Vibration Feature Extraction for Smart Sensors

Transcription

1 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

2 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

3 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

4 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.

5 iv Table of Contents LIST OF TABLES... v LIST OF FIGURES:... vi ACKNOWLEDGEMENTS:... 1 CHAPTER - 1 INTRODUCTION Smart Sensors Why Feature Extraction?...10 CHAPTER - 2 FEATURE EXTRACTION EXAMPLES Preprocessing for Gear Fault Detection Preprocessing Steps Interstitial Preprocessing Asynchronous Demodulation Preprocessing Feature Extraction Statistical Features Root Mean Square (RMS) Feature Skew Kurtosis Envelope Spectral Peak Feature...17 CHAPTER - 3 EXPERIMENTAL AND ANALYTICAL RESULTS Transitional Gear Failure Data Gearbox Features Interstitial RMS Interstitial Kurtosis Interstitial Envelope Spectral Peak Bearing Feature: Skew...31 CHAPTER - 4 EVALUATION OF GEARBOX FEATURES High-Pass Filtering Comparison Comparison with Traditional Gearbox Features Feature Fusion Model-Based Feature Identification...41 CHAPTER - 5 CONCLUSION... 48

6 v List of Tables: TABLE 1: SUMMARY OF INTERSTITIAL PARAMETER EFFECTIVENESS...40

7 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 Z 4 M...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 FM FIGURE 36: COMPARISON OF INTERSTITIAL KURTOSIS WITH NA4 AND FM4 (NOT NORMALIZED)...39

8 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 vii

9 1 Acknowledgements: This work was primarily supported by Multidisciplinary University Research Initiative (MURI) for Integrated Predictive Diagnostics (Grant Number N ) 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.

10 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 conditionmonitoring 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, shorttime 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

11 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 physicsbased. 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 attributes 2 : 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.

12 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 months 3. 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.

13 Merced Transistors Intel Data Linear Fit (Logarithmic) Pentium Pro Pentium Linear fit corresponds to doubling every 2.15 years Year Figure 1: Moore's Law as applied to Intel processors 1000 Twenty-five year history Pentium Pro Linear fit of twenty-five year history Pentium Linear fit of first decade 100 Linear fit of last decade 10 Twenty-five year History: Doubling every 1.96 years Last ten years: Doubling every 1.58 years MIPS 1 First ten years: Doubling every 1.87 years Year 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.

14 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 , 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 66% 17% system greatly restricts the Wiring Sensor Installation expansion of the system. In addition, it will often put smart Wire sensors in a position of being too 17% expensive. Figure 3 shows the estimated cost of installing a sensor onboard a ship. For Figure 3: Typical instrumentation costs 8 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. 6

15 On the basis of the current trends in wireless data communication, several sensor manufacturers have chosen the Bluetooth wireless protocol 9 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 Figure 4: Bluetooth OEM module Corporation, Nokia and Toshiba (circa 2001) 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 selfpowering. 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. 7

16 8 1 1 Communications Diagnostic Processor (ASIC) General Purpose Processor Digital Signal Processing Signal Conditioning/ADC Power interface/generation Sensing Element Self Calibration/Active Cancellation Figure 5: Idealized smart accelerometer LAN Intelligent Node Area Reasoner Operator/ Maintainer Intelligent Node The World via Internet Figure 6: Smart sensor architecture example for a pump

17 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. Wilcoxon Oceana Sensors Rockwell PC104 (PSU, others) Figure 7: Currently available forms of the smart sensor or intelligent node

18 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.

19 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. Accelerometer Data Bandpass Filter Between Higher GMF RMS Kurtosis Rectify Lowpass Filter DFT Analysis Peak Search 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 years 10. Enveloping has been used extensively for the

20 12 detection of rolling contact bearing faults in rotating machinery 10, 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 bearings 10. Bandpass filtering has also been used for bearing diagnostics in systems with significant mechanical energy in higher frequency bands, such as geared systems 12. Analogous filtering is used in some of the kurtosis-based gear figures of merit, such as NA4 13 and FM Preprocessing Steps 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.

21 13 Mean Square Acceleration ([in/sec] 2 ) Figure 9: Typical raw and filtered data from MDTB run Asynchronous Demodulation Preprocessing Envelope detection, or asynchronous demodulation 15, 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.

