vibration feature extraction for smart sensors
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The Pennsylvania State University
The Graduate School
College of Engineering
Vibration Feature Extraction for Smart Sensors
by
Kenneth P. Maynard
© 2001 Kenneth P. Maynard
Submitted in Partial Fulfillment of the Requirements
for the Degree of
Master of Engineering
November 2001
I grant The Pennsylvania State University the nonexclusive right to use this work for the University’s own purposes and to make single copies of the work available to the public on a not-for-profit basis if copies are not otherwise available.
__________________________________________
Kenneth P. Maynard
We approve the research report of Kenneth P. Maynard.
Date of Signature ___________________________________________ ______________ Dr. Martin W. Trethewey Professor of Mechanical Engineering Advisor ___________________________________________ ______________ Dr. Karl M. Reichard Research Associate/ Assistant Professor of Acoustics Co-Thesis Advisor ___________________________________________ ______________ Dr. Anthony A. Atchley Professor of Acoustics Chair, Graduate Program in Acoustics
iii
Abstract
Condition-based maintenance systems monitor the operation of
mechanical equipment to provide an accurate assessment of the system's
current condition and to facilitate prediction of problem evolution. Vibration
analysis for condition assessment and fault diagnostics has a long history of
application to power and mechanical equipment. The interpretation and
correlation of this data is often cumbersome, even for the most experienced
personnel. As a result, automated processing and analysis methods are often
sought. To facilitate automation, smart sensor systems are being implemented
for advanced diagnostics and prognostics. In conjunction with these smart
systems, advanced features are commonly used to provide a measure of the
vibration level that can be correlated to a fault condition. Many such feature
vectors have been developed over the years and are well documented in the
literature.
This paper introduces concepts related to feature extraction for smart
sensors for improved diagnostics within condition-based maintenance (CBM).
Novel data tools are introduced by examples that identify diagnostic and
prognostic features for transitional data from mechanical systems. These tools
facilitate the establishment of effective methodologies for CBM researchers and
practitioners, and promote environments in which the new methodologies can be
easily and systematically characterized and evaluated. The capability of different
features to identify and track failure modes are treated primarily using gearbox
run-to-failure accelerometer data acquired on the Mechanical Diagnostics Test
Bed (MDTB) at the Pennsylvania State University Applied Research Laboratory.
iv
Table of Contents
LIST OF TABLES ................................................................................................ v
LIST OF FIGURES:............................................................................................. vi
ACKNOWLEDGEMENTS: ................................................................................... 1
CHAPTER - 1 INTRODUCTION........................................................................... 2 1.1 Smart Sensors .......................................................................................................................3 1.2 Why Feature Extraction? ....................................................................................................10
CHAPTER - 2 FEATURE EXTRACTION EXAMPLES ...................................... 11 2.1 Preprocessing for Gear Fault Detection ...........................................................................11 2.2 Preprocessing Steps...........................................................................................................12
2.2.1 Interstitial Preprocessing..........................................................................................12 2.2.2 Asynchronous Demodulation Preprocessing...........................................................13
2.3 Feature Extraction...............................................................................................................14 2.3.1 Statistical Features ..................................................................................................14
2.3.1.1 Root Mean Square (RMS) Feature...................................................................15 2.3.1.2 Skew .................................................................................................................15 2.3.1.3 Kurtosis.............................................................................................................16
2.3.2 Envelope Spectral Peak Feature .............................................................................17
CHAPTER - 3 EXPERIMENTAL AND ANALYTICAL RESULTS...................... 21 3.1 Transitional Gear Failure Data ...........................................................................................21 3.2 Gearbox Features................................................................................................................23
3.2.1 Interstitial RMS.........................................................................................................23 3.2.2 Interstitial Kurtosis....................................................................................................25 3.2.3 Interstitial Envelope Spectral Peak ..........................................................................29
3.3 Bearing Feature: Skew........................................................................................................31
CHAPTER - 4 EVALUATION OF GEARBOX FEATURES................................ 35 4.1 High-Pass Filtering Comparison........................................................................................35 4.2 Comparison with Traditional Gearbox Features ..............................................................37 4.3 Feature Fusion.....................................................................................................................40 4.4 Model-Based Feature Identification...................................................................................41
CHAPTER - 5 CONCLUSION............................................................................ 48
v
List of Tables: TABLE 1: SUMMARY OF INTERSTITIAL PARAMETER EFFECTIVENESS .....................................................40
vi
List of Figures: FIGURE 1: MOORE'S LAW AS APPLIED TO INTEL PROCESSORS...............................................................5 FIGURE 2: ANALOGOUS APPLICATION OF MOORE'S LAW TO PROCESSOR SPEED ....................................5 FIGURE 3: TYPICAL INSTRUMENTATION COSTS .....................................................................................6 FIGURE 4: BLUETOOTH OEM MODULE (CIRCA 2001)............................................................................7 FIGURE 5: IDEALIZED SMART ACCELEROMETER ....................................................................................8 FIGURE 6: SMART SENSOR ARCHITECTURE EXAMPLE FOR A PUMP.........................................................8 FIGURE 7: CURRENTLY AVAILABLE FORMS OF THE SMART SENSOR OR INTELLIGENT NODE ......................9 FIGURE 8: SCHEMATIC OF INTERSTITIAL PROCESSING METHOD ...........................................................11 FIGURE 9: TYPICAL RAW AND FILTERED DATA FROM MDTB RUN .........................................................13 FIGURE 10: SKEW: MEASURE OF SYMMETRY OF THE PROBABILITY DENSITY FUNCTION .........................15 FIGURE 11: COMPARISON OF PDFS HAVING THE SAME STANDARD DEVIATION BUT DIFFERENT
KURTOSIS ................................................................................................................................16 FIGURE 12: SINE WAVE AT 200 HZ WITH AMPLITUDE MODULATION AT 5.5 HZ.......................................17 FIGURE 13: RECTIFIED SINE WAVE AT 200 HZ, AMPLITUDE MODULATION AT 5.5 HZ ..............................18 FIGURE 14: RECTIFIED SINE WAVE AT 200 HZ, AMPLITUDE MODULATION AT 5.5 HZ ..............................18 FIGURE 15: 200 & 126 HZ SINE WAVE WITH AMPLITUDE MODULATION AT 5.5 HZ (A) WAVEFORM; (B)
SPECTRUM; (C) ENVELOPE SPECTRUM AFTER 50 HZ LOW-PASS FILTER .......................................19 FIGURE 16: RANDOM DATA WITH AMPLITUDE MODULATION AT 5.5 HZ (A) WAVEFORM; (B) SPECTRUM;
