Patent Publication Number: US-8543341-B2

Title: System and method for monitoring health of airfoils

Description:
BACKGROUND 
     Embodiments of the disclosure relates generally to systems and methods for monitoring health of rotor blades or airfoils. 
     Rotor blades or airfoils play a crucial role in many devices with several examples including axial compressors, turbines, engines, turbo-machines, or the like. For example, an axial compressor has 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 play a crucial role to increase the pressure of the fluid. 
     Furthermore, the rotor blades or airfoils and the static airfoils are more crucial due to wide and varied applications of the axial compressors that include the airfoils. Axial compressors, for example, may be used in a number of devices, such as, land based gas turbines, jet engines, high speed ship engines, small scale power stations, or the like. In addition, the axial compressors may be used in varied applications, such as, large volume air separation plants, blast furnace air, fluid catalytic cracking air, propane dehydrogenation, or the like. 
     The airfoils operate for long hours under extreme and varied operating conditions such as, high speed, pressure and temperature that effect the health of the airfoils. In addition to the extreme and varied 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 leads to defects and cracks in the airfoils. One or more of the cracks may widen with time to result in a liberation of an airfoil or a portion of the airfoil. The liberation of airfoil may be hazardous for the device that includes the airfoils, and thus may lead to enormous monetary losses. In addition, it may be unsafe and horrendous for people near the device. 
     Accordingly, it is highly desirable to develop a system and method that may predict health of airfoils in real time. More particularly, it is desirable to develop a system and method that may predict cracks or fractures in real time. 
     BRIEF DESCRIPTION 
     Briefly in accordance with one aspect of the technique, a method for monitoring the health of one or more blades is presented. The method includes the steps of determining a delta TOA corresponding to each of the one or more blades based upon respective actual time of arrival (TOA) of the one or more blades, determining a normalized delta TOA corresponding to each of the one or more blades by removing effects of one or more operational data from the delta TOA, and determining a corrected delta TOA corresponding to each of the one or more blades by removing effects of reseating of the one or more blades from the normalized delta TOA. 
     In accordance with an aspect, a system including a processing subsystem is presented. The processing subsystem determines a delta TOA corresponding to each of the one or more blades based upon respective actual time of arrival (TOA) of the one or more blades, determines a normalized delta TOA corresponding to each of the one or more blades by removing effects of one or more operational data from the delta TOA, and determines a corrected delta TOA corresponding to each of the one or more blades by removing effects of reseating of the one or more blades from the normalized delta TOA. 
    
    
     
       DRAWINGS 
       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 in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is an exemplary diagrammatic illustration of a blade health monitoring system, in accordance with an embodiment of the present system; 
         FIG. 2  is a flow chart representing an exemplary method for determining static deflection and dynamic deflection of a blade, in accordance with an embodiment of the present techniques; 
         FIG. 3  is a flowchart representing an exemplary method for determining static deflection of a blade, in accordance with an embodiment of the present techniques; 
         FIG. 4  is a flowchart representing an exemplary method for determining static deflection of a blade, in accordance with another embodiment of the present techniques; 
         FIG. 5  is a flowchart representing an exemplary method for determining static deflection of a blade, in accordance with still another embodiment of the present techniques; and 
         FIG. 6  is a flowchart representing steps in a method for determining a reseating offset corresponding to a blade, in accordance with an embodiment of the present techniques. 
     
    
    
