Patent Publication Number: US-8532939-B2

Title: System and method for monitoring health of airfoils

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 12/262,783, entitled “System And Method For Article Monitoring”, filed on Oct. 31, 2008 now abandoned, which is herein incorporated by reference. This application is also a continuation-in-part of U.S. patent application Ser. No. 12/340,777 now having U.S. Pat. No. 7,941,281, entitled “System And Method For Rotor Blade Health Monitoring”, filed on Dec. 22, 2008, which is herein incorporated by reference. This application further claims priority as a continuation-in-part of U.S. patent application Ser. No. 12/825,763, entitled “System And Method For Monitoring Health Of Airfoils”, filed on Jun. 29, 2010, which is herein incorporated by reference. This application further claims priority as a continuation-in-part of U.S. patent application Ser. No. 12/825,895, entitled “System And Method For Monitoring Health Of Airfoils”, filed on Jun. 29, 2010, which is herein incorporated by reference. 
    
    
     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, a turbomachine, 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. Some part of the kinetic energy is converted into pressure energy due to decrease in relative velocity, and the rest of the kinetic energy is converted into pressure due to decrease in absolute velocity of the fluid. 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 vital 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, fluid load, and temperature that affect the health of the airfoils. In addition to the extreme and varied conditions, certain other factors lead to fatigue and stress on the airfoils. The factors, for example, may include centrifugal forces, fluid forces, thermal loads during transient events, load due to non-synchronous vibration such as rotating stall, and the cyclic load due to synchronous resonant vibration. Prolonged effects of the factors lead to defects and crack 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 embodiments, a system is presented. The system includes a data acquisition system that generates time of arrival (TOA) data corresponding to a plurality of blades in a device, a central processing subsystem that determines features of each of the plurality of blades utilizing the TOA data, and evaluates the health of each of the plurality of blades based upon the determined features. 
     In accordance with an aspect of the embodiments, a system is presented. The system includes a plurality of devices, wherein each of the plurality of devices comprises a plurality of blades, a plurality of data acquisition systems that generate time of arrival (TOA) data corresponding to the plurality of blades in each of the plurality of devices. The system further includes a central processing subsystem that determines features of each of the plurality of blades utilizing the TOA data, evaluates the health of each of the plurality of blades based upon the determined features to generate health evaluation results, and a web server for displaying the features and the health evaluation results of the plurality of blades. 
     In accordance with an aspect of the present technique, a method is presented. The method includes a method for monitoring the health of a plurality of blades in a device. The method includes the steps of generating time of arrival (TOA) data corresponding to each of the plurality of blades in a device, determining features of each of the plurality of blades utilizing the TOA data, and evaluating the health of each of the plurality of blades based upon the determined features. 
    
    
     