(C) ENVELOPE SPECTRUM (NO FILTERING) .................................................................................20 FIGURE 17: MECHANICAL DIAGNOSTIC TEST BED (MDTB) .................................................................22 FIGURE 18: CLOSE-UP OF THE GEARBOX SHOWING ACCELEROMETER LOCATIONS................................23 FIGURE 19: INTERSTITIAL RMS AS A FUNCTION OF TIME OVER THE ENTIRE TEST (RUN 14) ...................24 FIGURE 20: INTERSTITIAL RMS AS A FUNCTION OF TIME WHILE LOADED AT 3X RATED LOAD .................25 FIGURE 21: SAMPLE HISTOGRAMS OF MDTB GEARBOX DATA .............................................................26 FIGURE 22: DATA OF FIGURE 21 RESCALED TO COMPARE TAILS..........................................................26 FIGURE 23: CONTRIBUTION TO KURTOSIS Z4M ...................................................................................27 FIGURE 24: INTERSTITIAL KURTOSIS AS A FUNCTION OF TIME OVER THE ENTIRE TEST (RUN 14)............28 FIGURE 25: INTERSTITIAL KURTOSIS WHILE LOADED AT 3X RATED LOAD ..............................................29 FIGURE 26: INTERSTITIAL ENVELOPE SPECTRAL PEAK.........................................................................30 FIGURE 27: INTERSTITIAL ENVELOPE SPECTRAL PEAK.........................................................................31 FIGURE 28: (A) TYPICAL INSTALLATION OF PROXIMITY PROBE ON FLUID-FILM BEARING
(BENTLY-NEVADA); (B) RESULTING ORBIT .................................................................................32 FIGURE 29: SYNTHESIZED ORBIT WITH RUB AND NOISE .......................................................................33 FIGURE 30: HISTOGRAM OF ONE CHANNEL WITH 10% RUB, 28% NOISE .............................................34 FIGURE 31: SKEW AS A FUNCTION OF PERCENT FLATTENED ...............................................................34 FIGURE 32: COMPARISON OF RMS USING HIGH-PASS AND INTERSTITIAL FILTERING .............................36 FIGURE 33: COMPARISON OF KURTOSIS USING HIGH-PASS FILTERING (3000 HZ AND 5000 HZ) AND
INTERSTITIAL FILTERING (ACCELEROMETER 2) ...........................................................................36 FIGURE 34: COMPARISON OF ENVELOPING USING HIGH-PASS FILTERING (3000 HZ AND 5000 HZ)
AND INTERSTITIAL FILTERING (ACCELEROMETER 2) ....................................................................37 FIGURE 35: COMPARISON OF INTERSTITIAL KURTOSIS WITH NA4 AND FM4 .........................................38 FIGURE 36: COMPARISON OF INTERSTITIAL KURTOSIS WITH NA4 AND FM4 (NOT NORMALIZED) ............39
vii
FIGURE 37: GEAR COMPONENT HEALTH VECTOR BASED ON KURTOSIS AND RMS.................................41 FIGURE 38: FINITE ELEMENT MODEL OF MDTB GEAR TEETH (WITH CONTACT) .....................................42 FIGURE 39: DETAIL OF TOOTH MODEL: A) SHOWING ELEMENTS; B) SHOWING CRACK LOCATION .............42 FIGURE 40: CONTACT MODEL OF GEAR WITH NO CRACKS....................................................................43 FIGURE 41: CONTACT MODEL OF GEAR WITH CRACKED TOOTH............................................................43 FIGURE 42: EFFECTIVE TORSIONAL STIFFNESS PROFILE OF A CRACKED AND UNCRACKED TOOTH..........44 FIGURE 43: FINITE ELEMENT MODEL OF MDTB ROTOR (BEAM MODEL) ................................................45 FIGURE 44: CLOSE UP OF MDTB ROTOR BEAM MODEL SHOWING SCHEMATICALLY THE LOCATION OF
THE VARIABLE SPRING STIFFNESS ASSOCIATED WITH MESH ........................................................45 FIGURE 45: RESULTS OF COMPARISON OF FM4 FROM MDTB TEST AND FINITE ELEMENT MODEL
RESULTS .................................................................................................................................46
1
Acknowledgements:
This work was primarily supported by Multidisciplinary University
Research Initiative (MURI) for Integrated Predictive Diagnostics (Grant Number
N00014-95-1-0461) sponsored by the Office of Naval Research.
Personal gratitude goes to the Condition Based Maintenance (CBM)
department of the Applied Research Lab (ARL) of Penn State for their aid and
support in this research.
2
Chapter - 1 Introduction Vibration measurements have been used as the flagship of condition
monitoring of machinery health for almost a century. During the first half of the
twentieth century, most of the vibration information used involved overall
vibration (peak or RMS) from the time waveform. With the advent of advanced
filtering techniques during the last half-century, much work was been done to
identify vibration at specific frequencies and then correlate it with certain
maintenance issues, such as imbalance and misalignment, whirl, etc. With the
introduction of the Fast Fourier Transform (FFT)1 and the availability of fast
processing, spectrum-based diagnostic techniques enjoyed growth in attention
and importance. With the advent of other advanced technologies, such as oil
analysis, acoustic emissions, infrared thermography, ultrasonics, etc., the fleet of
condition monitoring technologies has grown, but vibration has still retained its
flagship status.
However, in the last few decades, new ways of looking at vibration have
emerged. Much of the information contained in the vibration is not visible in a
time waveform or a simple spectrum. Rather, it is hidden, encrypted in the signal
waveform. Various communication signal processing techniques used to encrypt
and decipher signals have found their way into the machinery condition-
monitoring arena, and new types of information and information portrayal have
been developed. These techniques include various types of demodulation
(asynchronous, AM, FM, phase), wavelets, time synchronous averaging, short-
time Fourier transforms (STFT), etc. By combining several of these techniques,
it has been found that features of the vibration waveform may be extracted and,
often empirically, correlated with various condition or damage states of
machinery components. The techniques employed in the extraction of these
features are varied; however, they generally employ three processing steps: (1)
preprocessing, such as filtering (high-pass, band-pass, low-pass), time
synchronous averaging, demodulation, etc.; (2) feature extraction, using
3
statistical properties, spectral properties, etc.; and (3) feature fusion, combining
the information obtained from several features. The appropriate preprocessing
techniques are most often empirically determined, where investigators may try
different techniques on the data until they find something that makes sense.
However, more and more system modeling is being used to help understand the
physics of the vibration, thereby making the feature selection more physics-
based.
The proliferation of smart sensors makes feature extraction more and
more essential. In smart sensors, we have moved high-speed processing power
close to the machine. However, the thought of transmitting high bandwidth data
for large numbers of signal channels, and then interpreting these signals as well,
is overwhelming. Feature extraction allows us to process the data and transmit
very low bandwidth information about the health of the system or component.
Such information can aid the decision-maker by providing interpretation along
with the data.
The purpose of this paper is to show by example some of the ways that
features may be extracted and correlated with machinery damage states. It is
hoped that the reader will gain insight into the process, and that some of the
features that are commonly used (such as kurtosis) will be demystified as a result
of studying the example process streams.
1.1 Smart Sensors A smart sensor is a system that includes a sensor element and various
other components, which facilitate the diagnostic and prognostic evaluation of
machinery components. The smart sensor is characterized by the following
attributes2:
• Smart sensor systems adapt to the environment by optimizing their sensor
detection performance, power consumption, and communication activity.
• Smart sensor systems record raw data and extract information.
4
• Smart sensor systems have some degree of self-awareness using built-in
calibration, internal process control checking and re-booting, and
measures of “normal” and “abnormal” operation of its internal processes.
• Smart sensor systems are completely re-programmable through their
communications port, allowing access to raw data, program variables, and
the processed data.
• In addition to pattern recognition ability, smart sensor systems are capable
of predicting pattern future states and providing meaningful confidence
metrics for these predictions.