     DETAILED DESCRIPTION 
     As discussed in detail below, embodiments of the present system and techniques evaluate the health of one or more blades or airfoils. More particularly, the present system and techniques determine static deflection of the blades or airfoils due to one or more defects or cracks in the blades or airfoils. Hereinafter, the terms “airfoils” and “blades” will be used interchangeably. The static deflection, for example, may be used to refer to a steady change in an original or expected position of a blade from the expected or original position of the blade. Certain embodiments of the present system and techniques also determine dynamic deflection corresponding to the blades. As used herein, the term, “dynamic deflection” may be used to refer to amplitude of vibration of a blade over the mean position of the blade. 
     In operation, a time of arrival (TOA) of blades at a reference position may vary from an expected TOA due to the one or more cracks or defects in the blades. Accordingly, the variation in the TOA of the blades may be used to determine the static deflection of the blades. As used herein, the term “expected TOA” may be used to refer to a TOA of a blade 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. Hereinafter, for ease of understanding, the word “TOA” and the term “actual TOA” will be used interchangeably. 
     However, in addition to the cracks or defects in the blades, the TOA may also vary due to one or more operational data and reseating of blades. The operational data, for example, may include an inlet guide vane (IGV) angle, a load, speed, mass flow, discharge pressure, or the like. As used herein, the term “reseating of a blade” may be used to refer to a locking of a blade at a position different from the original or expected position of the blade in joints, such as, a dovetail joint. Typically, the blades are fastened to a rotor via one or more joints, such as, dovetail joints. During start up of a device that includes the blades, the blades may shift from their original positions in the joints and may lock in the joints at positions that are different from the original positions of the blades. By way of an example, the device may include a gas turbine, a compressor, or the like. The locking of the blades in the joints at the positions different from the original positions of the blades is referred to as reseating of the blades. The change in the positions of the blades may vary actual TOA of the blades. 
     Consequently, due to the effects of the operational data and the reseating of blades, the static deflection that is determined based upon the actual TOA of the blades vary or exceed an exact or accurate static deflection due to the crack or defect in the blades. Accordingly, it is crucial to negate the effects of the operational data and the reseating of the blades on the actual TOA for the determination of the exact static deflection, hereinafter “static deflection.” Certain embodiments of the present techniques negate the effects of one or more of the operational data and the reseating of the blades from the actual TOA of the blades to determine the static deflection. Certain other embodiments of the present techniques normalize or compensate the effects of the operational data on the actual TOA. 
       FIG. 1  is a diagrammatic illustration of a rotor blade health monitoring system  10 , in accordance with an embodiment of the present system. As shown in  FIG. 1 , the system  10  includes one or more blades or airfoils  12  that are monitored by the system  10  to determine static deflection of the blades  12 . In certain embodiments, the system  10  also determines dynamic deflection corresponding to the blades  12 . As shown in the presently contemplated configuration, the system  10  includes one or more sensors  14 ,  16 . Each of the sensors  14 ,  16  generate TOA signals  18 ,  20 , respectively that are representative of actual TOA of the blades  12  at a reference point for a particular time period. In one embodiment, the sensors  14 ,  16  sense an arrival of the one or more blades  12  at the reference point to generate the TOA signals  18 ,  20 . The reference point, for example, may be underneath the sensors  14 ,  16  or adjacent to the sensors  14 ,  16 . In an embodiment, each of the TOA signals  18 ,  20  is sampled and/or measured for a particular time period and is used for determining actual TOA of a blade. The actual TOA, for example, may be measured in units of time or degrees. 
