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1、Lesson content:IntroductionWhat is aliasing?Preventing aliasingAbaqus/Viewer postprocessing filters Filter optionsFilter distortionsReferencesLesson 11: Output Filtering90 minutesIntroductionAbaqus/Explicit and Abaqus/Viewer both contain tools for filtering output. You can use both to attenuate high

2、-frequency solution noise.Solution noise can obscure the lower-frequency structural response. Filtering can be applied to reveal the underlying structural response.Abaqus/Viewer filters history output only.Abaqus/Explicit run-time filters also allow you to increase output time intervals without alia

3、sing the results.With run-time filters you can request field and history data less often, which in turn can reduce the size of the output database (.odb) file. Reaction forceComparison of raw history data with run-time filtered history dataWhat is aliasing? (1/8)Aliasing is a form of data corruption

4、.It occurs when a signal is sampled at a series of discrete points in time, but not enough data points are saved in order to correctly describe the signal. The Nyquist Sampling Theorem (a.k.a. Shannon Sampling Theorem):A signal must be sampled at a rate that is greater than twice the signals highest

5、 frequency in order to avoid alias distortions.Therefore, the maximum frequency content that can be described by a given sampling rate is half that rate (the Nyquist frequency). Sampling (storing) a signal with large-amplitude oscillations at frequencies greater than the Nyquist frequency of the sam

6、ple rate may produce significantly distorted results due to aliasing. What is aliasing? (2/8)Example: Aliasing of a 1 kHz sine wave Original 1kHz sine wave Sample rate must be greater than 2 kHz to avoid aliasing (Sampling Theorem).Sample rate 1.1 kHz; less than the required 2 kHz rate. This curve i

7、s said to have alias distortions.It is an extremely misleading representation of the original.What is aliasing? (3/8)Example: Aliasing of a 1 kHz sine wave (contd)Sample rate 3 kHz; this is greater than the required 2 kHz rate. The frequency content of the original signal is captured without aliasin

8、g. However, peak values are not accurately captured.To guarantee 95% accuracy of the recorded local peak values, the sampling rate must exceed the signal frequency by a factor of ten or more. What is aliasing? (4/8)Susceptibility of Abaqus results to aliasingRecall the Sampling Theorem: Signals with

9、 large-amplitude oscillations at frequencies greater than half the sampling rate may be significantly distorted due to aliasing.Therefore:Analyses with a smooth response are not susceptible to aliasing. E.g., static analyses Although, quasi-static analyses with Abaqus/Explicit can be susceptible to

10、aliasing, depending on a variety of factors.Analyses with high-frequency, large-amplitude oscillations are susceptible to aliasing.E.g., explicit dynamic analysesAny model characteristic that reduces the high-frequency response of the solution will decrease the analysiss susceptibility to aliasing.

11、What is aliasing? (5/8)Susceptibility to aliasing also depends on the output variable.Any integration procedure will reduce high-frequency content and, therefore, reduce susceptibility to aliasing. For example:High-frequency content progressively decreases as time integration transforms acceleration

12、 to velocity to displacement. History output integrated over a surface will have less high-frequency content than if the same quantity were requested at a single point. Displacements VelocityAccelerations Force at a single pointForce integrated over a surfaceStrain StressReaction forcesIncreasing su

13、sceptibility to aliasing What is aliasing? (6/8)To test whether the acceleration history output is plausible, integrate it twice and compare the result with the displacement output.Example: Acceleration history output from a drop test analysis displacement calculated from the aliased acceleration da

14、tadisplacement recorded during the analysisAcceleration recorded every incrementAcceleration recorded every 0.03 ms without filteringThis data has been aliased!Integrate the aliased acceleration twice and the results do not match the recorded displacement:What is aliasing? (7/8)Aliasing field output

15、 It is possible for aliasing to distort field output, which is used to create model plots and animations.For example, aliasing can cause a rotating part to appear to rotate backwardsBlade throw analysis:Step-1: Engine rotation rate 0.05 rotations/s Must be sampled at a rate greater than 0.1 s-1 (com