These basic characteristics represent the starting point for defining the smart
sensor node on a network integrating many sensors into a smart system. In
addition, the smart system architecture must be expandable: it must account for
generation gap between sensor hardware and software and the machinery being
monitored.
Gordon Moore (co-founder of Intel) predicted in 1965 that the transistor
density of semiconductor chips would double roughly every 18 months3. Figure 1
and Figure 2 show how Moore’s Law plays out in the realm of personal
computers. This exponential growth is to be compared to “...digging ditches —
the machines that do that don't improve at Moore's Law-type rates. They improve
about three percent a year.”4 This not so flattering description applies to most
mechanical machinery. One task of the smart sensor is to integrate these
technologies, permitting the growth of the smart sensor at a rapid rate on
machines that change at extremely slow rates.
5
Figure 1: Moore's Law as applied to Intel processors
Figure 2: Analogous application of Moore's Law to processor speed
The smart sensor must also allow for newly identified failure modes. As
our understanding of a machine matures, new algorithms may be developed to
assess the condition of the machine. The smart sensor must permit the
incorporation of this new understanding into its architecture.
4004
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80486
PentiumPentium Pro
Merced
1
10
100
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100000
1970 1975 1980 1985 1990 1995 2000Year
Tran
sist
ors
Intel Data
Linear Fit (Logarithmic)
Linear fit corresponds to doubling every 2.15 years
4004
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2028620386
20486
Pentium
Pentium Pro
0.01
0.1
1
10
100
1000
1970 1975 1980 1985 1990 1995 2000
Year
MIP
S
Twenty-five year history
Linear fit of twenty-five year history
Linear fit of first decade
Linear fit of last decade
Last ten years:Doubling every 1.58 years
First ten years:Doubling every 1.87
years
Twenty-five year History:Doubling every 1.96 years
4004
8086
2028620386
20486
Pentium
Pentium Pro
0.01
0.1
1
10
100
1000
1970 1975 1980 1985 1990 1995 2000
Year
MIP
S
Twenty-five year history
Linear fit of twenty-five year history
Linear fit of first decade
Linear fit of last decade
Last ten years:Doubling every 1.58 years
First ten years:Doubling every 1.87
years
Twenty-five year History:Doubling every 1.96 years
6
The smart sensor certainly must also be digital. No significant processing
of the sensor data can take place without first digitizing the data. In addition, the
sensor should incorporate current standards, such as IEEE 14515, which defines
the smart sensor interface; Open System Architecture for Condition-Based
Maintenance (OSA-CBM)6, which facilitates integration and interchangeability of
various hardware and software components in a smart sensor system for CBM
from a variety of sources; and Machinery Information Management Open
Systems Alliance (MIMOSA)7, a standard equipment database architecture.
Finally, for most
applications, the smart sensor
must be wireless. A wired
system greatly restricts the
expansion of the system. In
addition, it will often put smart
sensors in a position of being too
expensive. Figure 3 shows the
estimated cost of installing a
sensor onboard a ship. For
some industries, such as the
nuclear power industry, it is essentially impossible to add wires to equipment due
to the lack of penetrations for wires in the building. Finally, a wireless system
makes it possible for the maintenance worker or operator to simply walk out to a
machine, place a wireless sensor, and return to a workstation to reconfigure the
wireless network to include the new sensor.
Figure 3: Typical instrumentation costs 8
66%
17%
17%WiringInstallation
Sensor
Wire
7
On the basis of the current trends
in wireless data communication, several
sensor manufacturers have chosen the
Bluetooth wireless protocol9 for their
smart sensors. This protocol, originally
targeting wireless telephones,
handhelds, and PCs, was founded by a
special interest group (SIG) consisting
of Ericsson, IBM Corporation, Intel
Corporation, Nokia and Toshiba
Corporation, and has since been joined by such players as 3Com Corporation,
Lucent Technologies, Microsoft Corporation and Motorola Inc. to form the
promoter group of the Bluetooth SIG. Most recently, a Working Group for
Industrial Automation was formed, and includes many sensor manufacturers.
Some additional characteristics are desirable in the ideal smart sensor,
including full integration of electronics, signal processing, and power generation
in a small package. Figure 5 shows such an idealized transducer for measuring
vibration acceleration. Perhaps the most difficult attribute to achieve is self-
powering. Work is ongoing to attempt to power such a smart accelerometer
using ambient vibration, ambient thermal gradients, and ambient light.
The smart sensor occupies the lowest level in the smart system
architecture. The smart sensor architecture includes the sensing element and
intelligent node, which together comprise the smart sensor (they may or may not
be physically integrated into one unit), an area reasoner, which collects health
information from the intelligent nodes, and the operator/maintainer local area
network, by which the information is communicated to the operator/maintainer.
Figure 6 shows a typical architecture for a smart pump. Note that the area
reasoner may reside at the platform level, and integrate the information from
intelligent bearing nodes, intelligent motor nodes, and intelligent lubrication
system nodes, etc., to arrive at a health vector for the pump system.
Figure 4: Bluetooth OEM module (circa 2001)
8
Figure 5: Idealized smart accelerometer
Figure 6: Smart sensor architecture example for a pump
1”
1”
Communications
Diagnostic Processor (ASIC)
General Purpose Processor
Digital Signal Processing
Signal Conditioning/ADC
Power interface/Generation
Sensing Element
Self Calibration/Active Cancellation
1”
1”
Communications
Diagnostic Processor (ASIC)
General Purpose Processor
Digital Signal Processing
Signal Conditioning/ADC
Power interface/Generation
Sensing Element
Self Calibration/Active Cancellation
The Worldvia Internet
™
LAN
Area Reasoner Operator/Maintainer
™
Intelligent Node
Intelligent Node
The Worldvia Internet
™
LAN
Area Reasoner Operator/Maintainer
™
Intelligent Node
Intelligent Node
9
Examples of commercially available versions of the smart sensor or
intelligent node are shown in Figure 7. Note that some, such as the Wilcoxon
device, integrate the sensing element (in this case, an accelerometer) with the
electronics, digitizer, radio, etc., and some, such as the Oceana device and the
PC104, would have wired or wireless connection to the sensing element, and
may provide intelligence for several sensing elements. For example, an
intelligent node for a bearing might have two or more accelerometers, two or
more proximity probes, and a temperature-sensing element all attached to one
unit, which then wirelessly communicates information to the area reasoner.
Figure 7: Currently available forms of the smart sensor or intelligent node
Wilcoxonhttp://www.wilcoxonlabs.com
Oceana Sensorshttp://www.oceanasensor.com
Rockwellhttp://www.rsc.rockwell.com
PC104 (PSU, others)http://www.arl.psu.edu
10
1.2 Why Feature Extraction? Usually, raw data cannot provide information about the vibration without
feature extraction. Generally, humans understand data by feature extraction.
For example, one might look at a vibration time waveform, intuit that the peak
amplitude is important, and extract a visual estimate of that feature. Or, one
might examine a spectrum and recognize features, such as vibration at one times
and two times operating speed. Since only a few features associated with a time
waveform or spectrum might be of real interest, transmitting the large amounts of
data associated with vibration time waveforms and spectra is a waste of precious
bandwidth. Additionally, it may lead to data overload in the transmitting network
or information overload at the receiver. Often, this overload at the receiver tends
to lead to ignoring the data. So, rather than recording and transmitting large
amounts of data, features are extracted and information is sent to the
operator/maintainer. Finally, feature extraction facilitates automated reasoning
and information fusion to aid the user/maintainer in the decision-making process.