       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 an exemplary flowchart for monitoring one or more devices to evaluate the health of one or more blades in each of the devices, 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 monitor one or more devices to evaluate the health of one or more blades in each of the devices. Embodiments of the present system provide a central processing subsystem that monitors the devices in real-time, wherein the devices may be located at different remote locations. By way of an example, the devices may include a turbomachine, a gas turbine, a compressor, a jet engine, a high speed ship engine, a small scale power station, or the like. More particularly, the present system and techniques determine one or more features of the blades to evaluate the health of the blades. As used herein, the term “features” may be used to refer to characteristics of one or more blades that may be used to determine the health of the blades. The features, for example, may include static deflection, dynamic deflection, blade clearance, variations in resonance frequency, reseating of a blade, or the like. Hereinafter, the terms “blades” and “airfoils” will be used interchangeably. As used herein, the term “static deflection” is used to refer to a fixed change in an original or expected position of a blade from the expected or original position of the blade. Also, the term, “dynamic deflection” is used herein to refer to an amplitude of vibration of a blade over the mean or original position of the blade. Furthermore, as used herein, the term “resonance frequencies” may be used to refer to the frequencies of oscillations of a blade that match its natural frequencies of vibration. In addition, the term “reseating of a blade” is used herein 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. 
     In operation, a time of arrival (TOA) of a blade at a reference position may vary from an expected TOA due to one or more defects or cracks in the blades. Accordingly, the variation in the TOA of the blades may be used to determine one or more of the features. 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 defects or cracks 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 variation, asynchronous vibrations, synchronous vibrations, variation of speed, speed, mass flow, discharge pressure, or the like. Consequently, due to the effects of the operational data and the reseating of blades, the features that are determined based upon the variation in the actual TOA of the blades may not be accurate. 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 accurate static deflection, hereinafter “static deflection.” Certain embodiments of the present techniques negate the effects of the operational data and the reseating of the blades from the actual TOA of the blades to determine the features. 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 an exemplary rotor blade health monitoring system  10 . The system  10  monitors one or more devices  12 ,  14  to evaluate the health of one or more blades  16 ,  18  in the devices  12 ,  14 . The devices  12 ,  14 , for example, may be a turbomachine, a gas turbine, an axial compressor, or the like. It may be noted that the devices  12 ,  14  may be located at different remote locations. As shown in the presently contemplated configuration, the device  12  includes the one or more blades  16  and the device  14  includes the one or more blades  18 . 
     Furthermore, as shown in  FIG. 1 , the system  10  includes one or more sensors  20 ,  22 ,  24 ,  26  that sense the arrivals of the blades  16 ,  18  at respective reference points to generate respective blade passing signals (BPS)  28 ,  30 . In the presently contemplated configuration, the sensors  20 ,  22  sense the arrivals of the blades  16  at a respective reference point to generate the BPS signals  28 . Similarly, the sensors  24 ,  26  sense the arrivals of the blades  18  at a respective reference point to generate the BPS signals  30 . The reference point, for example, may be underneath or adjacent to the sensors  20 ,  22 ,  24 ,  26 . 
     In one embodiment, the sensors  20 ,  22 ,  24 ,  26  may sense an arrival of the leading edge of each of the blades  16 ,  18  to generate the BPS signals  28 ,  30 . In another embodiment, the sensors  20 ,  22 ,  24 ,  26  may sense an arrival of the trailing edge of each of the blades  16 ,  18  to generate the BPS signals  28 ,  30 . In still another embodiment, the sensor  20  may sense an arrival of the leading edge and the sensor  22  may sense an arrival of the trailing edge of each of the blades  16 , or vice versa. Similarly, the sensor  24  may sense an arrival of the leading edge and the sensor  26  may sense an arrival of the trailing edge of each of the blades  18 , or vice versa. The sensors  20 ,  22 ,  24 ,  26 , for example, may be mounted adjacent to the respective blades  16 ,  18  on a stationary object in a position such that the arrivals of each of the blades  16 ,  18  may be sensed efficiently. In one embodiment, at least one of the sensors  20 ,  22 ,  24 ,  26  is mounted on a casing (not shown) of the one or more blades  16 ,  18 . By way of a non-limiting example, the sensors  20 ,  22 ,  24 ,  26  may be magnetic sensors, capacitive sensors, eddy current sensors, or the like. 
     Subsequent to the generation of the BPS signals  28 ,  30  by the sensors  20 ,  22 ,  24 ,  26 , the BPS signals  28 ,  30  may be transmitted to respective data acquisition systems  32 ,  34 . More particularly, the sensors  20 ,  22  transmit the BPS signals  28  to the DAQ_ 1   32  and the sensors  24 ,  26  transmit the BPS signals  30  to the DAQ_ 2   34 . As shown in  FIG. 1 , the sensors  20 ,  22  are communicatively coupled to the data acquisition system (DAQ_ 1 )  32 , and the sensors  24 ,  26  are communicatively coupled to the data acquisition system (DAQ_ 2 )  34 . The DAQ_ 1   32  and DAQ_ 2   34  determine times of arrival (TOAs) of respective blades  16 ,  18  utilizing the respective BPS signals  28 ,  30 . More particularly, the DAQ_ 1   32  determines TOA of the blades  16  utilizing the BPS signals  28 , and the DAQ_ 2  determines TOA of the blades  18  utilizing the BPS signals  30 . Hereinafter, the terms “TOA” and “actual TOA” will be used interchangeably. It may be noted that while in the presently contemplated configurations, none of the sensors  20 ,  22 ,  24 ,  26  is shown as a component of the data acquisition systems  32 ,  34 , however, each of the sensors  20 ,  22 ,  24 ,  26  may be a component of the respective DAQs  32 ,  34 . It may be noted that the DAQ_ 1   32  and the DAQ_ 2   34  may be located at different remote locations from one another. 
     Furthermore, the DAQ_ 1   32  and the DAQ_ 2   34  generate TOA data  36  utilizing the actual TOA of the blades  16 ,  18 . The TOA data  36 , for example, may include clearance data, identity of the sensors  20 ,  22 ,  24 ,  26 , identity of the blades  16 ,  18 , identity of the devices  12 ,  14 , the actual TOA of the blades  16 ,  18 , the category of the sensor indicating whether the sensor is a leading edge or a trailing edge sensor, or the like. By way of a non-limiting example, an exemplary TOA data generated by data acquisition subsystems of a system A may be represented as shown in the following Table 1: 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                   
                 Identity 
                 Identity  
                 Identity  
                 Type  
                 Actual 
               
