Table 514.8F: -I: Lifetime Scenario Breakout – Example Only

MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests

Last Updated 29 Oct 2026

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LEVEL 1 BREAKOUT					LEVEL 2 BREAKOUT
TOTAL MILES:	1000
Terrain Type	Percent	Miles	Speed		Surface¹	Percent	Miles	Speed
Terrain Type	Percent	Miles	Max	Avg	Surface¹	Percent	Miles	Max	Avg
PRIMARY ROAD	70%	700	55	35	Paved	100%	700	55	35
						100%	700

SECONDARY ROAD	20%	200	40	22	Secondary Road	60%	120	40	25
					Gravel Road	23%	46	45	22
					Belgian Block	10%	20	25	15
					Embedded Rock	1%	2	10	7
					Radial Washboard	3%	6	15	9
					2" Washboard	3%	6	10	7
						100%	200

* Off Road	10%	100	25	14	Cross Country	85%	85	25	16.3
* A combination of trails and cross country					Embedded Rock	5%	5	10	7
					Radial Washboard	5%	5	15	9
					2" Washboard	5%	5	10	7
						100%	100

LEVEL 1	This information should be provided by the program manager and is required before LVTS development can begin. This information can sometimes be found in the LCEP or other system documentation.
LEVEL 2	This breakout has a significant impact on the test durations of the final LVTS and should therefore be given serious consideration. This information, too, should be provided but is seldom available. Development cannot begin without this breakout. Often the analyst is forced to recommend a breakout for the concurrence of user.

MIL-STD-810H METHOD 514.8, ANNEX F

514.8F -II: Selection of Alpha for Beta Distribution

Legend

Figure description:

Legend

Alpha — color: Dark blue; symbol: Line with diamond markers

Ratio of Avg to Max Speed	Alpha
10%	0.2
20%	0.5
30%	0.75
40%	1.25
50%	2
60%	3
70%	4
80%	6
90%	13

Notes: The image displays a data table and its corresponding line graph showing the relationship between the ratio of average speed to maximum speed and the parameter Alpha. The graph shows an exponential-like increase in Alpha as the ratio approaches 100%.

MIL-STD-810H

METHOD 514.8, ANNEX F

BETA DISTRIBUTION INPUTS
SURFACE	Paved Road
MIN SPEED OF DATA SET	5
MAX SPEED OF DATA SET	55
AVG SPEED FROM SCENARIO	35
SPEED INCREMENT OF DATA SET	5
TOTAL MILES FROM SCENARIO	700.00
TOTAL HOURS	20.000
Ratio Avg/Max Speed	64%

CALCULATED RESULTS
Dist Min Speed	0
Dist Max Speed	57.5
ALPHA	3.40
BETA	2.19
Average Speed	35.00
Total Miles	699.982
Total Hours	20.000
Error	0.00%

BETA Distribution of Speed BETA Distribution of Speed Legend

Figure description:

BETA Distribution of Speed

BETA Distribution of Speed

Legend

Miles — color: magenta; symbol: Solid line with square marker
Time — color: dark blue; symbol: Solid line with diamond marker

Speed	Miles (Percentage)	Time (Percentage)
5	0.1%	0.4%
10	0.5%	2.0%
15	1.9%	4.5%
20	4.3%	7.6%
25	7.8%	11.0%
30	12.0%	14.0%
35	15.9%	16.0%
40	18.6%	16.3%
45	18.6%	14.5%
50	14.5%	10.1%
55	5.5%	3.5%