16、puted as 2 * 0.05 s-1) to avoid aliasingStep-2: Blade releasedStep-1 frame rate 0.06 frames/sAliasing occurs Step-1 frame rate 0.5 frames/sAliasing avoidedWhat is aliasing? (8/8)Result oscillations and local peak values may not be included in animations and solution noise may distort the results (al

17、iasing)Field output filtering can be used to avoid these problemsElement used for history plotThe 1-direction is parallel to the short edges of the rectangular circuit boardPreventing aliasing (1/14)The safest way to ensure that aliasing will not occur is to request output at every increment.The out

18、put sampling rate is then determined by the stable time increment, which is based on the highest possible frequency response of the model.However, this is usually much more information than you need.Why record high-frequency solution noise when you are only interested in the lower-frequency structur

19、al response?A run-time, anti-aliasing filter should be used to avoid aliasing when results are not requested at every increment,particularly for situations when susceptibility to aliasing is highsuch as, when recording acceleration and force history output.Additional history output filtering can alw

20、ays be performed with Abaqus/Viewer. However, no amount of postprocessing can compensate for aliasing or over-filtering in the result written to the output database (.odb) file!Preventing aliasing (2/14)You can create user-defined output filters based on criteria that you specify.Available filter ty

21、pes: Butterworth,Chebyshev Type I, Chebyshev Type IIHowever, it is often more convenient to use the built-in anti-aliasing filter.The built-in anti-aliasing filter generally gives you the best un-aliased representation of the results when recorded at the output rate you specify on the output request

22、. If the output is requested at a relatively high frequency, only high frequency noise content of the signal will be filtered.Additional filtering operations can be performed after the analysis during postprocessing.Preventing aliasing (3/14)When you use the built-in anti-aliasing filter Abaqus inte

23、rnally defines a low-pass, second-order, Butterworth filter.The filter cutoff frequency is one-sixth the output sample rate.In most cases this is low enough to ensure that all frequency content less than one-half of the sample rate is removed before the signal is sampled, as required to prevent alia

24、sing.Example:Record output every 0.1667 ms with the built-in anti-aliasing filterOutput rate 6 kHz (1 / 0.1667e-3)Frequency content above 3 kHz (half of 6 kHz) can cause aliasing.Built-in anti-aliasing filter cutoff frequency 1 kHz (one-sixth of 6 kHz )Creating a history output request with a user-d

25、efined run-time filter:*FILTER, NAME=BW, TYPE=BUTTERWORTH 5000.0.*OUTPUT, HISTORY, FILTER=BW, TIME INTERVAL=5E-5 *NODE OUTPUT, PONENT_REFS U,V,APreventing aliasing (4/14)Define BUTTERWORTH filter. Type I Chebyshev (CHEBYS1) and Type II Chebyshev (CHEBYS2) filters are also available.Preventing aliasi

26、ng (5/14)Creating a history output request with the built-in anti-aliasing filter *OUTPUT, HISTORY, FILTER=ANTIALIASING, TIME INTERVAL=3E-5*NODE OUTPUT, PONENT_REFS U,V,AYou do not need to predefine a filter when using the built-in anti-aliasing filter. Abaqus internally defines a second-order, Butt

27、erworth filter.The filter cutoff frequency is one-third the output sample rate.Here, the output time interval is 3e-5 s, so the cut-off frequency used by the built-in anti-aliasing filter is 1 / (6*3e-5) = 5,556 Hz.Preventing aliasing (6/14)Example: Acceleration history output from a drop test analy

28、sis Acceleration recorded every incrementAcceleration recorded every 0.03 ms without filteringThis data has been aliased!Acceleration recorded every 0.03 ms with an anti-aliasing filter.Integrate twice and the results match the displacement recorded during the analysis. The anti-aliasing filter remo

29、ved all frequency content too high to be captured by the 33 kHz sample rate before the results were recorded.Preventing aliasing (7/14)When choosing an output rate to use with the built-in anti-aliasing filter you must ensure that only the solution noise is eliminated.A natural frequency extraction

30、analysis using Abaqus/Standard may help you estimate the highest structurally-significant frequency.The highest structurally-significant frequency of a model is typically 2 to 4 orders of magnitude less than the highest frequency of the model (which governs the stable time increment). Example: A dro