     In one embodiment, the sensors  14 ,  16  may sense an arrival of the leading edge of the one or more blades  12  to generate the TOA signals  18 ,  20 . In another embodiment, the sensors  14 ,  16  may sense an arrival of the trailing edge of the one or more blades  12  to generate the signals  18 ,  20 . In still another embodiment, the sensor  14  may sense an arrival of the leading edge of the one or more blades  12  to generate the TOA signals  18  and, the sensor  16  may sense an arrival of the trailing edge of the one or more blades  12  to generate the TOA signals  20 , or vice versa. The sensors  14 ,  16 , for example, may be mounted adjacent to the one or more blades  12  on a stationary object in a position such that an arrival of the one or more blades  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 one or more blades  12 . By way of a non-limiting example, the sensors  14 ,  16  may be magnetic sensors, capacitive sensors, eddy current sensors, or the like. 
     As illustrated in the presently contemplated configuration, the TOA signals  18 ,  20  are received by a processing subsystem  22 . The processing subsystem  22  determines actual TOA of the one or more blades  12  based upon the TOA signals  18 ,  20 . Furthermore, the processing subsystem  22  determines static deflection of the one or more blades  12  based upon the actual TOA of the one or more blades  12 . More particularly, the processing subsystem  22  is configured to determine the static deflection of the one or more of the blades  12  by processing the actual TOA of the one or more blades  12 . As previously noted the actual TOA of the blades  12  may be affected by one or more operational data and reseating of the blades  12 . 
     Consequently, the static deflection that is determined based upon the actual TOA of the one or more blades  12  may be an exaggerated value due to the effects of the operational data on the actual TOA and the reseating of the blades  12 . For example, due to the effects of the operational data and the reseating of blades  12  on the actual TOA of the blades  12 , the static deflection that is determined based upon the actual TOA of blades  12  may show one or more defects or cracks in the blades  12  even when no cracks or defects exist in the blades  12 . Accordingly, in one embodiment, the processing subsystem  22  determines the effects of the one or more operational data on the actual TOA of the one or more blades  12 . Furthermore, the processing subsystem  22  determines the static deflection by deducting the effects of the one or more operational data on the actual TOA of the one or more blades  12 . As previously noted, the operational data may include inlet guide vane (IGV) angle, a load variation, reseating of a blade, asynchronous vibration, synchronous vibration, variation of speed, temperature, speed, or the like. The processing subsystem  22 , for example, may receive the operational data from an onsite monitoring machine (OSM)  24  that monitors the operational data via sensors, cameras, and other devices. In addition, the processing subsystem  22  normalizes the effects of the reseating of the blades on the actual TOA of the blades  12 . The determination of the static deflection by deducting or normalizing the effects of the operational data on the actual TOA will be explained in greater detail with reference to  FIGS. 2-5 . The processing subsystem  22  is also configured to determine dynamic deflection corresponding to the one or more blades  12  based upon the static deflection and the actual TOA of the one or more blades  12 . In one embodiment, the processing subsystem  22  may have a data repository  26  that stores data, such as, static deflection, dynamic deflection, TOA, delta TOA, any intermediate data, or the like. 
     Referring now to  FIG. 2 , a flowchart representing an exemplary method  100  for determining static deflection and dynamic deflection of one or more blades, in accordance with an embodiment of the invention, is depicted. The one or more blades, for example, may be the one or more blades  12  (see  FIG. 1 ). The method starts at step  102  where TOA signals corresponding to each of the one or more blades may be received by a processing subsystem, such as, the processing subsystem  22  (see  FIG. 1 ). As previously noted with reference to  FIG. 1 , the TOA signals may be generated by a sensor, such as, the sensors  14 ,  16  (see  FIG. 1 ). In addition, the TOA signals, for example, may be the TOA signals  18 ,  20 . 
     Furthermore, at step  104  actual TOA corresponding to each of the one or more blades is determined by the processing subsystem. The processing subsystem determines the actual TOA utilizing TOA signals corresponding to each of the one or more blades. More particularly, the processing subsystem determines one or more actual TOA corresponding to a blade utilizing a TOA signal corresponding to the blade. At step  106 , a delta TOA corresponding to each of the one or more blades may be determined. The delta TOA corresponding to a blade, for example, may be a difference of an actual TOA corresponding to the blade that is determined at step  104  and an expected TOA  105  corresponding to the blade. It may be noted that the delta TOA corresponding to the blade is representative of a variation from the expected TOA  105  of the blade at a time instant. The delta TOA, for example, may be determined using the following equation (1):
 
