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VoldKalman Order Tracking Filter

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Tachometer repair and smoothing. BA7645-11, 7. Vold-Kalman ... Tachometer Analysis ... Tachometer Analysis RPM CurveFit. Cubic least squares spline fit ... – PowerPoint PPT presentation

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Title: VoldKalman Order Tracking Filter


1
Multi-analyzer System Type 3560
  • Vold-Kalman Order Tracking Filter

A PULSE LabShop Tool Pack for Order Tracking
Analysis
2
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman
    Filtering
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

3
LabShop Tool Packs - Application Packages
Excel
Word
Sound Power Type 7748
Sound Quality Type 7698
3rd Party Applications
Modal Analysis Type 7750
Customised Solutions
Communication Interface (OLE Automation and/or
file)
PULSE Interface to SONY DAT Type 7706
Data Recorder Type 7701
Order Analysis Type 7702
Zwicker Loudness Analysis Type 7704
Noise Vibration Analysis Type 7700
Vold-Kalman Order Tracking Filter Type 7703
Time Capture Type 7705
PULSE LabShop
Windows NT
Data Acquisition and Conditioning Interface
4
Order Analysis
  • Order Analysis is the art and science of
    extracting sinusoidal contents of measurements
    from acousto-mechanical systems under periodic
    loading
  • Order Analysis is used for
  • troubleshooting
  • design
  • synthesis

5
Applications of Vold-Kalman Filters
  • Examples
  • Order Tracking Analysis
  • Order analysis at extreme slew rates
  • including gear shifts
  • Separation of orders in multishaft systems
  • Order Waveform extraction
  • Playback of individual orders
  • Other order applications
  • Sound Quality synthesis studies
  • Removal of nuisance orders from total signal
  • Multiplane balancing
  • Operating Deflection Shapes
  • Dopplerized engine noise order tracking in
    pass-by test

6
Features of Vold-Kalman Filters
  • Order Extraction as
  • Phase assigned orders (Magnitude / Phase)
  • as function of RPM / time / process parameters
  • Order waveform extraction
  • without phase bias
  • No slew rate limitation
  • Beat-free estimation of interacting and crossing
    orders
  • Leakage- and smearing-free order extraction
  • Ultra-fine tracking resolution
  • Tachometer repair and smoothing

7
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

8
Overview of digital order analysis techniques
FFT/DFT based tracking analysis
Digital Filtering based analysis
including Overall levels
FFT based analysis
Vold-Kalman filter based analysis
9
Run-up/down Test using Digital Filters
  • Overall Lin, A, B, C, D levels as a function of
    RPM / time / other process parameters
  • 1/1, 1/3, 1/12, 1/24 octave spectra as a function
    of RPM / time / etc.
  • low orders may be identified
  • overall and frequency slices can be extracted
  • The technique can reveal frequency regions with
    annoying resonances
  • related to human perception of sound

10
Run-up/down Test using FFT Analysis
  • FFT spectra as a function of RPM / time / etc.
  • fixed sampling frequency
  • fixed frequency range
  • Advantages
  • fast, simple implementation
  • structural resonances parallel to RPM axis
  • order and frequency slices can be extracted
  • Disadvantages
  • smearing of orders
  • limited RPM range
  • wide RPM range requires large FFT transform size

11
Run-up/down test using Digital Order Tracking
  • FFT/DFT order spectra as a function of RPM / time
    / etc.
  • fixed order span
  • variable frequency span
  • oversampling, interpolation, resampling technique
  • Advantages
  • leakage- and smearing-free
  • identification of high orders
  • small number of lines required
  • easy order / slice extraction
  • Disadvantages
  • more complex processing
  • requires accurate tacho estimation

12
Run-up/down Test using Vold-Kalman Filters
  • Order extraction as a function of RPM / time /
    etc.
  • using time history data
  • fixed sampling frequency
  • adaptive filter approach
  • Advantages
  • no slew-rate limitation
  • can handle gearshifts
  • leakage- and smearing- free
  • separation of close and crossing orders
  • can handle very noisy signals
  • automatic tacho repair
  • Disadvantages
  • some priori knowledge required
  • postprocessing
  • tacho signal required