22 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 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 = Variance = σ 2 = N i=1 N N i=1 N x x i 2 i = 0 (1) (2) 3 xi Skew = S = i= 1 3 Nσ (3) 4 xi i= 1 Kurtosis = k = (4) 4 Nσ N N

23 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) 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 Skew = 0 (Gaussian Distribution) Skew = Skew = PDF σ Figure 10: Skew: measure of symmetry of the probability density function

24 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 kurtosis 17. 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 kurtosis 18 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

25 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 Envelope Spectral Peak Feature Envelope detection, or asynchronous demodulation 19, 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 Amplitude 0.0 Amplitude Time (sec) (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. Frequency (Hz)

26 Amplitude 0.1 Amplitude Time (sec) Frequency (Hz) (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 Amplitude 0.0 Amplitude Time (sec) (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) Frequency (Hz)

27 have sidebands at 5.5 Hz. The demodulation process is applied, and the resulting spectrum shows only the 5.5 Hz modulating frequency Amplitude Amplitude Time (sec) (a) Frequency (Hz) (b) Amplitude Frequency (Hz) (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.

28 Amplitude Amplitude Time (sec) (a) Frequency (Hz) (b) Amplitude Frequency (Hz) (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 faults 19, and will be shown to be useful for gear faults herein (see Chapter 3).

29 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

30 gear tooth failures on the output gear, and a few of the gearboxes have experience shaft failure. 22 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.

31 Gearbox Features Interstitial RMS Figure 18: Close-up of the gearbox showing accelerometer locations Interstitial RMS refers to a feature that includes the interstitial preprocessing (bandpass filtering) of Section followed by the statistical feature extraction of RMS (Section ). 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.

32 Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load Normalized RMS /15/98 0:00 3/15/98 12:00 3/16/98 0:00 3/16/98 12:00 3/17/98 0:00 3/17/98 12:00 3/18/98 0:00 Date/Time 3/18/98 12:00 0:00 12:00 0:00 12:00 3/21/98 0:00 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, 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, 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.

33 Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load 5:00 AM: Two broken teeth Normalized RMS :00 AM: One broken tooth, one cracked 2:00 AM: No visible damage 0.1 8:15 AM: 8 teeth missing 0 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00 Date/Time Figure 20: Interstitial RMS as a function of time while loaded at 3X rated load Interstitial Kurtosis Interstitial Kurtosis refers to a feature that includes the interstitial preprocessing (bandpass filtering) of Section and the statistical feature extraction of kurtosis (Section ). 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.

34 Data Set 136 (k=3.07) 8000 Data Set 307 (k=22.39) M (count) z (standard deviations) Figure 21: Sample histograms of MDTB gearbox data Data Set 136 (k=3.07) Data Set 307 (k=22.39) M (count) z (standard deviations) Figure 22: Data of Figure 21 rescaled to compare tails

35 27 Figure 23 is the more intuitive plot of the product z 4 i M i, where z i is the number of standard deviations from the mean of bin i and M i is the number of samples in i th bin (of I total) of the histogram. Now, kurtosis becomes simply: I k = i= 1 z 4 M i i The figure dramatically demonstrates the effects of the quartic weighting of the distribution tails (5) Kurtosis Contribution, z 4 M Data Set 136 (k=3.07) Data Set 307 (k=22.39) k = I i= 1 4 z i M i z (standard deviations) Figure 23: Contribution to kurtosis z 4 M 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.

36 Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load Kurtosis /15/98 0:00 3/15/98 12:00 3/16/98 0:00 3/16/98 12:00 3/17/98 0:00 3/17/98 12:00 3/18/98 0:00 3/18/98 12:00 0:00 12:00 0:00 12:00 3/21/98 0:00 Date/Time 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, 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

37 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 tests 13, Kurtosis Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load 3:00 One broken tooth, one cracked 5:00 Two broken teeth 6 2:00 No visible damage 3 0 8:15 am: 8 teeth missing 12:00 14:00 16:00 18:00 20:00 22:00 0:00 2:00 4:00 6:00 8:00 10:00 Date/Time Figure 25: Interstitial kurtosis while loaded at 3X rated load 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.

38 30 1 Normalized Amplitude Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load /15/98 0:00 3/15/98 12:00 3/16/98 0:00 3/16/98 12:00 3/17/98 0:00 3/17/98 12:00 3/18/98 0:00 3/18/98 12:00 0:00 12:00 0:00 12:00 3/21/98 0:00 Date/Time 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, The value of the parameter continued to rise as the damage increased.