BETA DISTRIBUTION OF SPEED
Repr	Start	End	Range	Percentage	Time			Percentage
Speed	Speed	Speed	Avg	Time	in Hours	in Min	Miles	Miles
n/a	0	2.5	1.25	0.012%	0.002	0.15	0.0031	0.00%
5	2.5	7.5	5	0.458%	0.092	5.50	0.46	0.07%
10	7.5	12.5	10	1.966%	0.393	23.59	3.93	0.56%
15	12.5	17.5	15	4.487%	0.897	53.84	13.46	1.92%
20	17.5	22.5	20	7.673%	1.535	92.08	30.69	4.38%
25	22.5	27.5	25	11.035%	2.207	132.42	55.18	7.88%
30	27.5	32.5	30	13.999%	2.800	167.99	84.00	12.00%
35	32.5	37.5	35	15.955%	3.191	191.46	111.68	15.95%
40	37.5	42.5	40	16.295%	3.259	195.54	130.36	18.62%
45	42.5	47.5	45	14.478%	2.896	173.74	130.31	18.62%
50	47.5	52.5	50	10.142%	2.028	121.71	101.42	14.49%
55	52.5	57.5	55	3.499%	0.700	41.99	38.49	5.50%
TOTAL				100.0%	20.000	1200.00	699.982	100.0%
TOTAL USED				100.0%	19.998	1199.85	699.979	100.0%

Figure 514.8F-1. Sample beta distribution (wheeled vehicle).

The Beta distribution calculations are performed in the “BETA DISTRIBUTION OF SPEED” table of Figure 514.8F-1. A description of the fields follows.

a. Repr Speed - The representative speed for this entry. This is the speed for which vibration data were acquired.
b. Start Speed – The beginning of the speed range for this entry.
c. End Speed – The ending of the speed range for this entry.
d. Range Average – The average of the speed range for this entry. This number should be equal to the representative speed for the entry.
e. Percentage Time – This is the actual Beta distribution as a percentage of the total drive time. This column, along with the Percentage Miles column, is plotted on the graph of Figure 514.8F-1.
f. Time in Hours – The time in hours represented by this data entry, calculated by multiplying the total hours by the percentages of the previous column. The total hours is calculated from the total miles and the average speed.
g. Time in Min. – The time in minutes represented by this data entry. This is the final output of the Beta distribution and is passed forward to the VSD process.
h. Miles – The miles represented by this data entry, calculated by multiplying the Time in Hours by the Range Average.
i. Percentage Miles – The percentage of the total miles represented by this entry. This column, along with the Percentage Time column, is plotted on the graph of Figure 514.8F-1.

Note that the widths (in units of speed) of each speed range in the table of Figure 514.8F-1 are equal to the speed increment for which data was acquired and are centered around the acquired speeds. This results in two slight inconsistencies at the endpoints of the Beta distribution. First, the percentage of the miles at very low speeds (below 2.5 mph in this example) is not included in the VSD process. It is expected that the vibration at these speeds will be quite low and have no effect on the resultant LVTS, even if included. Second, the maximum speed of the Beta distribution is one-half speed increment higher than the highest speed for which data was acquired. This too should have little effect on the VSD process since very little time is spent at this speed.

The endpoints of the Beta distribution technique are treated slightly different for NBROR or SOR LVTS. In those cases, the endpoints for Beta distribution are set to exactly the minimum and maximum speeds acquired. If the example presented here were for a tracked vehicle the range of the first entry would be from 5 to 7.5 mph instead of 2.5 to 7.5 mph. Likewise, the last entry would be from 42.5 to 45 mph instead of 42.5 to 47.5 mph. For a tracked vehicle the narrowband random sweeps dominate the fatigue exposure represented by an LVTS. The same is true for the swept sine LVTS. Therefore, more emphasis is placed on the sweep ranges when calculating the Beta distribution. The sweep ranges are bound by the frequencies associated with the minimum and maximum speeds acquired, and the Beta distribution ranges are selected to account for that. Note that the speed ranges of the endpoints are then one-half as wide as the intermediate points. This is accounted for in the VSD process when calculating the actual run time represented by each speed event. The run times of the first and last speeds are set to one half of the intermediate speeds. Note also that during testing on the shaker, the swept narrow bands are in the range of the endpoint speeds for one-half the time of the other speeds.