It is the intention of the author that the reader will glean from this paper an
understanding of the overall feature extraction methodology and how it fits into a
smart sensor architecture. In addition, it is hoped that the reader will gain some
insights into specific methods of preprocessing as well as feature extraction that
will enable experimentation with feature development and evaluation. The
specific objectives of this paper are:
• Review the process of feature extraction by showing typical examples.
• Test gear tooth failure feature examples using transition-to-failure data
from the Mechanical Diagnostic Test Bed (MDTB) at the Penn State
Applied Research Laboratory.
• Compare feature effectiveness using different preprocessing schemes.
• Compare features described herein to gear tooth failure feature
algorithms currently in use for helicopter gearboxes.
• Demonstrate a data fusion method for gear tooth diagnostics.
• Present example of model-based feature extraction for tooth failure.
11
Chapter - 2 Feature Extraction Examples To demonstrate the methodology employed in feature extraction, four
statistical features (second, third, and fourth moment) and one envelope spectral
peak feature are investigated for the detection of gear tooth cracking. Note that
the third moment was not found to be useful for gear fault detection. For all of
the gearbox features, an interstitial filtering preprocessing (a high-frequency
filtering technique) step is performed before feature extraction. For the envelope
spectral peak feature, an additional preprocessing step (asynchronous
demodulation, or envelope detection) is also employed. A diversion to a fluid-film
bearing diagnostic feature is made for a demonstration of a suitable application
for skew. This chapter summarizes the preprocessing and feature extraction
steps. The process for feature extraction for gearbox faults is shown
schematically in Figure 8.
Figure 8: Schematic of interstitial processing method
2.1 Preprocessing for Gear Fault Detection Various high-frequency techniques have been used for gear fault
detection for some years10. Enveloping has been used extensively for the
AccelerometerData
Bandpass FilterBetween
Higher GMF
RectifyLowpass
FilterDFT
AnalysisPeak
Search
RMS1
3Kurtosis2
12
detection of rolling contact bearing faults in rotating machinery10, 11. High-pass
filtering prior to enveloping has often been used to enhance the ability of the
envelope detection techniques to identify faults in rolling contact bearings10.
Bandpass filtering has also been used for bearing diagnostics in systems with
significant mechanical energy in higher frequency bands, such as geared
systems12. Analogous filtering is used in some of the kurtosis-based gear figures
of merit, such as NA413 and FM414.
2.2 Preprocessing Steps
2.2.1 Interstitial Preprocessing
The preprocessing technique associated with the example feature
extraction is designed to isolate a region in the gearbox acceleration spectra that
is relatively free from the dominant periodic signals associated with gear meshing
and its sidebands. This allows the identification of enveloping signals and the
use of kurtosis for impact detection in a “quiet” region of the spectrum, where the
acceleration distribution approaches Gaussian.
The most obvious area in the spectrum that would have Gaussian
distribution is at or near the noise floor of the data. The assumption is that when
impact-like events occur which are associated with gear tooth fracture, the
broadband effects will be evident in the bandpass region. After some
experimentation with the data, it was found that the region between the third and
fourth multiple of the gear mesh frequency produced good results. To isolate this
region, a bandpass filter was employed. The filter was a forward and reverse
FIR (finite-duration impulse response) filter using a Blackman window and 501
coefficients. Figure 9 shows typical spectra of the raw and bandpass filtered
data.
13
Figure 9: Typical raw and filtered data from MDTB run
2.2.2 Asynchronous Demodulation Preprocessing
Envelope detection, or asynchronous demodulation15, of a waveform may
be used to identify low-frequency impact events that modulate high frequency
data. The process is shown schematically in Process 3 in Figure 8. The
envelope of the bandpass filtered waveform is extracted by first rectifying, then
low-pass filtering the data. The low-pass filter used in this final step was a 25-
pole Butterworth filter. The resulting waveform is then transformed using a
discrete Fourier transform (DFT). Finally, the resulting spectrum is searched for
peaks near the two gear shaft speed frequencies, and the values at these peaks
are recorded.
Mea
n Sq
uare
Acc
eler
atio
n ([
in/s
ec]2 )
14
2.3 Feature Extraction Two basic statistical features (Interstitial Kurtosis and Interstitial RMS)16
and one advance feature (Interstitial Envelope Spectral Peak) are extracted from
the gearbox acceleration data, and one statistical feature (skew) is extracted
from simulated bearing data to demonstrate feature extraction methodology.
2.3.1 Statistical Features
The features considered here are the statistical moments. The first
moment, or mean, is assumed to be zero. Often some preprocessing is required
to enforce this assumption (subtracting the average from a block of data). The
statistical moments considered are shown below. Note that the formulation of
the second, third, and fourth moments shown below assumes zero-mean data.
Further, the third and fourth moments are normalized by the square root of the
variance to the third and fourth power, respectively, which facilitates comparison
from data set to data set.
Mean = µ = N
xN
ii∑
=1 = 0 (1)
Variance = σ2 = N
xN
ii∑
=1
2
(2)
Skew = S = 3
1
3
σN
xN
ii∑
= (3)
Kurtosis = k = 4
1
4
σN
xN
ii∑
= (4)
15
2.3.1.1 Root Mean Square (RMS) Feature
The first statistical feature is obtained from the second moment (see
Equation 2). This feature is a traditional vibration feature form, root mean square
(RMS), which, for zero-mean data, is simply the square root of the second
moment (variance).
2.3.1.2 Skew
The second feature is the normalized third moment, or skew (Equation 3).
This is a measure of the symmetry of the probability distribution function (PDF).
If the median is smaller than the mean, then the distribution is said to have a
"positive" skew. If the median is larger than the mean, then the distribution is said
to have a "negative" skew. Figure 10 shows a normal (Gaussian) distribution
and both positive and negative skewed distributions. Skew is useful in identifying
un-symmetric phenomena in machinery, such as rub or impacting.
Figure 10: Skew: measure of symmetry of the probability density function
0
0.1
0.2
0.3
0.4
0.5
-5 -4 -3 -2 -1 0 1 2 3 4 5
σ
PD
F
Skew = 0 (Gaussian Distribution)Skew = +0.686Skew = -0.686
16
2.3.1.3 Kurtosis
Kurtosis, like skew, is a measure of the shape of the PDF. It is defined as
the fourth moment normalized by the square root of the variance to the fourth
power (Equation 4). Kurtosis provides a measure of the size of the tails of a
distribution, or the “peakedness” of the data. Kurtosis is a measure of whether
the data is peaked or flat relative to a normal distribution. Data with high kurtosis
tend to have a distinct peak near the mean, decline rather rapidly, and have
heavy tails. Data sets with low kurtosis tend to be flat near the mean. A uniform
distribution would be the extreme case of low kurtosis17. Figure 11 shows the
shapes for mesokurtic (labeled “normal” in the figure), leptokurtic (kurtosis >3.0),
and platykurtic (kurtosis < 3.0) probability distribution functions. Note that there
exists some differences in the way that kurtosis is defined. Some would define
kurtosis (as herein) such that the kurtosis of a Gaussian distribution is 3. Others
define kurtosis by subtracting three from the normalized fourth moment of
Equation 4. Still others term such a value, “excess kurtosis”.
