WO2002095633A2 - Methodes et dispositif permettant de determiner la condition d'un composant au moyen d'indicateurs d'etat - Google Patents

Methodes et dispositif permettant de determiner la condition d'un composant au moyen d'indicateurs d'etat Download PDF

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Publication number
WO2002095633A2
WO2002095633A2 PCT/US2002/016380 US0216380W WO02095633A2 WO 2002095633 A2 WO2002095633 A2 WO 2002095633A2 US 0216380 W US0216380 W US 0216380W WO 02095633 A2 WO02095633 A2 WO 02095633A2
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WIPO (PCT)
Prior art keywords
determining
health
indicator
computer program
program product
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Application number
PCT/US2002/016380
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English (en)
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WO2002095633A3 (fr
Inventor
Eric Robert Bechhoefer
David Hochmann
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Simmonds Precision Products, Inc.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from US10/011,905 external-priority patent/US6754569B2/en
Priority claimed from US10/011,973 external-priority patent/US6847917B2/en
Priority claimed from US10/011,622 external-priority patent/US6651012B1/en
Priority claimed from US10/011,787 external-priority patent/US6728658B1/en
Priority claimed from US10/011,864 external-priority patent/US6711523B2/en
Priority claimed from US10/011,428 external-priority patent/US7136794B1/en
Application filed by Simmonds Precision Products, Inc. filed Critical Simmonds Precision Products, Inc.
Priority to AU2002339855A priority Critical patent/AU2002339855A1/en
Priority to CA002439734A priority patent/CA2439734A1/fr
Priority to EP02744172A priority patent/EP1390739A2/fr
Publication of WO2002095633A2 publication Critical patent/WO2002095633A2/fr
Publication of WO2002095633A3 publication Critical patent/WO2002095633A3/fr

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Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
    • G05B23/0262—Confirmation of fault detection, e.g. extra checks to confirm that a failure has indeed occurred
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
    • G01H1/003—Measuring characteristics of vibrations in solids by using direct conduction to the detector of rotating machines
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/11—Analysing solids by measuring attenuation of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/12—Analysing solids by measuring frequency or resonance of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/4445—Classification of defects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/449—Statistical methods not provided for in G01N29/4409, e.g. averaging, smoothing and interpolation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/46—Processing the detected response signal, e.g. electronic circuits specially adapted therefor by spectral analysis, e.g. Fourier analysis or wavelet analysis
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
    • G05B23/0254—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model based on a quantitative model, e.g. mathematical relationships between inputs and outputs; functions: observer, Kalman filter, residual calculation, Neural Networks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/26—Scanned objects
    • G01N2291/269—Various geometry objects
    • G01N2291/2693—Rotor or turbine parts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/26—Scanned objects
    • G01N2291/269—Various geometry objects
    • G01N2291/2696—Wheels, Gears, Bearings

Definitions

  • This application relates to the field of vibration analysis and more particularly to performing vibration analysis for the purpose of device monitoring.
  • the transmission of power to rotors which propel helicopters and other shafts that propel devices within the aircraft induce vibrations in the supporting structure.
  • the vibrations occur at frequencies that correspond to the shaft rotation rate, mesh rate, bearing passing frequency, and harmonics thereof.
  • the vibration is associated with transmission error (TE).
  • Increased levels ofTE are associated with transmission failure.
  • Similar types of vibrations are produced by transmissions in fixed installations as well.
  • Parts such as those that may be included in a helicopter transmission, may be replaced in accordance with a predetermined maintenance and parts replacement schedule. These schedules provide for replacement of parts prior to failure.
  • the replacement schedules may indicate replacement time intervals that are too aggressive resulting in needless replacement of working parts. This may result in incurring unnecessary costs as airplane parts are expensive. Additionally, new equipment may have installed faulty or defective parts that may fail prematurely.
  • a method executed in a computer system and a computer program product for determining a health indicator associated with a component.
  • a plurality of health classifications are determined.
  • At least one condition indicator is determined quantifying a characteristic of the component.
  • a probability associated with each of the health classifications is determined. The probability is an estimation that the component is of a particular health classification given the at least one indicator.
  • a determination is made as to which of said health classifications is associated with said component using said probabilities associated with said health classifications for a given set of observed values.
  • a method executed in a computer system and a computer program product for determining a health status of a component A plurality of condition indicators are selected having a value and each having a corresponding weighting factor, and at least one threshold value defining at least two classifications.
  • a contribution to a health indicator is determined for each of said condition indicators, wherein said determining further comprises, for each of said plurality of indicators: determining which of said at least two classifications said value of said each indicator belongs; and determining said contribution to said health indicator by said each condition indicator in accordance with a selected one of said at least two classifications and said weighted value.
  • the health indicator is determined in accordance with all contributions by each of said condition indicator values.
  • a method executed in a computer system and a computer program product for determining an health indicator of a component at a subsequent time are a method executed in a computer system and a computer program product for determining an health indicator of a component at a subsequent time.
  • a first health indicator of said component at a time, n is determined in accordance with at least one corresponding condition indicator.
  • a second health indicator of the component is determined using a three state Kalman filter at a time subsequent to time n.
  • a method executed in a computer system and a computer program product for ranking condition indicators used in determining a health indicator for a component A first set of a plurality of said condition indicators is determined. A covariance matrix corresponding to said plurality of condition indicators is determined. A transformation matrix that whitens the covariance matrix is determined. Differences between said first plurality of condition indicators and expected values for said condition indicators belonging to a health class are determined using the whitening matrix. Each health class has a corresponding health indicator. A portion of said plurality of condition indicators is selected in accordance with those condition indicators have the smallest of said differences.
  • a method executed in a computer system and computer program product for estimating a conditional indicator value associated with a gear pair.
  • the gear pair is modeled as a damped spring model having a contact line between said gears.
  • a force, P is determined at a point of contact along said contact line causing linear and torsional response to each of said two gears in said gear pair.
  • a relative movement, d is determined of said gear pair, in accordance with said force, P, as a sum of four responses and a contact deflection, said relative movement d representing a gear model having two degrees of freedom.
  • the relative movement, d is used in determining said conditional indicator value for transmission error associated with said gear pair.
  • a bearing frequency ratio is determined for the bearing.
  • a periodic impulse is determined in accordance with the bearing frequency ratio.
  • An intensity of an impulse on a bearing surface as a function of an angle relative to a bearing fault is determined.
  • a decay of a unit impulse is determined.
  • a movement of the bearing is determined.
  • a conditional indicator value is determined in accordance with the movement.
  • a method executed in a computer system and computer program product for normalizing a set of at least one observed condition indicator.
  • a plurality of conditional indicators and at least one associated factor are determined in accordance with previous data acquisitions.
  • a mean and at least one model coefficient corresponding to said at least one associated factor are determined.
  • the set of observed condition indicators is adjusted in accordance with model coefficients and said at least one associated factor producing a normalized set of condition indicators.
  • a method executed in a computer system and computer program product for determining a condition indicator about a characteristic of a component.
  • a distribution of observed data associated with said component is determined.
  • a difference between said distribution and a normal distribution is determined.
  • the condition indicator is determined using the difference.
  • a method executed in a computer system and computer program product for determining a condition indicator associated with a component.
  • a total impulse signal is determined in accordance with configuration data.
  • the total impulse signal is a superposition of gear and bearing noise represented as a convolution of a gear and bearing signal with a gearbox transfer function.
  • a condition indicator is determined in accordance with the total impulse signal.
  • At least one condition indicator is determined using at least one of: an impulse determination technique and a statistical normality test.
  • the health indicator is determined in accordance with the at least one indicator.