514.8F -C.I. Test Course Lengths, Speeds and Exposure Times

Test Course
Test Course	Length, m (ft)	Nominal Speed, km/hr (mph)	Exposure Time, sec
Belgian Block	1200 (3940)	32.2 (20)	134
Two-Inch Washboard	250 (822)	16.2 (10)	56
Radial Washboard	74 (243)	24.1 (15)	11
Three Inch Spaced Bump	233 (764)	32.2 (20)	26
Total	1757 (5769)		227

The exposure times can be used with equation C.1 and the appropriate test course ASDs to produce a fatigue damage spectrum for each test course. Using the same set of typical wheeled vehicle data as before, the fatigue spectra are shown in Figure 514.8F-C.1. For this example, $\zeta$ was chosen to be 0.05 (5-percent critical damping) and the exponent $m$ was substituted for $b$ , and was assigned a value of 7.5 .

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 Location Fatigue Damage Spectra

Figure description:

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 Location

Fatigue Damage Spectra

Legend

Course 1 — color: red; symbol: Solid line
Course 2 — color: dark blue; symbol: Solid line
Course 3 — color: green; symbol: Solid line
Course 4 — color: light blue; symbol: Solid line

Annotations

Exposure time = 1 lap per course (text_label - position: x = 40, y = 1.00E+01)
m = 7.5 (text_label - position: x = 40, y = 1.00E+00)
Damping = 0.05 (text_label - position: x = 40, y = 1.00E-01)

Frequency - Hertz	Course 1	Course 2	Course 3	Course 4
2	5.00E-02	6.00E-06	5.00E-04	6.00E-02
3	5.00E-03	2.00E-08	1.00E-05	5.00E-04
4	4.00E-05	1.00E-10	2.00E-03	2.00E-04
5	5.00E-04	1.00E-08	3.00E-01	8.00E-03
6	1.00E-03	5.00E-06	1.00E-01	1.00E-02
7	2.00E-03	2.00E+00	2.00E-04	1.00E-02
8	3.00E-03	1.00E+01	6.00E-05	3.00E-03
9	1.00E-03	3.00E-01	1.00E-04	5.00E-04
10	1.00E-04	2.00E-04	3.00E-03	1.00E-05
15	2.00E-06	5.00E-01	1.00E-05	3.00E-04
20	2.00E-07	5.00E-09	1.00E-05	1.00E-04
25	1.00E-07	1.00E-03	3.00E-07	3.00E-04
30	1.00E-09	1.00E-06	2.00E-08	1.00E-07
40	1.00E-10	1.00E-08	1.00E-07	1.00E-05
50	null	1.00E-10	1.00E-09	5.00E-09
70	null	2.00E-09	4.00E-07	2.00E-08
100	null	1.00E-10	1.00E-10	1.00E-09

Notes: The chart uses logarithmic scales for both the X-axis (Frequency in Hertz and the Y-axis (Damage Index. The data values in the markdown table are estimates derived from the plot. Exposure time, m factor, and damping ratio are specified in a note within the chart area.))

Figure 514.8F-C.1. Fatigue damage spectra for specific test courses.

The cumulative fatigue damage spectrum (equation C.2) is shown by the lavender line in Figure 514.8F-C.2 and represents a fatigue damage index derived from a complete lap of the four specified test courses.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 location Fatigue Damage Spectra

Figure description:

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 location

Fatigue Damage Spectra

Legend

Course 1 — color: red; symbol: Solid line
Course 2 — color: dark blue; symbol: Solid line
Course 3 — color: bright green; symbol: Solid line
Course 4 — color: light blue; symbol: Solid line
Sum — color: light purple; symbol: Solid line

Annotations

Note: Exposure time = 1 lap per course, m = 7.5, Damping = 0.05 (text_label - position: top right)

