Vibrationdata 1 Unit 20 Digital Filtering, Part 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

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

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

Vibrationdata 5 Time History

Vibrationdata 6 Histogram

Vibrationdata 7 PSD Verification

Vibrationdata 8 Octave Bands LowerCenterUpper 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

Vibrationdata 9 Octave Band 1 Input 6.06 RMS Filtered Data RMS

Vibrationdata 10 Octave Band 2 Input 6.06 RMS Filtered Data RMS

Vibrationdata 11 Octave Band 3 Input 6.06 RMS Filtered Data RMS

Vibrationdata 12 Octave Band 4 Input 6.06 RMS Filtered Data RMS

Vibrationdata 13 Octave Band 5 Input 6.06 RMS Filtered Data RMS

Vibrationdata 14 Octave Band 6 Input 6.06 RMS Filtered Data RMS

Vibrationdata 15 Octave Band 7 Input 6.06 RMS Filtered Data RMS

Vibrationdata 16 Octave Band 8 Input 6.06 RMS Filtered Data RMS

Vibrationdata 17 Results Lower (Hz) Center (Hz) Upper (Hz) (GRMS)GRMS^2 Bandwidth (Hz) Center (Hz) GRMS^2/Hz E E E E E E E E-04 The bandwidth is the upper frequency minus the lower frequency.

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 E E E E E E E E-04

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

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.

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

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

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

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