US20150184533A1  Methods and systems to monitor health of rotor blades  Google Patents
Methods and systems to monitor health of rotor blades Download PDFInfo
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 US20150184533A1 US20150184533A1 US14/140,654 US201314140654A US2015184533A1 US 20150184533 A1 US20150184533 A1 US 20150184533A1 US 201314140654 A US201314140654 A US 201314140654A US 2015184533 A1 US2015184533 A1 US 2015184533A1
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 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
 F01D—NONPOSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
 F01D21/00—Shuttingdown of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for
 F01D21/003—Arrangements for testing or measuring

 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
 F01D—NONPOSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
 F01D17/00—Regulating or controlling by varying flow
 F01D17/02—Arrangement of sensing elements
 F01D17/06—Arrangement of sensing elements responsive to speed

 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
 F01D—NONPOSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
 F01D21/00—Shuttingdown of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for
 F01D21/14—Shuttingdown of machines or engines, e.g. in emergency; Regulating, controlling, or safety means not otherwise provided for responsive to other specific conditions
Definitions
 Rotor blades or airfoils are used in many devices with several examples including axial compressors, turbines, engines, or other turbo machinery.
 an axial compressor has one or more rotors having a series of stages with each stage comprising a row of rotor blades or airfoils followed by a row of static blades or static airfoils. Accordingly, each stage comprises a pair of rotor blades or airfoils and static airfoils.
 the rotor blades or airfoils increase the kinetic energy of a fluid that enters the axial compressor through an inlet.
 the static blades or static airfoils generally convert the increased kinetic energy of the fluid into static pressure through diffusion. Accordingly, the rotor blades or airfoils and static airfoils increase the pressure of the fluid.
 the rotor blades generally vibrate at synchronous and asynchronous frequencies.
 the rotor blades may generally vibrate at the synchronous frequencies due to the rotor speed/frequency
 the rotor blades may vibrate at the asynchronous frequencies due to aerodynamic instabilities, such as, rotating stall and flutter.
 the rotor blades have a natural tendency to vibrate at larger amplitudes at certain synchronous frequencies of the rotor blades.
 Such synchronous frequencies are referred to as resonant frequencies of the rotor blades.
 the synchronous frequencies of the rotor blades are typically activated at fixed rotor speeds of the rotors.
 the activation of the resonant frequencies may increase the amplitudes of vibration of the rotor blades. Such increased amplitudes of vibration may damage the rotor blades or lead to cracks in the rotor blades.
 the rotor blades operate for long hours under extreme and varied operating conditions, such as, high speed, pressure, and temperature that affect the health of the airfoils.
 extreme and varied operating conditions such as, high speed, pressure, and temperature that affect the health of the airfoils.
 certain other factors lead to fatigue and stress of the airfoils.
 the factors may include inertial forces including centrifugal force, pressure, resonant frequencies of the airfoils, vibrations in the airfoils, vibratory stresses, temperature stresses, reseating of the airfoils, load of the gas or other fluid, or the like.
 a prolonged increase in stress and fatigue over a period of time damages the rotor blades resulting in defects or cracks in the rotor blades.
 Such defects, damages, or cracks in the rotor blades may vary the rotor speeds that activate the rotor blades' resonant frequencies. For example, in a healthy rotor blade if resonant frequencies are activated at a rotor speed R, then when the rotor blade has a crack, the resonant frequencies may get activated at a rotor speed of R ⁇ r. These variations in rotor speeds that activate the rotor blades' resonant frequencies may, therefore, be useful in monitoring the health of rotor blades.
 the system includes a processing subsystem that generates a plurality of frequency peak values corresponding to two or more respective windows of signals by iteratively shifting the two or more respective windows of signals along delta times of arrival signals corresponding to a blade in the rotor, determines one or more resonantfrequency rotor speeds of the blade by identifying rotor speeds corresponding to a subset of the plurality of frequency peak values, and monitors the blade to determine a presence of one or more defects in the blade during the resonantfrequency rotor speeds regions.
 FIG. 1 is a diagrammatic illustration of a blade health monitoring system, in accordance with an embodiment of the present systems
 FIG. 2 is a flow chart illustrating an exemplary method to identify resonantfrequency rotor speeds regions of the blade based upon delta TOAs, in accordance with certain aspects of the present techniques
 FIG. 3 is a flow chart illustrating an exemplary method to determine a plurality of frequency peak values by shifting a window of signals along delta TOAs signals, in accordance with one aspect of the present techniques
 FIG. 4 is a plot of a simulated delta TOAs vector signal, corresponding to a blade in a rotor, to show determination of a plurality of frequency peak values and resultant values;
 FIG. 5 is a simulated plot of a frequency signal to explain determination of a first frequency peak value based upon the frequency signal and the determined synchronous frequency threshold;
 FIG. 6 is a simulated plot of resonantfrequency rotor speed regions of a blade, in accordance with one embodiment of the present techniques
 FIG. 7 is a flowchart of a method for monitoring health of a rotor, in accordance with one embodiment of the present techniques
 FIG. 8 is a correlation chart, of an index value and a correlation value that may be used to determine the existence of the crack, or a probability of crack in a blade;
 FIG. 9( a ) shows a simulated plot of a historical resonance signal of a blade
 FIG. 9( b ) shows a simulated plot of a resonance signal of a blade
 FIG. 10 is a flowchart of a method to generate a measurement matrix based upon a resonantfrequency first delta TOAs and a resonantfrequency second delta TOAs, in accordance with one embodiment of the present techniques
 FIG. 11 is a flowchart of a method to generate a resonant matrix based upon a measurement matrix, in accordance with one embodiment of the present techniques
 FIG. 12 ( a ) shows a simulated plot of a resonantfrequency first delta times of arrival vectors signal corresponding to a blade and a first sensing device
 FIG. 12 ( b ) shows a simulated plot of a resonantfrequency second delta times of arrival vectors signal corresponding to a blade and a second sensing device
 FIG. 12 ( c ) shows a simulated plot of a subcleaned resonantfrequency delta TOAs vectors signal generated using a row of a whitened matrix
 FIG. 12 ( d ) shows a simulated plot of a seminoise signal generated using another row of the whitened matrix referred to in FIG. 12( c );
 FIG. 12 ( e ) shows a simulated plot of a resonance signal
 FIG. 12 ( f ) shows a simulated plot of a noise signal
 FIG. 13 is a flowchart of a method to generate a whitened matrix, in accordance with one embodiment of the present techniques.
 the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements.
 the terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.
 the term “and/or” includes any and all combinations of one or more of the associated listed items.
 Approximating language may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it may be about related. Accordingly, a value modified by a term such as “about” is not limited to the precise value specified. In some instances, the approximating language may correspond to the precision of an instrument for measuring the value.
 the term “expected time of arrival (TOA)” may be used to refer to a TOA of a blade, during rotation, at a reference position when there are no defects or cracks in the blade and the blade is working in an ideal situation, load conditions are optimal, and the vibrations in the blade are minimal.
 the term “resonantfrequency rotor speeds” refers to speeds, of a rotor of a device, that result in activation of one or more resonant frequencies of blades in the rotor.
 resonantfrequency rotor speeds In operation, natural frequencies or resonant frequencies of blades in a rotor get activated at certain rotor speeds of a rotor in a device, such as an axial compressor.
 resonantfrequency rotor speeds As discussed in detail below, the present systems and methods identify resonantfrequency rotor speeds of the blades based upon times of arrival (TOAs) (hereinafter referred to as actual TOAs) of the blades at a reference position in the rotor.
 TOAs times of arrival
 One or more cracks in the blades may vary the resonantfrequency rotor speeds of the blades.
 a technical effect of the present system and method according to one embodiment is to determine one or more variations in the resonantfrequency rotor speeds, and determine existence of cracks or probability of existence of cracks in the blades based upon the variations. This technical effect provides for enhanced maintenance prognostics and a lower percentage of unplanned downtime.
 FIG. 1 is a diagrammatic illustration of a blade health monitoring system 10 , in accordance with an embodiment of the present system.
 the system 10 includes one or more blades or airfoils, in a rotor 11 , that are monitored by the system 10 to determine existence of cracks or probability of existence of cracks in the blades.
 FIG. 1 shows a portion of the rotor 11 .
 the rotor 11 for example may be a component of device, such as, a compressor, an axial compressor, a land based gas turbine, or the like.
 the rotor 11 for example includes a blade 12 .
 the system 10 includes one or more sensors 14 , 16 that sense an arrival of the blade 12 at a reference point to generate blade passing signals BPS 18 , 20 representative of times of arrival (TOAs) 24 , 26 of the blade 12 at the reference point.
 BPS 18 , 20 representative of times of arrival
 TOAs of a blade at a reference point are referred to as actual TOAs.
 the first sensing device 14 generates the first BPS 18 representative of first actual TOAs 24 of the blade 12 at the reference point.
 the second sensing device 16 generates the second BPS 20 representative of second actual TOAs 26 of the blade 12 at the reference point.
 the reference point for example, may be underneath the sensors 14 , 16 or adjacent to the sensors 14 , 16 .
 the actual TOAs for example, may be measured in units of time or degrees.
 the BPS 18 , 20 for example, may be generated during a startup state of the rotor, a transient state of the rotor 11 , a steady state of the rotor 11 , overspeed state of the rotor 11 , or combinations thereof.
 the sensors 14 , 16 may sense an arrival of the leading edge of the blade 12 to generate the BPS 18 , 20 . In another embodiment, the sensors 14 , 16 may sense an arrival of the trailing edge of the blade 12 to generate the BPS 18 , 20 . In still another embodiment, the sensor 14 may sense an arrival of the leading edge of the blade 12 to generate the BPS 18 , and the sensor 16 may sense an arrival of the trailing edge of the blade 12 to generate the BPS 20 , or vice versa.
 the sensors 14 , 16 may be mounted adjacent to the blade 12 on a stationary object in a position such that an arrival of the blade 12 may be sensed efficiently.
 At least one of the sensors 14 , 16 is mounted on a casing (not shown) of the blades.
 the sensors 14 , 16 may be magnetostriction sensors, magnetic sensors, capacitive sensors, eddy current sensors, or the like.
 the BPS 18 , 20 are received by a processing subsystem 22 .
 the processing subsystem 22 determines the first actual TOAs 24 and the second actual TOAs 26 of the blade 12 based upon the BPS 18 , 20 .
 the processing subsystem 22 determines the first actual TOAs 24 based upon the first BPS 18
 the processing subsystem 22 determines the second actual TOAs 26 based upon the second BPS 20 .
 the processing subsystem 22 preprocesses the first actual TOAs 24 and the second actual TOAs 26 to remove noise and asynchronous frequencies from the first actual TOAs 24 and the second actual TOAs 26 .
 the processing subsystem 22 may preprocess the first actual TOAs 24 and the second actual TOAs 26 by applying at least one of a smoothening filtering technique and a median filtering technique on the first actual TOAs 24 and the second actual TOAs 26 .
 the processing subsystem 22 includes at least one processor that is coupled to memory and a communications section.
 the information such as sensor data can be communicated by wired or wireless mechanisms via the communications section and stored in memory for the subsequent processing.
 the memory in one example can also include the executable programs and associated files to run the application.
 the processing subsystem 22 monitors the health of the blade 12 based upon the first actual TOAs 24 and the second actual TOAs 26 .
 the processing subsystem 22 determines first delta TOAs 28 , corresponding to the blade 12 and corresponding to the first sensing device 14 , based upon the first actual TOAs 24 and an expected TOA of the blade 12 .
 the processing subsystem 22 determines second delta TOAs 30 , corresponding to the blade 12 and the corresponding to the second sensing device 16 , based upon the second actual TOAs 26 and the expected TOA of the blade 12 .
 the first delta TOAs 28 correspond to the first sensing device 14 as the first delta TOAs are determined based upon the first actual TOAs 24 determined based upon the first BPS 18 generated by the first sensing device 14 .