Δ TOA   k ( t )= TOA   ACT(k) ( t )− ToA   exp(k)   (1)
 
where ΔTOA k (t) is a delta TOA corresponding to a blade k at a time instant t or a variation from the expected TOA corresponding to the blade k at the time instant t, TOA act(k)  is an actual TOA corresponding to the blade k at the time instant t, and TOA exp(k)  is an expected TOA corresponding to the blade k.
 
     As used herein, the term “expected TOA” may be used to refer to an actual TOA of a blade at a reference position when there are no defects or cracks in the blade and the blade is working in an operational state when effects of operational data on the actual TOA are minimal. In one embodiment, an expected TOA corresponding to a blade may be determined by equating an actual TOA corresponding to the blade to the expected TOA of the blade when a device that includes the blade has been recently commissioned or bought. Such a determination assumes that since the device has been recently commissioned or bought, all the blades are working in an ideal situation, the load conditions are optimal, and the vibrations in the blade are minimal. In another embodiment, the expected TOA may be determined by taking an average of actual times of arrival (TOAs) of all the blades in the device. The device, for example, may include axial compressors, land based gas turbines, jet engines, high speed ship engines, small scale power stations, or the like. It may be noted that the delta TOA is represented in units of time or degrees. 
     In one embodiment, at step  108 , the units of the delta TOA corresponding to each of the one or more blades may be converted in to units of mils. In one embodiment, the delta TOA corresponding to each of the one or more blades that is in units of degrees may be converted in to units of mils using the following equation (2): 
                     Δ   ⁢           ⁢       ToA     mils   ⁡     (   k   )         ⁡     (   t   )         =       2   ⁢   π   ⁢           ⁢   R   ×   Δ   ⁢           ⁢       ToA     Deg   ⁡     (   k   )         ⁡     (   t   )         360             (   2   )               
where ΔToA mils(k)  (t) is a delta TOA of a blade k at a t instant of time and the delta TOA is in units of mils, ΔToA Deg(k) (t) is a delta TOA of the blade k at the t instant of time and the delta TOA is in units of degrees and, R is a radius measured from the centre of the rotor to the tip of the blade k. The radius R is in units of mils. In another embodiment, the delta TOA that is in units of seconds may be converted in to units of mils using the following equation (3):
 
                     Δ   ⁢           ⁢       ToA     mils   ⁡     (   k   )         ⁡     (   t   )         =       2   ⁢   π   ⁢           ⁢   R   ×   N   ×   Δ   ⁢           ⁢       ToA     se   ⁢           ⁢     c   ⁡     (   k   )           ⁡     (   t   )         60             (   3   )               
where ΔToA mils(k) (t) is a delta TOA of a blade k at a t instant of time and the delta TOA is in units of mils, ΔToA sec(k) (t) is a delta TOA of the blade k at the t instant of time and the delta TOA is in units of degrees and R is a radius of a blade from the centre of a rotor of the blade. The radius R is in units of mils.
 