  • Figure 1 is an example of an embodiment of a system that may be used in performing vibration analysis and performing associated monitoring functions
  • Figure 2 is an example representation of a data structure that includes aircraft mechanical data
  • Figure 3 is an example of parameters that may be included in the type-specific data portions when the descriptor type is an indexer
  • Figure 4 is an example of parameters that may be included in the type-specific data portions when the descriptor type is an accelerometer
  • Figure 5 is an example of parameters that may be included in the type-specific data portions when the descriptor type is a shaft
  • Figure 6 is an example of parameters that maybe included in the type-specific data portions when the descriptor type is for a gear
  • Figure 7 is an example of parameters that may be included in the type-specific data portions when the descriptor type is a planetary type
  • Figure 8 is an example of parameters that may be included in the type-specific data portions when the descriptor type is bearing type;
  • Figure 9 is an example of a data structure that includes analysis information
  • Figure 10 is a more detailed example of an embodiment of a header descriptor of Figure 9;
  • Figure 11 is an example of a descriptor that may be included in the acquisition descriptor group of Figure 9;
  • Figure 12 is an example of a descriptor that maybe included in the accelerometer group of Figure 9;
  • Figure 13 is an example of a descriptor that may be included in the shaft descriptor group of Figure 9;
  • Figure 14 is an example of a descriptor that may be included in the signal average descriptor group of Figure 9;
  • Figure 15 is an example of a descriptor that may be included in the envelope descriptor group of Figure 9;
  • Figure 16 is an example of a planetary gear arrangement
  • Figure 17A is an example of an embodiment of a bearing
  • Figure 17B is an example of a cut along a line of Figure 17A;
  • Figure 18A is an example of a representation of data flow in vector transformations
  • Figure 18B is an example of a representation of some of the CI algorithms that may be included in an embodiment, and some of the various inputs and outputs of each;
  • Figure 19 is an example of a graphical representation of a probability distribution function (PDF) of observed data
  • Figure 20 is an example of a graphical representation of a cumulative distribution function (CDF) observed data following a gamma (5,20) distribution and the normal CDF;
  • CDF cumulative distribution function
  • Figure 21 is an example of a graphical representation of the difference between the two CDFs of Figure 20;
  • Figure 22 is an example of a graphical representation of the PDF of observed data following a Gamma (5,20) distribution and a PDF of the normal distribution;
  • Figure 23 is an example of another graphical representation of the two PDFs from Figure 22 shown which quantities as intervals rather than continuous lines;
  • Figure 24A is an example of a graphical representation of the differences between the two PDFs of observed data and the normally distributed PDF;
  • Figures 24B-24D are examples of a graphical data displays in connection with a healthy system
  • Figures 24E-24G are examples of graphical data displays in connection with a system having a fault
  • Figure 25 is a flowchart of steps of one embodiment for deteraiining health indicators
  • Figure 26 is a graphical illustration of the probability of a false alarm (PFA) in one example
  • Figure 27 is a graphical illustration of the probability of detection (PD) in one example
  • Figure 28 is a graphical illustration of the relationship between PD and PFA and threshold values in one embodiment
  • Figure 29 is an graphical illustration of the probability of Ho and threshold values in one embodiment
  • Figure 30 is an example of an embodiment of a gear model
  • Figure 31 is a graphical representation of an estimated signal having an inner bearing fault
  • Figure 32 is a graphical representation of the signal of Figure 31 as a frequency spectrum.
  • FIG. 1 shown is an example of an embodiment of a system 10 that may be used in performing vibration analysis and monitoring of a machine such as a portion of an aircraft.
  • the machine being monitored 12 may be a particular element within an aircraft.
  • Sensors 14a through 14c are located on the machine to gather data from one or more components of the machine. Data may be collected by the sensors 14a through 14c and sent to a processor or a VPU16 for data gathering and analysis.
  • the VPU16 analyzes and gathers the data from the Sensors 14a through 14c.
  • the VPU16 may also use other data in performing analysis.
  • the VPU16 may use collected data 18.
  • One or more of the Algorithms 20 may be used as input into the VPU16 in connection with analyzing data such as may be gathered from the Sensors 14a through 14c.
  • configuration data 22 may be used by the VPU16 in connection with performing an analysis of the data received for example from the Sensors 14a through 14c.
  • configuration data may include parameters and the like that may be stored in a configuration data file. Each of these will be described in more detail in paragraphs that follow.
  • the VPU16 may use as input the collected data 18, one or more of the algorithms 20, and configuration data 22 to determine one or more condition indicators or CIs.
  • these condition indicators may be used in determining health indicators or His that may be stored for example in CI and HI storage 28.
  • CIs describe aspects about a particular component that may be useful in making a determination about the state or health of a component as may be reflected in an HI depending on one or more CIs.
  • CIs and His may be used in connection with different techniques in determining an indication about monitored components such as Machine 12.
  • the configuration data may include values for parameters that may vary in accordance with the type of the component being monitored.
  • the collected data 18 may include data collected over a period of time from sensors such as 14a through 14c mounted on Machine 12.
  • a user such as a Pilot 26, may use a special service processor, such as the PPU24, connected to the Machine 12 to obtain different types of data such as the CI and HI values 28.
  • the VPU16 may receive inputs from Sensors 14a through 14c.
  • Sensors 14a through 14c may be different types of data gathering monitoring equipment including, for example, high resolution accelerometers and index sensors (indexors) or tachometers that may be mounted on a component of Machine 12 at carefully selected locations throughout an aircraft. Data from these sensors may be sampled at high rates, for example, up to 100 kilohertz, in order for the VPU16 to produce the necessary CI and HI indicators. Data from these sensors and accelerometers may be acquired synchronously at precise intervals in measuring vibration and rotational speeds.
  • the different types of data gathering equipment such as 14a-14c may be sensors or tachometers and accelerometers.
  • Accelerometers may provide instantaneous acceleration data along whatever axis on which they are mounted of a particular device. Accelerometers may be used in gathering vibration analysis data and accordingly may be positioned to optimally monitor vibration generated by one or more mechanical components such as gears, shafts, bearings or planetary systems. Each component being monitored may generally be monitored using two independent sensors to provide confirmation of component faults and to enable detection of sensor faults.
  • No accelerometer is completely isolated from any other component.
  • the component rotational frequencies share as few common divisors as possible in order to maximize the effectiveness of the monitoring function being performed.
  • all gears being monitored should have differing number of teeth and all bearings should have differing numbers and sizes of balls or rollers. This may allow individual components to be spectrally isolated from each other to the extent that their rotational frequencies are unique.
  • the indexers may also be used as a particular monitoring component 14a through 14c to gather data about a particular component of Machine 12.
  • the indexers produce a periodic analog signal whose frequency is an integer multiple of the instantaneous rotation frequency of the shaft that they are monitoring.
  • These signals may be generated magnetically using one or more evenly spaced metallic protrusions on the shaft passing by the fixed sensor. Alternatively, these may be monitored optically using a piece of optically reflective material affixed to the shaft. It should be noted that each index point should be fixed in time as precisely as possible. In connection with magnetic sensors, this may be accomplished for example by interpolating the zero crossing times of each index pulse and similarly for optical sensors by locating either rising or falling edges.
  • the relative position and rate of any component may be calculated using a single index or wave form. Because of the high data rates and lengthy processing intervals, diagnostics may be performed, for example, on pilot command or on a predetermined flight regime or time interval.
  • Each of the algorithms 20 produces one or more CIs described elsewhere herein in more detail.
  • the CI may yield useful information about the health of a monitored component.
  • This condition indicator or CI as well as HI may be used in determining or predicting faults of different components.
  • VPU16 is intended to be used in a wide variety of mechanical and electrical environments. As described herein, different components of an aircraft may be monitored. However, this is only one example of a type of environment in which the system described herein may be used. As known to those skilled in the art, the general principles and techniques described herein have much broader and general applicability beyond a specific aircraft environment that may used in an example here.
  • the VPU16 uses the CIs as input and portions of the data such as, for example, used in connection with an algorithm to provide His. These are described in more detail in paragraphs that follow.
  • each mechanical part being monitored may have one or more sensors associated with it where a sensor may include for example an accelerometer or a tachometer.
  • a sensor may include for example an accelerometer or a tachometer.
  • accelerometers may be used, for example, to obtain data regarding vibrations and a tachometer may be used, for example, to gain information and data regarding rotation or speed of a particular object. Data may be obtained and converted from the time to the frequency domain.
  • a particular algorithm may provide one or more CIs.
  • Each of the algorithms may produce or be associated with a particular CI.
  • One or more CIs may be used in combination with a function to produce an HI for a particular part or type.
  • each of the algorithms may be associated or classified with a particular part or type.
  • the CI generally measures vibrations and applies a function as described in accordance for each algorithm. Generally, vibration is a function of the rotational frequency in the amount of torque. Using torque and a particular frequency, a CI is appropriately determined in accordance with a selected algorithm for a part.
  • the algorithms 20 may be classified into four families or groups in accordance with the different types of parts.
  • the families of algorithms may include shaft, gears, bearings, and planetary gears.
  • Associated with each particular part being monitored may be a number of CIs.
  • Each CI may be the result or output of applying a different one of the algorithms for a particular family.
  • each gear may have an associated 27 CIs
  • each bearing may have 19 CIs
  • each shaft may have 22 CIs
  • each planetary gear may have two or three CIs. It should be noted that each one of these numbers represents in this example a maximum number of CIs that may be used or associated with a particular type in accordance with the number of algorithms associated with a particular class or family.
  • a CI reflects a particular aspect or characteristic about a gear with regard to how it may fail.
  • Different techniques used in computing CIs are described, for example, in "Introduction to Machinery Analysis and Monitoring, Second Edition", 1993, Penn Well Publishing Company of Tulsa, OK, ISBN 0-87814-401-3, and "Machinery Vibration: measurement and analysis", 1991, McGraw-Hill Publishing, ISBN-0-07-071936-5.
  • this data structure includes one or more descriptors 56a through 56n.
  • a descriptor associated with a particular sensor includes the parameters relevant to the particular component being momtored.
  • Each of the descriptors such as 56a includes three portions of data.
  • the field 52 identifies a particular type of descriptor.
  • Each of the descriptors also includes a common data portion 54 which includes those data fields common to all descriptor types. Also included is a type specific data portion 56 which includes different data fields, for example, that may vary in accordance with the descriptor type 52.
  • Descriptor types may include, for example, an indexer, an accelerometer, a shaft, a gear, a planetary gear, or a bearing descriptor type value corresponding to each of the different types of descriptors.
  • the common data portion 54 may include, for example, a name, part number and identifier. In this example, the identifier in the common data filed 54 may uniquely identify the component and type.
  • descriptor type specific parameters or information that may be included in a descriptor of a particular type, such as in area 56 of the data structure 50.