 the second delta TOAs 30 correspond to the second sensing device 16 as the second delta TOAs 30 are determined based upon the second actual TOAs 26 determined based upon the second BPS 20 generated by the second sensing device 16 .
 the first delta TOAs 28 or the second delta TOAs 30 may be determined using the following equation (1):
 the first delta TOAs 28 may be represented as first delta TOAs vectors 32 by mapping the first delta TOAs 28 to corresponding rotor speeds of the rotor 11 .
 the second delta TOAs may be represented as second delta TOAs vectors 34 by mapping the second delta TOAs 30 to corresponding rotor speeds of the rotor 11 . For example, if a first actual TOA is generated based upon a BPS generated at a time stamp T 1 when the rotor speed is R 1 , then a first delta TOA is determined based upon the first actual TOA; and the first delta TOA is represented as a first delta TOA vector by mapping the first delta TOA to the rotor speed R 1 .
 first delta TOAs and “first delta TOAs signal” are interchangeably used as first delta TOAs are digital representation of the analog first delta TOAs signal.
 second delta TOAs and “second delta TOAs signal” are interchangeably used as second delta TOAs are digital representation of the analog second delta TOAs signal.
 first delta TOAs vectors and “first delta TOAs vectors signal” are interchangeably used as first delta TOAs vectors are digital representation of the analog first delta TOAs vectors signal.
 second delta TOAs vectors and “second delta TOAs vectors signal” are interchangeably used as the second delta TOAs vectors are digital representation of the analog first delta TOAs vectors signal.
 the rotor 11 operates at multiple rotor speeds. A subset of the rotor speeds activates the resonant frequencies of the blades in the rotor 11 .
 the ‘rotor speeds of the rotor that activate the resonant frequencies of the blades’ are hereinafter referred to as resonantfrequency rotor speeds.
 resonantfrequency rotor speeds of blades in a rotor may be different from resonantfrequency rotor speeds of blades in another rotor.
 the resonantfrequency rotor speeds of a blade in the rotor 11 may be different from resonant frequency rotor speeds of another blade in the rotor 11 .
 the processing subsystem 22 extracts resonantfrequency first delta TOAs/resonantfrequency first delta TOAs vectors from the first delta TOAs 28 /first delta TOAs vectors 32 , respectively.
 the resonantfrequency first delta TOAs/resonantfrequency first delta TOAs vectors are a subset of the first delta TOAs 28 /first delta TOAs vectors 32 , respectively.
 the processing subsystem 22 extracts resonantfrequency second delta TOAs/resonantfrequency second delta TOAs vectors from the second delta TOAs 30 /the second delta TOAs vectors 34 , respectively.
 the resonantfrequency second delta TOAs/resonantfrequency second delta TOAs vectors are a subset of the second delta TOAs 30 /the second delta TOAs vectors 34 , respectively.
 the processing subsystem 22 determines resonantfrequency rotor speeds of the blade 12 based upon the resonantfrequency first delta TOAs and the resonantfrequency second delta TOAs. In another embodiment, the processing subsystem 22 determines resonantfrequency rotor speeds of the blade 12 based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.
 the processing subsystem 22 determines existence of any variations in the resonantfrequency rotor speeds with respect to historical resonantfrequency rotor speeds to determine the existence of a crack in the blade 12 or a probability of existence of a crack in the blade 12 .
 the processing subsystem 22 determines that one or more variations exist in the resonantfrequency rotor speeds of the blade 12 , the processing subsystem 22 determines that a crack in the blade 12 exists, or determines that a probability of crack in the blade 12 exists. The determination of crack in the blade 12 is explained in greater detail with reference to FIG. 7 .
 FIG. 2 is a flow chart illustrating an exemplary method 200 to identify resonantfrequency rotor speed regions 220 of the blade 12 based upon delta TOAs 220 , in accordance with certain aspects of the present techniques.
 the resonantfrequency rotor speed regions 220 are broad ranges of rotor speeds of the blade 12 that result in activation of one or more resonant frequencies of the blade 12 .
 resonant frequencies of the blade 12 may get activated at rotor speeds in the range of 1200 rotations per minute to 1400 rotation per minute, therefore 1200 rotations per minute to 1400 rotation per minute is a resonantfrequency rotor speed range of the blade.
 Reference numeral 202 is representative of delta TOAs corresponding to the blade 12 .
 the delta TOAs 202 are determined based upon actual TOAs generated by the first sensing device 14 or the second sensing device 16 when there are no defects or cracks in the blade 12 ; the blade 12 and the rotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in the blade 12 are minimal.
 the delta TOAs 202 may be the first delta TOAs 28 (see FIG. 1 ) if the first actual TOAs 24 are generated by the first sensing device 14 when there are no defects or cracks in the blade 12 ; the blade 12 and the rotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in the blade 12 are minimal.
 the delta TOAs 202 may be the second delta TOAs 30 (see FIG. 1 ) if the second actual TOAs 26 are generated by the second sensing device 16 when there are no defects or cracks in the blade 12 ; the blade 12 and the rotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in the blade 12 are minimal.
 the delta TOAs signals 202 may be represented as delta TOAs vector signals by mapping the delta TOAs signals 202 to respective rotor speeds. An exemplary delta TOAs vector signal is shown in FIG. 3 . In the embodiment of FIG. 2 , each block of the method 200 is executed by the processing subsystem 22 of FIG. 1 .
 a first window of signals and a second window of signals are selected.
 the first window of signals and the second window of signals are rotor speed bands. Additionally, each of the first window of signals and second window of signals has a respective width.
 the first window of signals is a rotor speed band of 25 rotations per minute, and a width of the first window of signals is 25 rotations per minute.
 the second window of signals is a rotor speed band of 50 rotations per minute, and a width of the second window of signals is 50 rotations per minute. The width of the second window of signals is greater than the width of the first window of signals.
 a plurality of first frequency peak values are generated by iteratively shifting the first window of signals along the delta TOAs signal 202 .
 a plurality of second frequency peak values are generated by iteratively shifting the second window of signals along the delta TOAs signal 202 . Determination of the first frequency peak values and the second frequency peak values are explained in greater detail with reference to FIG. 3 and FIG. 4 .
 a plurality of resultant values are determined based upon the first frequency peak values and the second frequency peak values. Particularly, a resultant value is determined by subtracting a second frequency peak value from a respective first frequency peak value.
 a resultant value for example, may be determined using the following equation (2):
 RV First_Frequnecy_Peak_Value ⁇ Second_Frequnecy_Peak_Value (2)
 RV is a resultant value
 a check is carried out to determine whether the resultant values are less than a determined value.
 the control is transferred to block 214 .
 rotor speeds corresponding to the second frequency peak values are determined.
 a local maxima of the rotor speeds corresponding to the second frequency peak values are determined as the resonantfrequency rotor speeds regions 220 , when the resultant values are less than the determined value. For example, when a rotor speed corresponding to a second frequency peak value is 1200 rotation per minute, then a local maxima of 1200 ⁇ 50 is determined as a resonantfrequency rotor speed region.
 a subsequent window of signals is selected.
 a width of the subsequent window of signals is greater than the width of the first window of signals and the width of the second window of signals.
 the width of the subsequent window of signals may be 75 rotations per minute or greater than 75 rotations per minute.
 a plurality of subsequent frequency peak values are determined by iteratively shifting the subsequent window of signals along the delta TOAs 202 . The determination of the subsequent frequency peak values by iteratively shifting the subsequent window of signals along the delta TOAs signal 202 is explained with reference to FIG.
 the control is transferred to block 210 .
 a plurality of subsequent resultant values are determined based upon the subsequent frequency peak values and previous frequency peak values.
 the previous frequency peak values are the second frequency peak values.
 a check is carried out to determine whether one or more of the subsequent resultant values are less than the determined value.
 blocks 216 to 212 are executed again.
 the control is transferred to block 214 .
 a local maxima of each of the rotor speeds corresponding to the subsequent frequency peak values is identified as the resonantfrequency rotor speeds region 220 .
 r is a rotor speed corresponding to a subsequent frequency peak value
 r+50 may be selected as a resonantfrequency rotor speed region.
 FIG. 6 shows simulated resonantfrequency speed regions of a blade identified by using a process described with reference to FIG. 2 .
 FIG. 3 is a flow chart illustrating an exemplary method 300 to determine a plurality of frequency peak values 310 by shifting a window of signals 302 along the first delta TOAs signals 202 referred to in FIG. 1 , in accordance with one aspect of the present techniques. Particularly, FIG. 3 explains blocks 206 , 208 , and 218 of FIG. 2 in greater detail.
 the plurality of frequency peak values 310 may be the first frequency peak values when the window of signals 302 is the first window of signals referred to in FIG. 2 .
 the plurality of frequency peak values 310 may be the second frequency peak values when the window of signals 302 is the second window of signals referred to in FIG. 2 .
 the plurality of frequency peak values 310 may be the subsequent frequency peak values when the window of signals 302 is the subsequent window of signals. (See FIG. 2 ).
 the window of signals 302 is placed on the delta TOAs 202 , and a first subset of the delta TOAs 202 contained or covered by the window of signal 302 is selected. Furthermore, at block 306 , a frequency peak value is generated based upon the first subset of the delta TOAs signal 202 . For example, the frequency peak value is generated by determining a frequency signal by taking a fast Fourier transform of the first subset of the delta TOAs signal 202 , and selecting the frequency peak value from the frequency signal, wherein the frequency peak value is equal to or less than a determined synchronous frequency threshold.
 the term “determined synchronous frequency threshold” is a numerical frequency value selected such that frequencies, greater than the determined synchronous frequency threshold, substantially are asynchronous frequencies; and frequencies, equal to or less than the determined synchronous frequency threshold, substantially are synchronous frequencies.
 the magnitude of the determined synchronous frequency threshold may be about 2 Hertz. Determination of the frequency peak value is explained in greater detail with reference to FIG. 5 .
 the frequency peak value is added to the plurality of frequency peak values 310 , and the control is transferred to block 312 .
 a check is carried out to determine whether the window of signals 302 has been shifted a determined number of times along the delta times of signals 202 . While in FIG. 3 , a check is carried out to determine whether the window of signals 302 has been shifted a determined number of times, in certain embodiment a check may be carried out to determine whether the window of signals 302 has been shifted across the delta times of arrival 202 .
 a shifted window is determined by shifting the window of signals 302 along the delta TOAs signal 202 by a determined rotor speed band.
 a subsequent subset of the delta TOAs signal 202 contained or covered by the shifted window of signals is selected.
 a subsequent frequency peak value based upon the subsequent subset of the delta TOAs signal 202 is determined.
 the subsequent frequency peak value for example, is generated by taking a fast Fourier transform of the subsequent subset of the first delta TOAs signal 202 to generate a corresponding frequency signal, followed by selecting the subsequent frequency peak value from the frequency signal, wherein the subsequent frequency peak value is equal to or less than the determined synchronous frequency threshold.
 the control from the block 318 is transferred to block 308 .
 the subsequent frequency peak value is added to the plurality of frequency peak values 310 .
 the check is carried out to determine whether the window of signals 302 has been shifted, a determined number of times, along the delta TOAs signal 202 .
 the plurality of frequency peak values 310 are determined.
 FIG. 4 is a plot 400 of a simulated delta TOAs vector signal 402 , corresponding to a blade in a rotor, to show determination of a plurality of frequency peak values and resultant values.
 FIG. 4 explains steps 206 , 208 and 218 of FIG. 2 in greater detail.
 FIG. 4 explains step 210 of FIG. 2 .
 FIG. 4 explains step 306 of FIG. 3 in greater detail.
 the simulated delta TOAs vector signal 402 is generated by mapping delta TOAs, of a blade in a rotor, to respective rotor speeds.
 the delta TOAs vector signal 402 may be the first delta TOAs vector signal 32 (see FIG. 1 ).
 the delta TOAs vector signal 402 may be the second delta TOAs vector signal 34 (see FIG. 1 ).
 Xaxis 406 of the plot 400 represents rotor speeds of the rotor
 Yaxis 408 of the plot 400 represents delta TOAs corresponding to the blade.