Frequency (Hertz)	Course 1	Course 2	Course 3	Course 4	Sum
2	5.00E-02	6.00E-06	5.00E-04	5.00E-02	1.00E-01
3	1.00E-02	2.00E-09	1.00E-05	5.00E-03	1.50E-02
4	5.00E-05	1.00E-10	2.00E-02	1.00E-04	2.00E-02
5	1.00E-03	3.00E-08	2.00E-01	8.00E-03	2.10E-01
6	2.00E-03	1.00E-06	8.00E-02	1.20E-02	9.50E-02
7	3.00E-03	1.00E-01	1.00E-04	5.00E-03	1.10E-01
8	1.00E-03	8.00E+00	5.00E-04	2.00E-03	8.00E+00
9	5.00E-04	1.00E+00	1.00E-04	5.00E-04	1.00E+00
10	1.00E-05	1.00E-04	2.00E-03	1.00E-04	2.20E-03
12	1.00E-05	2.00E-03	5.00E-04	2.00E-04	2.70E-03
15	5.00E-05	1.00E+00	1.00E-04	3.00E-04	1.00E+00
20	1.00E-05	1.00E-05	1.00E-05	6.00E-04	6.30E-04
25	2.00E-07	5.00E-04	2.00E-06	2.00E-04	7.00E-04
30	1.00E-08	2.00E-06	1.00E-07	2.00E-06	4.10E-06
40	1.00E-09	1.00E-05	1.00E-07	1.00E-05	2.00E-05
50	1.00E-10	2.00E-09	5.00E-10	2.00E-09	5.00E-09
60	1.00E-10	1.00E-09	1.00E-09	2.50E-08	2.70E-08
70	1.00E-10	4.00E-07	3.00E-07	1.50E-08	7.20E-07
80	1.00E-10	1.00E-10	1.00E-10	1.00E-10	1.00E-10
100	1.00E-10	1.00E-10	1.00E-10	1.00E-10	1.00E-10

Notes: The data represents a Fatigue Damage Spectra (FDS for four test courses. Both axes are on a logarithmic scale. The Y-axis represents Damage index and the X-axis represents Frequency in Hertz.)

Figure 514.8F-C.2. Cumulative fatigue damage spectrum (lavender line).

The same process was performed for 2 measurement locations independently using cumulative data for 3 laps. The cumulative spectra for each location were then averaged and enveloped for comparison and are shown in Figure 514.8F-C.3.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra 4 Test Courses, 3 Laps, 2

Figure description:

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra 4 Test Courses, 3 Laps, 2 Locations

Sum of Fatigue Damage Spectra

Legend

Location 1 — color: dark blue; symbol: solid line
Location 2 — color: red; symbol: solid line
Average of Locations 1 and 2 — color: light green; symbol: solid line
Max of Locations 1 and 2 — color: purple; symbol: solid line

Annotations

Note: Exposure time = 3 laps per course m = 7.5 Damping = 0.05 (text_label - position: top right of plot area

Frequency - Hertz	Location 1	Location 2	Average of Locations 1 and 2	Max of Locations 1 and 2
2.0	4.70E-01	1.80E+01	9.24E+00	1.80E+01
3.0	1.10E-02	1.50E-02	1.30E-02	1.50E-02
4.0	5.50E-02	1.60E+01	8.03E+00	1.60E+01
5.0	6.50E-01	1.40E+02	7.03E+01	1.40E+02
6.0	2.00E-01	3.50E+00	1.85E+00	3.50E+00
8.0	1.80E+01	9.50E+02	4.84E+02	9.50E+02
10.0	2.50E-02	5.50E-02	4.00E-02	5.50E-02
12.0	2.10E-04	8.00E-04	5.05E-04	8.00E-04
14.0	5.00E-01	1.20E-01	3.10E-01	5.00E-01
15.0	1.10E+00	2.50E-01	6.75E-01	1.10E+00
17.0	1.00E-03	1.50E-04	5.75E-04	1.00E-03
20.0	2.00E-04	5.00E-06	1.03E-04	2.00E-04
23.0	9.00E-03	3.00E-04	4.65E-03	9.00E-03
27.0	1.00E-06	1.40E-07	5.70E-07	1.00E-06
30.0	2.00E-05	1.50E-06	1.08E-05	2.00E-05
33.0	3.30E-03	2.00E-05	1.66E-03	3.30E-03
37.0	1.00E-04	1.50E-06	5.08E-05	1.00E-04
40.0	1.20E-04	2.10E-06	6.11E-05	1.20E-04
45.0	5.00E-07	null	2.50E-07	5.00E-07
75.0	7.00E-06	2.00E-07	3.60E-06	7.00E-06
85.0	1.00E-07	null	null	1.00E-07

Notes: The Y-axis (Damage Index and X-axis (Frequency - Hertz are both on logarithmic scales. Data points were estimated based on the log-log grid provided.))