Figure 11: Comparison of PDFs having the same standard deviation but different kurtosis18
One significant advantage of using a kurtosis-based feature is the fact
that, for a Gaussian (or normal) distribution, kurtosis may be shown to equal 3.0
(for a sine wave, k=1.5; for a square wave, k= 1.0). Thus, if one could find a
region in which the signal is Gaussian when there is no mechanical fault, but
non-Gaussian when there is a fault, we could have a figure of merit, which does
17
not require the establishment of a baseline, e.g., one could know whether there is
a fault without knowing the details of history of the machine.
2.3.2 Envelope Spectral Peak Feature
Envelope detection, or asynchronous demodulation19, of a waveform may
be used to identify low-frequency impact events that modulate high frequency
data. The envelope of the bandpass filtered waveform is extracted by first
rectifying, then low-pass filtering the data. The resulting waveform is then
transformed using a discrete Fourier transform (DFT). Finally, the resulting
spectrum is searched for peaks near gear shaft speed frequencies, and the
values at these peaks are recorded.
Envelope detection is best understood by first examining amplitude
modulation. Figure 12a shows a sine wave at 200 Hz modulated by a sine wave
at 5.5 Hz. The spectrum of Figure 12b shows a peak at 200 Hz, but no peak at
5.5. Rather, the 5.5 Hz modulating frequency manifests itself as sidebands of
the 200 Hz peak.
(a) (b)
Figure 12: Sine wave at 200 Hz with amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum
The envelope detection process described above is then applied to the
waveform. First, the waveform is rectified by taking the absolute value. Figure
13 shows the resulting waveform and the associated spectrum. Note that the
spectrum now contains a peak at 5.5 Hz in addition to the 200 Hz peak and its
sidebands.
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Time (sec)
Am
plitu
de
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
18
(a) (b)
Figure 13: Rectified sine wave at 200 Hz, amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum
The final step is to pass the rectified waveform through a low-pass filter (3
dB point at 50 Hz) to remove the carrier and its sidebands. Figure 14 shows the
resulting waveform and its spectrum. The 5.5 Hz modulating frequency is all that
remains.
(a) (b)
Figure 14: Rectified sine wave at 200 Hz, amplitude modulation at 5.5 Hz After low-pass filtering (a) waveform; (b) spectrum
The above example represents the amplitude demodulation of a signal
where there is a single carrier frequency (200 Hz). To extend the example
further, we apply the same techniques to the modulation of the sum of two sine
waves of different frequencies. Figure 15a shows two sine waves, one at 200 Hz
and one at 126 Hz, modulated by a 5.5 Hz sin wave. Once again, the spectrum
(Figure 15b) shows no peak at 5.5 Hz, but both of the peaks (200 and 126 Hz)
-1.4
-0.9
-0.4
0.1
0.6
1.1
1.6
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Time (sec)
Am
plitu
de
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Time (sec)
Am
plitu
de
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
19
have sidebands at 5.5 Hz. The demodulation process is applied, and the
resulting spectrum shows only the 5.5 Hz modulating frequency.
(a) (b)
(c) Figure 15: 200 & 126 Hz sine wave with amplitude modulation at 5.5 Hz (a) waveform; (b) spectrum; (c) envelope spectrum after 50 Hz low-pass filter
Finally, asynchronous modulation, or enveloping, occurs when every
frequency is modulated, implying the there would be sidebands on every spectral
line. This makes interpretation in the time domain or the raw spectrum near to
impossible. Figure 16a shows random data modulated by 5.5 Hz, and Figure
16b its spectrum. As expected, there is no discernable peak at 5.5 Hz.
However, once the demodulation process is applied, the spectrum of Figure 16c
shows the 5.5 Hz modulating frequency. Note that, when the “carrier” is random,
low-pass filtering becomes optional, since there are no discrete carrier
frequencies to remove.
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Time (sec)
Am
plitu
de
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
0.00
0.05
0.10
0.15
0.20
0.25
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
20
(a) (b)
(c) Figure 16: Random data with amplitude modulation at 5.5 Hz (a) waveform;
(b) spectrum; (c) envelope spectrum (no filtering)
This type of broadband, asynchronous modulation (or enveloping) is
known to occur in signals associated with rotating assemblies. It has proven to
be particularly useful in the diagnosis of bearing faults19, and will be shown to be
useful for gear faults herein (see Chapter 3).
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
Time (sec)
Am
plitu
de
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0 50 100 150 200 250 300 350 400
Frequency (Hz)
Am
plitu
de
21
Chapter - 3 Experimental and Analytical Results The feature extraction techniques described in Chapter 2 are applied to
experimental accelerometer data from a gearbox test bed (Interstitial RMS,
Interstitial Kurtosis, and Interstitial Envelope Spectrum Peak features), and to
analytically synthesized fluid-film bearing data (skew feature). Interstitial RMS,
Interstitial Kurtosis, and Interstitial Envelope Spectrum Peak were found to be
good indicators of imminent damage for all runs in which gear tooth fracture
occurred. During the early runs, damage assessment was performed only at the
end of the run by post-mortem inspection, so that the actual time of tooth fracture
could only be surmised from the data. However, in the later runs, periodic optical
inspection via borescope was introduced, so that we have a much better
opportunity for correlation of features with damage. In this paper, only the results
from one of the runs (Run 14) with borescopic inspection will be reviewed.
3.1 Transitional Gear Failure Data The availability of high fidelity data associated with fault development in a
gearbox has been facilitated by the development of the Mechanical Diagnostics
Test Bed, in which off-the-shelf industrial gearboxes are run to failure. This has
created a unique opportunity to develop and tune diagnostic algorithms aimed at
the region of transition-to-failure, rather than at the failure itself, as has been
done previously for data from gearboxes with seeded faults. Such a focus may
provide earlier and better data to fuel accurate prognostic models.
The test platform used to generate the transitional data was the
Mechanical Diagnostics Test Bed (MDTB)20 (see Figure 17). This motor-driven
platform employs two digital vector drive motor motors: a 30 HP drive motor, and
a 75 HP load (absorption) motor. The MDTB has been used to date to run
commercial single-reduction gearboxes to failure by loading by a factor of two or
three over the manufacturer’s rated load. Most of the failures to date involve
22
gear tooth failures on the output gear, and a few of the gearboxes have
experience shaft failure.
Figure 17: Mechanical Diagnostic Test Bed (MDTB)
The overall test plan and operation of the MDTB are detailed in Reference
20. Basically, the MDTB is operated at normal, rated loading conditions for four
days as a “break-in” period. Then, the loading is increased by a factor of two or
three, and the gearbox is operated at that level until preset vibration levels have
been exceeded. For all the tests, postmortem examination indicated that these
levels were observed after significant damage to the gearbox had occurred.
Most of the damage was associated with gear tooth fracture, but there have been
several shaft failures as well. A close-up of the gearbox showing some of the
installed instrumentation is found in Figure 18.