13
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

14
Overview of Vold-Kalman Filtering
  • RPM determination
  • Order Waveform tracking
  • Structural equation
  • sinewave model
  • Data equation
  • energy conservation
  • Least square equation
  • filter bandwidth
  • Phase assigned order determination
  • i.e. Magnitude / Phase
  • Order Waveform (time histories) from RPM and
    phase assigned orders

15
Vold-Kalman Filter
  • First generation Kalman filtering
  • 2nd order real difference equation
  • Second generation Vold-Kalman filtering
  • 1st order complex difference equation
  • improved performance
  • reduced calculation time

16
Structural Equation, 1st Generation
Sinewave model using a linear, frequency
dependent, three data point constraints equation
  • 2nd order real difference equation
  • determined by instantaneous axle RPM and order
  • where
  • nonhomogeneity term??(n), which allows the
    sinewave to change amplitude, phase and frequency
    over the time points involved
  • solving for the waveform in a recursive manner
  • s?(n), standard deviation of nonhomogeneity term,
    ?(n)

17
Data Equation
  • Measured signal contains signal that satisfies
    the structural equation as well as noise and
    other periodic components

Based on Energy Conservation Data equation
  • where
  • y(n) measured signal
  • x(n) target signal
  • ?(n) nuisance component, random noise and
    periodic components at other frequencies than
    x(n)
  • s??(n) standard deviation of nuisance component,
    ?(n)

18
Least Squares Equation
Satisfy a weighted average of Structural and Data
Equation
  • Unweighted form
  • Weighted form
  • where
  • Global solution minimizes variance error

19
Weighting Factor, r(n)
  • ratio of standard deviations between
    non-homogeneity term and nuisance term
  • expresses confidence between structural and data
    equation
  • small r(n) yields a narrow filter with long
    settling time
  • large r(n) yields a broad filter with short
    settling time
  • 1 / r(n) Harmonic confidence factor
  • By varying r(n) along the record Constant
    Bandwidth, CB and Constant Percentage Bandwidth,
    CPB filter shapes can be obtained

20
Magnitude / Phase determination
  • Time Variant Vandermonde Equation used
  • Real / Imaginary parts, a(n), b(n) for data point
    n
  • Magnitude,
  • Phase,

21
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

22
Phasors and Phase Assigned Orders
  • An order can be visualized as an AM/FM radio
    signal
  • Complex phasor, generic carrier wave
  • the integral gives the angle travelled by the
    axle up to the current time
  • the phasor is always on the complex unit circle
  • Carrier is amplitude/phase modulated by the
    orders, Ak(t)
  • phase assigned orders occur in complex conjugate
    pairs to sum a real signal

23
Visualization of Order Extraction
  • Time Variant Zoom (Radio Receiver)
  • Functional relationship between phasors
  • in particular
  • Any order can be centred at DC, (Time Variant
    Zoom)
  • Low frequency order Aj(t) is straightened and can
    be extracted in the time domain by any suitable
    lowpass filter (time smoothing)

24
Structural Equation 2nd Generation
  • Phase assigned order should be smooth
  • one sufficient condition for smoothness is that
    the function locally can be presented by a low
    order polynomial
  • complex difference equation for sampled data
  • ?(n) represent noise / error term
  • difference operator annihilates all polynomials
    of one order less

25
Data Equation 2nd Generation
  • Signal Energy is distributed between orders
  • sum of orders differs from total signal only by
    an error term
  • decoupling of close and crossing orders possible
  • using several tacho signals
  • correspond to the repeated root problem in Modal
    Analysis
  • Iterative solution scheme possible
  • different orders may be estimated independently
    using structural equation
  • then the data equation is applied for iterative
    refinement

26
Filter Shapes
  • First order filter
  • knife edge peak and wide skirts
  • good for very fine bandwidth tracking and slowly
    varying orders
  • Second order filter
  • flatter top and better selectivity
  • better for rapidly modulated orders
  • Filter bandwidth can be specified in
  • order resolution
  • frequency resolution

27
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second Generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

28
Tachometer Analysis RPM Estimation
  • RPM estimation is a post processing facility
    found in the Function Organizer
  • Level crossings determined to define a table of
    RPM values as a function of time
  • including slope, hysteresis and gearing