     Moreover, at step  110 , the static deflection of each of the one or more blades is determined based upon the delta TOA. The determination of the static deflection of the one or more blades will be explained in greater detail with reference to  FIGS. 3-5 . Subsequently at step  112 , the dynamic deflection corresponding to the one or more blades may be determined. In one embodiment, a dynamic deflection corresponding to a blade may be determined by subtracting a static deflection corresponding to the blade from a delta TOA corresponding to the blade. In another embodiment, a dynamic deflection corresponding to a blade may be determined by subtracting a static deflection corresponding to the blade from a filtered delta TOA corresponding to the blade. The filtered delta TOA, for example, may be determined by filtering a delta TOA corresponding to the blade that is determined at step  106 . The delta TOA may be filtered utilizing one or more techniques including average filtering, median filtering, or the like. 
     As previously noted, actual TOA of one or more blades may be used to determine static deflection of the blades. However, one or more operational data and reseating of the blades may effect the actual TOA of the blades. Consequently, the static deflection that is determined based upon the actual TOA of the blades may not be accurate static deflection. Accordingly, it is essential to remove or deduct the effects of the one or more operational data and reseating of the blades on the actual TOA for the determination of the exact static deflection. An exemplary method for determining the static deflection by deducting the effects of the one or more operational data and reseating of the blades from the actual TOA or delta TOA that is determined based upon the actual TOA will be explained with reference to  FIG. 3 . Referring now to  FIG. 3 , a flowchart representing an exemplary method  110  for determining static deflection of a blade, in accordance with an embodiment of the invention, is depicted. More particularly, step  110  of  FIG. 2  is described in greater detail in accordance with an exemplary aspect of the present techniques. 
     As shown in  FIG. 3 , reference numeral  302  is representative of a delta TOA corresponding to the blade. In one embodiment, the delta TOA  302  may be determined utilizing the techniques described with reference to step  106  of  FIG. 2 . Furthermore, at step  304 , one or more operational data corresponding to the blade or a device that includes the blade may be received. As previously noted, the operational data, for example, may include (IGV) angle, load, temperature, speed, mass flow, discharge pressure, or the like. The operational data, for example, may be received by the processing subsystem  22  from the onsite monitor  24  (see  FIG. 1 ). 
     Furthermore, at step  306 , a check may be carried out to verify if the blade is operating for the first time after a start up of the device that includes the blade. At step  306 , if it is the determined that the blade is operating for the first time after the start up, then the control may be transferred to step  308 . At step  308 , one or more coefficients are determined based upon one or more portions of the operational data. The coefficients, for example, may be determined by utilizing the following equation (4):
 
ΔTOA k =  AD   (4)
 
where ΔTOA k  is a delta TOA of a blade k,  D  is one or more portions of operational data and Ā is a coefficient. In one embodiment, the coefficients may be determined by forming a linear combination of the one or more portions of operational data. Furthermore, the values of the one or more portions of operational data may be substituted to determine the coefficients. Moreover, at step  312 , the coefficients that have been determined at step  308  are stored in a data repository, such as, the data repository  26  (see  FIG. 1 ). It may be noted that when the coefficients are stored in the data repository any other existing coefficients in the data repository may be erased.
 
     With returning reference to step  306  if it is determined that the blade is not operating for the first time after a start up, then the control may be transferred to step  310 . At step  310 , the coefficients are retrieved from the data repository. The coefficients are retrieved at step  310  with an assumption that the coefficients have already been determined during a start up of the device that includes the blade and thus, already exist in the data repository. Subsequently at step  314 , effects due to IGV angle on the delta TOA  302  may be determined. In one embodiment, the effects due to IGV may be determined using the following exemplary equation (5):
 
 T   IGV ( t )= ƒ ( IGV ( t ))  (5)
 
where T IGV (t) is effects of IGV on a delta TOA at a t instant of time, IGV (t) is IGV angle at the t instant of time and ƒis a function of the IGV(t). In one embodiment, the function of IGV may be determined by determining a multiple of IGV(t) and a coefficient corresponding to the IGV(t).
 
     At step  316 , effects on the delta TOA  302  due to load may be determined. The effects on the delta TOA  302  due to the load may be determined utilizing the following equation (6):
 
 T   load ( t )= g ( DWATT ( t ))  (6)
 
where T load (t) is effects of load on a delta TOA at a t instant of time, DWATT is load at the t instant of time, and g is a function of the load. In one embodiment, the function of DWATT may be determined by determining a multiple of DWATT(t) and a coefficient corresponding to the DWATT. In another embodiment, the function of DWATT may be determined by determining a linear combination of the multiple of DWATT(t) and the coefficient and, another coefficient corresponding to the DWATT.
 
     Subsequently, at step  318 , effects due to inlet temperature (CTIM) on the delta TOA  302  may be determined. The effects due to the inlet temperature (CTIM) may be determined utilizing the following equation (7):
 
 T   CTIM ( t )= d ( CTIM ( t ))  (7)
 
where T CTIM  is a value of the effects on a delta TOA due to an inlet temperature at a t instant of time, CTIM(t) is the inlet temperature at the t instant of time, d is a coefficient corresponding to the inlet temperature. Subsequent to the determination of the effects on the delta TOA  302  due to IGV at step  314 , load at step  316  and CTIM at step  318 , a normalized delta TOA is determined at step  320 . The normalized delta TOA, for example, may be determined by subtracting the effects of the operational data, such as, the IGV, the load and the inlet temperature (CTIM) from the delta TOA  302 .
 