 Reference numeral 410 is representative of a first window of signals having a width W 1
 reference numeral 412 is representative of a second window of signals having a width W 2 .
 the first window of signals 410 selects a first subset of the delta TOAs vector signal 402 contained or covered by the first window of signals 410 .
 the first subset of the delta TOAs vector signal 402 starts at a point 414 and ends at a point 416 .
 the frequency signal 502 is determined by taking a Fourier transform or a Fast Fourier transform of the first subset of the delta TOAs vectors signal 402 .
 a first frequency peak value 508 (shown in FIG. 5 ), corresponding to the first window of signals 410 and the first subset of the delta TOAs vectors signal 402 , is determined based upon the frequency signal 502 and a determined synchronous frequency threshold 510 (shown in FIG. 5 ).
 the determination of the first frequency peak value, corresponding to the first window and the first subset of the delta TOAs is explained in greater detail with reference to FIG. 5 .
 the second window of signals 412 selects a second subset of the delta TOAs vector signal 402 contained or covered by the second window of signals 412 .
 the second subset of the delta TOAs vector signal 402 starts at a point 418 and ends at a point 420 .
 a frequency signal is generated based upon the second subset of the delta TOAs vector signal 402 .
 the frequency signal is determined by taking a Fourier transform or a Fast Fourier transform of the second subset of the delta TOAs vector signal.
 a second frequency peak value, corresponding to the second window of signals 412 and the second subset of the delta TOAs is determined based upon the frequency signal and a determined synchronous frequency threshold.
 the second frequency peak value for example, may be determined using the method explained with reference to FIG. 5 .
 a first resultant value is determined by subtracting the second frequency peak value from the first frequency peak value.
 the first window of signals 410 is shifted by a rotor speed band SB 1 to generate a shifted first window SW 1
 the second window 412 is shifted by the rotor speed band SB 1 to generate a shifted second window of signals SW 2 .
 subsequent first frequency peak value, corresponding to the shifted first window of signals SW 1 is determined based upon a subset of the delta TOAs vector signal 402 covered by the shifted first window of signals SW 1 .
 subsequent second frequency peak value, corresponding to the shifted second window of signals SW 2 is determined based upon a subset of the delta TOAs vector signal 402 covered by the shifted second window of signals SW 2 .
 a second resultant value is determined by subtracting the subsequent second frequency peak value from the subsequent first frequency peak value.
 the first window of signals 410 and the second window of signals 412 are shifted unless the delta TOAs vector signal 402 is traversed completely. Furthermore, a plurality of first frequency peak values, a plurality of second frequency peak values, and a plurality of resultant values are determined by shifting the first window of signals 410 , and the second window of signals 412 .
 the plurality of first frequency peak values includes the first frequency peak value, and the subsequent first frequency peak.
 the plurality of second frequency peak values includes the second frequency peak value, and the subsequent second frequency peak.
 the plurality of resultant values includes the first resultant value and the second resultant value.
 FIG. 5 is a plot 500 of the frequency signal 502 referred to in FIG. 4 to explain determination of the first frequency peak value 508 based upon the frequency signal 502 and a determined synchronous frequency threshold 510 .
 Xaxis 504 of the plot 500 represents frequency of the first subset of the delta TOAs vector signal 402
 Yaxis 506 of the plot 500 represents amplitude of the frequency.
 the first frequency peak value 508 for example, is determined by the processing subsystem 22 referred to in FIG. 1 .
 the processing subsystem 22 selects frequencies that are less than the determined synchronous frequency threshold 510 .
 the selected frequencies are synchronous frequencies.
 a frequency that has the highest amplitude is selected from the synchronous frequencies or the selected frequencies.
 a frequency 512 has the highest amplitude 508 .
 the highest amplitude 508 is determined as the first frequency peak value 508 .
 FIG. 6 is a simulated plot 600 of resonantfrequency rotor speed regions 602 , 604 of a blade determined using the method explained with reference to FIG. 2 .
 Xaxis 606 is representative of rotor speeds of a rotor
 Yaxis is representative of frequency peak values.
 the frequency peak values may be the second frequency peak values determined at the block 208 in FIG. 2 , or the subsequent frequency peak values determined at the block 218 referred to in FIG. 2 .
 two resonantfrequency rotor speed regions 602 , 604 are identified.
 FIG. 7 is a flowchart of a method 700 for monitoring health of the blade 12 referred to in FIG. 1 , in accordance with one embodiment of the present techniques.
 Reference numeral 220 is representative of the resonantfrequency rotor speeds regions of the blade 12 in the rotor 11 (see FIG. 2 ).
 Reference numeral 32 is representative of the first delta TOAs vectors determined by the processing subsystem 22 in FIG. 1 .
 reference numeral 34 is representative of the second delta TOAs vectors determined by the processing subsystem 22 in FIG. 1 .
 resonantfrequency first delta TOAs vectors are selected from the first delta TOAs vectors 32 .
 resonantfrequency first delta TOAs vectors are used to refer to a subset of the first delta TOAs vectors 32 , wherein the subset corresponds to resonantfrequency rotor speeds regions of the blade 12 .
 resonantfrequency second deltas TOAs vectors are selected from the second delta TOAs vectors 34 .
 resonantfrequency second delta TOAs vectors are used to refer to a subset of the second delta TOAs vectors 34 , wherein the subset corresponds to resonantfrequency rotor speeds regions of the blade 12 .
 a measurement matrix is generated based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.
 the measurement matrix for example may be generated by arranging the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors to generate an initial matrix, and detrending the initial matrix to generate the measurement matrix.
 the initial matrix for example, may be detrended using one or more techniques including a polynomial curve fitting technique, or a wavelet based curve fitting technique. Furthermore, generation of the measurement matrix is explained in greater detail with reference to FIG. 10 .
 a resonant matrix is generated based upon the measurement matrix such that entries in the resonant matrix are substantially linearly uncorrelated and linearly independent.
 the resonant matrix may be determined by applying at least one technique on the measurement matrix, wherein the at least one technique comprises a whitening technique, a cumulant matrix estimation technique, and a matrix rotation technique.
 the resonant matrix comprises cleaned resonantfrequency delta TOAs vectors 712 and noise data 710 .
 a row of the resonant matrix comprises the resonantfrequency delta TOAs vectors 712
 another row of the resonant matrix comprises the noise data 714 .
 the cleaned resonantfrequency delta TOAs vector signal 712 includes common observations or measurements of the first sensing device 14 and the second sensing device 16 after removal of noise from the resonantfrequency first delta TOAs vectors signal and the resonantfrequency second delta TOAs vectors signal.
 the term “cleaned resonantfrequency delta TOAs vectors” will be referred to as a resonance signal.
 the noise signal 710 includes noise of the resonantfrequency first delta TOAs vectors signal and the resonantfrequency second delta TOAs vectors signal.
 the “cleaned resonantfrequency delta TOAs vectors signal 712 ” are interchangeably referred to as resonance signal 712 .
 An example of a resonance signal using the method of FIG. 7 is shown in FIG. 9( a ) and FIG. 12( e ).
 An example of a noise signal using the method of FIG. 7 is shown in FIG. 12( f ).
 Reference numeral 714 is representative of historical resonance signals, of the blade 12 , generated when there are no defects or cracks in the blade 12 , and the blade 12 is working in an ideal situation, load conditions are optimal, and the vibrations in the blade 12 are minimal.
 the historical resonance signals 714 show historical resonantfrequency rotor speeds of the blade 12 mapped to historical cleaned delta TOAs of the blade 12 when there are no defects or cracks in the blade 12 .
 the variation in resonantfrequency rotor speeds of the blade 12 with respect to historical resonantfrequency rotor speeds of the blade 12 is determined by applying a correlation function to the resonance signal 712 and the historical resonance signals 714 .
 the application of the correlation function results in determination of an index value and a correlation value.
 correlation value is a measurement of a correlation or similarity between a resonance signal and a historical resonance signal.
 the term “index value” is a measurement of a phase shift between a resonance signal and a historical resonance signal. Higher the correlation value, higher is the similarity between the resonance signal 712 and the historical resonance signals 714 . Again higher the index value, higher is a phase shift in the resonance signal 712 with respect to the historical resonance signals 714 . Accordingly, the correlation value and the index value may be used to determine the variation in the resonance signal 712 with respect to the historical resonance signals 714 .
 a presence of crack, an absence of crack or a probability of crack may be determined based upon the variation in the resonance signal 712 with respect to the historical resonance signals 714 . For example, when a variation exists in the resonance signal 712 with respect to the historical resonance signals 714 , it may be determined that a crack exists in the blade 12 . In one embodiment, the presence of crack, the absence of crack or the probability of crack may be determined based upon the index value, the correlation value, and a correlation chart. Determination of the presence of crack, the absence of crack, or the probability of crack based upon the index value, the correlation value and the correlation chart is shown in FIG. 8 .
 FIG. 8 shows a correlation chart 800 that may be used to determine a presence of crack, an absence of crack or a probability of crack in the blade 12 , in accordance with one embodiment of the present techniques.
 FIG. 8 explains step 718 of FIG. 7 .
 the correlation chart 800 comprises four quadrants including a first quadrant 802 , a second quadrant 804 , a third quadrant 806 , and a fourth quadrant 808 .
 the first quadrant 802 represents low index value and high correlation value.
 the second quadrant 804 represents high index value and high correlation value.
 the third quadrant 806 represents high index value and low correlation value.
 the fourth quadrant 808 represents low index value and low correlation value.
 the index value and the correlation value determined at the block 716 in FIG. 7 are positioned in the correlation chart 800 to determine the existence of the crack or a probability of existence of the crack in the blade 12 . For example, when the index value and the correlation value fall in the first quadrant 802 of the correlation chart 800 , it may be determined that no cracks exist in the blade 12 . Furthermore, when the index value and the correlation value, determined at the block 716 , fall in the second quadrant 804 of the correlation chart 800 , it may be determined that one or more cracks exist in the blade 12 .
 index value and the correlation value, determined at the block 716 fall in the third quadrant 806 of the correlation chart 800 , it may be determined that a probability of existence of a crack exist in the blade 12 .
 index value and the correlation value, determined at the block 716 fall in the fourth quadrant 808 of the correlation chart 800 , it may be determined that a probability of existence of a crack exist in the blade 12 .
 FIG. 9( a ) shows a simulated plot 900 of a historical resonance signal 902 of a blade
 FIG. 9( b ) shows a simulated plot 904 of a resonance signal 906 , of the blade, generated using the method explained in FIG. 7
 Xaxis 908 of the plot 900 , 904 is representative of resonantfrequency rotor speeds range
 Yaxis 910 of the plot 900 , 904 is representative of cleaned resonantfrequency delta TOAs.
 the resonance frequency of the blade is activated at a resonantfrequency rotor speed 912 .
 the resonant frequencies of the blade are activated at a shifted resonantfrequency rotor speed 914 . Accordingly, due to the variation or the shift in the resonantfrequency rotor speed 912 of the blade shown by the historical resonance signal 902 , it may be determined that the blade has a crack.
 FIG. 10 is a flowchart of a method 1000 to generate a measurement matrix based upon resonantfrequency first delta TOAs and resonantfrequency second delta TOAs, in accordance with one embodiment of the present techniques.
 FIG. 10 explains block 706 of FIG. 7 in greater detail.
 the resonantfrequency first delta TOAs are selected from the first delta TOAs 32 at the block 702 in FIG. 7 .
 the resonantfrequency second delta TOAs are selected from the second delta TOAs 34 at block 704 in FIG. 7 .
 an initial matrix is generated based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs.
 the initial matrix I may be represented as follows:
 a measurement matrix may be generated by detrending the initial matrix I.
 the initial matrix for example, may be detrended by applying at least one technique on the initial matrix I.
 the technique for example includes a polynomial curve fitting, a wavelet based curve fitting, or combinations thereof.
 FIG. 11 is a flowchart of a method 1100 to generate a resonant matrix based upon a measurement matrix, in accordance with one embodiment of the present techniques.