  • a descriptor 60 which is an indexer descriptor type.
  • the parameters that may be included are a channel 62, a type 64, a shaft identifier 66, a pulses per revolution parameter 68, a pulse width parameter 70, and a frequency of interest 72 for this particular type of descriptor.
  • the type in this example for the index or descriptor may be one of sinusoidal, pulse such as 1/ rev, or optical.
  • the shaft identifier 66 is that as may be read or viewed by the indexer that calculates the shaft rate.
  • the pulse width 70 is in seconds as the unit value.
  • the frequency of interest 72 for this descriptor type is a nominal pulse frequency that is used in computing the data quality signal to noise ratio.
  • the descriptor for an accelerometer type may include the channel 82, a type 84, a sensitivity 86 and a frequency of interest 88.
  • the type may be one of normal, or remote charge coupled.
  • the frequency of interest may be used in computing the data quality signal to noise ratio.
  • the frequency of interest for a gear is the mesh rate which may be calculated from the gear shaft rate and the number of teeth of the gear.
  • a shaft descriptor 90 includes path parameter or data 92 and nominal RPM data 94.
  • the path data is an even length sequence of gear tooth counts in the mechanical path between the shaft in question and a reference shaft.
  • the driving gears alternate with driven gears such that the expected frequency of a gear, shaft, bearing and the like may be determined based on an input shaft RPM.
  • gear descriptor 100 included in the gear descriptor 100 is the shaft identifier 102 to which the gear is mounted and a parameter 104 indicating the number of teeth in the gear.
  • the planetary descriptor 110 may include an input shaft identifier 112, an output shaft identifier 114, a parameter indicating the number of planet gears 116, a parameter indicating the number of teeth on the planet gear, a parameter 120 indicating the number of teeth on the ring gear, and a parameter 122 indicating the number of teeth on the sun gear. It should be noted that the number of teeth on a planet gear relates to a planet carrier that is assumed to be mounted to the output shaft.
  • the ring gear is described by parameter 120 is assumed to be stationery and the sun gear 122 as related to parameter 122 is assumed to be mounted to the input shaft. It should be noted that the path between the input and the output shaft may be reduced to using a value S for the driving path tooth count and R+S as the driven path tooth count where R and S are the ring and sun tooth counts respectively.
  • An example of a planetary type gear is described in more detail elsewhere herein.
  • the bearing descriptor 130 may include descriptor type specific fields including a shaft identifier 132, a cage ratio 134, a ball spin ratio 136, an outer race ratio 138 and an inner race ratio 140.
  • a bearing is described in more detail elsewhere herein.
  • data structures described in connection with Figures 2 through 8 are those that may be used in storing data obtained and gathered by a sensor such as 14a when monitoring a particular component of a machine 12. Data maybe gathered and stored in the data structure for a particular descriptor or descriptors and sent to the VPU 16 for processing. It should be noted that a particular set of data may be gathered at a particular instance and time, for example, in connection with the synchronous data gathering described elsewhere herein. In connection with this, a data set may include multiple descriptors from sampling data at a particular point in time which is sent to the VPU 16.
  • Each instance of analysis data 150 as represented in the data structure includes a header descriptor 152 and descriptor groups noted as 164. In this example there are five descriptor groups although the particular number may vary in an embodiment.
  • Each of the descriptor groups 154 through 162 as identified by the group identifier 164 includes one or more descriptors associated with a particular group type.
  • descriptor group 154 is the acquisition group that includes a descriptor for each sensor to be acquired.
  • the accelerometer group 156 consists of a descriptor for each accelerometer to be processed.
  • the shaft group 158 includes a descriptor for each shaft to be processed.
  • the signal average group 160 includes a descriptor for each unique parameter set.
  • the envelope group 162 includes a descriptor for each unique parameter.
  • a header descriptor 170 Parameters that may be included in a header descriptor 170 include: an analysis identifier 172, acquisition time out parameter 174 and processing time out parameter 176. In this example, the acquisition, time out and processing time out parameters are in seconds.
  • a descriptor 180 included in the acquisition group may include a sensor identifier 182, a sample rate parameter in Hz 184, a sample duration in seconds 186, a gain control setting, such as "auto" or “fixed” 188, an automatic gain control (AGC) acquisition time in seconds 190, an automatic gain control (AGC) headroom factor as a number of bits 192 and a DC offset compensation enable 194.
  • AGC automatic gain control
  • a descriptor in the accelerometer group may include a parameter that is an accelerometer acquisition analysis group identifier 202, a list of associated planetary identifiers to be processed 204, a list of associated shaft analysis group identifiers to be processed 206, a processor identifier 208, a transient detection block size 210, a transient detection RMS factor 212, a power spectrum decimation factor 214 specified as a power of 2 and a power spectrum block size also specified as a power of 2.
  • the list of associated planetary identifiers 204 also includes two signal average analysis group identifiers for each planetary identifier, first identifier co ⁇ esponding to the input shaft and a second corresponding to an output shaft.
  • processor identifier 208 will be used in connection with assigning processing to a particular DSP or digital signal processor.
  • the descriptor 220 may include a shaft identifier 222, a signal average analysis group identifier 224, a list of gear identifiers to be processed 226, a list of bearing identifiers to be processed 228 and a list of associated envelope analysis group identifiers 230.
  • each descriptor 232 may be included in the signal average group. It should be noted that the signal average group includes a descriptor for each unique parameter set. The signal average processing group is run for each accelerometer and shaft combination even if it has the same parameters as another combination. Each descriptor 232 may include a number of output points per revolution 234 and a number of revolutions to average 236.
  • Each descriptor 240 may include a duration parameter 242 specifying the seconds of raw data to process, an FFT size 244 which is a power of 2, a lower bound frequency in Hz 246, and an upper bound frequency, also in, Hz 248.
  • a planetary gear a ⁇ angement as described in connection with the different types of gears and items to be monitored by the system 10 of Figure 1 may include a plurality of gears as configured, for example, in the embodiment 300.
  • a ring gear 302 a plurality of planet gears 304a through 304c and of sun gear 306.
  • the gears that are designated as planets move around the sun gear similar to that as a solar system, hence the name of planet gear versus sun gear.
  • the arrangement shown in Figure 16 is a downward view representing the different types of gears included in an arrangement 300.
  • the bearing 320 includes a ring or track having one or more spherical or cylindrical elements (rolling elements) 324 moving in the direction of circular rotation as indicated by the arrows.
  • Different characteristics about such a structure of a bearing may be important as described in connection with this embodiment.
  • One characteristic is an “inner race” which represents the circumference of circle 322a of the inner portion of the ring.
  • the "outer race” or circumference 322b representing the outer portion of the ring may be a consideration in connection with a bearing.
  • FIG. 17B shown is an example of a cut along line 17B of Figure 17A.
  • this is cut through the ring or track within which a bearing or bearings 324 rotate in a circular direction.
  • the ball bearings move in unison with respect to the shaft within a cage that follows a track as well as rotate around each of their own axis.
  • FIG. 18 A shown is an example of a representation 550 of different transformations that may be performed and the associated data flow and dependencies for each particular sensor.
  • the output of the transformations are transformation vectors and may be used in addition to analysis data or raw data, such as bearing frequency, mesh frequency, and the like, by an algorithm in producing a CI.
  • an in going arrow represents data flow input to a transformation.
  • the FF or Fast Fourier transform takes as an input data from the Al signal average data transform.
  • Al has as input the accelerometer data AD.
  • other embodiments may produce different vectors and organize data inputs/outputs and intermediate calculations in a variety of different ways as known to those skilled in the art.
  • each type of component in this example is one of: indexer, accelerometer, shaft, gear, planetary, or bearing.
  • Certain algorithms may be used in connection with determining one or more CIs for more than one component type. It should be noted that a variety of different algorithms may be used and are known by one of ordinary skill in the art, as described elsewhere herein in more detail. The following are examples of some of the different techniques that may be used in producing CIs.
  • Figure 18B illustrates an example of relationships between some algorithms, a portion of their respective inputs and outputs, as well as how the algorithms may be associated with different component types. However, it should be noted that this illustration is not all inclusive of all algorithms, all respective inputs and outputs, and all component types.
  • the data quality (DQ) algorithm 356 may be used as a quality assurance tool for the DTD CI.
  • DQ performs an assessment of the raw uncalibrated sensor data to insure that the entire system is performing nominally.
  • DQ may be used to identify, for example, bad wiring connections, faulty sensors, clipping, and other typical data acquisition problems.
  • the DQ indicator checks the output of an accelerometer for "bad data”. Such "bad data” causes the SI to be also be “bad” and should not be used in determining health calculations.
  • ADC Bit Use measures the number of ADC bits used in the current acquisition.
  • the ADC board is typically a 16 bit processor.
  • the log base 2 value of the maximum raw data bit acquired is rounded up to the next highest integer.
  • Channels with inadequate dynamic range typically use less than 6 bits to represent the entire dynamic range.
  • ADC Sensor Range is the maximum range of the raw acquired data. This range cannot exceed the operational range of the ADC board, and the threshold value of 32500 is just below the maximum permissible value of +32767 or -32768 when the absolute value is taken.
