine engine order order (EO) (EO) == 13. 13. Figure 10. Model fitting result of blade 6# at 8200 rpm, engine order (EO) = 13. Table 2. Model fitting results of blade 6#. Table 2. Model fitting results of blade 6#. Table 2. Model fitting results of blade 6#. Engine Order Amplitude (mm) Frequency (Hz) Center Speed (rpm)

Engine Order Engine Order 13 13 13 14 14 14 15 15 16 15 16 17 16 18 17 17 19 18 18 20 19 19 21 20 20 21 21

Amplitude (mm) Amplitude (mm) 0.07 0.07 0.070.07 0.07 0.070.04 0.040.02 0.04 0.020.04 0.020.05 0.04 0.040.04 0.05 0.050.03 0.04 0.040.03 0.03 0.03 0.03 0.03

Frequency (Hz) Frequency (Hz) 1777.02 1777.02 1776.07 1777.02 1776.07 1775.02 1776.07 1775.02 1774.22 1775.02 1773.28 1774.22 1774.22 1773.38 1773.28 1773.28 1772.00 1773.38 1772.59 1773.38 1772.00 1770.06 1772.00 1772.59 1772.59 1770.06 1770.06

Center Speed (rpm) Center 8201.61 Speed (rpm) 8201.61 7611.72 8201.61 7611.72 7100.07 7611.72 7100.07 6653.32 7100.07 6258.62 6653.32 6653.32 5911.26 6258.62 6258.62 5595.79 5911.26 5317.77 5911.26 5595.79 5057.30 5595.79 5317.77 5317.77 5057.30 5057.30

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Sensors 2019, 19, x FOR PEER REVIEW SensorsThe 2019,model 19, 1482fitting results are

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listed in the Campbell diagram (Figure 11). Figure 11 could also 10 of 12 proveThe that the vibration events of blade 6# were correct. Synchronous vibration occurred when, model fitting results are listed in the Campbell diagram (Figure 11). Figure 11 could also theoretically, thevibration blade natural integral multiple of rotational frequency. The results prove that the eventsfrequency of blade is 6#an were correct. Synchronous vibration occurred when, The model fitting results are listed in the Campbell diagram (Figure 11). Figure 11 could also prove in Figure 11 accurately on allfrequency of the intersect points between theoffirst-order wave and theoretically, the bladefell natural is an integral multiple rotationalvibration frequency. Theline results that the vibration events of blade 6# were correct. Synchronous vibration occurred when, theoretically, EO lines. in Figure 11 accurately fell on all of the intersect points between the first-order vibration wave line and the blade natural frequency is an integral multiple of rotational frequency. The results in Figure 11 EO lines. accurately fell on all of the intersect points between the first-order vibration wave line and EO lines.

Figure 11. Campbell diagram of blade 6#. Figure Figure11. 11. Campbell Campbelldiagram diagramof ofblade blade6#. 6#.