     In one embodiment, the normalized delta TOA, for example, may be determined using the following exemplary equation (8):
 
Norm_ΔTOA k ( t )=ΔTOA k ( t )− T   load ( t )− T   CTIM ( t )− T   IGV ( t )  (8)
 
where Norm_ΔTOA k (t) is a normalized delta TOA corresponding to a blade k at a t instant of time, ΔTOA k (t) is a delta TOA corresponding to the blade k at the t instant of time and T load (t),T CTIM (t), T IGV (t) are the effects of the load, inlet temperature and IGV on the delta TOA at the t instant of time, respectively.
 
     Typically, one or more blades are fastened to a rotor via one or more joints, such as, dovetail joints. During start up of the device that includes the blades, the blades may shift from their original positions in the joints and may lock in the joints at positions that are different from the original positions of the blades. The locking of the blades in the joints at the positions different from the original positions of the blades is referred to as reseating of the blades. The change in the positions of the blades may vary actual TOA of the blades. Accordingly, delta TOA and normalized delta TOA that are determined based upon the actual TOA of the blades may not be accurate. More particularly, the delta TOA and the normalized delta TOA may not be accurate due to the reseating of the blades. Accordingly, it is essential to correct the actual TOA, delta TOA or the normalized delta TOA corresponding to the blades to remove effects due to the reseating of the blades. The steps  322 - 330  correct the normalized delta TOA determined at step  320  and the delta TOA  302  of the blade to remove effects due to a reseating of the blade. 
     At step  322 , a check may be carried out to verify whether the blade is operating for the first time after a start up. At step  322 , if it is determined that the blade is operating for the first time after a start up, then the control may be transferred to step  324 . At step  324 , a reseating offset corresponding to the blade may be determined. As used herein, the term “reseating offset” may be used to refer to a numerical value that may be used to remove effects due to reseating of a blade from delta TOA, actual TOA or a normalized delta TOA of the blade. The determination of the reseating offset will be explained in greater detail with reference to  FIG. 6 . Subsequently, the reseating offset determined at step  324  may be stored in the data repository at step  326 . The reseating offset, for example, may be stored in the data repository  26  (see  FIG. 1 ). It may be noted that in the presently contemplated configuration, the reseating offset is determined when the blade is operating for the first time after the start up as it is assumed that the blade may lock at a position different from the original position of the blade during the start up of the device that includes the blade. 
     With returning reference to step  322 , if it is determined that the blade is not operating for the first time after a start up of the device that includes the blade, then the control may be transferred to step  328 . It may be noted that when the blade is not operating for the first time after a start up, it indicates that the reseating offset corresponding to the blade has already been determined after a start up of the device that includes the blade and has already been stored in the data repository. Accordingly, at step  328 , a reseating offset corresponding to the blade may be retrieved from the data repository. 
     Subsequent to the storage of the reseating offset at step  326  or the retrieval of the reseating offset at step  328 , a corrected delta TOA may be determined at step  330 . In one embodiment, the corrected delta TOA may be determined by correcting the normalized delta TOA that has been determined at step  320  for the reseating of the blade. The corrected delta TOA, for example, may be determined by subtracting the reseating offset from the normalized delta TOA corresponding to the blade. In another embodiment, the corrected delta TOA may be determined by correcting the delta TOA  302 . In this embodiment, the corrected delta TOA may be determined by subtracting the reseating offset from the delta TOA  302  corresponding to the blade. Moreover, at step  332 , the corrected delta TOA may be filtered to generate static deflection  334 . The filtering of the corrected delta TOA may reduce noise from the corrected delta TOA. The corrected delta TOA, for example, may be filtered using median filtering, moving average filtering, or combinations thereof. 
     As previously noted, one or more operational data effect actual TOA of a plurality of blades. However, the operational data may not affect the actual TOA of the blades uniformly. Accordingly, the actual TOA of one or more of the blades may be affected more in comparison to the actual TOA of other blades in the plurality of blades. Consequently, static deflection corresponding to the one or more of the blades may show defects or cracks in the blades due to the additional effects of the operational data in comparison to static deflection corresponding to the other blades. In addition, the static deflection that is determined based upon the actual TOA of the blades may not be accurate static deflection. Accordingly, it is essential to normalize the effects of the operational data on the actual TOA of the plurality of blades in a device. Exemplary methods for determining static deflection by normalizing effects of one or more operational data on actual TOA or delta TOA that is determined based upon the actual TOA will be explained with reference to  FIGS. 4 and 5 . 
     Referring now to  FIG. 4 , a flowchart representing steps in an exemplary method  110 ′ for determining static deflection in accordance with another embodiment, is depicted. More particularly,  FIG. 4  explains step  110  of  FIG. 2  in accordance with an embodiment of the present technique for determining the static deflection. As shown in  FIG. 4 , reference numeral  402  is representative of delta times of arrival (TOAs) corresponding to a plurality of blades in a device, such as, a turbine, axial compressor, or the like. A delta TOA corresponding to each of the plurality of blades may be determined utilizing the techniques explained with reference to step  106  of  FIG. 2 . In one embodiment, the delta TOAs  402  may be similar to the delta TOA determined at step  106  of  FIG. 2 . 
     Furthermore, at step  404 , a standard deviation of the delta TOAs corresponding to the plurality of blades may be calculated. For example, when the plurality of blades includes five blades and each of the five blades has a delta TOA as delta TOA 1 , delta TOA 2 , delta TOA 3 , delta TOA 4 , delta TOA 5  then, a standard deviation of the delta TOA 1 , delta TOA 2 , delta TOA 3 , delta TOA 4  and delta TOA 5  may be calculated at the step  404 . Subsequently at step  406 , a check may be carried out to determine if the blades are operating for the first time after a start up of a device that includes the plurality of blades. At step  406 , if it is determined that the blades are operating for the first time after a start up, then the control may be transferred to step  408 . 
     For ease of understanding, the term “standard deviation” will be hereinafter referred to as “current standard deviation.” As shown in  FIG. 4 , at step  408  the standard deviation that is calculated at step  404  may be stored as an initial standard deviation  410 . The initial standard deviation  410  may be stored in a data repository, such as, the data repository  26 . As used herein, the term “initial standard deviation” may be referred to as a current standard deviation that is determined when the blades start operating for the first time after a start up. More particularly, the standard deviation that is determined at step  404  may be stored as the initial standard deviation  410  in the data repository. 
     Referring back to step  406  if it is determined that the blades are not operating for the first time after the start up, then the control may be transferred to step  412 . At step  412 , a delta sigma — 1 may be determined utilizing the current standard deviation determined at step  404  and the initial standard deviation  410 . More particularly, the delta sigma — 1 may be determined by determining a difference between the current standard deviation that is determined at step  404  and the initial standard deviation  410 . It may be noted that when the step  412  is processed for the first time after a start up of the device that includes the plurality of blades, then the values of the initial standard deviation  410  and the current standard deviation determined at step  404  are equivalent. Accordingly, the value of delta sigma — 1 may be equal to zero at step  412 . 
     Furthermore, at step  414 , a normalized delta TOA corresponding to one or more of the plurality of blades may be determined. The normalized delta TOA, for example, may be determined based upon the following equation (9):
 
