Digital Filtering, Part 2

1
Unit 20
Digital Filtering, Part 2
2
Introduction

• 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

3
Navmat P-9492 PSD
PSD Overall Level 6.06 GRMS
Accel (G2/Hz)
Frequency (Hz) Accel (G2/Hz)
20 0.01
80 0.04
350 0.04
2000 0.007
Frequency (Hz)
4
Synthesis Steps

• vibrationdata gt PSD Analysis gt Acceleration PSD
  Time History Synthesis
• Input file navmat_spec.psd
• Duration 60 sec
• sps16384, df2.13 Hz, sdof256
• Save Acceleration time history as input_th.txt
  
• Save Acceleration PSD as input_psd.txt

5
Time History
6
Histogram
7
PSD Verification
8
Octave Bands
Perform bandpass filtering on for each band using
the lower upper frequencies from table.
vibrationdata gt Time History gt Filters, Various
gt Butterworth Filter Input file is
input_th.txt Y-axis Label Accel (G) Filter
Type Bandpass Refiltering No Record each
Filtered Data RMS value
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
9
Octave Band 1
Input 6.06 RMS Filtered Data 0.3619 RMS
10
Octave Band 2
Input 6.06 RMS Filtered Data 0.7885 RMS
11
Octave Band 3
Input 6.06 RMS Filtered Data 1.457 RMS
12
Octave Band 4
Input 6.06 RMS Filtered Data 2.134 RMS
13
Octave Band 5
Input 6.06 RMS Filtered Data 2.906 RMS
14
Octave Band 6
Input 6.06 RMS Filtered Data 3.109 RMS
15
Octave Band 7
Input 6.06 RMS Filtered Data 3.076 RMS
16
Octave Band 8
Input 6.06 RMS Filtered Data 1.305 RMS
17
Results
Lower (Hz) Center (Hz) Upper (Hz) (GRMS) GRMS2 Bandwidth(Hz) Center(Hz) GRMS2/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.
18
Filtered PSD Coordinates

Copy and paste last two columns from previous
table into ASCII text files using Wordpad or some
other editor Suggested name bpf_psd.txt
20 9.36E-03 40 2.14E-02 80
3.79E-02 160 4.03E-02 320 3.72E-02
640 2.14E-02 1280 1.05E-02 2560
9.41E-04
19
Plotting
bpf_psd.txt
navmat_spec.txt
vibrationdata gt Plot Utilities gt Multiple Curves
20
PSD Comparison
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.
21
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 lt 0.8 Nyquist
  frequency
• Practice exercise
• Miscellaneousgt Signal Editing gt Decimate,
  Downsample
• input file input_th.txt
• downsample factor 10

22
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 post-flight data reco
  nstruction using flight accelerometer data

23
Launch Vehicle Filtering Applications

• 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

24
Typical Guideline

• 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
  low-frequency dynamic response can be up to 150
  Hz