23
Figure 18: Close-up of the gearbox showing accelerometer locations
3.2 Gearbox Features
3.2.1 Interstitial RMS
Interstitial RMS refers to a feature that includes the interstitial
preprocessing (bandpass filtering) of Section 2.2.1 followed by the statistical
feature extraction of RMS (Section 2.3.1.1 ). Figure 19 shows the normalized
results of the Interstitial RMS feature (12:00 on 3/18/98 in Figure 19). Note that
the gearbox was operated at its rated load for about four days for break-in. Then
the load was increased to three times its rated load to accelerate damage. It is
evident that Interstitial RMS increased significantly not only when damage
occurred, but also due to the load change.
24
Figure 19: Interstitial RMS as a function of time over the entire test (Run 14)
Figure 20 shows the same RMS acceleration after increasing load to 3X
rated load. Periodic borescopic inspection revealed no damage at 2:00 AM on
March 20, 1998. As seen in the figure, except for accelerometer 5, there is about
factor of two increase in the amplitude just prior to the onset of macroscopic
(e.g., visible via borescope) damage, which occurred between 2 and 3:00 AM on
March 20, 1998. At 3:00 AM, the first visible evidence of damage was noted in
the borescopic photographs: one tooth was broken and one showed signs of
cracking. By 5:00 AM, the second tooth had broken off, and by 8:15 AM, there
were 8-9 broken teeth. The value of the Interstitial RMS continued to rise as the
damage increased.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
3/15/980:00
3/15/9812:00
3/16/980:00
3/16/9812:00
3/17/980:00
3/17/9812:00
3/18/980:00
3/18/9812:00
3/19/980:00
3/19/9812:00
3/20/980:00
3/20/9812:00
3/21/980:00
Date/Time
Nor
mal
ized
RM
SAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
25
Figure 20: Interstitial RMS as a function of time while loaded at 3X rated load
3.2.2 Interstitial Kurtosis
Interstitial Kurtosis refers to a feature that includes the interstitial
preprocessing (bandpass filtering) of Section 2.2.1 and the statistical feature
extraction of kurtosis (Section 2.3.1.3 ). Figure 21 shows the histograms of
normal (break-in) MDTB data and data at the point of highest kurtosis in a run.
Note that Figure 22 shows the broad tails of the high kurtosis data.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
3/20/984:00
3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Nor
mal
ized
RM
SAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
2:00 AM: No visible damage
3:00 AM: One broken tooth, one cracked
8:15 AM: 8 teeth missing
5:00 AM: Two broken teeth
26
Figure 21: Sample histograms of MDTB gearbox data
Figure 22: Data of Figure 21 rescaled to compare tails
0
2000
4000
6000
8000
10000
12000
-12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0z (standard deviations)
M (c
ount
)Data Set 136 (k=3.07)Data Set 307 (k=22.39)
0
20
40
60
80
100
120
140
160
180
200
-12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0z (standard deviations)
M (c
ount
)
Data Set 136 (k=3.07)
Data Set 307 (k=22.39)
27
Figure 23 is the more intuitive plot of the product zi
4Mi, where zi is the
number of standard deviations from the mean of bin i and Mi is the number of
samples in ith bin (of I total) of the histogram. Now, kurtosis becomes simply:
∑=
=I
iii Mzk
1
4 (5)
The figure dramatically demonstrates the effects of the quartic weighting of the
distribution tails.
Figure 23: Contribution to kurtosis z4M
Figure 24 shows the Interstitial Kurtosis feature as a function of time
during Run 14. Note that the value of this feature remains at about 3.0 before
the onset of damage, and there is little sensitivity to the load increase to three
times rated load.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0z (standard deviations)
Kur
tosi
s C
ontri
butio
n, z
4 M
Data Set 136 (k=3.07)Data Set 307 (k=22.39)
∑=
=I
iii Mzk
1
4
28
Figure 24: Interstitial kurtosis as a function of time over the entire test (Run 14)
Figure 25 shows the data of Figure 24 during the overload period. As with
the Interstitial RMS, the Interstitial Kurtosis performs well, and gives an indication
of a fault before macroscopic damage is observable via borescope. Periodic
borescopic inspection revealed no damage at 2:00 AM on March 20, 1998.
However, except for accelerometer 5, kurtosis already indicates a significant
change in the distribution before the damage is visible. At 3:00 AM, the first
visible evidence of damage was noted in the borescopic photographs: one tooth
was broken and one showed signs of cracking. By 5:00 AM, the second tooth
had broken off, and by 8:15 AM, there were 8-9 broken teeth. Note that kurtosis
maximized at about 4:00 AM, implying that kurtosis, although an excellent
indicator of the onset of tooth impact, may not always be a good measure of the
extent of the damage. Barkov and Barkova noted that, for rolling contact
bearings, “peaks may rise more slowly and may even decrease as impact
0
3
6
9
12
15
18
21
3/15/980:00
3/15/9812:00
3/16/980:00
3/16/9812:00
3/17/980:00
3/17/9812:00
3/18/980:00
3/18/9812:00
3/19/980:00
3/19/9812:00
3/20/980:00
3/20/9812:00
3/21/980:00
Date/Time
Kur
tosi
s
Accelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
29
producing discontinuities are worn away”21. In fact, in other kurtosis features
kurtosis has been observed to decrease as damage increases on other gearbox
tests13,14.
Figure 25: Interstitial kurtosis while loaded at 3X rated load
3.2.3 Interstitial Envelope Spectral Peak
Figure 26 and Figure 27 show the normalized amplitude of the envelope
spectral peak at the output gear shaft speed. Note that the parameter is best
viewed using logarithmic scaling due to the significant increases in its value.
Figure 26 shows that there is about an order of magnitude increase in the
amplitude when the load is increased to three times rated load.
0
3
6
9
12
15
18
21
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
3/20/984:00
3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Kur
tosi
s
Accelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
2:00 No visible damage
3:00 One broken tooth, one cracked
8:15 am: 8 teeth missing
5:00 Two broken teeth
30
Figure 26: Interstitial envelope spectral peak at output gear speed as a function of time
Figure 27 shows the normalized values of the spectral peak during the
loading at 3X rated load only. As seen in the figure, except for accelerometer 5,
there is about an order of magnitude increase in the amplitude just prior to the
onset of visible damage, which occurred between 2:00 AM and 3:00 AM on
March 20, 1998. The value of the parameter continued to rise as the damage
increased.
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
3/15/980:00
3/15/9812:00
3/16/980:00
3/16/9812:00
3/17/980:00
3/17/9812:00
3/18/980:00
3/18/9812:00
3/19/980:00
3/19/9812:00
3/20/980:00
3/20/9812:00
3/21/980:00
Date/Time
Nor
mal
ized
Am
plitu
de
Accelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
31
Figure 27: Interstitial envelope spectral peak at output gear speed as a function of time while loaded at 3X rated load
3.3 Bearing Feature: Skew It was found that the skew feature did not provide meaningful information
when applied to gearbox accelerometer data during gear tooth failure. To
demonstrate the potential application of this feature, a fluid film bearing is
considered during shaft-to-bearing rub. Such rub leads to premature bearing
wear and, sometimes, catastrophic damage to the rotating equipment. Figure 28
shows a typical installation of proximity probes on a fluid film bearing22. The
resulting data from the orthogonally mounted proximity probes may be displayed
as an orbit by synchronously plotting one channel versus the other channel.