  • Dynamic Range is similar to the ADC Sensor Range, except the indicator reports dynamic channel range as a percent rather than a fixed bit number.
  • Low Frequency Slope Low Frequency Slope
  • Low Frequency Intercept lowFreqlnt
  • SNR is the signal to noise ratio observed in each specific data channel.
  • a power spectral density is calculated from the raw uncalibrated vibration data. For each data channel, there are known frequencies associated with certain components. Examples include, but are not limited to, gear mesh frequencies, shaft rotation rates, and indexer pulse rates.
  • S ⁇ R measures the rise of a known tone (corrected for operational speed differences) above the typical minimum baseline levels in a user-defined bandwidth (generally +/- 8 bins).
  • the Statistics (ST) algorithm 360 is associated with producing a plurality of statistical indicators 360a.
  • the Root-Mean-Square (RMS) value of the raw vibration amplitude represents the overall energy level of the vibration.
  • the RMS value can be used to detect major overall changes in the vibration level.
  • the Peak-To-Peak value of the raw vibrating amplitude represents the difference between the two vibration extrema. When failures occur, the vibration amplitude tends to increase in both upward and downward directions and thus the Peak-To-Peak value increases.
  • the Skewness coefficient (which is the third statistical moment) measures the asymmetry of the probability density function (p.d.f.) of the raw vibration amplitude. Since it is generally believed that the p.d.f.
  • any large deviations of this value from zero may be an indication of faults.
  • a localized defect in a machine usually results in impulsive peaks in the raw vibration signal, which affects the tails of the p.d.f. of the vibration amplitude.
  • the fourth moment (Kurtosis) of the distribution has the ability to enhance the sensitivity of such tail changes. It has a value of 3 (Gaussian distribution) when the machinery is healthy. Kurtosis values larger than 3.5 are usually an indication of localized defects. However, distributed defects such as wear tend to smooth the distribution and thus decrease the Kurtosis values.
  • the ST algorithm may be performed on the following vectors: AD raw accelerometer data, Al signal average data, RS residual data, NB na ⁇ ow band data, and EV envelope data and others, some of which are listed in 360b.
  • Tone andBase Energy algorithm(TB) 362 uses tone energy and base energy. Tone Energy is calculated as the sum of all the strong tones in the raw vibration spectrum. Localized defects tend to increase the energy levels of the strong tones. This indicator is designed to provide an overall indication of localized defects. "Strong tones" are determined by applying a threshold which is set based on the mean of all the energy contents in the spectrum. Any tones that are above this threshold are attributed to this indicator. The Base Energy measures the remaining energy level when all the strong tones are removed from the raw vibration spectrum. Certain failures such as wear, do not seem to affect the strong tones created by shaft rotation and gear mesh, the energy in the base of the spectrum could potentially be a powerful detection indicator for wear-related failures.
  • Tone Energy and Base Energy equals the overall energy level in the spectrum.
  • SI are miscellaneous shaft indicators.
  • SOI shaft Order 1 in g
  • SO2 shaft Order 2 in g
  • GDF Near detector fault
  • GDF may be an effective detector for distributed gear faults such as wear and multiple tooth cracks, and is a complement of the indicator signal AverageLl (also known as gearLocalFault).
  • the SI algorithm takes input from the indexer zero-crossing vector (ZC).
  • the Demodulation analysis (DM) 370 is designed to further reveal side band modulation by using the Hubert transform on either the na ⁇ ow band signal (na ⁇ ow band demodulation) or the signal average itself (wide band demodulation) to produce the Amplitude Modulation (AM) and Phase Modulation (FM) signals.
  • the procedures involved to obtain such signals are:
  • the DM algorithm is performed on the band passed filtered data at a frequency of interest by taking a Hubert Window function of the frequency domain data and converting the data back to the time domain.
  • the Sideband Modulation (SM) 368 analysis is designed to reveal any sideband activities that may be the results of certain gear faults such as eccentricity, misalignment, or looseness.
  • the DSMn is calculated as the sum of both the nth high and low sideband energies around the strongest gear meshing harmonic.
  • the SM algorithm is performed on the Fast Fourier transform vector (FF).
  • the Planetary Analysis (PL) 364 extracts the Amplitude Modulation (AM) signal produced by individual planet gears and compares the "uniformity" of all the modulation signals.
  • AM Amplitude Modulation
  • Calculate the Planet Gear Fault (PGF) indicator as included in 364a according to the equation PGF MAX(AM) / MIN (AM).
  • the inputs to the PL algorithm are the raw accelerometer data (AD) and the indexer zero- crossing data (ZC).
  • the Zero-Crossing Indicators (Zl) algorithm 354 is performed on the zero-crossing vector (ZC).
  • the zero crossing indicators may be determined as follows:
  • the Shaft Indicators (SI) algorithm 358 calculates miscellaneous shaft indicators included in 358a.
  • SO/ Shaft Order 1 in g
  • SO2 Shaft Order 2 in g
  • SO2 shaft Order 2 in g
  • S ⁇ 3 (Shaft Order 3), is the three-per-rev energy in the signal average, and is used to detect shaft misalignment.
  • the miscellaneous shaft indicators may also be included in an embodiment defined as follows: p — numPathPairs
  • indexRatio 7 ⁇ ⁇ , dnveRatio pulsesUsed shaftRatio 60 shaftSpeed pulselntervalMean • driveRatio
  • gearDistFault is an effective detector for distributed gear faults such as wear and multiple tooth cracks, and is a complement of the indicator signalAverageLl (also known as gearLocalFault).
  • the SI algorithm takes input from the indexer zero-crossing vector (ZC) and may also use others and indicated above.
  • shaftPath is defined for the shaft descriptor indexPath is the path of the shaft seen by the indexer used for signal averaging numPathPairs is the number of path pairs defined for shaftPath and indexPath pulsesUsed is the number of pulses used per revolution of the indexer shaft pulselntervalMean is the mean of the zero-crossing (ZC) intervals pointsPerRev is the number of output points per revolution in the signal average
  • the Bearing Energy (BE) algorithm 376 performs an analysis to reveal the four bearing defect frequencies (cage, ball spin, outer race, and inner race frequencies) that usually modulate the bearing shaft frequency. As such, these four frequencies are calculated based on the measured shaft speed and bearing geometry. Alternatively, the four frequency ratios may be obtained from the bearing manufacturers. The energy levels associated with these four frequencies and their harmonics are calculated for bearing fault detection. They are:
  • Cage Energy the total energy associated with the bearing cage defect frequency and its harmonics. Usually it is detectable only at the later stage of a bearing failure, but some studies show that this indicator may increase before the others.
  • - Ball Energy the total energy associated with the bearing ball spin defect frequency and its harmonics.
  • - Outer Race Energy the total energy associated with the bearing outer race defect frequency and its harmonics.
  • the Total Energy indicator gives an overall measure of the bearing defect energies.
  • one or more algorithms may be used in determining a CI representing a score quantifying a difference between observed or actual test distribution data and a normal probability distribution function (PDF) or a normal cumulative distribution function (CDF).
  • PDF normal probability distribution function
  • CDF normal cumulative distribution function
  • these one or more algorithms may be categorized as belonging to a class of algorithms producing CIs using hypothesis tests (“hypothesis testing algorithms”) that provide a measure of difference in determining whether a given distribution is not normally distributed.
  • hypothesis testing algorithms produce a score that is used as a CI.
  • the score may be described as a sum of differences between an observed or actual test distribution function based on observed data and a normal PDF or normal CDF.
  • An algorithm may exist, for example, based on each of the following tests: Chi-Squared Goodness of fit (CS), Kolmogorov-Smirnov Goodness of fit (KS), Lilliefors test of normality, and Jarque-Bera test of normality (JB).
  • Other embodiments may also include other algorithms based on other tests for normality, as known to those of ordinary skill in the art.
  • the hypothesis tests compare the test distribution to the normal PDF, for example as with CS test, or the normal CDF, for example as with the KS and Lilliefor tests.
  • the test distribution of observed data forms a Gamma (5, 20) distribution function, having and alpha value of 5 and a beta value of 20.
  • the mean of this Gamma(5,20) distribution is alpha * beta having a variance of alpha * beta 2 .
  • the Gamma (5,20) distribution function is a tailed distribution which graphically is similar to that of a normal distribution.
  • FIG. 19 shown is an example of a graphical representation 400 of observed data.
  • FIG 20 shown is an example of a graphical representation 410 of the normal CDF and the Gamma (5,20) CDF of random data.
  • Figure 21 shown is an example of a graphical representation 420 of the difference between the normal CDF and the Gamma (5,20) CDF.
  • the graphical representation for example, in Figure 21 represents differences in 1000 instances where the difference between the expected value (Normal CDF) and the maximum deviation of the (in this case defined as the score) observed gamma CDF can exceed some critical value.
  • the critical value is that statistic which represents some predefined alpha e ⁇ or (the probability that the test indicates the distribution is not normal when in fact it is normal - this is typically set at 5%.) If the score exceeds the critical value, the distribution is said to be not normal statistic. The score is the maximum deviation from this statistic or alpha value.
  • the normal PDF is used.
  • the representations of Figure 22 are drawn as continuous lines rather than discrete intervals.