 FIG. 11 explains step 708 in FIG. 7 .
 a whitened matrix is determined based upon the measurement matrix.
 the whitened matrix is determined by substantially removing linear correlation between entries in the measurement matrix.
 the whitened matrix is determined by substantially removing linear correlation between entries in a first row of the measurement matrix and entries in a second row of the measurement matrix. Accordingly, entries in a first row of the whitened matrix and entries in a second row of the whitened matrix are linearly uncorrelated.
 the whitened matrix comprises two rows, wherein a first row substantially comprises common observations/components of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors, and a second row substantially comprises noise of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.
 the first row of the whitened matrix may be used to generate a subcleaned resonant frequency delta TOAs vectors signal 1104 that substantially comprises common observations/components of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.
 the second row of the whitened matrix may be used to generate a seminoise signal 1106 that substantially comprises noise of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.
 a cumulant matrix is determined based upon the whitened matrix by applying a cumulantgenerating function on the whitened matrix.
 the cumulant matrix is a fourth order cumulant matrix.
 the cumulant matrix is a measure of independence of entries in the whitened matrix.
 a rotation matrix may be determined based upon the cumulant matrix. The rotation matrix is determined by substantially removing linear correlation between entries in the cumulant matrix. Particularly, the rotation matrix is determined by removing linear correlation between entries in a first row of the cumulant matrix and entries in a second row of the cumulant matrix. Accordingly, entries in a first row of the rotation matrix and entries in a second row of the rotation matrix are linearly uncorrelated. Determination of a rotation matrix is explained in greater detail with reference to FIG. 13 .
 a unitary matrix is determined by rotating the rotation matrix based upon the rotation matrix and a determined rotation matrix by substantially removing linear dependence between entries in the rotation matrix.
 the resonant matrix is determined by determining a product of the unitary matrix and the whitened matrix.
 the entries in the resonant matrix are linearly uncorrelated and linearly independent.
 the entries in the unitary matrix are linearly uncorrelated.
 entries in a first row of the resonant matrix and entries in a second row of the resonant matrix are linearly uncorrelated and linearly independent.
 the resonant matrix for example is the resonant matrix determined at block 708 in FIG. 7 .
 the resonant matrix comprises the cleaned delta TOAs vectors 712 , and the noise data 710 referred to in FIG. 7 .
 FIG. 12 ( a ) shows a simulated plot 1200 of a resonantfrequency first delta times of arrival vectors signal 1202 corresponding to the blade 12 and the first sensing device 14 .
 the resonantfrequency first delta times of arrival vectors signal 1202 may be the resonantfrequency first delta times of arrival vectors selected from the first delta TOAs 32 at block 702 in FIG. 7 .
 FIG. 12 ( b ) shows a simulated plot 1204 of a resonantfrequency second delta times of arrival vectors signal 1206 corresponding to the blade and the second sensing device 16 .
 the resonantfrequency second delta times of arrival vectors signal 1206 may be the resonantfrequency second delta times of arrival vectors selected from the second delta TOAs 34 at block 704 in FIG. 7 .
 Xaxis 1208 of the plot 1200 is representative of resonantfrequency rotor speeds range of the blade.
 Yaxis 1210 of the plot 1200 is representative of resonantfrequency first delta TOAs 1202 .
 Xaxis 1212 of the plot 1204 is representative of resonantfrequency rotor speeds range of the blade.
 Yaxis 1214 of the plot 1204 is representative of resonantfrequency second delta TOAs 1206 .
 the resonantfrequency first delta times of arrival vectors signal 1202 and the resonantfrequency second delta times of arrival vectors signal 1206 are processed to form a measurement matrix using the method explained in block 706 in FIG. 7 , and in FIG. 10 . Furthermore, a whitened matrix is determined by transforming the measurement matrix. The whitened matrix is used to generate subcleaned resonantfrequency delta TOAs vectors signal 1216 and seminoise signal 1218 shown in FIGS. 12( c ), and 12 ( d ), respectively. The subcleaned resonantfrequency delta TOAs vectors signal 1216 and seminoise signal 1218 are generated using a method explained in block 1102 in FIG. 11 .
 the subcleaned resonantfrequency delta TOAs vectors signal 1216 As shown in the subcleaned resonantfrequency delta TOAs vectors signal 1216 , common observations of the signals 1202 , 1206 (see FIG. 12( a ), FIG. 12( b )) are captured in the subcleaned resonantfrequency delta TOAs vectors signal 1216 . However, still the subcleaned resonantfrequency delta TOAs vectors signal 1216 has minimal remaining noise. Furthermore, as shown in FIG. 12( d ), the noise signal 1218 contains substantial noise of the signals 1202 , 1204 .
 the whitened matrix, or the signals 1216 , 1218 are processed using the blocks 1108  1112 in FIG. 11 to generate a resonance signal 1220 shown in FIG. 12( e ) and a noise signal 1222 shown in FIG. 12( f ).
 the resonance signal 1220 and the noise signal 1222 are generated by using the method explained with reference to block 708 in FIG. 7 and FIG. 11 .
 FIG. 12( e ) common observations of the signals 1202 , 1206 (see FIG. 12( a ), FIG. 12( b )) are captured in the resonance signal 1220 , and the noise signal 1222 has nil or zero noise.
 the noise signal 1222 contains noise of the signals 1202 , 1204 .
 FIG. 13 is a flowchart of a method to generate a whitened matrix 1314 , in accordance with one embodiment of the present techniques.
 FIG. 13 explains block 1102 of FIG. 11 in greater detail.
 FIG. 13 explains block 1110 of FIG. 11 in greater detail.
 Reference numeral 1302 is representative of a tobewhitened matrix.
 the tobewhitened matrix 1302 may be the measurement matrix referred to in block 1102 in FIG. 11 , or the tobe whitened matrix 1302 may be the cumulant matrix referred to in block 1108 in FIG. 11 .
 the whitened matrix 1314 is the whitened matrix referred to in block 1102 of FIG. 11 .
 the whitened matrix is the unitary matrix referred to in block 1110 of FIG. 11 .
 a covariance matrix is generated by determining a covariance of the tobe whitened matrix 1302 .
 an Eigen value matrix and Eigen values are determined by applying an Eigen vector decomposition technique on the covariance matrix.
 a square root of the Eigen values is determined.
 a product matrix is determined by multiplying the Eigen Vector matrix and the square root of the Eigen values.
 the whitened matrix 1314 is determined by multiplying the product matrix and the measurement matrix.
 the present systems and methods monitor the health of rotor blades by identifying resonantfrequency rotor speeds of the rotor blades when the rotor blades, a rotor containing the rotor blades and a device containing the rotor blades, and the rotor are healthy. Furthermore, the present systems and methods determine variations in the resonantfrequency rotor speeds of the rotor blades. The present systems and methods determine presence or absence of cracks in the rotor blades based on the variations in the resonantfrequency of the rotor blades.
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Abstract
A system for monitoring health of a rotor is presented. The system includes a processing subsystem that generates a plurality of frequency peak values corresponding to two or more respective windows of signals by iteratively shifting the two or more respective windows of signals along delta times of arrival signals corresponding to a blade in the rotor, determines one or more resonantfrequency rotor speeds ranges of the blade by identifying rotor speeds corresponding to a subset of the plurality of frequency peak values, and monitors the blade to determine a presence of one or more defects in the blade during the resonantfrequency rotor speeds regions.
Description
 Rotor blades or airfoils are used in many devices with several examples including axial compressors, turbines, engines, or other turbo machinery. For example, an axial compressor has one or more rotors having a series of stages with each stage comprising a row of rotor blades or airfoils followed by a row of static blades or static airfoils. Accordingly, each stage comprises a pair of rotor blades or airfoils and static airfoils. Typically, the rotor blades or airfoils increase the kinetic energy of a fluid that enters the axial compressor through an inlet. Furthermore, the static blades or static airfoils generally convert the increased kinetic energy of the fluid into static pressure through diffusion. Accordingly, the rotor blades or airfoils and static airfoils increase the pressure of the fluid.
 During operation, the rotor blades generally vibrate at synchronous and asynchronous frequencies. For example, while the rotor blades may generally vibrate at the synchronous frequencies due to the rotor speed/frequency, the rotor blades may vibrate at the asynchronous frequencies due to aerodynamic instabilities, such as, rotating stall and flutter. The rotor blades have a natural tendency to vibrate at larger amplitudes at certain synchronous frequencies of the rotor blades. Such synchronous frequencies are referred to as resonant frequencies of the rotor blades. The synchronous frequencies of the rotor blades are typically activated at fixed rotor speeds of the rotors. Furthermore, the activation of the resonant frequencies may increase the amplitudes of vibration of the rotor blades. Such increased amplitudes of vibration may damage the rotor blades or lead to cracks in the rotor blades.
 The rotor blades operate for long hours under extreme and varied operating conditions, such as, high speed, pressure, and temperature that affect the health of the airfoils. In addition to the extreme and varied operating conditions, certain other factors lead to fatigue and stress of the airfoils. The factors, for example, may include inertial forces including centrifugal force, pressure, resonant frequencies of the airfoils, vibrations in the airfoils, vibratory stresses, temperature stresses, reseating of the airfoils, load of the gas or other fluid, or the like. A prolonged increase in stress and fatigue over a period of time damages the rotor blades resulting in defects or cracks in the rotor blades. Such defects, damages, or cracks in the rotor blades may vary the rotor speeds that activate the rotor blades' resonant frequencies. For example, in a healthy rotor blade if resonant frequencies are activated at a rotor speed R, then when the rotor blade has a crack, the resonant frequencies may get activated at a rotor speed of R±r. These variations in rotor speeds that activate the rotor blades' resonant frequencies may, therefore, be useful in monitoring the health of rotor blades.
 Accordingly, it is desirable to determine rotor speeds that activate resonant frequencies of healthy rotor blades. Furthermore it is desirable to determine existence of variations in the rotor speeds that activate resonant frequencies to monitor and assess the health of the rotor blades.
 These and other drawbacks associated with such conventional approaches are addressed here by providing, in various embodiments, a system for monitoring health of a rotor is presented. The system includes a processing subsystem that generates a plurality of frequency peak values corresponding to two or more respective windows of signals by iteratively shifting the two or more respective windows of signals along delta times of arrival signals corresponding to a blade in the rotor, determines one or more resonantfrequency rotor speeds of the blade by identifying rotor speeds corresponding to a subset of the plurality of frequency peak values, and monitors the blade to determine a presence of one or more defects in the blade during the resonantfrequency rotor speeds regions.
 These and other features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying drawings, wherein:

FIG. 1 is a diagrammatic illustration of a blade health monitoring system, in accordance with an embodiment of the present systems; 
FIG. 2 is a flow chart illustrating an exemplary method to identify resonantfrequency rotor speeds regions of the blade based upon delta TOAs, in accordance with certain aspects of the present techniques; 
FIG. 3 is a flow chart illustrating an exemplary method to determine a plurality of frequency peak values by shifting a window of signals along delta TOAs signals, in accordance with one aspect of the present techniques; 
FIG. 4 is a plot of a simulated delta TOAs vector signal, corresponding to a blade in a rotor, to show determination of a plurality of frequency peak values and resultant values; 
FIG. 5 is a simulated plot of a frequency signal to explain determination of a first frequency peak value based upon the frequency signal and the determined synchronous frequency threshold; 
FIG. 6 is a simulated plot of resonantfrequency rotor speed regions of a blade, in accordance with one embodiment of the present techniques; 
FIG. 7 is a flowchart of a method for monitoring health of a rotor, in accordance with one embodiment of the present techniques; 
FIG. 8 is a correlation chart, of an index value and a correlation value that may be used to determine the existence of the crack, or a probability of crack in a blade; 
FIG. 9( a) shows a simulated plot of a historical resonance signal of a blade; 
FIG. 9( b) shows a simulated plot of a resonance signal of a blade; 
FIG. 10 is a flowchart of a method to generate a measurement matrix based upon a resonantfrequency first delta TOAs and a resonantfrequency second delta TOAs, in accordance with one embodiment of the present techniques; 
FIG. 11 is a flowchart of a method to generate a resonant matrix based upon a measurement matrix, in accordance with one embodiment of the present techniques; 
FIG. 12 (a) shows a simulated plot of a resonantfrequency first delta times of arrival vectors signal corresponding to a blade and a first sensing device; 
FIG. 12 (b) shows a simulated plot of a resonantfrequency second delta times of arrival vectors signal corresponding to a blade and a second sensing device; 
FIG. 12 (c) shows a simulated plot of a subcleaned resonantfrequency delta TOAs vectors signal generated using a row of a whitened matrix; 
FIG. 12 (d) shows a simulated plot of a seminoise signal generated using another row of the whitened matrix referred to inFIG. 12( c); 
FIG. 12 (e) shows a simulated plot of a resonance signal; 
FIG. 12 (f) shows a simulated plot of a noise signal; and 
FIG. 13 is a flowchart of a method to generate a whitened matrix, in accordance with one embodiment of the present techniques.  When introducing elements of various embodiments of the present invention, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.
 Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it may be about related. Accordingly, a value modified by a term such as “about” is not limited to the precise value specified. In some instances, the approximating language may correspond to the precision of an instrument for measuring the value.
 As used herein, the term “expected time of arrival (TOA)” may be used to refer to a TOA of a blade, during rotation, at a reference position when there are no defects or cracks in the blade and the blade is working in an ideal situation, load conditions are optimal, and the vibrations in the blade are minimal. As used herein, the term “resonantfrequency rotor speeds” refers to speeds, of a rotor of a device, that result in activation of one or more resonant frequencies of blades in the rotor.
 In operation, natural frequencies or resonant frequencies of blades in a rotor get activated at certain rotor speeds of a rotor in a device, such as an axial compressor. Hereinafter the phrase “speeds of the rotor that result in activation of the resonantfrequencies of the blades” are referred to as resonantfrequency rotor speeds. As discussed in detail below, the present systems and methods identify resonantfrequency rotor speeds of the blades based upon times of arrival (TOAs) (hereinafter referred to as actual TOAs) of the blades at a reference position in the rotor. One or more cracks in the blades may vary the resonantfrequency rotor speeds of the blades. A technical effect of the present system and method according to one embodiment is to determine one or more variations in the resonantfrequency rotor speeds, and determine existence of cracks or probability of existence of cracks in the blades based upon the variations. This technical effect provides for enhanced maintenance prognostics and a lower percentage of unplanned downtime.

FIG. 1 is a diagrammatic illustration of a bladehealth monitoring system 10, in accordance with an embodiment of the present system. As shown inFIG. 1 , thesystem 10 includes one or more blades or airfoils, in arotor 11, that are monitored by thesystem 10 to determine existence of cracks or probability of existence of cracks in the blades. It is noted thatFIG. 1 shows a portion of therotor 11. Therotor 11, for example may be a component of device, such as, a compressor, an axial compressor, a land based gas turbine, or the like. Therotor 11, for example includes ablade 12. For ease of understanding, the present systems and techniques are explained with reference to theblade 12, however, the present systems and techniques are applicable to each of the blades in therotor 11. As shown in the presently contemplated configuration, thesystem 10 includes one ormore sensors blade 12 at a reference point to generate blade passingsignals BPS blade 12 at the reference point. Hereinafter, the phrase “TOAs of a blade at a reference point” are referred to as actual TOAs. For example, thefirst sensing device 14 generates thefirst BPS 18 representative of firstactual TOAs 24 of theblade 12 at the reference point. For example, thesecond sensing device 16 generates thesecond BPS 20 representative of secondactual TOAs 26 of theblade 12 at the reference point. The reference point, for example, may be underneath thesensors sensors BPS rotor 11, a steady state of therotor 11, overspeed state of therotor 11, or combinations thereof.  In one embodiment, the
sensors blade 12 to generate theBPS sensors blade 12 to generate theBPS sensor 14 may sense an arrival of the leading edge of theblade 12 to generate theBPS 18, and thesensor 16 may sense an arrival of the trailing edge of theblade 12 to generate theBPS 20, or vice versa. Thesensors blade 12 on a stationary object in a position such that an arrival of theblade 12 may be sensed efficiently. In one embodiment, at least one of thesensors sensors  As illustrated in the presently contemplated configuration, the
BPS processing subsystem 22. Theprocessing subsystem 22 determines the first actual TOAs 24 and the secondactual TOAs 26 of theblade 12 based upon theBPS processing subsystem 22 determines the firstactual TOAs 24 based upon thefirst BPS 18, and theprocessing subsystem 22 determines the secondactual TOAs 26 based upon thesecond BPS 20. In certain embodiments, theprocessing subsystem 22 preprocesses the first actual TOAs 24 and the secondactual TOAs 26 to remove noise and asynchronous frequencies from the first actual TOAs 24 and the second actual TOAs 26. Theprocessing subsystem 22, for example, may preprocess the first actual TOAs 24 and the secondactual TOAs 26 by applying at least one of a smoothening filtering technique and a median filtering technique on the first actual TOAs 24 and the second actual TOAs 26. In one example, theprocessing subsystem 22 includes at least one processor that is coupled to memory and a communications section. The information such as sensor data can be communicated by wired or wireless mechanisms via the communications section and stored in memory for the subsequent processing. The memory in one example can also include the executable programs and associated files to run the application.  Furthermore, the
processing subsystem 22 monitors the health of theblade 12 based upon the first actual TOAs 24 and the second actual TOAs 26. Theprocessing subsystem 22 determines first delta TOAs 28, corresponding to theblade 12 and corresponding to thefirst sensing device 14, based upon the first actual TOAs 24 and an expected TOA of theblade 12. Additionally, theprocessing subsystem 22 determines second delta TOAs 30, corresponding to theblade 12 and the corresponding to thesecond sensing device 16, based upon the second actual TOAs 26 and the expected TOA of theblade 12. The first delta TOAs 28 correspond to thefirst sensing device 14 as the first delta TOAs are determined based upon the firstactual TOAs 24 determined based upon thefirst BPS 18 generated by thefirst sensing device 14. The second delta TOAs 30 correspond to thesecond sensing device 16 as the second delta TOAs 30 are determined based upon the secondactual TOAs 26 determined based upon thesecond BPS 20 generated by thesecond sensing device 16.  The first delta TOAs 28 or the second delta TOAs 30 may be determined using the following equation (1):

DeltaTOA=ActualTOA−ExpectedTOA (1)  In one embodiment, the first delta TOAs 28 may be represented as first
delta TOAs vectors 32 by mapping the first delta TOAs 28 to corresponding rotor speeds of therotor 11. In another embodiment, the second delta TOAs may be represented as seconddelta TOAs vectors 34 by mapping the second delta TOAs 30 to corresponding rotor speeds of therotor 11. For example, if a first actual TOA is generated based upon a BPS generated at a time stamp T_{1 }when the rotor speed is R_{1}, then a first delta TOA is determined based upon the first actual TOA; and the first delta TOA is represented as a first delta TOA vector by mapping the first delta TOA to the rotor speed R_{1}. Hereinafter, the phrase “first delta TOAs” and “first delta TOAs signal” are interchangeably used as first delta TOAs are digital representation of the analog first delta TOAs signal. Furthermore, the phrase “second delta TOAs” and “second delta TOAs signal” are interchangeably used as second delta TOAs are digital representation of the analog second delta TOAs signal. Additionally, the phrase “first delta TOAs vectors” and “first delta TOAs vectors signal” are interchangeably used as first delta TOAs vectors are digital representation of the analog first delta TOAs vectors signal. Additionally, the phrase “second delta TOAs vectors” and “second delta TOAs vectors signal” are interchangeably used as the second delta TOAs vectors are digital representation of the analog first delta TOAs vectors signal.  It is noted that the
rotor 11 operates at multiple rotor speeds. A subset of the rotor speeds activates the resonant frequencies of the blades in therotor 11. The ‘rotor speeds of the rotor that activate the resonant frequencies of the blades’ are hereinafter referred to as resonantfrequency rotor speeds. It is noted that the resonantfrequency rotor speeds of blades in a rotor may be different from resonantfrequency rotor speeds of blades in another rotor. Furthermore, it is noted that the resonantfrequency rotor speeds of a blade in therotor 11 may be different from resonant frequency rotor speeds of another blade in therotor 11.  In the embodiment of
FIG. 1 , theprocessing subsystem 22 extracts resonantfrequency first delta TOAs/resonantfrequency first delta TOAs vectors from the first delta TOAs 28/firstdelta TOAs vectors 32, respectively. The resonantfrequency first delta TOAs/resonantfrequency first delta TOAs vectors are a subset of the first delta TOAs 28/firstdelta TOAs vectors 32, respectively. Additionally, theprocessing subsystem 22 extracts resonantfrequency second delta TOAs/resonantfrequency second delta TOAs vectors from the second delta TOAs 30/the seconddelta TOAs vectors 34, respectively. The resonantfrequency second delta TOAs/resonantfrequency second delta TOAs vectors are a subset of the second delta TOAs 30/the seconddelta TOAs vectors 34, respectively. In one embodiment, theprocessing subsystem 22 determines resonantfrequency rotor speeds of theblade 12 based upon the resonantfrequency first delta TOAs and the resonantfrequency second delta TOAs. In another embodiment, theprocessing subsystem 22 determines resonantfrequency rotor speeds of theblade 12 based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.  Additionally, the
processing subsystem 22 determines existence of any variations in the resonantfrequency rotor speeds with respect to historical resonantfrequency rotor speeds to determine the existence of a crack in theblade 12 or a probability of existence of a crack in theblade 12. When theprocessing subsystem 22 determines that one or more variations exist in the resonantfrequency rotor speeds of theblade 12, theprocessing subsystem 22 determines that a crack in theblade 12 exists, or determines that a probability of crack in theblade 12 exists. The determination of crack in theblade 12 is explained in greater detail with reference toFIG. 7 . 
FIG. 2 is a flow chart illustrating anexemplary method 200 to identify resonantfrequencyrotor speed regions 220 of theblade 12 based upondelta TOAs 220, in accordance with certain aspects of the present techniques. The resonantfrequencyrotor speed regions 220 are broad ranges of rotor speeds of theblade 12 that result in activation of one or more resonant frequencies of theblade 12. For example, resonant frequencies of theblade 12 may get activated at rotor speeds in the range of 1200 rotations per minute to 1400 rotation per minute, therefore 1200 rotations per minute to 1400 rotation per minute is a resonantfrequency rotor speed range of the blade. 
Reference numeral 202 is representative of delta TOAs corresponding to theblade 12. The delta TOAs 202 are determined based upon actual TOAs generated by thefirst sensing device 14 or thesecond sensing device 16 when there are no defects or cracks in theblade 12; theblade 12 and therotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in theblade 12 are minimal. In one embodiment, thedelta TOAs 202 may be the first delta TOAs 28 (seeFIG. 1 ) if the firstactual TOAs 24 are generated by thefirst sensing device 14 when there are no defects or cracks in theblade 12; theblade 12 and therotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in theblade 12 are minimal. In another embodiment, thedelta TOAs 202 may be the second delta TOAs 30 (seeFIG. 1 ) if the secondactual TOAs 26 are generated by thesecond sensing device 16 when there are no defects or cracks in theblade 12; theblade 12 and therotor 11 are working in an ideal situation, load conditions are optimal, and the vibrations in theblade 12 are minimal. In one embodiment, the delta TOAs signals 202 may be represented as delta TOAs vector signals by mapping the delta TOAs signals 202 to respective rotor speeds. An exemplary delta TOAs vector signal is shown inFIG. 3 . In the embodiment ofFIG. 2 , each block of themethod 200 is executed by theprocessing subsystem 22 ofFIG. 1 .  At
block 204, a first window of signals and a second window of signals are selected. The first window of signals and the second window of signals are rotor speed bands. Additionally, each of the first window of signals and second window of signals has a respective width. For example, in the embodiment ofFIG. 2 , the first window of signals is a rotor speed band of 25 rotations per minute, and a width of the first window of signals is 25 rotations per minute. Again in the embodiment ofFIG. 2 , the second window of signals is a rotor speed band of 50 rotations per minute, and a width of the second window of signals is 50 rotations per minute. The width of the second window of signals is greater than the width of the first window of signals.  At
block 206, a plurality of first frequency peak values are generated by iteratively shifting the first window of signals along the delta TOAs signal 202. Atblock 208, a plurality of second frequency peak values are generated by iteratively shifting the second window of signals along the delta TOAs signal 202. Determination of the first frequency peak values and the second frequency peak values are explained in greater detail with reference toFIG. 3 andFIG. 4 .  At
block 210, a plurality of resultant values are determined based upon the first frequency peak values and the second frequency peak values. Particularly, a resultant value is determined by subtracting a second frequency peak value from a respective first frequency peak value. A resultant value, for example, may be determined using the following equation (2): 
RV=First_Frequnecy_Peak_Value−Second_Frequnecy_Peak_Value (2)  where RV is a resultant value.