Often, diagnostics for rub are performed by visually inspecting the orbit to look for
“flat spots” associated with rub. We will examine some synthetic data to
investigate the application of skew to bearing rub diagnostics.
0.00001
0.0001
0.001
0.01
0.1
1
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
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3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Nor
mal
ized
Am
plitu
deAccelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load
2:00 AM: No visible damage
3:00 AM:One broken tooth, one cracked
8:15 AM: 8 teeth missing
5:00 AM: Two broken teeth
32
(a) (b)
Figure 28: (a) Typical installation of proximity probe on fluid-film bearing (Bently-Nevada)22; (b) Resulting orbit
Figure 29 shows some synthesized data with and without rub. Note that a
value of 10% is displayed to allow visualization. Actual incipient rub would be
significantly less than 10 %. To explore the sensitivity of skew to noise, we have
injected various amount of random noise to the synthesized signal, as seen in
Figure 29(b) and (c). Clearly, even with exaggerated values of rub, noise can
obscure visual interpretation of the orbit.
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
33
(a) (b)
(c) (d) Figure 29: Synthesized orbit with rub and noise
Figure 30 shows a typical histogram of the synthesized data. Note that
the “double hump” distribution underlying this data is associated with sinusoidal
data. Although there is significant rub (10%) for the data associated with this
histogram, the skew is not visibly obvious.
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
Normal Orbit
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
Orbit with 10% Rub
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
Orbit with 10% Rub, 14% Noise
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
Orbit with 10% Rub, 28% Noise
34
Figure 30: Histogram of one channel with 10% Rub, 28% Noise
Skew was then extracted from the synthesized data. Figure 31 shows the
results. It is evident that (1) skew is a good measure of the flattening due to rub;
and (2) skew is reasonably immune to noise. Additional research is required to
demonstrate the efficacy of a skew feature in an actual fluid-film bearing system.
Figure 31: Skew as a function of percent flattened
-1.5 -1 -0.5 0 0.5 1 1.50
5
10
15
20
25
30
35
40
45
0.001
0.01
0.1
1
0 2 4 6 8 10 12 14 16 18 20
Percent Flattened
Ske
w
No Noise14% Noise14% Noise14% Noise28% Noise28% Noise28% Noise
35
Chapter - 4 Evaluation of Gearbox Features The three gearbox features (Interstitial RMS, Interstitial Kurtosis, and
Interstitial Envelope Spectral Peak) are evaluated in two ways: first, by
comparing with the more traditional preprocessing step of high-pass filtering; and
second, by comparing the experimental results for these features with the
commonly used gearbox features FM4 and NA4.
4.1 High-Pass Filtering Comparison The interstitial results for a single accelerometer (Accelerometer 2) are
compared with the more traditional high-pass filtering (3000 Hz and 5000 Hz)
results in Figure 32, Figure 33, and Figure 34. For all of the three features, the
interstitial results showed clear indications before there was any visible damage.
The parameters obtained after high-pass filtering did show evidence of damage
after the gear tooth cracking was visible. However, the interstitial parameters are
better prognostic indicators and are more robust.
36
Figure 32: Comparison of RMS using high-pass and interstitial filtering
Figure 33: Comparison of kurtosis using high-pass filtering (3000 Hz and 5000 Hz) and interstitial filtering (Accelerometer 2)
0
3
6
9
12
15
18
21
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
3/20/984:00
3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Kur
tosi
s
Unfiltered3000 Hz Highpass5000 Hz HighpassBandpassStart 3X Load
2:00 AM: No visible damage
3:00 AM: One broken tooth, one cracked
5:00 AM: Two broken teeth
8:15 AM: 8 teeth missing
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
3/20/984:00
3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Nor
mal
ized
RM
S
Unfiltered3000 Hz HP5000 Hz HPBandpassStart 3X Load
3:00 AM:One broken tooth, one cracked
2:00 AM: No visible damage
8:15 AM: 8 teeth missing
5:00 AM: Two broken teeth
37
Figure 34: Comparison of enveloping using high-pass filtering (3000 Hz and 5000 Hz) and interstitial filtering (Accelerometer 2)
4.2 Comparison with Traditional Gearbox Features Several features have been developed over the years for the detection of
gear tooth failures. Most are based on time synchronous averaging (TSA)
preprocessing schemes, followed by some peak removal, and, finally kurtosis
extraction. A few, such as M6A and M8A23, use higher statistical moments (6th
and 8th respectively). TSA is usually done by interpolating the raw data, aligning
the data corresponding to one revolution at a time, averaging and then
decimating back to the original sampling frequency. It is effective in removing
information not associated with the rotation of the machine. TSA is followed by
various schemes to normalize the kurtosis (or higher moment), such as removing
the gear mesh frequency and its multiples using digital filtering, and sometimes
removing the first and occasionally the second order side bands. Again, the
primary goal of the preprocessing is to force the kurtosis to be 3.0 (corresponding
to Gaussian distribution) when there is no gear damage. It does appear that
different gear systems may require different schemes.
0.00001
0.0001
0.001
0.01
0.1
1
3/19/9812:00
3/19/9814:00
3/19/9816:00
3/19/9818:00
3/19/9820:00
3/19/9822:00
3/20/980:00
3/20/982:00
3/20/984:00
3/20/986:00
3/20/988:00
3/20/9810:00
Date/Time
Nor
mal
ized
Am
plitu
de
3000 Hz Highpass5000 Hz HighpassBandpassStart 3X Load
2:00 AM: No visible damage
3:00 AM:One broken tooth, one cracked
8:15 AM: 8 teeth missing
5:00 AM: Two broken teeth
38
A number of gearbox features were evaluated on the MDTB24,25, and it
was found that the most consistent and robust were FM414 and NA413. These
two kurtosis-based features are compared to Interstitial Kurtosis in Figure 35.
Figure 35: Comparison of interstitial kurtosis with NA4 and FM4
(Normalized to 1.0)
As seen in the figure, both FM4 and Interstitial Kurtosis provide similar
early warning, and both drop off in value, with FM4 retaining its amplitude longer.
NA4 does not show as clear an early change. Note that normalization was
performed because (1) the values for NA4 were two orders of magnitude larger
than for FM4 and Interstitial Kurtosis; and (2) the values of kurtosis before
damage for NA4 had considerable scatter about the expected value of 3.0. This
is seen in Figure 36, in which normalization was not performed.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00
Time
Nor
mal
ized
Env
elop
e Sp
ectr
al A
mpl
itude
at O
utpu
t G
ear S
peed
, Nor
mal
ize
RM
S
Start 3X LoadInterstital KurtosisNA4FM4
2:00 AM: No visible
3:00 AM: One broken tooth, one cracked
8:15 AM: 8 teeth missing
5:00 AM: Two broken
39
Figure 36: Comparison of interstitial kurtosis with NA4 and FM4 (not normalized)
So, Interstitial Kurtosis and FM4 are equally good at identifying a gear
tooth fault without a baseline (due to kurtosis being 3.0 when undamaged). For
this case, NA4 did not yield the expected robust behavior of the other two
kurtosis-based features.
The extraction of Interstitial Kurtosis may be performed without a
tachometer, since the positioning of the interstitial band-pass filter may be
accomplished without a direct measure of speed. However, FM4 and NA4
require a tachometer to perform time-synchronous averaging. An effect of the
time synchronous averaging, however, is that an increase in FM4, for instance,
ensures that the fault is associated with gear meshing. Interstitial kurtosis could
be affected by other faults that manifest themselves in sharp events, such as
rolling element contact bearing flaws.