  • bin 1 includes values between [0,0.25)
  • bin 2 includes values between [0.25, 0.50
  • bin 3 includes values between [.050,0.75)
  • bin 4 includes values between [0.75, 1.0).
  • For each bin determine the number of observed and expected values, and their difference. Square each of the differences for each bin and then add all the differences and divide by the expected value for each bin.
  • the CS test which sums all the differences for each category divided by the expected value for each category represented as:
  • the critical value is the ⁇ at k-1 degrees of freedom may be, for example, 90.72
  • Figure 24A represents graphically a difference between observed and expected values for each bin or interval of Figure 23.
  • This may be refe ⁇ ed to as an impulse determination algorithm that produces a CI indicating an amount of vibration that may be used in detecting a type of fault.
  • the impulse determination algorithm takes into account the physical model of the system.
  • One type of fault that this technique may be used to detect is a pit or spall on either: gear tooth, inner bearing race, outer bearing race or bearing roller element.
  • This technique uses a model designed to detect this type of fault where the model is based on knowledge of the physical system. For example, if there is a pit or spall on a bearing, this may produce a vibration on a first bearing which may further add vibrations to other components connected to or coupled to the bearing.
  • a model can be determined for a particular configuration by using configuration data, for example.
  • a signal received at a sensor may be a superposition of gear and bearing noise that may be represented as a convolution of gear/bearing noise and a convolution of the Gear/Bearing signal with the gearbox transfer function.
  • LPC Linear Predictive Coding
  • LPC Linear Predictive Coding
  • the base signal components are an impulse train generated by the fault hitting a surface (e.g gear tooth with geartooth, inner race with roller element, etc) and the bearing/case transfer function.
  • the bearing, gear and case have there own transfer functions.
  • Convolution here is transitive and multiplicative.
  • LPC techniques may be used to estimate the total convolution function of the total vibration that may be produced.
  • the total amount of vibration representing the total impulse signal generated by a configuration may be represented as:
  • convolution is a homomorphic system such that it is monotonically increasing and that logarithmic transformations hold.
  • a "dual nature" of convolution is used in following representations to equate operations using convolution in the time domain to equivalent multiplication operation in the frequency domain.
  • the convolution in the time domain may be equated to a multiplication in the frequency domain represented as:
  • the system transfer function " ⁇ " may be estimated for the Gear/Bearing and Case to recover the impulse response allocated with a Gear or Bearing pit/spall fault.
  • the estimation of this transfer function " ⁇ ” may be accomplished using Linear Predictive Coding (LPC) techniques.
  • LPC assumes that the Transfer Function is a FIR filter, and as such, the auto-co ⁇ elation of the time domain signal may be used to solve for the filter coefficients in a minimum sum of square e ⁇ or sense.
  • LPC there is an impulse that is convoluted with a FLR filter, such that:
  • y[n] — 1] + a 2 x[n - 2J+ a 3 x[n - 3J+ ...
  • Y may also be expressed as:
  • Y FFT(y[l, 2, .. n]) in which y[l ..n] are values in the time domain expressed in the frequency domain as a Fourier transform of the time domain values. Y represents cu ⁇ ent time vector measurements in the frequency domain.
  • the transfer function H may be estimated and represented as a/2?, (freq. Domain). Note that "a” is a vector of the values al ... an obtained above.
  • IMP exp(log(Y) - log(H)) IMP Equation
  • the impulse for example, may be characterized as "white noise". As the fault progresses, the impulse or the value of H becomes larger.
  • the CI is the power spectral density at a bearing passing frequency for a bearing fault, or a mesh frequency for a gear fault.
  • Other CIs based on the foregoing value may be a "score" of the Lilifers test for normality, or other such test.
  • a pit or spall may cause a vibration or tapping. Subsequently, other elements in contact with the ball bearing may also vibrate exhibiting behavior from this initial vibration. Thus, the initial vibration of the pit or spall may cause an impulse spectrum to be exhibited by such a component having unusual noise or vibration.
  • the value of IMP as may be determined using the IMP Equation above represents the impulse function that may be used as a "raw" value and at a given frequency and used as an input into an HI determination technique.
  • the IMP at a particular frequency, since this the spectrum, determined above may be compared to expected values, such as may be obtained from the stored historic data and configuration data.
  • An embodiment may also take the power spectrum of this raw impulse spectrum prior to being used, for example, as input to an HI calculation where the power spectrum is observed at frequencies of interest, such as the inner race frequency. For example, if the impulse function is within some predetermined threshold amount, it may be concluded that there is no fault.
  • FIG. 24B and Figure 24C are relative to a healthy system, such as a main gearbox, for example, such as in connection with a planetary race fault of an SH-60B U.S. Navy Helicopter built by Silorsky.
  • the Figure 24B representation 700 shows an impulse train in the frequency domain of the healthy system.
  • an embodiment may estimate the transfer function H using LPC using different techniques.
  • An embodiment may estimate the transfer function H using an autoco ⁇ elation technique(AutoLPC).
  • An embodiment may also estimate the transfer function H using a covariance technique (CovLPC).
  • Use of autoco ⁇ elation may use less mathematical operations, but require more data than using the covariance.
  • use of the covariance technique may use more mathematical operations but require less data.
  • the autoco ⁇ elation LPC result converges to the covariance LPC result.
  • data samples are at lOOKHz with 64,000 data points used with the autoco ⁇ elation technique due to the relatively large number of data points.
  • Figure 24C representation 710 shows the data of 700 from Figure 24B in the time domain rather than the frequency domain.
  • Figure 24D representation 720 shows the power spectral density of the above figures as deconvolved time data of frequency v. dB values in a healthy system.
  • Figures 24B-24D represent data in a graphical display in connection with a healthy system.
  • Figures 24E-24G in connection with an unhealthy system, such as a starboard ring channel which exhibit data that may be expected in connection with a pit or spall fault.
  • Figure 24E, representation 730 illustrates an impulse train as maybe associated with an unhealthy system in the time domain.
  • Figure 24F, representation 740 illustrates a graphical display of the impulse train in the frequency domain.
  • FIG 24G shown is an illustration 740 is a graphical representation of the power spectrum of the impulse train represented in connection with the other two figures for the unhealthy system identified by a period impulse train associated with an inner race bearing fault.
  • a spike may be viewed in the graphical display as well as the harmonics thereof.
  • raw data acquisition is performed. This maybe, for example, issuing appropriate commands causing the VPU to perform a data acquisition.
  • the raw data may be adjusted, for example, in accordance with particular configuration information producing analysis data as output. It is at step 504, for example, that an embodiment may make adjustments to a raw data item acquired as may be related to the particular arrangement of components.
  • data transformations may be performed using the analysis data and other data, such as raw data.
  • the output of the data transformations includes transformation output vectors.
  • CIs are computed using the analysis data and transformation vector data as may be specified in accordance with each algorithm.
  • one or more CIs may be selected. Particular techniques that may be included in an embodiment for selecting particular CIs is described elsewhere herein in more detail.
  • CIs may be normalized. This step is described in more detail elsewhere herein.
  • the selected and normalized CIs are used in determining His. Particular techniques for determining His are described in more detail elsewhere herein.
  • HI computations may not be executed in real time. Rather, they may be performed, for example, when a command or request is issued, such as from a pilot or at predetermined time intervals.
  • the hardware and/or software included in each embodiment may vary, in one embodiment, data acquisition and/or computations may be performed by one or more digital signal processors (DSPs) running at a particular clock speed, such as 40MHz, having a predetermined numerical precision, such as 32 bits.
  • the processors may have access to shared memory.
  • sensors may be multiplexed and data may be acquired in groups, such as 8. Other embodiments may vary the number in each group for data sampling. The sampling rates and durations within an acquisition group may also vary in an embodiment.
  • Data may be placed in the memory accessed by the DSPs on acquisition, hi one embodiment, the software may be a combination of ADA95 and machine code.
  • Processors may include the VPU as described herein as well as a DSP chip. What will now be described are techniques for nonnalizing CIs in connection with determining His providing more detailed processing of step 512 as described in connection with flowchart 500.
  • Transmission e ⁇ or depends upon torque. Additionally, vibration depends upon the frequency response of a gear. As such, the CI, which also depends upon T.E. and vibration, is a function (generally linear) of torque and rotor speed (which is frequency), and airspeed as this may change the shape of the airframe.
  • T.E. Transmission e ⁇ or
  • CI Transmission e ⁇ or
  • vibration depends upon the frequency response of a gear.
  • the CI which also depends upon T.E. and vibration, is a function (generally linear) of torque and rotor speed (which is frequency), and airspeed as this may change the shape of the airframe.
  • techniques that may be used in connection with determining the "health state" or HI of a component may normalize CIs to account for the foregoing since His are determined using CIs.
  • a number of CIs may be determined.
  • An embodiment may compare CI values to threshold values, apply a weighting factor, and sum the weighted CIs to determine an HI value for a component at a particular time.
  • the threshold values may be different for each torque value. For example, an embodiment may use 4 torque bands, requiring 4 threshold values and weights for each CI. Additionally, the coarseness of the torque bands will result in increased, uncontrolled system variance. Alternatively, rather than use multiple threshold values and have an uncontrolled variance, an embodiment may use a normalization technique which normalizes the CI for torque and rotor RPM (Nr), and airspeed, expressed as a percentage, for example, in which a percentage of 100% is perfect. Use of these normalized CIs allows for a reduction of configuration such that, for example, only one threshold is used and variance may also be reduced.