Figure 514.8F-C.3. Cumulative fatigue spectra from locations 1 and 2.

If an overall exposure time is selected, equation C.1 can be reworked to provide an ASD level based on the fatigue spectrum computed from Equation C.2.

G\left(f_{n}\right)=f_{n} \zeta\left(\frac{D P\left(f_{n}\right)}{f_{T}}\right)^{\frac{\bar{\kappa}}{b}}

C.3

where:
DP(f_n) =	Cumulative damage index as a function of system natural frequency
f_n =	System natural frequency (variable), Hz
T =	Total exposure time in environment, seconds
G(f_n) =	Equivalent ASD for a given DP(f_n), T, g²/Hz
ζ =	Damping ratio of system at dominant natural frequency expressed as a decimal
b =	Fatigue curve slope value when computed as a linear fit in log-log domain.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Using an exposure time equal to 3 times the total value listed in Table 514.8F-C.I (to account for 3 laps) and the fatigue damage spectra (average and max) shown in Figure 514.8F-C.3, an equivalent representative ASD was calculated from equation C.3. The spectra derived from the average and maximum fatigue damage spectra are shown in Figure 514.8F-C.4. For this data set, the fatigue damage spectra for locations 1 and 2 were nearly the same producing an average spectrum that is about the same as the enveloped spectrum. The enveloped or maximum spectrum is compared to the resultant spectrum computed from the statistical process and from a spectrum derived from the envelope of all original spectra and is shown in Figure 514.8F-C.5.

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum PSD From Fatigue Damage Sum

Figure description:

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum

PSD From Fatigue Damage Sum

Legend

Based on Max Fatigue Spectrum — color: blue; symbol: Solid line
Based on Average Fatigue Spectrum — color: red; symbol: Solid line

Annotations

Note: Exposure time = 681 seconds (3 Munson laps m = 7.5 Damping = 0.05 (text_label - position: top right of graph area))

Frequency - Hertz	Based on Max Fatigue Spectrum (G sq/Hz)	Based on Average Fatigue Spectrum (G sq/Hz)
2.0	0.033	0.027
3.0	0.007	0.0065
4.0	0.054	0.048
5.0	0.107	0.092
6.0	0.046	0.039
7.1	0.198	0.176
8.0	0.264	0.233
9.5	0.036	0.028
10.3	0.017	0.015
13.5	0.009	0.0068
15.3	0.068	0.061
17.5	0.013	0.011
20.3	0.0089	0.0074
23.0	0.024	0.021
27.5	0.0035	0.0031
35.0	0.025	0.022
40.5	0.0071	0.0063
50.5	0.012	0.0094
62.0	0.0011	0.00086
71.0	0.0083	0.0071
95.0	0.0011	0.00092
104.0	0.0012	0.0011
130.0	0.0016	0.0013
160.0	0.00042	0.00033
185.0	0.0010	0.00085
235.0	0.00018	0.00014
265.0	0.0011	0.00095
320.0	0.000078	0.000057
420.0	0.00068	0.00052
500.0	0.00042	0.00031

Notes: The chart uses a logarithmic scale for both axes. Frequency ranges from 1 to 1000 Hertz, and PSD Magnitude ranges from 0.00001 to 1 G sq/Hz.

Figure 514.8F-C.4. Combined vibration power spectra developed from average and maximum fatigue damage Spectra.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum Compared to Statistically

Figure description:

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum Compared to Statistically Generated PSD

Legend

Fatigue (Max Spectrum — color: red; symbol: Solid line
Statistical — color: dark blue; symbol: Solid line
Individual Spectral Envelope — color: green; symbol: Solid line

Annotations

Note: Exposure time = 681 seconds (3 Munson laps, m = 7.5, Damping = 0.05 (text_label - position: top right))