3.4. Comparison of the IAD Correlation Method with the Probe Displacement Distribution (PDD) 3.4. Comparison of the IAD Correlation Method with the Probe Displacement Distribution (PDD) Correlation Method 3.4. Comparison of the IAD Correlation Method with the Probe Displacement Distribution (PDD) Correlation Method Correlation Method[16], it was suggested that the displacement value of a single blade at each probe In Reference In Reference [16], it was suggested that the displacement value of a single blade at each probe is correlated to the values for the next rotation. This reference then proposed method to identify In Reference it was that theThis displacement of a singleaa blade at each probe is correlated to the[16], values for suggested the next rotation. reference value then proposed method to identify blade vibration events by calculating Pearson correlation coefficient between the probe is correlated to the values for the next rotation. This reference then proposed a method to identify blade vibration events by calculating Pearson correlation coefficient between the probe displacement displacement distributions of previous and current revolutions (also called PDD correlation blade vibration eventsand by calculating Pearson coefficient between themethod probe distributions of previous current revolutions (also correlation called PDD correlation method in this paper). in this paper). The identification results of blade 6# based on the PDD correlation method are displacement distributions of previous and current revolutions (also called PDD correlation method The identification results of blade 6# based on the PDD correlation method are shown in Figure 12. shown in Figure 12. The displacements of blade 6# from five probes are also shown in Figure 12, which in this paper). Theofidentification of blade 6# based PDD are The displacements blade 6# fromresults five probes are also shownon in the Figure 12,correlation which weremethod separated were separated 0.1 mm apart from each other. Compared to the IAD correlation method, it is shown Figure 12. each The displacements of blade probes aremethod, also shown Figure 12, 0.1 mmin apart from other. Compared to 6# thefrom IADfive correlation it isindifficult to which set a difficult to set a threshold value to indicate the occurrences of vibration events according to the were separated 0.1indicate mm apart from each other. Compared toaccording the IAD to correlation it is threshold value to the occurrences of vibration events the resultsmethod, of the PDD results of the PDD correlation method. As the data applied in that calculation of correlation were difficult to method. set a threshold to indicate thecalculation occurrences vibration were events according to the correlation As the value data applied in that of of correlation from five different from five different probes, the inconsistency of applied different probes, including the noiseswere in results of the PDD correlation method. As the data in that calculation of correlation probes, the inconsistency of different probes, including the noises in displacement signals, affected the displacement signals, affected the correlation value. from five value. different probes, the inconsistency of different probes, including the noises in correlation displacement signals, affected the correlation value.

Figure 12. Identification results of blade 6# using the probe displacement distribution (PDD) Figure 12. method. Identification results of blade 6# using the probe displacement distribution (PDD) correlation correlation method. Figure 12. Identification results of blade 6# using the probe displacement distribution (PDD) 4. Conclusions correlation method.

In this paper, an IAD correlation method to identify vibration events automatically for rotational blades of machinery was proposed. All included rotor angles between any two adjacent blades were

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accurately detected by only one fiber optical tip timing sensor, and then three formulas for calculating the IAD correlation were proposed to identify three types of blades vibration events: the blades’ overall vibrations, vibration of the adjacent two blades, and vibration of a specific blade. Further, the IAD correlation method was optimized in the calculating process to reduce computation load while identifying every blade’s vibration events. The method can meet the requirements of real-time, embedded, and automatic processing applications. The experimental results showed that the proposed method could effectively identify all vibration events. Compared with the visual observation method or the simple threshold value triggering method, the present method eliminated fake vibration signals, which may be wrongly recognized as vibration events by human judgment. The coupled vibration signals of adjacent blades were also accurately identified. The three calculating formulas described in this paper provide objective criterions for the identification of the blades’ overall vibration, vibration of adjacent two blades, and vibration events of a specific blade, and are suitable for different applications. Although synchronous vibration events in the experiments were only air-excited, other types of blade vibration events will also lead to changes in the included angle distribution of rotor blades, such as foreign object damage (FOD) events and blade asynchronous vibration events. Therefore, the IAD correlation method has general applicability to be used for the identification of such types of events. The response of the blade to FOD events is complex. There is no effective method to identify FOD events of blades at present. This can be further studied in combination with the technology described in this paper. Author Contributions: Conceptualization, D.Y. and F.D.; methodology, D.Y. and F.D.; software, D.Y.; validation, D.Y. and Z.L.; formal analysis, D.Y.; investigation, G.N.; resources, Z.L.; data curation, D.Y.; writing—original draft preparation, D.Y.; writing—review and editing, J.J. and F.L.; visualization, F.L.; supervision, J.J.; project administration, F.D.; funding acquisition, F.D. Funding: This research was funded by the National Natural Science Foundations of China (51775377), National Key Research and Development Plan (2017YFF0204800), the TianJin Natural Science Foundations of China (17JCQNJC01100) and Young Elite Scientists Sponsorship Program by Cast of China (2016QNRC001). Acknowledgments: The author would like to thank the administrative support of State Key Laboratory of Precision Measuring Technology and Instruments. Conflicts of Interest: The authors declare no conflict of interest.

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