 At
block 212, a check is carried out to determine whether the resultant values are less than a determined value. Atblock 212, when the resultant values are less than the determined value, the control is transferred to block 214. Atblock 214, rotor speeds corresponding to the second frequency peak values are determined. A local maxima of the rotor speeds corresponding to the second frequency peak values are determined as the resonantfrequencyrotor speeds regions 220, when the resultant values are less than the determined value. For example, when a rotor speed corresponding to a second frequency peak value is 1200 rotation per minute, then a local maxima of 1200±50 is determined as a resonantfrequency rotor speed region.  However, with returning reference to block 212, when the resultant values are not less than the determined value, the control is transferred to block 216. At
block 216, a subsequent window of signals is selected. A width of the subsequent window of signals is greater than the width of the first window of signals and the width of the second window of signals. For example, by way of a nonlimiting example, the width of the subsequent window of signals may be 75 rotations per minute or greater than 75 rotations per minute. Furthermore, atblock 218, a plurality of subsequent frequency peak values are determined by iteratively shifting the subsequent window of signals along thedelta TOAs 202. The determination of the subsequent frequency peak values by iteratively shifting the subsequent window of signals along the delta TOAs signal 202 is explained with reference toFIG. 3 andFIG. 4 . Furthermore, the control is transferred to block 210. Atblock 210, a plurality of subsequent resultant values are determined based upon the subsequent frequency peak values and previous frequency peak values. In one embodiment, the previous frequency peak values are the second frequency peak values. Again atblock 212, a check is carried out to determine whether one or more of the subsequent resultant values are less than the determined value. When atblock 212, the subsequent resultant values are not less than the determined value, blocks 216 to 212 are executed again. However atblock 212, when the subsequent resultant values are less than the determined value, the control is transferred to block 214. Atblock 214, a local maxima of each of the rotor speeds corresponding to the subsequent frequency peak values is identified as the resonantfrequency rotor speedsregion 220. For example, if r is a rotor speed corresponding to a subsequent frequency peak value, then r+50 may be selected as a resonantfrequency rotor speed region.FIG. 6 shows simulated resonantfrequency speed regions of a blade identified by using a process described with reference toFIG. 2 . 
FIG. 3 is a flow chart illustrating anexemplary method 300 to determine a plurality of frequency peak values 310 by shifting a window ofsignals 302 along the first delta TOAs signals 202 referred to inFIG. 1 , in accordance with one aspect of the present techniques. Particularly,FIG. 3 explainsblocks FIG. 2 in greater detail. The plurality of frequency peak values 310, for example, may be the first frequency peak values when the window ofsignals 302 is the first window of signals referred to inFIG. 2 . Similarly, the plurality of frequency peak values 310 may be the second frequency peak values when the window ofsignals 302 is the second window of signals referred to inFIG. 2 . Again, the plurality of frequency peak values 310 may be the subsequent frequency peak values when the window ofsignals 302 is the subsequent window of signals. (SeeFIG. 2 ).  At
block 304, the window ofsignals 302 is placed on thedelta TOAs 202, and a first subset of thedelta TOAs 202 contained or covered by the window ofsignal 302 is selected. Furthermore, atblock 306, a frequency peak value is generated based upon the first subset of the delta TOAs signal 202. For example, the frequency peak value is generated by determining a frequency signal by taking a fast Fourier transform of the first subset of the delta TOAs signal 202, and selecting the frequency peak value from the frequency signal, wherein the frequency peak value is equal to or less than a determined synchronous frequency threshold. As used herein, the term “determined synchronous frequency threshold” is a numerical frequency value selected such that frequencies, greater than the determined synchronous frequency threshold, substantially are asynchronous frequencies; and frequencies, equal to or less than the determined synchronous frequency threshold, substantially are synchronous frequencies. By way of a nonlimiting example, the magnitude of the determined synchronous frequency threshold may be about 2 Hertz. Determination of the frequency peak value is explained in greater detail with reference toFIG. 5 .  Furthermore, at
block 308, the frequency peak value is added to the plurality of frequency peak values 310, and the control is transferred to block 312. Atblock 312, a check is carried out to determine whether the window ofsignals 302 has been shifted a determined number of times along the delta times ofsignals 202. While inFIG. 3 , a check is carried out to determine whether the window ofsignals 302 has been shifted a determined number of times, in certain embodiment a check may be carried out to determine whether the window ofsignals 302 has been shifted across the delta times ofarrival 202. Atblock 312, when it is determined that the window ofsignals 302 has not been shifted, along the first delta TOAs signal 202, a determined number of times; the control is transferred to block 314. Atblock 314, a shifted window is determined by shifting the window ofsignals 302 along the delta TOAs signal 202 by a determined rotor speed band. Furthermore, atblock 316, a subsequent subset of the delta TOAs signal 202, contained or covered by the shifted window of signals is selected. Atblock 318, a subsequent frequency peak value based upon the subsequent subset of the delta TOAs signal 202 is determined. The subsequent frequency peak value, for example, is generated by taking a fast Fourier transform of the subsequent subset of the first delta TOAs signal 202 to generate a corresponding frequency signal, followed by selecting the subsequent frequency peak value from the frequency signal, wherein the subsequent frequency peak value is equal to or less than the determined synchronous frequency threshold. The control from theblock 318 is transferred to block 308. Atblock 308, the subsequent frequency peak value is added to the plurality of frequency peak values 310. Subsequently, atblock 312, the check is carried out to determine whether the window ofsignals 302 has been shifted, a determined number of times, along the delta TOAs signal 202. Atblock 312, when it is determined that the window ofsignals 302 has been shifted the determined number of times, the plurality of frequency peak values 310 are determined. 
FIG. 4 is aplot 400 of a simulated deltaTOAs vector signal 402, corresponding to a blade in a rotor, to show determination of a plurality of frequency peak values and resultant values. In one embodiment,FIG. 4 explainssteps FIG. 2 in greater detail. Furthermore,FIG. 4 explainsstep 210 ofFIG. 2 . Additionally,FIG. 4 explainsstep 306 ofFIG. 3 in greater detail. The simulated deltaTOAs vector signal 402 is generated by mapping delta TOAs, of a blade in a rotor, to respective rotor speeds. In one embodiment, the deltaTOAs vector signal 402 may be the first delta TOAs vector signal 32 (seeFIG. 1 ). In another embodiment, the deltaTOAs vector signal 402 may be the second delta TOAs vector signal 34 (seeFIG. 1 ). 
Xaxis 406 of theplot 400 represents rotor speeds of the rotor, and Yaxis 408 of theplot 400 represents delta TOAs corresponding to the blade.Reference numeral 410 is representative of a first window of signals having a width W_{1}, andreference numeral 412 is representative of a second window of signals having a width W_{2}. The first window ofsignals 410 selects a first subset of the deltaTOAs vector signal 402 contained or covered by the first window ofsignals 410. As shown inFIG. 4 , the first subset of the deltaTOAs vector signal 402 starts at apoint 414 and ends at apoint 416. Furthermore, afrequency signal 502 shown inFIG. 5 is generated based upon the first subset of the deltaTOAs vector signal 402. Thefrequency signal 502 is determined by taking a Fourier transform or a Fast Fourier transform of the first subset of the delta TOAs vectors signal 402. Furthermore, a first frequency peak value 508 (shown inFIG. 5 ), corresponding to the first window ofsignals 410 and the first subset of the delta TOAs vectors signal 402, is determined based upon thefrequency signal 502 and a determined synchronous frequency threshold 510 (shown inFIG. 5 ). The determination of the first frequency peak value, corresponding to the first window and the first subset of the delta TOAs, is explained in greater detail with reference toFIG. 5 .  The second window of
signals 412 selects a second subset of the deltaTOAs vector signal 402 contained or covered by the second window ofsignals 412. As shown inFIG. 4 , the second subset of the deltaTOAs vector signal 402 starts at apoint 418 and ends at apoint 420. Furthermore, a frequency signal is generated based upon the second subset of the deltaTOAs vector signal 402. The frequency signal is determined by taking a Fourier transform or a Fast Fourier transform of the second subset of the delta TOAs vector signal. Furthermore, a second frequency peak value, corresponding to the second window ofsignals 412 and the second subset of the delta TOAs, is determined based upon the frequency signal and a determined synchronous frequency threshold. The second frequency peak value, for example, may be determined using the method explained with reference toFIG. 5 . Furthermore, a first resultant value is determined by subtracting the second frequency peak value from the first frequency peak value.  Subsequently, the first window of
signals 410 is shifted by a rotor speed band SB_{1 }to generate a shifted first window SW_{1}, and thesecond window 412 is shifted by the rotor speed band SB_{1 }to generate a shifted second window of signals SW_{2}. Again subsequent first frequency peak value, corresponding to the shifted first window of signals SW_{1}, is determined based upon a subset of the deltaTOAs vector signal 402 covered by the shifted first window of signals SW_{1}. Additionally, subsequent second frequency peak value, corresponding to the shifted second window of signals SW_{2}, is determined based upon a subset of the deltaTOAs vector signal 402 covered by the shifted second window of signals SW_{2}. Furthermore, a second resultant value is determined by subtracting the subsequent second frequency peak value from the subsequent first frequency peak value.  The first window of
signals 410 and the second window ofsignals 412 are shifted unless the deltaTOAs vector signal 402 is traversed completely. Furthermore, a plurality of first frequency peak values, a plurality of second frequency peak values, and a plurality of resultant values are determined by shifting the first window ofsignals 410, and the second window ofsignals 412. The plurality of first frequency peak values includes the first frequency peak value, and the subsequent first frequency peak. The plurality of second frequency peak values includes the second frequency peak value, and the subsequent second frequency peak. Furthermore, the plurality of resultant values includes the first resultant value and the second resultant value. 
FIG. 5 is aplot 500 of thefrequency signal 502 referred to inFIG. 4 to explain determination of the firstfrequency peak value 508 based upon thefrequency signal 502 and a determinedsynchronous frequency threshold 510.Xaxis 504 of theplot 500 represents frequency of the first subset of the deltaTOAs vector signal 402, and Yaxis 506 of theplot 500 represents amplitude of the frequency. The firstfrequency peak value 508, for example, is determined by theprocessing subsystem 22 referred to inFIG. 1 . Theprocessing subsystem 22 selects frequencies that are less than the determinedsynchronous frequency threshold 510. The selected frequencies are synchronous frequencies. It is noted that selection of the frequencies, that are less than the determinedsynchronous frequency threshold 510, from thefrequency signal 502 results in selection of synchronous frequencies from thefrequency signal 502. Furthermore, a frequency that has the highest amplitude is selected from the synchronous frequencies or the selected frequencies. In the embodiment ofFIG. 5 , afrequency 512 has thehighest amplitude 508. Thehighest amplitude 508 is determined as the firstfrequency peak value 508. 