39 Accelerometer 2 Accelerometer 3 Accelerometer 4 Accelerometer 5 Start 3X Load 3:00 AM:One broken tooth, one cracked Normalized Amplitude :00 AM: No visible damage 5:00 AM: Two broken teeth :00 14:00 16:00 18:00 20:00 22:00 0:00 Date/Time 2:00 8:15 AM: 8 teeth missing 4:00 6:00 8:00 Figure 27: Interstitial envelope spectral peak at output gear speed as a function of time while loaded at 3X rated load 10: 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 bearing 22. 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.

40 (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.

41 Normal Orbit (a) Orbit with 10% Rub (b) Orbit with 10% Rub, 14% Noise Orbit with 10% Rub, 28% Noise (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.

42 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 No Noise 14% Noise 14% Noise 14% Noise 28% Noise 28% Noise 28% Noise Skew Percent Flattened Figure 31: Skew as a function of percent flattened

43 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 NA 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.

44 36 Normalized RMS Unfiltered 3000 Hz HP 5000 Hz HP Bandpass Start 3X Load 3:00 AM:One broken tooth, one cracked 5:00 AM: Two broken teeth 0.2 2:00 AM: No visible damage :00 14:00 16:00 18:00 20:00 22:00 0:00 Date/Time 2:00 8:15 AM: 8 teeth missing 4:00 6:00 8:00 10:00 Figure 32: Comparison of RMS using high-pass and interstitial filtering 21 Kurtosis Unfiltered 3000 Hz Highpass 5000 Hz Highpass Bandpass Start 3X Load 3:00 AM: One broken tooth, one cracked 5:00 AM: Two broken teeth 8:15 AM: 8 teeth missing 6 2:00 AM: No visible damage :00 14:00 16:00 18:00 20:00 22:00 0:00 Date/Time 2:00 4:00 6:00 8:00 10:00 Figure 33: Comparison of kurtosis using high-pass filtering (3000 Hz and 5000 Hz) and interstitial filtering (Accelerometer 2)

45 Hz Highpass 5000 Hz Highpass Bandpass Start 3X Load 3:00 AM:One broken tooth, one cracked Normalized Amplitude :00 AM: No visible damage 5:00 AM: Two broken teeth :15 AM: 8 teeth missing :00 14:00 16:00 18:00 20:00 22:00 0:00 Date/Time 2:00 4:00 6:00 8:00 10:00 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 M8A 23, use higher statistical moments (6 th and 8 th 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.

46 38 A number of gearbox features were evaluated on the MDTB 24,25, and it was found that the most consistent and robust were FM4 14 and NA4 13. These two kurtosis-based features are compared to Interstitial Kurtosis in Figure 35. Normalized Envelope Spectral Amplitude at Output Gear Speed, Normalize RMS Start 3X Load Interstital Kurtosis NA4 FM4 2:00 AM: No visible 3:00 AM: One broken tooth, one cracked 5:00 AM: Two broken 8:15 AM: 8 teeth missing 0 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 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.

47 39 Normalized Envelope Spectral Amplitude at Output Gear Speed, Normalize RMS Start 3X Load Interstital Kurtosis NA4 FM4 2:00 AM: No visible 3:00 AM: One broken tooth, one cracked 5:00 AM: Two broken 8:15 AM: 8 teeth missing 0 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 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.

48 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. Able to clearly distinguish between load change and imminent tooth damage Able to indicate imminent damage during transition to failure (prior to tooth cracking visible via borescope) Able to provide some indication of the extent of the gear tooth damage Interstitial Kurtosis Interstitial Envelope Spectrum Interstitial RMS Yes No No Yes Yes Yes No Yes Yes 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 vector 26. 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.

49 41 Normalized Gear Tooth Health Parameters 1 11:29 No visible damage 12:29 One broken tooth, one cracked 14:29 Two broken teeth 17:44 8 teeth missing Time from Shutdown (Hours) 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.

50 42 Figure 38: Finite element model of MDTB gear teeth (with contact) Crack Figure 39: Detail of tooth model: a) showing elements; b) showing crack location

51 43 Figure 40: Contact model of gear with no cracks Figure 41: Contact model of gear with cracked tooth