Norm_ΔTOA k ( t )=ΔTOA k ( t )− K *(Δσ( t ) — 1)−Mean(ΔTOA 1toj ( t ))  (9)
 
where Norm_ΔTOA k (t) is a normalized delta TOA corresponding to a blade k at a t instant of time, ΔTOA k (t) is a delta TOA corresponding to the blade k at the t instant of time and Δσ(t) — 1 is a delta sigma — 1 at the t instant of time and K is a constant.
 
     In one embodiment, the value of the constant K may be determined based upon a mean of delta TOA corresponding to the blades. In one embodiment, the value of K may be 1. In another embodiment, the value of K may be −1. In still another embodiment the value of K may be 0. 
     Moreover, at step  416 , a current standard deviation of the normalized delta TOA corresponding to the one or more of the plurality of blades may be determined. Subsequently at step  418 , a delta sigma — 2 may be determined. The delta sigma — 2, for example, may be determined by determining a difference between the current standard deviation of the normalized delta TOA and a previous standard deviation of normalized delta TOA. The term “previous standard deviation of normalized delta TOA” may be used to refer to a current standard deviation of normalized delta TOA that is determined at a time step T−1 in comparison to a current standard deviation of normalized delta TOA that is determined at a time step T. 
     Subsequent to the determination of the delta sigma — 2, at step  420  a check may be carried out to verify if the delta sigma — 2 is greater than a predetermined first threshold and/or if the plurality of blades are operating for the first time after a start up. The predetermined first threshold may be determined empirically based upon historical delta TOA corresponding to the blades. At step  420  if it is determined that the delta sigma — 2 is greater than the predetermined first threshold or the plurality of blades are operating for the first time after a start up, then the control may be transferred to step  422 . At step  422 , a reseating offset corresponding to the one or more of the plurality of blades may be determined. The determination of the reseating offset will be explained in greater details with reference to  FIG. 6 . Subsequent to the determination of the reseating offset, at step  424  the reseating offset may be stored in the data repository, such as, the data repository  26  (see  FIG. 1 ). 
     With returning reference to step  420 , when it is determined that the delta sigma — 2 is not greater than the predetermined first threshold and the plurality of blades are not operating for the first time after a start up then, the control may be transferred to step  426 . At step  426 , the reseating offset may be retrieved from the data repository. It may be noted that no reseating offset is generated when the delta sigma — 2 is not greater than the predetermined first threshold and the blades are not operating for the first time after a start up. Accordingly, an existing reseating offset from the data repository is retrieved at step  426 . Subsequent to the retrieval of the reseating offset, a corrected delta TOA corresponding to the one or more of the plurality of blades may be determined at step  428 . The corrected delta TOA, for example, may be determined utilizing the techniques explained with reference to step  330  of  FIG. 3 . As previously noted with reference to  FIG. 3 , the corrected delta TOA may be determined utilizing the techniques explained with reference to step  330  of  FIG. 3 . For example, the corrected delta TOA corresponding to a blade may be determined utilizing the normalized delta TOA corresponding to the blade that is determined at step  414  and a reseating offset corresponding to the blade that is retrieved from the data repository at step  426 . In one embodiment, a corrected delta TOA corresponding to a blade may be determined by subtracting a reseating offset corresponding to the blade from delta TOA corresponding to the blade. The delta TOA, for example, may be one of the delta TOA  402  corresponding to the plurality of blades. 
     Furthermore, at step  430 , the corrected delta TOA may be filtered to generate static deflection  432  corresponding to the one or more of the plurality of blades. As previously noted with reference to  FIG. 3 , the filtering of the corrected delta TOA may reduce noise from the corrected delta TOA. The corrected delta TOA, for example, may be filtered using a median filtering technique, a moving average filtering technique, or combinations thereof. 
     Referring now to  FIG. 5 , a flowchart representing steps in an exemplary method  110 ″ for determining static deflection in accordance with another embodiment, is depicted. More particularly,  FIG. 5  explains step  110  of  FIG. 2  in accordance with an embodiment of the present techniques for determining the static deflection. As shown in  FIG. 5 , reference numeral  502  is representative of delta times of arrival (TOAs) corresponding to a plurality of blades in a device, such as, a turbine, axial compressor, or the like. A delta TOA corresponding to each of the plurality of blades may be determined utilizing the techniques explained with reference to step  106  of  FIG. 2 . In one embodiment, the delta TOAs  502  may be similar to the delta TOA determined at step  106  of  FIG. 2 . 
     Furthermore, at step  504 , a standard deviation of the delta TOAs corresponding to the plurality of blades may be calculated. For example, when the plurality of blades includes five blades and each of the five blades has a delta TOA as delta TOA 1 , delta TOA 2 , delta TOA 3 , delta TOA 4 , delta TOA 5  then, a standard deviation of the delta TOA 1 , delta TOA 2 , delta TOA 3 , delta TOA 4  and delta TOA 5  may be determined at the step  504 . Subsequently at step  506 , a normalized delta TOA corresponding to one or more of the plurality of blades may be determined. The normalized delta TOA, for example, may be determined based upon the following equation (10):
 
Norm_ΔTOA k ( t )=(ΔTOA k ( t )−Mean ΔTOA 1toj ( t ))/standard_deviation( t )  (10)
 
where Norm_ΔTOA k (t) is a normalized delta TOA corresponding to a blade k at a t instant of time, ΔTOA k (t) is a delta TOA corresponding to the blade k at the t instant of time, Mean ΔTOA 1toj (t) is a mean of delta TOA corresponding to blades  1  to j that includes the blade k.
 