               
                 Serial 
                 of a 
                 of a 
                 of a 
                 of 
                 TOA of 
               
               
                 No. 
                 device 
                 blade 
                 sensor 
                 sensor 
                 the blade 
               
               
                   
               
             
            
               
                 1. 
                 dev_l 
                 blade1_dev_l 
                 sen1_dev_l 
                 Leading 
                  2200 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
                   
               
               
                 2. 
                 dev_l 
                 blade1_dev_l 
                 sen2_dev_1 
                 Trailing 
                  2500 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
                   
               
               
                 3. 
                 dev_l 
                 blade2_dev_1 
                 sen2_dev_1 
                 Trailing 
                  9200 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
                   
               
               
                 4. 
                 dev_2 
                 blade1_dev_2 
                 sen1_dev_2 
                 Leading 
                  2000 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
                   
               
               
                 5. 
                 dev_2 
                 blade2_ dev_2 
                 sen2_dev_2 
                 Leading 
                  9100 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
                   
               
               
                 6. 
                 dev_2 
                 blade3_dev_2 
                 sen2_dev_2 
                 Leading 
                 16300 mils 
               
               
                   
                   
                   
                   
                 edge 
                   
               
               
                   
                   
                   
                   
                 sensor 
               
               
                   
               
            
           
         
       
     