31、p test with stable time increment of 8.8e-7 s. The maximum output sample rate is about 1,000 kHz (1 / stable time increment). According to the Sampling Theorem, the maximum frequency that can be described by a 1,000 kHz sample rate is 500 kHz (half the sample rate). The maximum structural frequency

32、of the same model is likely to be in the 5 to 0.05 kHz range (approximately 2 to 4 orders of magnitude less than 500 kHz). Preventing aliasing (8/14)For the cutoff frequency of the built-in anti-aliasing filter to be 5 kHz, the output request must have a sample rate of 30 kHz (6*5 kHz).Output with t

33、ime increments of 0.03 ms (1 / 30 kHz). There may still be solution noise in the results recorded at this rate; additional filtering can be applied as a postprocessing operation. Note: the Butterworth low-pass filter actually attenuates frequency content somewhat below the cutoff frequency. To compe

34、nsate for this, consider increasing the output rate by a factor of ten Preventing aliasing (9/14)Example: Over-filtered acceleration history output from a drop test analysis Acceleration recorded every 0.3 ms with an anti-aliasing filter. This curve is over filtered. Many of the oscillations in the

35、acceleration output are filtered outSignificant time delay in the filtered acceleration dataAcceleration recorded every incrementAcceleration recorded every 0.03 ms with an anti-aliasing filter.Preventing aliasing (10/14)For history output, it is best to use a minimal amount of filtering in Abaqus/E

36、xplicit. Output a rich, un-aliased representation for the solution recorded at a reasonable number of time points. If additional filtering is necessary, it can be done as a postprocessing operation. For field output, it may not be practical or desirable to capture the highest structurally-significan

37、t frequencyOften it is only peak values and their locations that are of interest when viewing field output.Operators can be used to record maximum, minimum, and absolute maximum values over time, regardless of the output rate.These operators can be applied to:both field output and history output and

38、both digitally filtered and unfiltered dataPreventing aliasing (11/14)Creating a field output request with a user-defined run-time filter*FILTER, NAME=MAX, TYPE=BUTTERWORTH, OPERATOR=MAX 2000.0.*OUTPUT, FIELD, NUMBER INTERVAL=16, FILTER=MAX*ELEMENT OUTPUT LE,Define BUTTERWORTH filter with the maximu

39、m value operator If you are only interested in the final peak values, specify a value of 1 for the number of output intervalsPreventing aliasing (12/14)Example: Maximum log strain (LE11) in a dropped circuit boardElement used for history plotThe 1-direction is parallel to the short edges of the rect

40、angular circuit boardThe maximum operator records the maximum result even if an output frame is not requested at the time the peak occurredThe maximum values for the tensor components are likely to have occurred at different points in time. Hence, you cannot plot tensor invariants based on the recor

41、ded maximum valuesPreventing aliasing (13/14)Additional comments regarding filtered field outputWhen using filtering to find the maximum, minimum, absolute maximum, or limiting value of a variable, the time at which the value is reached is also written to the output database.It is written as a separ

42、ate field output variable named of the form TIME_variableName_filterName.Maximum LE11 occurs in this element at time 0.0106Preventing aliasing (14/14)Additional comments (contd)When using field filtering for vector or tensor output, each component is filtered separately. You may also filter and moni

43、tor an invariant quantity.Examples include displacement magnitude, Mises stress, etc.The maximum/minimum of the invariants are monitored (according to the Operator and/or the Limit parameters)*FILTER, NAME=.INVARIANT=FIRST/SECOND,OPERATOR =MAX/MIN/ABSMAXThe operator parameter is requiredAbaqus/Viewe

44、r postprocessing filters (1/7)The Abaqus/Viewer history output filtering tools complement those in Abaqus/Explicit.You can perform some filtering in Abaqus/Explicit to produce a rich, un-aliased representation for the solution recorded at a reasonable number of time points,and additional filtering w

45、hile postprocessing in Abaqus/Viewerto remove any remaining solution noise and isolate the low-frequency response. This section highlights some advantages to filtering as a postprocessing operation.Recall, however, that Abaqus/Viewer filters cannot compensate for aliasing or over-filtering in the re

