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Unit 20
Vibrationdata
Digital Filtering, Part 2
1
Introduction



Vibrationdata
Successive bandpass filtering can be used to calculate a power
spectral density (PSD) from a time history
This method is very educational but inefficient for general use
Begin with a review exercise by synthesizing a time history to
satisfy a PSD
2
Vibrationdata
Navmat P-9492 PSD
PSDPSDOverall
Level
GRMS
OVERALL
LEVEL== 6.06
6.06 GRMS
ACCEL (G /Hz)
0.1
2
Accel
(G^2/Hz)
0.01
0.001
20
100
1000
Frequency
(Hz)
Accel
(G^2/Hz)
20
0.01
80
0.04
350
0.04
2000
0.007
2000
FREQUENCY (Hz)
Frequency (Hz)
3
Synthesis Steps
Vibrationdata
♦ vibrationdata > PSD Analysis > Acceleration PSD Time History Synthesis
♦ Input file: navmat_spec.psd
♦ Duration = 60 sec
♦ sps=16384, df=2.13 Hz, sdof=256
♦ Save Acceleration time history as: input_th.txt
♦ Save Acceleration PSD as: input_psd.txt
4
Time History
Vibrationdata
5
Histogram
Vibrationdata
6
PSD Verification
Vibrationdata
7
Vibrationdata
Octave Bands
Perform bandpass filtering on for each band using the
lower & upper frequencies from table.
Full Octave Band
Frequencies (Hz)
Lower
Center
Upper
14
20
28
28
40
57
57
80
113
113
160
226
226
320
453
453
640
905
905
1280
1810
1810
2560
3620
vibrationdata > Time History > Filters, Various >
Butterworth Filter
Input file is: input_th.txt
Y-axis Label: Accel (G)
Filter Type: Bandpass
Refiltering: No
Record each Filtered Data RMS value
8
Octave Band 1
Vibrationdata
Input
6.06 RMS
Filtered Data
0.3619 RMS
9
Octave Band 2
Vibrationdata
Input
6.06 RMS
Filtered Data
0.7885 RMS
10
Octave Band 3
Vibrationdata
Input
6.06 RMS
Filtered Data
1.457 RMS
11
Octave Band 4
Vibrationdata
Input
6.06 RMS
Filtered Data
2.134 RMS
12
Octave Band 5
Vibrationdata
Input
6.06 RMS
Filtered Data
2.906 RMS
13
Octave Band 6
Vibrationdata
Input
6.06 RMS
Filtered Data
3.109 RMS
14
Octave Band 7
Vibrationdata
Input
6.06 RMS
Filtered Data
3.076 RMS
15
Octave Band 8
Vibrationdata
Input
6.06 RMS
Filtered Data
1.305 RMS
16
Vibrationdata
Results
Lower
(Hz)
Center
(Hz)
Upper
(Hz)
(GRMS)
GRMS^2
Bandwidth
(Hz)
Center
(Hz)
GRMS^2/Hz
14
20
28
0.362
0.131
14
20
9.36E-03
28
40
57
0.789
0.622
29
40
2.14E-02
57
80
113
1.457
2.123
56
80
3.79E-02
113
160
226
2.134
4.554
113
160
4.03E-02
226
320
453
2.906
8.445
227
320
3.72E-02
453
640
905
3.109
9.666
452
640
2.14E-02
905
1280
1810
3.076
9.462
905
1280
1.05E-02
1810
2560
3620
1.305
1.703
1810
2560
9.41E-04
The bandwidth is the upper frequency minus the lower frequency.
17
Filtered PSD Coordinates
20
40
80
160
320
640
1280
2560
9.36E-03
2.14E-02
3.79E-02
4.03E-02
3.72E-02
2.14E-02
1.05E-02
9.41E-04
Vibrationdata
Copy and paste last two columns
from previous table into ASCII text
files using Wordpad or some other
editor
Suggested name: bpf_psd.txt
18
bpf_psd.txt
Plotting
navmat_spec.txt
vibrationdata > Plot Utilities > Multiple Curves
Vibrationdata
19
PSD Comparison
Vibrationdata
Good Agreement!
The dropout for the last
point is not a concern
because the bandwidth
extended from 1810 to
3620 Hz.
But the spec stopped at
2000 Hz.
20
Vibrationdata
Decimation
•
Data needs to be downsampled in some cases
•
Example: retain every other point
•
Possible reasons:
Original sample rate was too high
Only low frequency energy is of interest
•
Lowpass filtering should be performed prior to downsamping to prevent aliasing
•
Filter frequency should be < 0.8 * Nyquist frequency
•
Practice exercise:
Miscellaneous> Signal Editing > Decimate, Downsample
input file: input_th.txt
downsample factor = 10
lowpass filter = 100 Hz
21
Vibrationdata
Supplementary Topic
•
Atlas V Launch
•
Coupled Loads Analysis (CLA) predicts
payload & launch vehicle responses due
to major dynamic and quasi-static
loading events
•
CLA is performed prior to launch
•
CLA can also be performed as postflight data reconstruction using flight
accelerometer data
22
Launch Vehicle Filtering Applications
Vibrationdata

Flight accelerometer data is lowpass filtered for coupled-loads analyses

The cut-off frequency varies by launch vehicle, payload, key events, etc.

The primary sources of these low frequency loads are
•
•
Pre-launch events: ground winds, seismic loads
Liftoff: engine/motor thrust build-up, ignition overpressure,
pad release
•
Airloads: buffet, gust, static-elastic
•
Liquid engine ignitions and shutdowns
23
Typical Guideline

Vibrationdata
European Cooperation for Spacecraft Standardization (ECSS), Spacecraft
Mechanical Loads Analysis Handbook:
•
•
The low-frequency dynamic response, typically from 0 Hz
to 100 Hz, of the launch vehicle/payload system to
transient flight events
For some small launch vehicles the range of lowfrequency dynamic response can be up to 150 Hz
24
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