# Vibration Testing & Analysis Standard References

The European Cooperation for Space Standardization

http://www.ecss.nl/

ECSS-E-HB-32-26A_19February2013

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SMC-S-016, Air Force Space Command, Space and Missile Systems Center, Standard Test Requirements for Launch, Upper-Stage and Space Vehicles, 2014  Download Link

AEROSPACE REPORT No. TOR-2010(8591)-20
Flight Unit Qualification Guidelines

AEROSPACE REPORT NO. TR-2004(8583)-1 REV. A
Test Requirements for Launch, Upper-Stage, and Space Vehicles (aka SMC-TR-06-11)

AEROSPACE REPORT NO.TOR-2008(8583)-8215
Space and Missile Systems Center Compliance Specifications and Standards

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Acronym: maximum predicted environment (MPE)

Question:

SMC-S-016 specifies adding 4.9 dB to the log-mean for vibration and shock to get to the 95/50 probability/confidence level to define an MPE.  This is quite conservative relative to the Range Safety RCC319 that simply says to envelope at least 3 flights of limit level data to define the MPE. Just wondering what your thoughts are on this.

Answer from a Colleague at the Aerospace Corporation:

SMC-S-016 defines the MPE for vibration, shock, and acoustic environments at a P95/50 statistical levels.  The P95/50 MPE is defined as 4.9 dB above the log-mean of the available flight data set to account for flight-to-flight variability.  This approach is based on measurements of 24 static firings and over 40 flight tests which defines a standard deviation sigma of 3 dB.   From normal tolerance limit table, the statistical factor Z at P95 with large number of samples is 1.65.  Therefore, the 4.9 dB is calculated from 3 dB x 1.65.  As a result the P95/50 level is defined as 4.9 dB above the log-mean level.

The log-mean is just the average of the logarithmic of the spectral values at each frequency of all the available flight data sets.  The reason for calculating the log-mean is because each spectral value of each data set is considered as log-normally distributed.  That is the normal distribution of the logarithmic value of the spectral values at each frequency.

The flight-to-flight variability is estimated using a statistical approach.  The SMC-S-016MPE is defined as P95/50 statistical level.  The RCC-319 MPE is defined as an envelope of three or more flight data sets.  We do not know statistical level the RCC-319 MPE is defined at.  In order to judge the conservatism between the SMC-S-016 and the RCC-319 MPEs, the RCC-319 MPE needs to be assessed in the same statistical basis as in the SMC-S-016 MPE.

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SMC-S-016 Excerpt

3.27  Maximum Predicted Environment (MPE) for Random Vibration

The MPE is statistically the P95/50 random vibration spectrum, subject to a constraint discussed in B.1.1. The random vibration MPE is expressed as a spectral density in g2/Hz (commonly, termed the auto spectral density, ASD, or power spectral density, PSD) calculated at intervals no greater than 1/6 octave over the frequency range of at least 20 to 2000 Hz. For the liftoff and ascent acoustic environments during a flight, the spectra for each of a series of 1-second times, overlapped by 50%, are enveloped to produce the so-called maxi-max flight spectrum. Below 40 Hz, the resolution bandwidth need not be less than 5 Hz. The resulting P95/50 spectrum is 4.9 dB above the log-mean maximax spectrum from a series of flights or tests (B.1.1).

(End excerpt)

The individual PSD function is available in the Vibration Matlab GUI package

>> vibrationdata > PSD, Spectral Densities, Transmissibility, etc. > PSD MPE per SMC-S-016, 3.27

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Tom Irvine