  • the normalization technique that will now be described in more detail may be used in connection with methods of HI generation, such as the non-linear mapping method and the hypothesis testing method of HI generation that are also described in more detail elsewhere herein.
  • a deflection in a spring is linearly related to the force applied to the spring.
  • the transmission may be similar in certain aspects to a large, complex spring.
  • the displacement of a pinion and its co ⁇ esponding Transmission E ⁇ or (T.E.) is proportional to the torque applied.
  • T.E. is a what causes vibration, while the intensity of the vibration is a function of the frequency response (N r ), where frequency is a function of RPM.
  • vibration and the co ⁇ esponding CI calculated using a data acquisition are approximately linearly proportional to torque, N r, . (over the operating range of interest) and/or airspeed although at times there may be a linear torque*Nr interaction effect.
  • gear box manufacturers may design a gearbox to have minimum T.E. under load, and a graphical representation of T.E. vs. Torque is linear, or at least piece wise linear.
  • test data for example used in connection with a Bell helicopter H-l loss of lube test, shows a relationship between CI and torque suggesting linearity. Additionally, tests show that airspeed is also relevant factor.
  • Other embodiments may take into account any one or more of these factors as well as apply the techniques described herein to other factors that may be relevant in a particular embodiment or other application although in this example, the factors of torque, airspeed and Nr are taken into account.
  • An equation representing a model minimizing the sum of square e ⁇ or of a measured CI for a given torque value in a healthy gear box is:
  • the order of the model may be determined by statistical significance of the coefficients of Equation 1.
  • the T.E. of a "healthy" component may have, for example, a mean of zero (0) with some expected variance. It should be noted that if the model fits well for the lower order. Higher order coefficients are not required and may actually induce e ⁇ or in some instances.
  • Each of the CIs included in the vector y is a particular recorded value for a CI from previous data acquisitions, for example, as maybe stored and retrieved from the collected data 18. Also stored with each occu ⁇ ence of a CI for a data acquisition in an embodiment may be a co ⁇ esponding value for torque (t), ⁇ r, and Airspeed. These values may also be stored in the collected data 18.
  • the model coefficients for B may be estimated by minimizing the sum of square e ⁇ or between the measured CI and the model or estimated CI using the observed performance
  • coefficient Bo represents the mean of the data set for a particular component which, for example, may be represented as an offset value.
  • Each of the other values Bl ... Bn are coefficients multiplied by the co ⁇ esponding factors, such as airspeed, torque, and Nr.
  • the foregoing B values or coefficients may be determined at a time other than in real- time, for example, when flying a plane, and then subsequently stored, along with co ⁇ esponding X info ⁇ nation, for example, in the collected data store 18. These stored values may be used in determining a normalized CI value for a particular observed instance of a Clobs in determining an HI.
  • the normalized CI may be represented as:
  • the foregoing techniques are based upon a healthy gear characterized as having noise that is stationary and Gaussian in which the noise approximates a normal distribution.
  • a first technique may be refe ⁇ ed to as the non-linear map technique.
  • the second technique may be refe ⁇ ed to as the hypothesis test method of HI generation.
  • CI values other than normalized CI values may be used in connection with HI determination techniques described herein.
  • an embodiment may use CI values that are not normalized in connection with the HI determination techniques described herein.
  • multiple torque bands may be used, one for each CI or group of CIs belonging to different torque bands.
  • a larger covariance matrix may be used as there may be a larger variance causing decrease in separation between classes.
  • CIs diagnostics indicators or CIs
  • the CIs which are best suited to specify the fault indication may be developed over time through data analysis. Faults may be calculated at the component level and an HI may be calculated for a given component. If there is a component fault, then there is a sub-assembly fault, and therefore a drive train fault.
  • each indicator or CI is weighted and contributes a portion to the HI determination. Subsequently all the Hi contributions for the selected CIs are summed and maybe compared to threshold values for determining one of two possible outcomes of "healthy” or "not healthy".
  • the sum of the HI contributions is 11.4.
  • Indicator 13 has a value of 3.45, which contributes a 1 toward the index since the weight value is also 1.
  • Indicator 16 contributes a 1.4 to the index because it crosses the warning level (contributing a value of 1 to the index) while being weighted by a factor of 1.4.
  • the HI may be represented as a value of 1 for healthy and 0 for not healthy as associated with a component represented by the foregoing CI values.
  • the HI may be determined by dividing 11.4/19, the maximum of worst case outcome to obtain 0.6. This overall health index output ratio can then be compared to another final output threshold, where normal components produce His, for example, less than 0.5; values between 0.5 and 0.75 represent warning levels, and values over 0.75 represent alarm.
  • weights may be determined using a variety of different techniques.
  • the weights of each CI may be determined using any one or more of a variety of techniques.
  • One embodiment may determine weights for the CIs as:
  • threshold values may be used in HI determination and may vary with each embodiment.
  • the Warning threshold is 3 standard deviations and the Alarm level is 6 standard deviations. It should be noted that other threshold values may be used in and may vary in accordance with each embodiment.
  • the technique for HI determination may be refe ⁇ ed to as Hypothesis testing technique for HI determination which minimizes the occu ⁇ ence of a false alarm rate, or inco ⁇ ectly diagnosing the health of a part as being included in the alarm classification when in fact the part is not in this particular state.
  • three classes of health indication may be used, for example, normal, warning and alarm classifications with alarm being the least "healthy" classification.
  • Other embodiments may use the techniques described herein with a different number of classes.
  • the class of a part indicating the health of the part may be determined based on measured vibrations associated with the part.
  • the technique described herein may use a transformation, such as the whitening transformation to maximize the class distributions or separation of values thus decreasing the likelihood or amount of overlap between the classes. In particular, this maximization of class separation or distance attempts to minimize the misclassification of a part.
  • a transformation such as the whitening transformation
  • the HI or classification h(X) of a vector of normalized CI values denoted as X may be determined in which, as discussed elsewhere herein in more detail, X may be normalized.
  • X normalized CI values
  • the hypothesis testing technique may be performed more than once in accordance with the particular number of classes of an embodiment. For three classes, there are two degrees of freedom such that if the sample X is not from A or B classes, then it is from Class C.
  • X may belong to class ⁇ y or ⁇ 2 , such that: q ⁇ (X)oq 2 (X) (the notation ⁇ > means
  • q t is the a posteriori probability of ⁇ , given X, which can be
  • the mixed density function is the probability function for all cases where q , ⁇ is the unconditional probability of "i” given the probability of "i” conditioned on the mixed density function.
  • likelihood ratio is a quantity in hypothesis test.
  • the value P 2 /P / is the threshold value, hi some instances, it may be easier to calculate the minus log likelihood ratio.
  • the decision rule becomes (e.g. now called the discriminate function):
  • ⁇ . j ⁇ / / - h order that a non-null Z exits, ' ⁇ must be chosen to
  • n x n matrix e.g. a covariance matrix
  • n real eigenvalues ⁇ / ... ⁇ district
  • n real eigenvectors ⁇ 7 ... ⁇ district.
  • Y ⁇ T ,
  • the whitening transformation may be defined such that:
  • h(X) -Y T A ⁇ - [(-K-'Jy ]Y + [--L T K ⁇ l L - -ln
  • the component is a member of the normal or healthy class. Otherwise, the component is classified as having an HI in the broken class, such as one of alarm or warning. In the latter case, another iteration of the hypothesis testing technique described herein may be further perfo ⁇ ned to determine which "broken" classification, such as alarm or warning in this instance, characterizes the health of the component under consideration.
  • values such as the a posteriori probabilities ⁇ ⁇ and q 2 , may be obtained and determined prior to executing the hypothesis testing technique on a particular set of CI normalized values represented as X above.
  • Bayes theorem may be used in determining, for example, how likely a cause is given that an effect has occu ⁇ ed.
  • the effect is the particular CI normalized values and it is being determined how likely each particular cause, such as a normal or broken part, given the particular effects.
  • operating characteristics of a system define the probability of a false alarm (PFA) and the probability of detection (PD).
  • PFA probability of a false alarm
  • PD probability of detection
  • the transformation used to maximize the distance function optimizes the discrimination between classes.
  • the threshold value selected given a discriminate function may be used in determining the PD and PFA.
  • the cost of a false alarm may be higher than the cost of a missed detection.
  • the PFA may be set to define threshold values, and then accept the PD (e.g., a constant false alarm rate (CFAR) type of process).
  • the threshold may be the In (P 2 /P ⁇ ). This integration is the incomplete gamma function. Conversely, the probability of a detection (PD) is:
  • FIG 26 shown is an example of a graphical illustration of the probability of a false alarm PFA represented by the shaded region A3 which designates the overlap between the distribution of class HO, denoted by the curve formed by line Al, and class HI, denoted by the curve formed by line A2.
  • FIG. 27 shown is an example of a graphical illustration of the probability of an appropriate detection (PD) represented as area A4 as belonging to class represented by HI as represented by the curve formed by line A2.