     As shown in Table 1, the system A includes devices, such as, dev_ 1  and dev_ 2 . Furthermore, the dev_ 1  includes blades, such as, blade 1 _dev_ 1  and blade 2 _dev_ 1 . Similarly, the dev_ 2  includes blades, such as, blade l_dev_ 2 , blade 2 _dev_ 2  and blade 3 _dev_ 2 . In addition, the arrivals of the blades in the dev_ 1  are sensed by sensors, such as, sen 1 _dev_ 1  and sen 2 _dev_ 1 . Similarly, the arrivals of the blades in the dev_ 2  are sensed by sensors, such as, sen 1 _dev_ 2  and sen 2 _dev_ 2 . Furthermore, the last column of Table 1 includes actual TOA of the blades in the devices dev_ 1  and dev_ 2 . 
     In addition, the system  10  includes one or more onsite monitoring machines (OSM), such as, an onsite monitoring machine  38  (OSM) for collecting one or more operational data  40  of the devices  12 ,  14  and the blades  16 ,  18  in the devices  12 ,  14 . The operational data  40 , for example, may include an inlet guide vane (IGV) angle, a load, speed, mass flow, discharge pressure, or the like. The OSM  38 , for example, may be a combination of hardware and software that collects the operational data  40 . 
     As shown in the presently contemplated configuration, a central processing subsystem  42  is communicatively coupled to the DAQs  32 ,  34  and the OSM  38 . Subsequent to the generation of the TOA data  36  and the collection of the operational data  40 , the TOA data  36  and the operational data  40  may be transmitted to the central processing subsystem  42 . More particularly, the DAQs  32 ,  34  transmit the TOA data  36 , and the OSM  38  forwards the operational data  40  to the central processing subsystem  42 . In certain embodiments, the central processing subsystem  42  may store the TOA data  36  and the operational data  40  as a backup file  44 . 
     Moreover, the central processing subsystem  42  determines one or more features  46  of the blades  16 ,  18  utilizing the TOA data  36  and the operational data  40 . As previously noted, the features  46 , for example, may include static deflection, blade clearance, dynamic deflection, variations in resonance frequency, reseating of a blade, or the like. More particularly, the central processing subsystem  42  determines the features  46  of the blades  16 ,  18  after taking into account the effects of the operational data  40  on the actual TOA in the TOA data  36 . In certain embodiments, the central processing subsystem  42  determines the features  46  of the blades  16 ,  18  after deducting the effects of reseating of the blades  16 ,  18  from the actual TOA of the blades  16 ,  18 . For example, with reference to Table 1, features corresponding to the blade 1 _dev_ 1  in the dev_ 1  may be determined utilizing the respective actual TOA that is shown as 2200 mils and other operational data that may be received from the OSM  38 . In addition, the central processing subsystem  42  evaluates the health of the blades  16 ,  18  utilizing the features  46 . Consequent to the determination of evaluation of the health of the blades, one or more health evaluation results may be generated by the central processing subsystem  42 . The health evaluation results may include plots, charts, graphs, visuals, or the like. In certain embodiments, the health evaluation results may include declarations, such as, probability of a propagation of a crack in a blade, probability of a twist in a blade, or the like. The determination of the features  46  and evaluation of the health of the blades  16 ,  18  will be explained in greater detail with reference to  FIGS. 2-6 . 
     In certain embodiments, the central processing subsystem  42  may store the features  46  and the health evaluation results in a data repository  48 . Furthermore, as shown in  FIG. 1 , the system  10  may include a web server  50  that may be coupled to the data repository  48 . The web server  50  may be configured to display the features  46  and the health evaluation results stored in the data repository  48 . The web server  50 , for example, may display the features  46  as tables, charts, and other visuals. 
     Referring now to  FIG. 2 , an exemplary flowchart  100  for monitoring one or more devices to evaluate the health of one or more blades in each of the devices, is depicted. The method starts at step  102  where BPS signals corresponding to the blades may be generated. The BPS signals, for example, may be generated by sensors, such as, the sensors  20 ,  22 ,  24 ,  26  (see  FIG. 1 ). As previously noted with reference to  FIG. 1 , the BPS signals may be generated by the sensors by sensing the arrivals of the blades at respective reference points. 
     Subsequently, at step  104  the BPS signals may be received by respective data acquisition systems (DAQs). The DAQs, for example, may be the DAQ_ 1   32  and the DAQ_ 2   34  (see  FIG. 1 ). Furthermore, at step  106  actual TOAs of the blades are determined utilizing the BPS signals. The actual times of arrival (TOAs), for example, may be determined by the DAQs. Subsequently, at step  108 , TOA data may be generated by the DAQs. For example, the TOA data may be the TOA data  36  (see  FIG. 1 ). As previously noted, the TOA data may include clearance data, identity of the devices that include the blades, identity of one or more sensors that sense the TOA of the blades, the category of the sensor indicating whether the sensor is a leading edge or a trailing edge sensor, identity of the blades, the actual TOA of the blades, or the like. 
     Furthermore, at step  110 , a central processing subsystem receives the TOA data from the DAQs. In certain embodiments, subsequent to the receipt of the TOA data from the DAQs, the central processing subsystem may store the TOA data as a back up file. As shown in  FIG. 2 , at step  112 , a delta TOA corresponding to each of the blades may be determined. The delta TOA corresponding to each of the blades may be determined by the central processing subsystem. 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  106  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):
 
