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 measurement matrix based upon a plurality of resonant-frequency first delta times of arrival vectors corresponding to a blade and a first sensing device, and a plurality of resonant-frequency second delta times of arrival vectors corresponding to the blade and a second sensing device, generates a resonant matrix based upon the measurement matrix such that entries in the resonant matrix are substantially linearly uncorrelated and linearly independent, and generates a resonance signal using a first subset of the entries of the resonant matrix, wherein the resonance signal substantially comprises common observations and components of the plurality of resonant-frequency first delta times of arrival vectors and the plurality of resonant-frequency second delta times of arrival vectors.
A method is presented. The method includes steps of generating a measurement matrix based upon a plurality of resonant-frequency first delta times of arrival vectors corresponding to a blade and a first sensing device, and a plurality of resonant-frequency second delta times of arrival vectors corresponding to the blade and a second sensing device, generating a resonant matrix based upon the measurement matrix such that entries in the resonant matrix are substantially linearly uncorrelated and linearly independent, and generating a resonance signal using a first subset of the entries of the resonant matrix, wherein the resonance signal substantially comprises common observations and components of the plurality of resonant-frequency first delta times of arrival vectors and the plurality of resonant-frequency second delta times of arrival vectors.
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:
a) shows a simulated plot of a historical resonance signal of a blade;
b) shows a simulated plot of a resonance signal of a blade;
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 “resonant-frequency 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 resonant-frequencies of the blades” are referred to as resonant-frequency rotor speeds. As discussed in detail below, the present systems and methods identify resonant-frequency 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 resonant-frequency 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 resonant-frequency 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.
In one embodiment, 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, for example, 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. In one embodiment, at least one of the sensors 14, 16 is mounted on a casing (not shown) of the blades. By way of a non-limiting example, the sensors 14, 16 may be magnetostriction sensors, magnetic sensors, capacitive sensors, eddy current sensors, or the like.
As illustrated in the presently contemplated configuration, 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. Particularly, the processing subsystem 22 determines the first actual TOAs 24 based upon the first BPS 18, and the processing subsystem 22 determines the second actual TOAs 26 based upon the second BPS 20. In certain embodiments, 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, for example, 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. In one example, 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.
Furthermore, 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. Additionally, 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):
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 the rotor 11. In another embodiment, 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 T1 when the rotor speed is R1, 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 R1. 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 the rotor 11. The ‘rotor speeds of the rotor that activate the resonant frequencies of the blades’ are hereinafter referred to as resonant-frequency rotor speeds. It is noted that the resonant-frequency rotor speeds of blades in a rotor may be different from resonant-frequency rotor speeds of blades in another rotor. Furthermore, it is noted that the resonant-frequency rotor speeds of a blade in the rotor 11 may be different from resonant frequency rotor speeds of another blade in the rotor 11.
In the embodiment of
Additionally, the processing subsystem 22 determines existence of any variations in the resonant-frequency rotor speeds with respect to historical resonant-frequency 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. When the processing subsystem 22 determines that one or more variations exist in the resonant-frequency 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
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. In one embodiment, the delta TOAs 202 may be the first delta TOAs 28 (see
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 of
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. At block 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 to
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. At block 212, when the resultant values are less than the determined value, the control is transferred to block 214. At 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 resonant-frequency 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 resonant-frequency 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 non-limiting example, the width of the subsequent window of signals may be 75 rotations per minute or greater than 75 rotations per minute. Furthermore, at block 218, 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
At block 304, 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. 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 non-limiting 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 to
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. At 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
X-axis 406 of the plot 400 represents rotor speeds of the rotor, and Y-axis 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 W1, and reference numeral 412 is representative of a second window of signals having a width W2. 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. As shown in
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. As shown in
Subsequently, the first window of signals 410 is shifted by a rotor speed band SB1 to generate a shifted first window SW1, and the second window 412 is shifted by the rotor speed band SB1 to generate a shifted second window of signals SW2. Again subsequent first frequency peak value, corresponding to the shifted first window of signals SW1, is determined based upon a subset of the delta TOAs vector signal 402 covered by the shifted first window of signals SW1. Additionally, subsequent second frequency peak value, corresponding to the shifted second window of signals SW2, is determined based upon a subset of the delta TOAs vector signal 402 covered by the shifted second window of signals SW2. 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 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. Furthermore, the plurality of resultant values includes the first resultant value and the second resultant value.
Furthermore, at block 706, a measurement matrix is generated based upon the resonant-frequency first delta TOAs vectors and the resonant-frequency second delta TOAs vectors. The measurement matrix, for example may be generated by arranging the resonant-frequency first delta TOAs vectors and the resonant-frequency 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
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 resonant-frequency delta TOAs vectors 712 and noise data 710. Particularly, a row of the resonant matrix comprises the resonant-frequency delta TOAs vectors 712, and another row of the resonant matrix comprises the noise data 714. The cleaned resonant-frequency 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 resonant-frequency first delta TOAs vectors signal and the resonant-frequency second delta TOAs vectors signal. For ease of understanding, the term “cleaned resonant-frequency delta TOAs vectors” will be referred to as a resonance signal. Furthermore, the noise signal 710 includes noise of the resonant-frequency first delta TOAs vectors signal and the resonant-frequency second delta TOAs vectors signal. For ease of understanding, the “cleaned resonant-frequency delta TOAs vectors signal 712” are interchangeably referred to as resonance signal 712. An example of a resonance signal using the method of
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 resonant-frequency 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.
At block 716, it is determined whether a variation exists in the resonant-frequency rotor speeds of the blade 12 with respect to historical resonant-frequency rotor speeds of the blade 12. For example, the variation in resonant-frequency rotor speeds of the blade 12 with respect to historical resonant-frequency 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. 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 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.
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 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
The index value and the correlation value determined at the block 716 in
a) shows a simulated plot 900 of a historical resonance signal 902 of a blade, and
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.
Furthermore, at block 1108, a cumulant matrix is determined based upon the whitened matrix by applying a cumulant-generating 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. At block 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 to
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. At block 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 at block 708 in
The resonant-frequency first delta times of arrival vectors signal 1202 and the resonant-frequency second delta times of arrival vectors signal 1206 are processed to form a measurement matrix using the method explained in block 706 in
Furthermore, the whitened matrix, or the signals 1216, 1218 are processed using the blocks 1108-1112 in
At block 1304, a covariance matrix is generated by determining a covariance of the to-be whitened matrix 1302. At block 1306, an Eigen value matrix and Eigen values are determined by applying an Eigen vector decomposition technique on the covariance matrix. At block 1308, a square root of the Eigen values is determined. Furthermore, at block 1310, a product matrix is determined by multiplying the Eigen Vector matrix and the square root of the Eigen values. At block 1312 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 resonant-frequency 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 resonant-frequency 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 resonant-frequency 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.