Unit 20

1. Unit 20 Digital Filtering, Part 2

2. Introduction • Successive bandpassfiltering 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 (G^2/Hz) Frequency (Hz)

4. Synthesis Steps • vibrationdata > Power Spectral Density > Time History Synthesis from White Noise • Input file: navmat_spec.psd • Duration = 60 sec • Row 8, df = 2.13 Hz, dof = 256 • Save Acceleration time history as: input_th • Save Acceleration PSD as: input_psd

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 > Time History > Filters, Various > Butterworth Filter Input file is: input_th Y-axis Label: Accel (G) Filter Type: Bandpass Refiltering: No Record each Filtered Data RMS value Full Octave Band Frequencies (Hz)

9. Octave Band 1 Input 6.058 RMS Filtered Data 0.3557 RMS

10. Octave Band 2 Input 6.058 RMS Filtered Data 0.7981 RMS

11. Octave Band 3 Input 6.058 RMS Filtered Data 1.468 RMS

12. Octave Band 4 Input 6.058 RMS Filtered Data 2.161 RMS

13. Octave Band 5 Input 6.058 RMS Filtered Data 2.931 RMS

14. Octave Band 6 Input 6.058 RMS Filtered Data 3.149 RMS

15. Octave Band 7 Input 6.058 RMS Filtered Data 3.003 RMS

16. Octave Band 8 Input 6.058 RMS Filtered Data 1.265 RMS

17. Results The bandwidth is the upper frequency minus the lower frequency.

18. Filtered PSD Coordinates bpf_psd=[20 0.00904 40 0.02196 80 0.03848 160 0.04133 320 0.03784 640 0.02194 1280 0.00996 2560 0.00088 ] Copy and paste last two columns from previous table into Matlab command window.

19. Import Spec Select input file: navmat_spec.psd

20. Introduction vibrationdata> Plot Utilities > Multiple Curves

21. 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.

22. 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: • Time History > Signal Editing > Decimate, Downsample • input file: input_th • downsample factor = 10 • lowpass filter = 100 Hz

23. 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

24. 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

25. 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