Frequency - Hertz	Fatigue (Max Spectrum - PSD Magnitude (G sq/Hz))	Statistical - PSD Magnitude (G sq/Hz)	Individual Spectral Envelope - PSD Magnitude (G sq/Hz)
2.0	0.03	0.025	0.04
3.0	0.007	0.008	0.012
4.0	0.05	0.045	0.14
5.0	0.11	0.11	0.25
6.5	0.05	0.06	0.11
7.5	0.15	0.13	0.3
8.5	0.26	0.21	0.42
10.0	0.017	0.025	0.043
15.0	0.07	0.065	0.105
18.0	0.013	0.015	0.026
23.0	0.025	0.02	0.047
30.0	0.0035	0.004	0.006
37.0	0.02	0.009	0.048
55.0	0.001	0.0009	0.002
70.0	0.007	0.006	0.021
100.0	0.0006	0.0007	0.0023
135.0	0.001	0.001	0.0048
170.0	0.00025	0.0003	0.0012
210.0	0.0008	0.0006	0.0018
250.0	0.0001	0.00015	0.00035
290.0	0.0003	0.0002	0.0035
350.0	0.00004	0.00006	0.00012
420.0	0.0003	0.00025	0.0015
500.0	0.0002	0.00015	0.0008

Notes: The chart is a log-log plot representing PSD Magnitude vs. Frequency for wheeled vehicle vibration data.

Figure 514.8F-C.5. Comparison of combined vibration power spectrum developed from the fatigue damage

spectrum, from the statistical process and from an envelope process.

The three processes (fatigue spectrum, statistical and envelope) produce specifications that are roughly the same shape. The specification derived from the fatigue damage spectrum technique has lower levels than those produced by the envelope process and nearly the same (but generally lower) levels than those produced by the technique developed in Appendix B. The statistical technique contains an implied assumption that each environment has the same exposure time and weights the spectral values toward the most severe spectrum due to the inclusion of spectral variance (the addition of a standard deviation) in the process. Therefore, it is likely that the statistical process will produce higher levels than the fatigue damage process unless the most severe spectra also have the longest exposure times.

The process was repeated for an exponent value of m = 5 as a comparison. A comparison of the fatigue damage spectra (maximum) for the two exponents is shown in Figure 514.8F-C.6, and a comparison of the vibration power spectra developed from each exponent is presented in Figure 514.8F-C.7.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra, 4 Test Courses, 3 Laps, 2

Figure description:

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra, 4 Test Courses, 3 Laps, 2 Locations

Sum of Fatigue Damage Spectra

Legend

m = 5 — color: blue; symbol: Solid line
m = 7.5 — color: red; symbol: Solid line

Annotations

Note: Exposure time = 3 laps per course, m = 5, 7.5, Damping = 0.05 (text_label - position: top right of plot area)

Frequency - Hertz	m = 5	m = 7.5
2.0	6.50E+01	1.80E+01
3.0	7.00E-01	1.80E-02
5.0	1.40E+02	1.10E+02
6.5	2.00E+01	4.00E+00
8.0	1.00E+03	1.10E+03
10.0	5.00E-01	2.00E-02
13.0	6.00E-02	4.00E-04
15.0	1.50E+01	1.10E+00
20.0	6.00E-02	2.20E-04
25.0	6.00E-01	1.00E-02
35.0	3.00E-01	3.50E-03
40.0	2.50E-02	3.50E-05
45.0	3.50E-02	1.20E-04
55.0	4.00E-05	null
70.0	5.00E-03	7.00E-06
80.0	1.50E-03	1.00E-06
100.0	3.00E-05	null
130.0	3.00E-05	null
145.0	5.00E-06	null
180.0	1.00E-05	null
250.0	3.50E-06	null
300.0	4.00E-07	null
400.0	2.50E-07	null
480.0	6.00E-07	null

Notes: The x-axis (Frequency in Hertz and y-axis (Damage Index both use logarithmic scales. Data points represent the sum of fatigue damage spectra for 4 test courses, 3 laps, and 2 locations.))

