MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests
Last Updated 29 Oct 2026
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3 tables appear under this heading.
1. PDF page 991
AECTP
Allied Environmental Conditions Test Publication
ASD
auto spectral density (also referred to as the power spectral density (PSD)
CG
center of gravity
CSD
cross spectral density
dB
decibel
DFT
discrete Fourier transform
DOF
degree of freedom
DTC
US Army Developmental Test Command
FRF
frequency response function
g/V
gravitational units/volts of drive
Hz
hertz
I/O
input/output
IEEE
Institute of Electrical and Electronics Engineers
IES
Institute of Environmental Sciences
IEST
Institute of Environmental Sciences and Technology
LCEP
Life Cycle Environment Profile
LOA
line of action
LVTS
Laboratory Vibration Test Schedule
MA
multi-axis
MDOF
multiple degree-of-freedom
MEMA
multiple-exciter multiple-axis
MESA
multiple-exciter single-axis
MET
multiple exciter test
MIL-STD
Military Standard
MIMO
multiple-input multiple-output
MISO
multiple-input single-output
2. PDF page 992
NATO
North Atlantic Treaty Organization
NBROR
narrowband random on random
pinv
Moore Penrose pseudo inverse
PSD
power spectral density
rms
root mean square
RTC
US Army Redstone Test Center
SA
single-axis
SDM
spectral density matrix
SDOF
single degree-of-freedom
SESA
single-exciter/single-axis
SIMO
single-input multiple-output
SISO
single-input single-output
SOR
sine-on-random
TWR
Time Waveform Replication
UUT
unit under test
VSD
Vibration Schedule Development
3. PDF page 993
Term
Definition
{ }
A vector where each element is a discrete time history or function of frequency, the discrete Fourier transform (DFT) of a time history. In general lower case letters will be used for functions of time and upper case letters will be used for functions of frequency. Sometimes lower case letters are used to designate an element in a matrix.
[ ]
Will denote a matrix. Usually a third dimension will denote time samples or samples as a function of frequency.
[ ]T
The transpose of a matrix.
[ ]′
The transpose of a real matrix or often used as a compact notation to represent the complex conjugate transpose of a matrix.
[ ]*′
The complex conjugate transpose of a matrix (also see [ ]′ above).
[ ]†
The Moore Penrose pseudo inverse of a matrix.
^
Over a variable will denote an estimated value.
{a}
The vector of return acceleration signals.
A
The spectral density matrix of the return signals, typically in units of G2/Hz .
{c}
A vector of the control signals from a MIMO system. Each element in the vector is a function of time. It can be thought of as a 2 dimensional matrix. First dimension is the input number. The second dimension is the time index.
{C}
The DFT of {c}.
C
The spectral density matrix of the control signals. The diagonal elements are the real auto-spectral densities of the control signals. The off diagonal elements are complex functions of frequency giving the cross spectral density between pairs of control signals.
{d}
A vector of drive signals into a MIMO system. Each element in the vector is a function of time. It can be thought of as a 2 dimensional matrix. First dimension is the input number. The second dimension is the time index.
[D]
The drive signals in the frequency domain. {d} is formed from [D] using a method called time domain randomization. Initially D = ZRZ' .