46、sults written to the output database (.odb) file!Abaqus/Viewer postprocessing filters (2/7)With Abaqus/Viewer you can interactively filter XY data and plot the results. You can quickly iterate to find appropriate filter parameters. Abaqus/Viewer postprocessing filters (3/7)With Abaqus/Viewer you can

47、 interactively filter XY data and plot the results. You can quickly iterate to find appropriate filter parameters. Both the filtered and unfiltered data are always available for comparison. Add unfiltered data to plot before saving the filtered dataAbaqus/Viewer postprocessing filters (4/7)The filte

48、rs in Abaqus/Viewer are bi-directional by default. The filter is applied twice, once in the forward direction and once in the reverse direction. Consequently: bi-directional filters do not result in the time delay that is unavoidable when filtering is applied in a single pass.Note: the Abaqus/Explic

49、it filters are single-pass filters.Reference curve (Abaqus/Explicit filter, cutoff 4,800 Hz)Abaqus/Viewer filter, cutoff 500 Hz (applied to output at every increment)Abaqus/Explicit filter, cutoff 500 HzAbaqus/Viewer postprocessing filters (5/7)The filters in Abaqus/Viewer are bi-directional by defa

50、ult. The filter is applied twice, once in the forward direction and once in the reverse direction.Consequently,bi-directional filters do not result in the time delay that is unavoidable when filtering is applied in a single pass, and the amplitude attenuation (gain) of bi-directional filters is squa

51、red compared to that of a single-pass filter. * Single-pass filter time shift is not constant; there is some dependence on the frequency content of the filtered signal. However, in many cases, this example included, the single-pass filter time shift is relatively uniform and the filtered result can

52、be sifted back as shown.*Abaqus/Viewer postprocessing filters (6/7)Additional filter types are available in Abaqus/Viewer. Both Abaqus/Viewer and Abaqus/Explicit include Butterworth, Chebyshev Type I, and Chebyshev Type II filters. Abaqus/Viewer also includes SAE filters: A special case of Butterwor

53、th filtering is provided for postprocessing automobile crash test results. The SAE filters use the Signal Analysis Software obtained from the National Highway Traffic Safety Administration (NHTSA). Abaqus/Viewer also includes: a sine-Butterworth filter, a moving average smoothing operation, and a de

54、cimation function automatically applies an anti-aliasing filter before reducing the sample size. Abaqus/Viewer postprocessing filters (7/7)An Abaqus/Viewer plug-in is available to convert history data from the time domain to the frequency domainThe plug-in allowsyou toplotthe discrete Fourier transf

55、orm of a set of time history data. See “Abaqus/CAE plug-in to compute the discrete Fourier transform of time history data”Knowledge Base Article QA (DSx.Client Care: )Filter options (1/5)Typical low-pass filter responsesCompared to Butterworth filters, the Chebyshev filters of the same order typical

56、ly have sharper transitions at the expense of ripples in the pass and stop bands (Type I and II, respectively).Typical magnitude response curves for low-pass filtersShown for single-pass filters (Abaqus/Explicit). The magnitude gain is squared for bi-directional filters (Abaqus/Viewer default)Higher

57、 frequency oscillations removed Lower frequency oscillations minimally affected by filterButterworthType I ChebyshevType II ChebyshevIdeal filterfc Type I Chebyshev has a ripple in the pass bandType II Chebyshev has a ripple in the stop bandfrequencyMagnitude gaincutoff frequencyFilter options (2/5)

58、Higher-order filtersIncreasing the order of the filter will result in a narrower transition band (also commonly referred to as a sharper filter).However:filter-induced end distortions in Abaqus/Viewer may increase with larger filter orders (6th-order or less mended), andthe filter-induced time delay

59、 in Abaqus/Explicit may e significant will larger filter orders (4th-order or less mended).Filter options (3/5)Example: Single-pass (Abaqus/Explicit) 4th-order Butterworth filter versus 2nd-order filter Unfiltered2nd-order Butterworth filter 4th-order Butterworth filterSmoother than 2nd-order, but w

60、ith larger time delayFilter options (4/5)For Chebyshev filters your choice of ripple factor will influence the width of the transition band:the smaller the ripple, the wider the transition bandFor a Type I Chebyshev filter with a very flat pass band (ripple only 0.5%) use:a ripple factor of 0.1 for