     Moreover, at step  508 , a standard deviation of the normalized delta TOA corresponding to the one or more of the plurality of blades may be determined. Subsequently at step  510 , a delta sigma — 3 may be determined. The delta sigma — 3, for example, may be determined by determining a difference between the standard deviation of the normalized delta TOA and a previous standard deviation of normalized delta TOA. The term “previous standard deviation of normalized delta TOA” may be used to refer to a standard deviation of normalized delta TOA that is determined at a time step T−1 in comparison to a standard deviation of normalized delta TOA that is determined at a time step T. 
     Subsequent to the determination of the delta sigma — 3 at step  510 , a check may be carried out at step  512  to verify if the delta sigma — 3 is greater than a predetermined second threshold and/or if the plurality of blades are operating for the first time after a start up. The predetermined second threshold may be determined empirically based upon historical delta TOA. At step  512  if it is determined that the delta sigma — 3 is greater than the predetermined second threshold or the plurality of blades are operating for the first time after a start up, then the control may be transferred to step  514 . At step  514 , a reseating offset corresponding to each of the one or more of the plurality of blades may be determined. The determination of the reseating offset will be explained in greater details with reference to  FIG. 6 . Subsequent to the determination of the reseating offset, at step  516  the reseating offset may be stored in the data repository, such as, the data repository  26  (see  FIG. 1 ). 
     With returning reference to step  512 , when it is determined that the delta sigma — 3 is not greater than the predetermined second threshold and the plurality of blades are not operating for the first time after a start up then the control may be transferred to step  518 . At step  518 , a reseating offset corresponding to each of the one or more of the plurality of blades may be retrieved from the data repository. It may be noted that no reseating offset is generated when the delta sigma — 3 is not greater than the predetermined second threshold and the blades are not operating for the first time after a start up. Accordingly, an existing reseating offset from the data repository is retrieved at step  518 . Subsequent to the retrieval of the reseating offset, a corrected delta TOA corresponding the one or more of the plurality of blades may be determined at step  520 . The corrected delta TOA, for example, may be determined utilizing the techniques explained with reference to step  330  of  FIG. 3 . As previously noted with reference to  FIG. 3 , the corrected delta TOA may be determined utilizing the techniques described with reference to step  330  of  FIG. 3 . For example, the corrected delta TOA corresponding to a blade may be determined utilizing the normalized delta TOA corresponding to the blade that is determined at step  506  and a reseating offset corresponding to the blade that is retrieved from the data repository at step  518 . In one embodiment, a corrected delta TOA corresponding to a blade may be determined by subtracting a reseating offset corresponding to the blade from a normalized delta TOA corresponding to the blade. In another embodiment, a corrected delta TOA corresponding to a blade may be determined by subtracting a reseating offset corresponding to the blade from delta TOA corresponding to the blade. The delta TOA, for example, may be one of the delta TOA  502  corresponding to the plurality of blades. 
     Furthermore, at step  522 , the corrected delta TOA may be filtered to generate static deflection  524 . As previously noted with reference to  FIG. 3 , the filtering of the corrected delta TOA may reduce noise from the corrected delta TOA. The corrected delta TOA, for example, may be filtered using a median filtering technique, a moving average filtering technique, or combinations thereof. 
     Referring now to  FIG. 6 , a flowchart representing steps in a method  600  for generating a reseating offset corresponding to a blade, in accordance with an embodiment of the present techniques, is depicted. More particularly, method  600  explains steps  328  of  FIG. 3 ,  422  of  FIG. 4 and 514  of  FIG. 5 . As shown in  FIG. 6 , reference numeral  602  is representative of normalized delta times of arrival (TOAs) corresponding to the blade. In one embodiment, the normalized delta TOAs  602  may be one or more of normalized delta TOAs that have been determined using the techniques described with reference to steps  320  of  FIG. 3 ,  414  of  FIG. 4 ,  506  of  FIG. 5 . In one embodiment, the normalized delta TOAs  602  are one or more of normalized delta TOAs corresponding to the blade that has been determined after transient events of the blade. The transient events, for example, may include a start up or shutdown of a device that includes the blades, continuous change in the speed of the blades, or the like. 
     Furthermore, reference numeral  604  is representative of one or more corrected delta TOAs corresponding to the blade that has been determined utilizing normalized delta TOAs that were generated before the transient events. The transient events are transient events after which the normalized delta TOAs  602  were determined. At step  606 , a check is carried out to determine if the blade is running for the first time after a start up. At step  606  if it is determined, that the blade is running for the first time after a start up then the control is transferred to step  608 . Furthermore, at step  608 , a check may be carried out to determine if the blade is running at a base load. At step  608 , if it is determined that the blade is not running at a base load then the control may be transferred to step  610 . With returning reference to step  606  if it is determined that the blade is not running for the first time after a start up, then control may be transferred to the step  610 . At step  610  it is declared that a reseating offset corresponding to the blade already exists in a data repository, such as, the data repository  26  (see  FIG. 1 ). Therefore, a reseating offset is not determined. 
     With returning reference to step  608 , if it is determined that the blade is running at a base load, then the control may be transferred to step  612 . At step  612 , a first mean of the one or more normalized delta TOAs  602  may be determined. Furthermore, at step  614 , a second mean of the one or more corrected delta TOAs  604  may be determined. Subsequent to the determination of the first mean and the second mean, a reseating offset  618  corresponding to the blade may be determined by subtracting the second mean from the first mean at step  616 . 
     The embodiments of the present techniques result in determination of the effects of operational data on TOAs. In addition, the present techniques deduct the effects of operational data from the TOAs to determine normalized delta TOAs. Furthermore, the present techniques normalize the effects of operational data on the TOAs of the blades to determine the normalized delta TOAs. The normalized delta TOAs may be used for determining defects or cracks in the blades. Certain embodiments of the present techniques also facilitate detection of variations in the TOAs of the blade due to reseating of the blades. Also, the determination of the normalized delta TOAs may be used for monitoring the health of the blades. For example, the normalized delta TOAs may be used to determine whether there are one or more cracks in the blades. 
     It is to be understood that not necessarily all such objects or advantages described above may be achieved in accordance with any particular embodiment. Thus, for example, those skilled in the art will recognize that the systems and techniques described herein may be embodied or carried out in a manner that achieves or optimizes one advantage or group of advantages as taught herein without necessarily achieving other objects or advantages as may be taught or suggested herein. 
     While the invention has been described in detail in connection with only a limited number of embodiments, it should be readily understood that the invention is not limited to such disclosed embodiments. Rather, the invention can be modified to incorporate any number of variations, alterations, substitutions or equivalent arrangements not heretofore described, but which are commensurate with the spirit and scope of the invention. Additionally, while various embodiments of the invention have been described, it is to be understood that aspects of the invention may include only some of the described embodiments. Accordingly, the invention is not to be seen as limited by the foregoing description, but is only limited by the scope of the appended claims.