  • PD appropriate detection
  • FIG 28 shown is a graphical illustration of a relationship in one embodiment between the PFA and PD and the threshold value. Note that as the threshold increases, the PD increases, but also the PFA increases. If the performance is not acceptable, such as the PFA is too high, an alternative is to increase the dimensionality of the classifier, such as by increasing the population sample size, n. Since the variance is related by l/sqroot(n), as n increases the variance is decreased and the normalized distance between the distributions will increase. This may characterize the performance of the system.
  • the likelihood ratio test used herein is a signal to noise ratio such that the larger the ratio, (e.g., the larger the distance between the two distributions), the greater the system performance.
  • the process of taking an orthonormal transfo ⁇ nation may be characterized as similar to the of a matched filter maximizing the signal to noise ratio.
  • false alarm rate and detection rate are two factors that may affect selection of particular values, such as thresholds within a particular system.
  • false alarm rate is a determining factor, for example, because of the high cost associated with false alarms and the fact that they may co ⁇ ode confidence when a real fault is detected. It should be noted that other embodiments and other applications may have different considerations. Further in this example of the system of Figure 1 , certain factors may be considered. An acceptable false alarm rate, for example, such as 1 false alarm per 100 flight hours, is established.
  • An estimate of the number of collection opportunities per flight hours may be determined, such as four data collections.
  • a number of His may be selected for the system, such as approximately 800.
  • a confidence level may be selected, such as that there is a 90% probability that a false alarm rate is less than 1 per 100 flight hours.
  • each HI is a an independent classification event such that the law of total probability may give the system alarm rate using the foregoing:
  • the logarithm likelihood ratio test for classification may be simplified in that the model may be reduced to a linear rather than quadratic problem having the following model:
  • the maximum distance of the distribution is an axis y (e.g. 2 nd dimension, the distribution was whitened and the project dimension (e.g. x, y or z) was plotted), but this axis has the minimum separability. Using this as one of the two features will result in higher false alarm rates than another feature. This may identify the importance of feature selection in maximizing the separability.
  • the problem of separability may be characterized as a "mixed" problem in that differences in means may be normalized by different class covariance. If the mean values are the same, or the covariance are the same, techniques such as the Bhattacharyya Distance may be used to measure class separability. However, same mean or covariance values may not be likely and thus such techniques may not be applicable. Statistical tools developed in discriminant analysis may be used to estimate class separability.
  • a measure of within class scatter may be represented as the weighted average of the
  • ( 1 of the covariance ⁇ i for that class.
  • unhealthy status for example, when performing a second round of hypothesis testing described herein, there may be alarm and warning classes.
  • a measure of between class scatter, Sb may be represented as the mixture of class means:
  • Mo represents the mean or expected value of the classes and Mi- Mo is a difference or variation from the expected value for the classes under consideration.
  • the formulation for a criteria for class separability may result in values that are larger when the between class scatter is larger, or when the within class scatter is smaller.
  • a typical criteria may result in values that are larger when the between class scatter is larger, or when the within class scatter is smaller.
  • CIs may be selected in accordance with the technique described above to obtain and examine the diagonals of the "whitened" Sb, represented as Sbw.
  • An embodiment may use normalized CIs and select a portion of these for use.
  • An embodiment may also use CIs however, those selected should belong to the same torque band.
  • A is the transformation matrix that whitens the covariance ⁇ . If Sb is defined as above as the between mean covariance of the classes, the whitening matrix A may be used to normalize the differences and give a distance between the mean values of the different classes, such that
  • a particular HI may be desired to use techniques in connection with trending or predicting HI values of the component at future points in time.
  • Techniques such as trending, may be used in establishing, for example, when maintenance or replacement of a component may be expected.
  • techniques may be used in determining an HI in accordance with a vector of CI values having expected CI values included in vector Mj for a given HI classification, i, having a covariance matrix ⁇ j.
  • One technique uses a three state Kalman filter for predicting or trending future HI values.
  • the Kalman filter may be used for various reasons due to the particular factors taken into account in the embodiment and uses described herein. It should be noted that other systems embodying concepts and techniques described herein may also take into account other noise factors.
  • the Kalman filter may be prefe ⁇ ed in that it provides for taking into account the noise of a particular a ⁇ angement of components. There may be noise corruption, such as indicated, for example, by the covariance matrices described and used herein. It may be desirous to filter out such known noise, such as using the Kalman filter, providing for smoothing of data values.
  • the Kalman filter provides a way to take into account other apriori knowledge of the system described herein.
  • the health of a component may not change quickly with time.
  • the difference between the health of a component at a time t, and time t+delta may not be large.
  • This technique may also be used in connection with determining future His of a particular part, for example, where the part is old. A part may have reached a particular state of relatively bad health, but still a working and functional part.
  • the techniques described herein may be used with an older part, for example, as well as a newer part.
  • state reconstruction may be performed using the Ricatti equation, as known to those of ordinary skill in the art.
  • the technique that is described herein uses a three-state Kalman filter of HI, and the first and second derivatives thereof with respect to changes in time, denoted, respectively, dt 2 and dt 3 .
  • the Ricatti equation in this instance uses a [1x3] vector of time values rather than a single value, for example, as may be used in connection with a single state Kalman filter.
  • ⁇ is the power spectral density of the system
  • R is the measurement e ⁇ or
  • K is the Kalman gain
  • ⁇ is the state transition matrix
  • ⁇ may be characterized as the Jacobian matrix. Since the value of a single HI is desired, only the first entry in the H vector is 1 with remaining zeroes. There are n entries in the n x 1 vector H for the n state Kalman filter. Similarly, the X vector above is column vector of 3 HI entries in accordance with the three-state Kalman filter. The end value being determined is the vector X, in this instance which represents a series of HI values, for which the first entry, HI_est in the vector X is the one of interest as a projected HI value being
  • HI represents the first derivative of HI_est and HI
  • t represents the average amount of time
  • t represents the average of the delta values representing time changes.
  • t-l refers to determining a value of at a time t conditioned on the measurement at a time of "t-1 ".
  • t refers to, for example, determining an estimate at a time “t” conditioned on a measurement of time "t”.
  • Equation T5 The cu ⁇ ent HI dete ⁇ nined, for example, using other techniques described herein, may be input into Equation T5 to obtain a projected value for HI_est, the best estimate of the cu ⁇ ent HI.
  • Equation T5 To project the expect HI "n” units of time into the future, input the number of units of time "dt” into ⁇ (as described above), and use the state update equation (Equation
  • Equation TI X t+ dt
  • t ⁇ X t
  • an initial value for P representing the covariance may be (1/mean time value between failures).
  • An embodiment may use any one of a variety of different techniques to select an initial value for P. Additionally, since P converges rapidly to an appropriate value and the time between data acquisitions is small in comparison to the mean failure time, selecting a particularly good initial value for P may not be as important as
  • a value for ⁇ may be selecting in accordance with apriori
  • the mean failure time may be approximately 20,000 hours.
  • the spectral density may be set to (l/20,000) 2 .
  • the failure rates may be generally characterized as an exponential type of distribution.
  • the mean time between expected failures is a rate, and the variance is that rate to the second power.
  • R may also be determined using apriori information, such as manufacturer's data, for example, an estimated HI variance of manufacturer's data of a healthy component.
  • Q may be characterized as the mean time between failures and dt (delta change in time between readings). As the value of dt increases, Q increases by the third power.
  • Input data used in the foregoing trending equations may be retrieved from collected data, for example, as may be stored in the system of Figure 1.
  • His may be derived using one or more CIs.
  • data acquisitions may occur by recording observed data values using sensors that monitor different components.
  • There may be a need for estimating data used in connection with CI calculations for example, in instances in which there may be too little or no observed empirical.
  • gear or bearing related measurements such as, for example, those in connection with a gear or bearing related measurements, such as, for example, those in connection with a gear or bearing fault due to the rare occu ⁇ ence of such events.
  • mean and threshold values may be derived using other techniques.
  • a CI may indicate a level of transmission e ⁇ or, for example, in which transmission e ⁇ or is a measure of the change in gear rigidity and spacing.
  • Modeling transmission e ⁇ or may allow one to gauge CI sensitivity and derive threshold and mean values indicative of gear/bearing failure.
  • This transmission e ⁇ or modeling may be refe ⁇ ed to as dynamic analysis. What will now be described is a technique that may be used to model a gears to obtain such estimated values.
  • transmission e ⁇ or may be estimated. It should be noted that this model uses two degrees of freedom or movement. Other systems may use other models which may be more complex having more degrees of freedom. However, for the purposes of estimating values, this model has proven accurate in obtaining estimates. Other embodiments may use other models in estimating values for use in a system such as that of Figure 1.
  • FIG. 30 shown is an example of an illustration of a pair of gears for which a model will now be described.
  • a force P at the contact gives linear and torsional response to each of the 2 gears for a total of four responses as indicated in Figure 30.