FIG. 6 is asimulated plot 600 of resonantfrequencyrotor speed regions FIG. 2 . Xaxis 606 is representative of rotor speeds of a rotor, and Yaxis is representative of frequency peak values. The frequency peak values may be the second frequency peak values determined at theblock 208 inFIG. 2 , or the subsequent frequency peak values determined at theblock 218 referred to inFIG. 2 . As shown inFIG. 6 , two resonantfrequencyrotor speed regions 
FIG. 7 is a flowchart of amethod 700 for monitoring health of theblade 12 referred to inFIG. 1 , in accordance with one embodiment of the present techniques.Reference numeral 220 is representative of the resonantfrequency rotor speeds regions of theblade 12 in the rotor 11 (seeFIG. 2 ).Reference numeral 32 is representative of the first delta TOAs vectors determined by theprocessing subsystem 22 inFIG. 1 . Furthermore,reference numeral 34 is representative of the second delta TOAs vectors determined by theprocessing subsystem 22 inFIG. 1 . Atblock 702, resonantfrequency first delta TOAs vectors are selected from the firstdelta TOAs vectors 32. As used herein, the phrase “resonantfrequency first delta TOAs vectors” are used to refer to a subset of the firstdelta TOAs vectors 32, wherein the subset corresponds to resonantfrequency rotor speeds regions of theblade 12. Atblock 704, resonantfrequency second deltas TOAs vectors are selected from the seconddelta TOAs vectors 34. As used herein, the phrase “resonantfrequency second delta TOAs vectors” are used to refer to a subset of the seconddelta TOAs vectors 34, wherein the subset corresponds to resonantfrequency rotor speeds regions of theblade 12.  Furthermore, at
block 706, a measurement matrix is generated based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors. The measurement matrix, for example may be generated by arranging the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors to generate an initial matrix, and detrending the initial matrix to generate the measurement matrix. The initial matrix, for example, may be detrended using one or more techniques including a polynomial curve fitting technique, or a wavelet based curve fitting technique. Furthermore, generation of the measurement matrix is explained in greater detail with reference toFIG. 10 .  At
block 708, a resonant matrix is generated based upon the measurement matrix such that entries in the resonant matrix are substantially linearly uncorrelated and linearly independent. The resonant matrix, for example, may be determined by applying at least one technique on the measurement matrix, wherein the at least one technique comprises a whitening technique, a cumulant matrix estimation technique, and a matrix rotation technique.  The resonant matrix comprises cleaned resonantfrequency
delta TOAs vectors 712 andnoise data 710. Particularly, a row of the resonant matrix comprises the resonantfrequencydelta TOAs vectors 712, and another row of the resonant matrix comprises thenoise data 714. The cleaned resonantfrequency deltaTOAs vector signal 712 includes common observations or measurements of thefirst sensing device 14 and thesecond sensing device 16 after removal of noise from the resonantfrequency first delta TOAs vectors signal and the resonantfrequency second delta TOAs vectors signal. For ease of understanding, the term “cleaned resonantfrequency delta TOAs vectors” will be referred to as a resonance signal. Furthermore, thenoise signal 710 includes noise of the resonantfrequency first delta TOAs vectors signal and the resonantfrequency second delta TOAs vectors signal. For ease of understanding, the “cleaned resonantfrequency delta TOAs vectors signal 712” are interchangeably referred to asresonance signal 712. An example of a resonance signal using the method ofFIG. 7 is shown inFIG. 9( a) andFIG. 12( e). An example of a noise signal using the method ofFIG. 7 is shown inFIG. 12( f). 
Reference numeral 714 is representative of historical resonance signals, of theblade 12, generated when there are no defects or cracks in theblade 12, and theblade 12 is working in an ideal situation, load conditions are optimal, and the vibrations in theblade 12 are minimal. The historical resonance signals 714 show historical resonantfrequency rotor speeds of theblade 12 mapped to historical cleaned delta TOAs of theblade 12 when there are no defects or cracks in theblade 12.  At
block 716, it is determined whether a variation exists in the resonantfrequency rotor speeds of theblade 12 with respect to historical resonantfrequency rotor speeds of theblade 12. For example, the variation in resonantfrequency rotor speeds of theblade 12 with respect to historical resonantfrequency rotor speeds of theblade 12 is determined by applying a correlation function to theresonance signal 712 and the historical resonance signals 714. The application of the correlation function results in determination of an index value and a correlation value. As used herein, the term “correlation value” is a measurement of a correlation or similarity between a resonance signal and a historical resonance signal. As used herein, the term “index value” is a measurement of a phase shift between a resonance signal and a historical resonance signal. Higher the correlation value, higher is the similarity between theresonance signal 712 and the historical resonance signals 714. Again higher the index value, higher is a phase shift in theresonance signal 712 with respect to the historical resonance signals 714. Accordingly, the correlation value and the index value may be used to determine the variation in theresonance signal 712 with respect to the historical resonance signals 714.  Furthermore, at
block 718, a presence of crack, an absence of crack or a probability of crack may be determined based upon the variation in theresonance signal 712 with respect to the historical resonance signals 714. For example, when a variation exists in theresonance signal 712 with respect to the historical resonance signals 714, it may be determined that a crack exists in theblade 12. In one embodiment, the presence of crack, the absence of crack or the probability of crack may be determined based upon the index value, the correlation value, and a correlation chart. Determination of the presence of crack, the absence of crack, or the probability of crack based upon the index value, the correlation value and the correlation chart is shown inFIG. 8 . 
FIG. 8 shows acorrelation chart 800 that may be used to determine a presence of crack, an absence of crack or a probability of crack in theblade 12, in accordance with one embodiment of the present techniques. In one embodiment,FIG. 8 explainsstep 718 ofFIG. 7 . Thecorrelation chart 800 comprises four quadrants including afirst quadrant 802, asecond quadrant 804, athird quadrant 806, and afourth quadrant 808. Thefirst quadrant 802 represents low index value and high correlation value. Thesecond quadrant 804 represents high index value and high correlation value. Thethird quadrant 806 represents high index value and low correlation value. Furthermore, thefourth quadrant 808 represents low index value and low correlation value.  The index value and the correlation value determined at the
block 716 inFIG. 7 are positioned in thecorrelation chart 800 to determine the existence of the crack or a probability of existence of the crack in theblade 12. For example, when the index value and the correlation value fall in thefirst quadrant 802 of thecorrelation chart 800, it may be determined that no cracks exist in theblade 12. Furthermore, when the index value and the correlation value, determined at theblock 716, fall in thesecond quadrant 804 of thecorrelation chart 800, it may be determined that one or more cracks exist in theblade 12. Additionally, when the index value and the correlation value, determined at theblock 716, fall in thethird quadrant 806 of thecorrelation chart 800, it may be determined that a probability of existence of a crack exist in theblade 12. Additionally, when the index value and the correlation value, determined at theblock 716, fall in thefourth quadrant 808 of thecorrelation chart 800, it may be determined that a probability of existence of a crack exist in theblade 12. 
FIG. 9( a) shows asimulated plot 900 of ahistorical resonance signal 902 of a blade, andFIG. 9( b) shows asimulated plot 904 of aresonance signal 906, of the blade, generated using the method explained inFIG. 7 .Xaxis 908 of theplot axis 910 of theplot historical resonance signal 902 inFIG. 9( a), when the blade is healthy without cracks and vibrations, the resonance frequency of the blade is activated at a resonantfrequency rotor speed 912. However, as is evident from theresonance signal 906, the resonant frequencies of the blade are activated at a shifted resonantfrequency rotor speed 914. Accordingly, due to the variation or the shift in the resonantfrequency rotor speed 912 of the blade shown by thehistorical resonance signal 902, it may be determined that the blade has a crack. 
FIG. 10 is a flowchart of amethod 1000 to generate a measurement matrix based upon resonantfrequency first delta TOAs and resonantfrequency second delta TOAs, in accordance with one embodiment of the present techniques. In one embodiment,FIG. 10 explainsblock 706 ofFIG. 7 in greater detail. The resonantfrequency first delta TOAs are selected from the first delta TOAs 32 at theblock 702 inFIG. 7 . Furthermore, the resonantfrequency second delta TOAs are selected from the second delta TOAs 34 atblock 704 inFIG. 7 . Atblock 1002, an initial matrix is generated based upon the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs. In one embodiment, if LE_{1 }is representative the resonantfrequency first delta TOAs vectors, and LE_{2 }is representative of the resonantfrequency second delta TOAs vectors, then the initial matrix I may be represented as follows: 
$\begin{array}{cc}I={\left[\begin{array}{c}{\mathrm{LE}}_{1}\\ {\mathrm{LE}}_{2}\end{array}\right]}_{2*n}& \left(3\right)\end{array}$  Furthermore, at
block 1004, a measurement matrix may be generated by detrending the initial matrix I. The initial matrix, for example, may be detrended by applying at least one technique on the initial matrix I. The technique, for example includes a polynomial curve fitting, a wavelet based curve fitting, or combinations thereof. 
FIG. 11 is a flowchart of amethod 1100 to generate a resonant matrix based upon a measurement matrix, in accordance with one embodiment of the present techniques. In one embodiment,FIG. 11 explainsstep 708 inFIG. 7 . Atblock 1102, a whitened matrix is determined based upon the measurement matrix. The whitened matrix is determined by substantially removing linear correlation between entries in the measurement matrix. Particularly, the whitened matrix is determined by substantially removing linear correlation between entries in a first row of the measurement matrix and entries in a second row of the measurement matrix. Accordingly, entries in a first row of the whitened matrix and entries in a second row of the whitened matrix are linearly uncorrelated. It is noted that two signals ‘x’ and ‘y’, or two entries ‘x’ and ‘y’ are linearly uncorrelated when E{xy^{T}}=0, where ‘E’ is the expectation or mean and xy^{T} _{1 }is correlation operation. Determination of a whitened matrix by transforming the measurement matrix to the whitened matrix is explained in greater detail with reference toFIG. 13 . In one embodiment, the whitened matrix comprises two rows, wherein a first row substantially comprises common observations/components of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors, and a second row substantially comprises noise of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors. Accordingly, the first row of the whitened matrix may be used to generate a subcleaned resonant frequency delta TOAs vectors signal 1104 that substantially comprises common observations/components of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors. Furthermore, the second row of the whitened matrix may be used to generate aseminoise signal 1106 that substantially comprises noise of the resonantfrequency first delta TOAs vectors and the resonantfrequency second delta TOAs vectors.  Furthermore, at
block 1108, a cumulant matrix is determined based upon the whitened matrix by applying a cumulantgenerating function on the whitened matrix. In one embodiment, the cumulant matrix is a fourth order cumulant matrix. In one embodiment, the cumulant matrix is a measure of independence of entries in the whitened matrix. Atblock 1110, a rotation matrix may be determined based upon the cumulant matrix. The rotation matrix is determined by substantially removing linear correlation between entries in the cumulant matrix. Particularly, the rotation matrix is determined by removing linear correlation between entries in a first row of the cumulant matrix and entries in a second row of the cumulant matrix. Accordingly, entries in a first row of the rotation matrix and entries in a second row of the rotation matrix are linearly uncorrelated. Determination of a rotation matrix is explained in greater detail with reference toFIG. 13 .  At
block 1112, a unitary matrix is determined by rotating the rotation matrix based upon the rotation matrix and a determined rotation matrix by substantially removing linear dependence between entries in the rotation matrix. Atblock 1114, the resonant matrix is determined by determining a product of the unitary matrix and the whitened matrix. The entries in the resonant matrix are linearly uncorrelated and linearly independent. Furthermore, the entries in the unitary matrix are linearly uncorrelated. In one embodiment, entries in a first row of the resonant matrix and entries in a second row of the resonant matrix are linearly uncorrelated and linearly independent. The resonant matrix, for example is the resonant matrix determined atblock 708 inFIG. 7 . The resonant matrix comprises the cleaneddelta TOAs vectors 712, and thenoise data 710 referred to inFIG. 7 . 