ΔTOA 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 in which the effects on the actual TOA of the operational conditions reflected by the operational data 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, bought, or otherwise verified as healthy. 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. 
     Furthermore, at step  114 , a static deflection corresponding to each of the blades is determined utilizing the delta TOA of the blades. The static deflection corresponding to each of the blades, for example, may be determined by the central processing subsystem. In one embodiment, the static deflection corresponding to each of the blades is determined after deducting the effects of one or more operational data on the delta TOA of each of the blades. In another embodiment, the static deflection of the blades is determined after deducting the effects of the reseating of the blades during a start up of the devices. Exemplary methods for determining the static deflection of the blades will be explained in greater detail with reference to  FIGS. 3-5 . 
     In addition, at step  116 , a filtered delta TOA corresponding to each of the blades may be determined. The filtered delta TOA corresponding to each of the blades, for example, may be determined by filtering each of the delta TOA utilizing one or more filtering techniques. The one or more filtering techniques, for example, may include a Savitzky-Golay technique, an average filtering technique, a median filtering technique, or other filtering techniques. 
     At step  118 , a dynamic deflection corresponding to each of the 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 the filtered delta TOA corresponding to the blade that has been determined at step  116 . Subsequently, at step  120 , a detrended filtered delta TOA corresponding to each of the blades may be determined. For example, the deterended filtered delta TOA corresponding to each of the blades may be determined by detrending the filtered delta TOA that have been determined at step  116 . 
     Subsequent to the determination of the detrended filtered delta TOA, one or more resonance parameters may be determined at step  122 . The one or more resonance parameters, for example, may be determined by application of one or more techniques on each of the deterended filtered delta TOA that have been determined at step  120 . The one or more techniques, for example, may include a single degree of freedom (SDOF) technique, a multiple degree of freedom (MDOF) technique, or the like. By way of a non-limiting example, the resonance parameters may include amplitude, frequency, damping ratio, phase, or the like. Furthermore, at step  124 , one or more variations in resonance frequencies of the blades in comparison to baseline resonance frequencies may be determined. As used herein, the term “baseline resonance frequency” is used to refer to the resonance frequency of one or more blades when a device that includes blades is operating in an ideal situation and the blades do not have cracks or defects. The baseline resonance frequencies corresponding to a blade A in a device A, for example, may be determined by determining a statistical distribution of resonance frequencies of the blade A during start up of device A when the device is operating in ideal conditions. 
     Moreover, at step  126 , the health of the blades may be evaluated based upon the features of the blades that have been determined at step  114 ,  116  and  124 . More particularly, the health of blades is evaluated based upon the static deflection that has been determined at step  114 , the dynamic deflection that has been determined at step  116 , and the variations in the resonance frequencies that have been determined at step  124 . Consequent to the evaluation of the health of the blades, one or more health evaluation results may be generated. The health evaluation results, for example, may include graphs, charts, plots, visuals, or the like. In certain embodiments, the health evaluation results may include declarations, such as, probability of propagation of a crack in a blade, probability of a twist in a blade, status of the health of a device, or the like. As previously noted, the static deflection has been determined by deducting the effects of reseating of the blades, thus, the health of the blades is determined based upon the static deflection that does not include the affects due to the reseating of the blades. By way of a non-limiting example, the health evaluation results may show a propagation of a crack in a blade when static deflections of the blade show a monotonic change and resonance frequencies of the blade show a monotonic decrease. By way of another example, a propagation of a crack towards the leading edge of a blade may be declared when static deflections corresponding to the blade (that have been determined based upon delta TOA of a leading edge) show a monotonic change and dynamic deflections of the blade show an increase. 
     As previously noted, respective actual TOA of one or more blades may be used to determine static deflection of each of the blades. However, the operational state and reseating of the blades may affect 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. Accordingly, it is essential to remove or deduct the effects of the one or more operational data associated with the operational state and reseating of the blades on the actual TOA for the determination of the accurate 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  114  for determining static deflection of a blade, in accordance with an embodiment of the invention, is depicted. More particularly, step  114  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  112  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 an (IGV) angle, load, temperature, speed, mass flow, discharge pressure, or the like. The operational data, for example, may be received by the central processing subsystem  42  from the OSM  38  (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 (2):
 
ΔTOA k   =  AD     (2)
 
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  48  (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 (3):
 
 T   IGV ( t )=ƒ(IGV( t ))  (3)
 
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 ƒ is 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 (4):
 
 T   load ( t )= g ( DWATT ( t ))  (4)
 
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 (5):
 
 T   CTIM ( t )= d ( CTIM ( t ))  (5)
 
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 (6):
 
Norm_ΔTOA k ( t )=ΔTOA k ( t )− T   load ( t )− T   CTIM ( t )− T   IGV ( t )  (6)
 
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  48  (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 affect 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 falsely 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  114 ′ for determining static deflection in accordance with another embodiment, is depicted. More particularly,  FIG. 4  explains step  114 ′ 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  48 . 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 that has been 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 utilizing the following equation (7):
 
Norm_ΔTOA k ( t )=ΔTOA k ( t )− K *(Δσ( t ) — 1)−Mean(ΔTOA 1toj ( t ))  (7)
 
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 detail 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  48  (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  114 ″ for determining static deflection in accordance with another embodiment, is depicted. More particularly,  FIG. 5  explains step  114  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 (8):
 
Norm_ΔTOA k ( t )=(ΔTOA k ( t )−MeanΔTOA 1toj ( t ))/standard_deviation( 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, MeanΔTOA 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 detail 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  48  (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  FIGS. 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  48  (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 system and techniques result in real-time determination of features of one or more blades. The one or more features may be used to evaluate the health of the blades in real-time. Furthermore, the present system and techniques provides a central processing subsystem to determine the features of one or more blades in one or more devices, wherein the devices may be located at different remote locations. 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. In addition, 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. The present system may continuously monitor health of turbomachinary blades located in geographically dispersed locations around the world 24×7. The present system has in-built redundancy to recover quickly after a hardware crash. The present system also provides visualization tools to analyze health of blades using features extracted from TOA data. 
     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.