1. Vibrationdata 1 Unit 20 Digital Filtering, Part 2

2. Vibrationdata 2 Introduction n Successive bandpass filtering can be used to calculate a power spectral density (PSD) from a time history n This method is very educational but inefficient for general use n Begin with a review exercise by synthesizing a time history to satisfy a PSD

3. Vibrationdata 3 Navmat P-9492 PSD Frequency (Hz) Accel (G^2/Hz) 200.01 800.04 3500.04 20000.007 PSD Overall Level = 6.06 GRMS Frequency (Hz) Accel (G^2/Hz)

4. Vibrationdata 4 Synthesis Steps ♦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

5. Vibrationdata 5 Time History

6. Vibrationdata 6 Histogram

7. Vibrationdata 7 PSD Verification

8. Vibrationdata 8 Octave Bands LowerCenterUpper 142028 4057 80113 160226 320453 640905 12801810 25603620 Full Octave Band Frequencies (Hz) Perform bandpass filtering on for each band using the lower & upper frequencies from table. 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

9. Vibrationdata 9 Octave Band 1 Input 6.06 RMS Filtered Data 0.3619 RMS

10. Vibrationdata 10 Octave Band 2 Input 6.06 RMS Filtered Data 0.7885 RMS

11. Vibrationdata 11 Octave Band 3 Input 6.06 RMS Filtered Data 1.457 RMS

12. Vibrationdata 12 Octave Band 4 Input 6.06 RMS Filtered Data 2.134 RMS

13. Vibrationdata 13 Octave Band 5 Input 6.06 RMS Filtered Data 2.906 RMS

14. Vibrationdata 14 Octave Band 6 Input 6.06 RMS Filtered Data 3.109 RMS

15. Vibrationdata 15 Octave Band 7 Input 6.06 RMS Filtered Data 3.076 RMS

16. Vibrationdata 16 Octave Band 8 Input 6.06 RMS Filtered Data 1.305 RMS

17. Vibrationdata 17 Results Lower (Hz) Center (Hz) Upper (Hz) (GRMS)GRMS^2 Bandwidth (Hz) Center (Hz) GRMS^2/Hz 1420280.3620.13114209.36E-03 2840570.7890.62229402.14E-02 57801131.4572.12356803.79E-02 1131602262.1344.5541131604.03E-02 2263204532.9068.4452273203.72E-02 4536409053.1099.6664526402.14E-02 905128018103.0769.46290512801.05E-02 1810256036201.3051.703181025609.41E-04 The bandwidth is the upper frequency minus the lower frequency.

18. Vibrationdata 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. Vibrationdata 19 Plotting vibrationdata > Plot Utilities > Multiple Curves bpf_psd.txt navmat_spec.txt

20. Vibrationdata 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. Vibrationdata 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 < 0.8 * Nyquist frequency Practice exercise: Miscellaneous> Signal Editing > Decimate, Downsample input file: input_th.txt downsample factor = 10 lowpass filter = 100 Hz

22. Vibrationdata 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 reconstruction using flight accelerometer data

23. Vibrationdata 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. Vibrationdata 24 Typical Guideline n 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