29
Tachometer Analysis RPM CurveFit
  • Cubic least squares spline fit to smooth data
  • continuity and first derivative continuity
    between segments
  • Singular events such as gearshifts allowed
  • relaxing first derivative continuity condition at
    shift points
  • Shave algorithm rejects outlier data
  • Data refitted using cubic least squares spline
    fit to obtain instantaneous RPM (as a function of
    time)

30
Corrupted Tachometer Waveform
  • A Tachometer signal
  • from 950 RPM to 350 RPM
  • run-down in 26 sec.
  • was corrupted 4 times
  • simulating severe tacho drop-outs

31
RPM Estimate and First Spline Fit
  • Deviations are ranked
  • Rejecting 20th percentile of RPM estimate
  • user definable parameter
  • Data refitted

32
Shaved RPM Estimate
  • Censored data with corrected spline fit
  • Conclusion
  • wild points have been removed
  • spline fit sufficiently stiff to straddle the
    empty section

Curves offset for ease of comparison
33
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

34
Beating Phenomena Crossing Orders
  • sum of two sinewaves is a slowly modulated high
    frequency wave
  • Example Two constant amplitude sinewaves
    crossing in frequency
  • rapid modulation until the sinewaves are almost
    identical in frequency

35
Synthetic Multiaxle Data
  • Three axles simulated
  • one with constant speed
  • two other slewing independently
  • all orders with constant amplitude
  • Focus on the axle that monotonically loses speed

36
1st Generation Kalman filter
  • First order Kalman filter used
  • No decoupling
  • using one tacho signal
  • Extracted order severely contaminated

37
2nd Generation Kalman filter
  • First order Vold-Kalman filter used
  • Decoupling applied
  • using three tacho signals in simultaneous
    estimation
  • Dramatic improvement in quality of order function
    extraction
  • small ripples due to extreme closeness and
    crossing of many orders in the neighbourhood of
    target order

38
Gear Shift Example
  • Gear shifting events
  • Second, third, fourth and fifth gear engaged
  • RPM profile as a function of time
  • Vold-Kalman Filtering can handle pin joint events
    better than traditional techniques

5th Gear
39
Vold-Kalman Filtering
  • Contents
  • PULSE LabShop Tool Pack Type 7703
  • Order Analysis
  • Applications and Features of Vold-Kalman Filters
  • Overview of Order Analysis techniques
  • Vold-Kalman Order Tracking Filters
  • First generation implementation
  • Second generation implementation
  • RPM Estimation
  • Close and Crossing Orders
  • Gearshifts events
  • PULSE Property Page
  • Summary / Conclusion

40
PULSE Setup
  • Use Time Capture Analyzer Type 7705 to select
    data
  • from input / frontend
  • from 7701 Data Recorder
  • (NB FFT-records can be used)
  • Vold-Kalman Order Tracking Filtering Type 7703
    chosen as a postprocessing facility
  • Step by step procedure
  • use conventional techniques first
  • inspect contour / waterfall plots
  • decide and allow for pin joints
  • compare raw and processed RPM profiles
  • select filter characteristics
  • apply Vold-Kalman filtering

41
Vold-Kalman Offers 1
  • Compared to all previous methods
  • Beat free decoupling of close and crossing orders
  • Advanced tachometer processing, wild point
    rejection
  • Compared to FFT based order cuts
  • No leakage
  • Finer resolution
  • Order waveform
  • No slew rate limitation
  • Compared to digital order tracking
  • Finer resolution
  • Order waveform
  • No slew rate limitation

42
Vold-Kalman Offers 2
  • Compared to digital tracking filters
  • Much shorter transients
  • No phase bias
  • Order waveform as well as Phase Assigned Orders
  • No slew rate limitation
  • Compared to previous Kalman tracking filters
  • Explicit bandwidth specification
  • Multipole filters for
  • flatter passband
  • better selectivity
  • Faster calculations

43
Conclusion
Second Generation Vold-Kalman Order Tracking
Filtering
  • Order Tracking Analysis with
  • No slew-rate limitation
  • Beat-free decoupling of close and crossing orders
  • think SDOF - MDOF curvefitters
  • think single reference - polyreference
    curvefitters
  • Advanced Tacho Calculation
  • and improved performance such as
  • Higher order filters
  • flatter passband and higher selectivity
  • Explicit Bandwidth Specification
  • Faster Calculation

State of the art Order Tracking Analysis
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