  • sp is the linear stiffness of the pinion
  • j is the square root of -1
  • 10 ⁇ is the angular rate that may be obtained from the configuration file (e.g., shaft rpm
  • bp is the linear damping coefficient of the pinion
  • mp is the mass of the pinion
  • rp is the radius of the pinion
  • 15 kp is the angular effective stiffness of the pinion
  • qp is the angular damping coefficient of the pinion
  • Ip is the angular effective mass of the pinion
  • Iw is the angular effective mass of the wheel
  • sc is the linear stiffness of the contact patch where the two gears come into contact
  • be is the linear damping coefficient of the contact patch
  • values for the above-referenced variables on the rights hand side of EQUATION Gl above, except for P (described below), may be obtained using manufacturer's specifications for a particular a ⁇ angement used in an embodiment.
  • An embodiment may include quantities for the above-referenced variables in units, for example, such as stiffness in units of force/distance (e.g., newtons/meter), mass in kg units, and the like.
  • the relative movement, d is the T.E., so from d, the above-referenced equation can be solved for P, the tooth force.
  • Deflection is the force (input torque divided by the pinion base radius) * the elastic deflection of the shafts, which may be used in estimating P represented as:
  • the displacement such as a vibration transmitted through the bearing housing and transmission case (which acts an additional transfer function)
  • the displacement such as a vibration transmitted through the bearing housing and transmission case (which acts an additional transfer function)
  • Lp may represent the longitudinal stiffness of the pinion
  • Lw may represent the longitudinal stiffness of the wheel. It should be noted that these elements may not be included in an embodiment using the two degrees of freedom model.
  • Bearings may also be modeled to obtain estimates of fault conditions in instances where there is little or no empirical data available.
  • a periodic impulse is of interest.
  • the impulse is the result of a bearing rolling over a pit or spall on the inner or outer bearing race.
  • the intensity of the impulse on the bearing surface is a function of the angle relative to the fault, which may be represented as, for example, described in the Stribeck equation in a book by T.A. Harris, 1966, Rolling Bearing Analysis. New York: John Wiley p 148 as:
  • n 3/2 for ball bearings and 10/9 for rolling elements bearing, ⁇ ⁇ .5, and ⁇ is less than
  • An impulse in a solid surface has an exponential decay constant, which may be taken into account, along with a periodic system due to rotation of the shaft.
  • the bearing model may then be represented as a quantity, "s", which is the multiplication of the impulse, "imp"
  • T is the exponential decay and t is the time.
  • T varies with the material of the solid surface.
  • Exp(T/t) may be obtained, for example, using a modal hammer, to generate the decay response experimentally. An embodiment may also obtain this value using other information as may be supplied in accordance with manufacturer's information.
  • the value of "t” may be a vector of times starting with the first time sample and extending to the end of the simulation. T is generally small, so the expression “exp(T/t)" approaches zero rapidly even using a high sampling rate.
  • “imp” is the impulse train that may be represented as the shaft rate * bearing frequncy ratio * sampling rate for the simulation period.
  • the Power Spectral Density of S at a bearing passing frequency may be used as a CI.
  • other CI values may be obtained, such as in connection with the CI algorithm comparing the spectrum "S" to those associated with transmission e ⁇ or in connection with a normal distribution using the PDF/ CDF CI algorithms that may be generally described as hypothesis testing techniques providing a measure of difference with regard whether the spectrum is normally distributed.
  • values may be used in the foregoing equations in connection with simulating various fault conditions and severity levels.
  • the particular values may be determined in accordance with what small amount of observed data or manufacturer's data may be available. For example, in accordance with observed values, an impulse value of 0.02 for the impulse, "imp", may co ⁇ espond to a fairly severe fault condition. Values ranging from 0.001 to 0.03, for example, may be used to delimit the range of "imp" values used in simulations.
  • Figure 32 represents the estimated spectrum "S" as may be determined using EQUATION B2 above.
  • FIG 32 represents the estimated spectrum "S" as may be determined using EQUATION B2 above.
  • Localized bearing faults induce an excitation which can be modeled as an impulse train, expressed as imp in the above equation. This impulse "imp" co ⁇ esponds to the passing of the rolling elements of the fault. Assuming a constant. inner ring rotation speed, the impulse train is periodic and the periodicity depends on the fault location.
  • the bearing frequency ratio, f d may be represented as:
  • f r is the rotation frequency of the inner race (e.g. shaft rate)
  • the bearing frequency ratio, f d , ⁇ may be represented as:
  • the vibrations at a given frequency may be specified by the amplitude and phase of the response and the time constant of the exponential decay.
  • the impulse response function h(t) and the transfer function H(f) may be replaced by a function a( ⁇ ) giving the amplitude and sign of the transfer function H(f)
  • the cos(t) may be used for the function a(t).
  • the impulse train is exponentially decaying.
  • the decay of a unit impulse can be defined by:
  • T e is the time constant of decay.
  • h(t) is the frequency response of the gear case, as may be determined, for example, using an estimate produced with linear predictive coding (LPC) techniques or with a modal hammer analysis
  • d(t) is the signal associated with gear/shaft T.E. as may be determined using the gear model EQUATION Gl; and other variables are as described elsewhere herein.
  • the frequency spectrum of signals representing a combined bearing and gear model from EQUATION B8 may be represented as:
  • healthy data such as may be obtained using manufacturer's information
  • different values such as those in connection with stiffnesses for gear simulation, amplitude and exponential decay for bearing faults.
  • amplitude and exponential decay for bearing faults.
  • a reduction in the stiffness for a tooth e.g. 50 and 20 percent of normal
  • these values may be varied, for example, using the Monte Carlo simulation to quantify variance.
  • shaft alignment within the model may be varied to estimate mean fault values •
  • the "size" of an impulse may be determined through trial and e ⁇ or, and by comparing simulation values with any limited observed fault data previously collected.
  • Sensitivity analysis may be performed, for example using range of different input values for the different parameters, to provide for increasing the effectiveness of fault detection techniques, for example, as described and used herein.
  • an embodiment may be better able to simulate a family of bearing faults to tailor a particular CI algorithm to be sensitive to that particular fault.
  • the modulated transmission e ⁇ or of a gear mesh may be simulated or estimated.
  • This signal may subsequently be processed using any one or more of a variety of CI algorithms such that estimates for the mean and threshold values can then be derived for fault conditions. (It is assumed that the stiffness and torque are known apriori).
  • Parameter values used in the above equations co ⁇ esponding to a healthy gear may be modified to estimate parameter values in connection with different types of faults being simulated. By modifying these parameter values, different output values may be determined co ⁇ esponding to different fault conditions.
  • known values for stiffness, masses, and the like used in EQUATION Gl may be varied.
  • a cracked gear tooth may be simulated by making the stiffness time varying.
  • the contact pitch may be varied with time in simulating a shaft alignment fault.
  • a modulated input pulse on d may be used in simulating a spall on a gear tooth.
  • Different parameter values may be used in connection with specifying different degrees of fault severity, such as alarm levels and warning levels.
  • a particular parameter value such as a tooth stiffness of 70% of the normal manufacturer's specified stiffness, maybe used in simulating warning levels.
  • a value of 20% of the normal manufacturer's specified stiffness may be used in simulating alarm levels.
  • the particular values may be determined in accordance with comparing calculated values with the characteristics of real CI data on any few real faults collected.

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Abstract

Cette invention concerne des techniques s'utilisant pour déterminer un indicateur de condition (ou de « santé »)(HI) d'un composant, tel qu'un composant d'aéronef. A cette fin, on utilise des indicateurs d'état (CI) qui paramètrent des caractéristiques sur un composant dans le but de réduire les risques d'alarme erronée. L'invention concerne divers algorithmes servant à déterminer un ou plusieurs CI. L'indicateur de condition HI peut être déterminé au moyen d'une valeur CI normalisée. Sont également décrites des techniques en rapport avec le choix de CI qui permettent de maximiser la séparation entre classifications HI. A partir d'un HI donné à un moment particulier pour un composant, les techniques décrites permettant de prévoir un état futur ou un niveau de santé du composant au moyen d'un filtre Kalman. Sont décrites des techniques permettant, en lieu et place d'acquisition de données, d'estimer des valeurs de données, comme cela se fait en l'absence de données préexistantes.
PCT/US2002/016380 2001-05-24 2002-05-23 Methodes et dispositif permettant de determiner la condition d'un composant au moyen d'indicateurs d'etat WO2002095633A2 (fr)

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EP02744172A EP1390739A2 (fr) 2001-05-24 2002-05-23 Methodes et dispositif permettant de determiner la condition d'un composant au moyen d'indicateurs d'etat

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US10/011,905 US6754569B2 (en) 2001-05-24 2001-12-04 Method and apparatus for normalizing condition indicators
US10/011,973 US6847917B2 (en) 2001-05-24 2001-12-04 Method and apparatus for selecting condition indicators in determining the health of a component
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US10/011,905 2001-12-04
US10/011,787 2001-12-04
US10/011,622 US6651012B1 (en) 2001-05-24 2001-12-04 Method and apparatus for trending and predicting the health of a component
US10/011,622 2001-12-04
US10/011,864 2001-12-04
US10/011,428 2001-12-04
US10/011,787 US6728658B1 (en) 2001-05-24 2001-12-04 Method and apparatus for determining the health of a component using condition indicators
US10/011,864 US6711523B2 (en) 2001-05-24 2001-12-04 Method and apparatus for determining a condition indicator for use in evaluating the health of a component
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AU2002339855A1 (en) 2002-12-03

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