0
5
10
15
20
25
30
12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00
Time
Nor
mal
ized
Env
elop
e Sp
ectr
al A
mpl
itude
at O
utpu
t G
ear S
peed
, Nor
mal
ize
RM
S
Start 3X LoadInterstital KurtosisNA4FM4
2:00 AM: No visible
3:00 AM: One broken tooth, one cracked
8:15 AM: 8 teeth missing
5:00 AM: Two broken
40
4.3 Feature Fusion None of the features employed herein are effective by themselves. Data
fusion should be performed to ensure correct interpretation of the action of
various features. For instance, if only the interstitial features were used, it would
be useful to employ some data fusion algorithms to aid in interpretation. Table 1
shows the effectiveness of the interstitial features for three important capabilities:
the ability to clearly distinguish between load change and tooth damage, the
ability to indicate imminent damage prior to macroscopically observable damage
(via the borescope), and the ability to provide indication of the extent of the
damage. It is seen that Interstitial Kurtosis provides an excellent indication of
imminent damage; however, it is not very good at providing a measure of the
extent of the damage.
Table 1: Summary of interstitial parameter effectiveness
Figure 37 shows the results of fusing a kurtosis-based feature and an
RMS based feature using fuzzy logic blending functions to provide an overall
health vector26. This kind of data fusion allows us to take advantages of the
strengths of various features and therefore track with high confidence the health
of the machine.
Interstitial Kurtosis
Interstitial Envelope Spectrum
InterstitialRMS
Able to clearly distinguish between load change and imminent tooth damage
Yes
No
No
Able to indicate imminent damage during transition to failure (prior to tooth cracking visible via borescope)
Yes
Yes
Yes
Able to provide some indication of the extent of the gear tooth damage
No
Yes
Yes
41
Figure 37: Gear component health vector based on kurtosis and RMS
4.4 Model-Based Feature Identification To further enhance the ability to correlate machine health with features,
machine models may be used. One approached being used on the MDTB is to
model the tooth cracking as a change in stiffness of the gear teeth. Figure 38
and Figure 39 show a finite element model of the MDTB gear teeth. Figure 40
and Figure 41 show the results without and with a crack. The result of nonlinear
analysis of this model was different stiffness profiles for cracked and uncracked
teeth, as shown in Figure 42.
0
1
-24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0Time from Shutdown (Hours)
Nor
mal
ized
Gea
r Too
th H
ealth
Par
amet
ers 11:29 No
visible damage
14:29 Two broken teeth
17:44 8 teeth missing
12:29 One broken tooth, one cracked
42
Figure 38: Finite element model of MDTB gear teeth (with contact)
Figure 39: Detail of tooth model: a) showing elements; b) showing crack
location
Crack
43
Figure 40: Contact model of gear with no cracks
Figure 41: Contact model of gear with cracked tooth
44
Figure 42: Effective torsional stiffness profile of a cracked and uncracked tooth
The stiffness of Figure 42 may then be input to a beam model of the
MDTB shaft (Figure 43), and the model may be exercised to produce time
waveforms. To exercise the model, a constant torque is applied at the motor and
generator ends, and the variable stiffness is introduced as a spring at the gear
mesh (Figure 44). Features may be extracted from the output time waveforms
and compared to test data27,28.
0
100000
200000
300000
400000
500000
600000
700000
0 5 10 15 20 25 30
φ (Degrees)
Stif
fnes
s (in
-lb/ra
d)
Cracked
Uncracked
One Tooth
45
Figure 43: Finite element model of MDTB rotor (beam model)
Figure 44: Close up of MDTB rotor beam model showing schematically the
location of the variable spring stiffness associated with mesh
Variable Stiffness SpringRigid Links
(Constraint Equations)
Variable Stiffness SpringRigid Links
(Constraint Equations)
46
Some preliminary results of feature extraction on the waveform output
from the finite element analysis are shown in Figure 4529. Note that, for this finite
element model, only one cracked tooth was input, so that results may only be
compared to MDTB data up to the time the first tooth crack was detected via
borescope. Note further that the gears in the MDTB, which are actually helical,
were modeled as spur gears. In addition, only torsional degrees of freedom were
allowed in the rotor model. Additional modeling is required to include the effects
of the helical gear and to allow coupling of the torsional motion with translation,
which will allow direct comparison with accelerometer data.
Figure 45: Results of comparison of FM4 from MDTB test and finite element model results
0
5
10
15
20
25
3/19/98 23:00 3/20/98 0:00 3/20/98 1:00 3/20/98 2:00 3/20/98 3:00Date/Time
FM4
Experimental FM4
Model Results
2:00 AM: No visible damage
3:00 AM: One broken, one cracked tooth
47
Research associated with model-based feature correlation is in its infancy.
However, the promise is great. To extend the experimental transition-to-failure
testing and correlation to a complex helicopter gearbox, for instance, would be
prohibitively expensive. However, if we are able to generate models of
experimental systems such as the MDTB and correlate experimental feature
extraction with features from the model, we will be able to understand the
relationship between extracted vibration features and damage. This
understanding may be transferred via only moderately complex models to a very
complex gear system without requiring that the complex system actually be run
to failure. This would provide immeasurable benefit to machinery OEMs,
operators and maintainers.
Another potential benefit of model-based feature development is the ability
to apply the methodology to assess the effects of changing operating conditions
on the life of a component. This allows the operator/maintainer to employ the
right machine for the right job. For example, using model-based feature
assessment and prognostics, a helicopter with damage to a bearing might be
demonstrated able to safely operate for only ten hours at full torque, but may be
permitted to continue to operate at low torque for one hundred hours. This
allows the fleet manager flexibility and facilitates full asset utilization.
48
Chapter - 5 Conclusion This paper has reviewed by example the basic methodology of feature
extraction. Facilitated by the use of actual transition-to-failure data from the
MDTB, we examined specific example features and compared the effectiveness
of various preprocessing schemes. We also compared the example features to
two features often used for helicopter gearbox diagnostics. We examined the
advantages of feature fusion and of model-based feature extraction by
considering examples. As a result, we have increased our understanding of the
overall feature extraction methodology and how it fits into a typical smart sensor
architecture.
On the basis of our increase in understanding, we arrive at the following
conclusions:
• Feature extraction emulates how a human assesses data
• Different features may be required for different failure modes.
• Feature extraction allows storage and transmission of large amounts of
information in the form of small amounts of data. This facilitates the
incorporation of large numbers of smart sensors in a system without
data/information overload.
• Feature extraction requires intelligent preprocessing. Preprocessing is
one of the most important and one of the least emphasized aspects of the
feature extraction process.
• Feature selection requires a prior knowledge of the failure process.
• Feature extraction requires automated evaluation of the condition of the
sensor, signal conditioning, etc.
• Component health evaluation may require the fusion of information from
several features.
• Model-based feature extraction will allow information gleaned from simple
systems to be applied to more complex systems.
49
Many research topics associated with feature extraction remain
incompletely explored. Nevertheless, it is evident that feature extraction, clothed
in smart sensor systems and system health management systems, is making its
way onto industrial and military platforms.
50
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