FIG. 12 (a) shows asimulated plot 1200 of a resonantfrequency first delta times of arrival vectors signal 1202 corresponding to theblade 12 and thefirst sensing device 14. The resonantfrequency first delta times of arrival vectors signal 1202, for example, may be the resonantfrequency first delta times of arrival vectors selected from the first delta TOAs 32 atblock 702 inFIG. 7 . Additionally,FIG. 12 (b) shows asimulated plot 1204 of a resonantfrequency second delta times of arrival vectors signal 1206 corresponding to the blade and thesecond sensing device 16. The resonantfrequency second delta times of arrival vectors signal 1206, for example, may be the resonantfrequency second delta times of arrival vectors selected from the second delta TOAs 34 atblock 704 inFIG. 7 .Xaxis 1208 of theplot 1200 is representative of resonantfrequency rotor speeds range of the blade. Yaxis 1210 of theplot 1200 is representative of resonantfrequencyfirst delta TOAs 1202. Similarly,Xaxis 1212 of theplot 1204 is representative of resonantfrequency rotor speeds range of the blade. Yaxis 1214 of theplot 1204 is representative of resonantfrequencysecond delta TOAs 1206.  The resonantfrequency first delta times of arrival vectors signal 1202 and the resonantfrequency second delta times of arrival vectors signal 1206 are processed to form a measurement matrix using the method explained in
block 706 inFIG. 7 , and inFIG. 10 . Furthermore, a whitened matrix is determined by transforming the measurement matrix. The whitened matrix is used to generate subcleaned resonantfrequency delta TOAs vectors signal 1216 andseminoise signal 1218 shown inFIGS. 12( c), and 12(d), respectively. The subcleaned resonantfrequency delta TOAs vectors signal 1216 andseminoise signal 1218 are generated using a method explained inblock 1102 inFIG. 11 . As shown in the subcleaned resonantfrequency delta TOAs vectors signal 1216, common observations of thesignals 1202, 1206 (seeFIG. 12( a),FIG. 12( b)) are captured in the subcleaned resonantfrequency delta TOAs vectors signal 1216. However, still the subcleaned resonantfrequency delta TOAs vectors signal 1216 has minimal remaining noise. Furthermore, as shown inFIG. 12( d), thenoise signal 1218 contains substantial noise of thesignals  Furthermore, the whitened matrix, or the
signals FIG. 11 to generate aresonance signal 1220 shown inFIG. 12( e) and anoise signal 1222 shown inFIG. 12( f). Theresonance signal 1220 and thenoise signal 1222 are generated by using the method explained with reference to block 708 inFIG. 7 andFIG. 11 . As shown inFIG. 12( e), common observations of thesignals 1202, 1206 (seeFIG. 12( a),FIG. 12( b)) are captured in theresonance signal 1220, and thenoise signal 1222 has nil or zero noise. Furthermore, as shown inFIG. 12( f), thenoise signal 1222 contains noise of thesignals 
FIG. 13 is a flowchart of a method to generate a whitenedmatrix 1314, in accordance with one embodiment of the present techniques. In one embodiment,FIG. 13 explainsblock 1102 ofFIG. 11 in greater detail. In another embodiment,FIG. 13 explainsblock 1110 ofFIG. 11 in greater detail.Reference numeral 1302 is representative of a tobewhitened matrix. The tobewhitened matrix 1302, for example, may be the measurement matrix referred to inblock 1102 inFIG. 11 , or the tobe whitenedmatrix 1302 may be the cumulant matrix referred to inblock 1108 inFIG. 11 . When the tobewhitened matrix 1302 is the measurement matrix, the whitenedmatrix 1314 is the whitened matrix referred to inblock 1102 ofFIG. 11 . When the tobewhitened matrix 1302 is the cumulant matrix, the whitened matrix is the unitary matrix referred to inblock 1110 ofFIG. 11 .  At
block 1304, a covariance matrix is generated by determining a covariance of the tobe whitenedmatrix 1302. Atblock 1306, an Eigen value matrix and Eigen values are determined by applying an Eigen vector decomposition technique on the covariance matrix. Atblock 1308, a square root of the Eigen values is determined. Furthermore, atblock 1310, a product matrix is determined by multiplying the Eigen Vector matrix and the square root of the Eigen values. Atblock 1312 the whitenedmatrix 1314 is determined by multiplying the product matrix and the measurement matrix.  The present systems and methods monitor the health of rotor blades by identifying resonantfrequency rotor speeds of the rotor blades when the rotor blades, a rotor containing the rotor blades and a device containing the rotor blades, and the rotor are healthy. Furthermore, the present systems and methods determine variations in the resonantfrequency rotor speeds of the rotor blades. The present systems and methods determine presence or absence of cracks in the rotor blades based on the variations in the resonantfrequency of the rotor blades.
 While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.
Claims (20)
1. A system for monitoring health of a rotor, comprising a processing subsystem, memory, and communications section that:
generates a plurality of frequency peak values corresponding to two or more respective windows of signals by iteratively shifting the two or more respective windows of signals along delta times of arrival signals corresponding to a blade in the rotor;
determines one or more resonantfrequency rotor speeds regions of the blade by identifying rotor speeds corresponding to a subset of the plurality of frequency peak values; and
monitors the blade to determine a presence of one or more defects in the blade during the resonantfrequency rotor speeds regions.
2. The system of claim 1 , wherein the one or more resonantfrequency rotor speeds regions are a local maxima of the rotor speeds corresponding to the subset of the plurality of frequency peak values.
3. The system of claim 1 , wherein the processing subsystem further monitors the health of the blade during the resonantfrequency rotor speeds range of the blade.
4. The system of claim 1 , wherein the processing subsystem further determines the delta times of arrival signals based upon times of arrival generated during a startup state of the rotor, a transient state of the rotor, a steady state of the rotor, overspeed state of the rotor, or combinations thereof.
5. The system of claim 1 , wherein a width of a first window of signals in the two more windows of signals is greater than a width of a second window of signals in the two or more window of signals.
6. The system of claim 1 , wherein the processing subsystem generates a plurality of first frequency peak values corresponding to a first window of signals in the two or more respective window of signals by:
selecting a first subset of the delta times of arrival signals contained in the window of signals;
generating a first frequency peak value in the plurality of first frequency peak values based upon the first subset of the delta times of arrival signals;
shifting the first window of signals along the delta times of arrival signals to determine a shifted first window of signals;
selecting a second subset of the delta times of arrival signals contained in the shifted first window of signals;
generating a subsequent first frequency peak value in the plurality of first frequency peak values based upon the second subset of the delta times of arrival signals; and
determining the plurality of first frequency peak values by iteratively shifting the first window of signals along the delta times of arrival signals and selecting a respective subset of the delta times of arrival,
wherein the plurality of first frequency peak values is a subset of the plurality of frequency peak values.
7. The system of claim 6 , wherein the shifted first window of signals does not completely overlap the first window of signals.
8. The system of claim 6 , wherein the processing subsystem generates the first frequency peak value in the plurality of first frequency peak values based upon the first subset of the delta times of arrival signals by:
determining a frequency signal corresponding to the first subset of the delta times of arrival signals by determining a Fourier transform of the first subset of the delta times of arrival signals;
selecting synchronous frequencies from the frequency signal; and
selecting a frequency having a highest amplitude in the synchronous frequencies; and
determining the first frequency peak value equal to the highest amplitude in the synchronous frequencies.
9. A method for monitoring health of a rotor, comprising:
generating a plurality of first frequency peak values by iteratively shifting a first window of signals along delta times of arrival signals corresponding to a blade in the rotor;
generating a plurality of second frequency peak values by iteratively shifting a second window of signals along the delta times of arrival signals corresponding to a blade;
processing a plurality of initial resultant values based upon the plurality of first frequency peak values and the plurality of second peak values;
determining whether one or more of the plurality of initial resultant values are less than a determined value; and
processing one or more resonantfrequency rotor speeds regions of the rotor by identifying rotor speeds corresponding to the plurality of second frequency peak values when the one or more of the plurality of resultant values are less than the determined value.
10. The method of claim 9 , wherein the one or more resonantfrequency rotor speeds regions are a local maxima of the rotor speeds corresponding to the subset of the plurality of second frequency peak values.
11. The method of claim 9 , wherein further comprising:
generating a plurality of subsequent frequency peak values by iteratively shifting a subsequent window of signals along the delta times of arrival signals when the one or more of the plurality of resultant values are greater than the determined value;
generating a plurality of subsequent resultant values based upon the plurality of subsequent frequency peak values and a plurality of previous frequency peak values determined using a previous window of signals;
determining whether one or more of the plurality of subsequent resultant values are less than the determined value; and
processing the resonantfrequency rotor speeds of the rotor by identifying rotor speeds corresponding to the plurality of subsequent peak values when one or more of the plurality of subsequent resultant values are less than the determined value.
12. The method of claim 11 , wherein the previous window comprises the second window, and the plurality of previous peak values comprises the plurality of second peak values.
13. The method of claim 9 , further comprising determining the delta times of arrival signals based upon times of arrival generated during multiple rotor speeds of the rotor.
14. The method of claim 9 , wherein the delta times of arrival signals comprise delta times of arrival vectors comprising delta times of arrival mapped to respective rotor speeds of the rotor.
15. The method of claim 11 , wherein a width of the second window is greater than a width of the first window, and a width of the subsequent window is greater than the previous window.
16. The method of claim 15 , wherein the width of the first window, the width of the second window, the width of the previous window, and the width of the subsequent window comprises a rotor speed band.
17. The method of claim 9 , further comprising determining a plurality of resultant values based upon the plurality of first frequency peak values and the plurality of second frequency peak values by subtracting the plurality of second frequency peak values from the plurality of first peak values.
18. The method of claim 9 , wherein the one or more resonant frequency rotor speeds ranges comprise a subset of rotor speeds of the rotor that activate at least one resonant frequency of the blade.
19. The method of claim 9 , further comprising:
generating resonantfrequency delta times of arrival by extracting a subset of the delta times of arrival determined based upon times of arrival generated during the resonantfrequency rotor speeds range of the rotor; and
determining one or more defects in the blade based upon the resonantfrequency delta times of arrival.
20. The method of claim 9 , further comprising:
receiving times of arrival corresponding to the blade;
generating preprocessed times of arrival signals by applying at least one of a smoothening filtering technique and a median filtering technique to remove asynchronous signals from the times of arrival signals; and
determining the delta times of arrival signals based upon the preprocessed times of arrival signals and an expected time of arrival.
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US14/140,654 US20150184533A1 (en)  20131226  20131226  Methods and systems to monitor health of rotor blades 
DE102014118695.8A DE102014118695A1 (en)  20131226  20141216  Processes and systems for monitoring the functioning of blades 
CH01963/14A CH709085A8 (en)  20131226  20141217  Method and systems for monitoring the functioning of blades. 
JP2014259655A JP2015125147A (en)  20131226  20141224  Methods and systems to monitor health of rotor blades 
CN201410815966.0A CN104748952A (en)  20131226  20141224  Methods And Systems To Monitor Health Of Rotor Blades 
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CN114264366A (en) *  20211222  20220401  南水北调东线江苏水源有限责任公司  Method for monitoring multiangle vibration components of pump shell of water pump unit 
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CN109974849B (en) *  20190403  20200505  上海交通大学  Blade vibration online monitoring method based on blade tip timing technology under condition of no reference signal 
CN113586177B (en) *  20210810  20220809  西安交通大学  Blade natural frequency identification method based on singlebladeend timing sensor 
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2014
 20141216 DE DE102014118695.8A patent/DE102014118695A1/en not_active Withdrawn
 20141217 CH CH01963/14A patent/CH709085A8/en not_active Application Discontinuation
 20141224 JP JP2014259655A patent/JP2015125147A/en active Pending
 20141224 CN CN201410815966.0A patent/CN104748952A/en active Pending
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CH709085A8 (en)  20150828 
CN104748952A (en)  20150701 
CH709085A2 (en)  20150630 
JP2015125147A (en)  20150706 
DE102014118695A1 (en)  20150702 
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