Figure 514.8F-C.6. Fatigue damage spectra for two exponents.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data", "subtitle": "PSD From Fatigue Damage Sum

Figure description:

Typical Wheeled Vehicle Vibration Data", "subtitle": "PSD From Fatigue Damage Sum (Maximum of Locations 1 and 2\nValues of m = 5 and m = 7.5", "additional_notes": "The axes are on a logarithmic scale. Data values are estimated from the graph grid lines and represent key peaks and troughs to capture the profile of the fatigue damage sum spectrum. Red (m=7.5 shows higher sensitivity to peak values compared to blue (m=5.

PSD From Fatigue Damage Sum (Maximum of Locations 1 and 2

Legend

PSD From Cumm FDS m = 5 — color: blue; symbol: Solid line
PSD From Cumm FDS m = 7.5 — color: red; symbol: Solid line

Annotations

Exposure Time = 681 seconds, (3 Munson laps, m = 5 and 7.5, Damping = 0.05 (text_label - position: top right box))

Frequency - Hertz	PSD From Cumm FDS m = 5	PSD From Cumm FDS m = 7.5
2.0	0.030	0.033
3.1	0.006	0.007
4.8	0.070	0.100
7.8	0.200	0.250
10.0	0.013	0.018
12.0	0.005	0.007
15.0	0.055	0.065
19.0	0.007	0.010
22.0	0.019	0.024
28.0	0.003	0.004
30.0	0.008	0.024
40.0	0.008	0.012
50.0	0.0008	0.0012
60.0	0.0008	0.0015
70.0	0.0055	0.0080
100.0	0.0005	0.0008
150.0	0.0008	0.0015
180.0	0.0006	0.0010
250.0	0.0007	0.0011
300.0	0.0002	0.0004
400.0	0.0002	0.0005
500.0	0.00015	0.0003

Figure 514.8F-C.7. Comparison of combined vibration power spectra developed from two exponents.

For this set of measured environments (acceleration spectra) and associated exposure times, the final combined spectrum is somewhat independent of the value of the exponent chosen. Forty percent of the spectral amplitudes for the two exponents were within 1 dB (based on m=7.5 as the reference), 80 percent were within 2 dB and all were within 2.4 dB.

Documentation of the spectral combination process, including assumptions (e.g., value of b), is essential. The final combined spectrum should be compared to the original input spectra to ensure that the resultant spectrum is a reasonable representation of the measured environment.

FDS APPROACH TO DEVELOPMENT OF A LVTS.

In summarizing the example provided in the previous section, a single ASD was computed, representative of the ensemble of data acquired from making three passes over four specific road courses. The ASD derived from the inverse of the cumulative FDS is compared to the envelope of the data ensemble as shown in Figure 514.8F-C.5. From Figure 514.8F-C.7 it is clear that the spectral shapes and amplitudes are very similar for the ASD’s derived in the examples in previous section for both selections of m (m=5 and m=7.5). From Figure 514.8F-C.5 it is also clear that the ASD computed from the inverse cumulative FDS falls significantly below the envelope of the data ensemble. Employing equation 9.5, one could easily compress the test time by increasing the magnitude of the ASD. This can be accomplished by changing the T parameter of equation C.3. As in Annex F, paragraph 9, one should always use caution in employing time compression techniques. When dealing with data of a similar spectral characteristic, a conservative approach would be to limit the final compressed spectral shape to the spectral shape of the envelope of the original data ensemble. Reviewing the spectral shapes of the ASD’s computed from the inverse cumulative FDS and the envelope of the original data ensemble, it is clear that the ratio between the two curves is not the same at each spectral line. Therefore, one will need to set some criteria, which is often test specific, for addressing the amount of

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

time compression employed. In the example discussed in this Appendix, the average ratio between 2 and 100 Hz was set at the compression ratio. This spectral band was considered to be of primary importance for this example since the data set was from a wheeled vehicle and the spectrum is dominated by energy below 100 Hz. Figure 514.8F-C.8 illustrates the effect of time compression based on the ratio described above. Using the time compressed spectral shape, the test time reduces from 681 seconds (the actual time spent on the courses) to either 72 seconds (when $m=5$ ) or 54 seconds (when $m=7.5$ ). As a final step, the analyst will usually reduce the number of breakpoints (smooth the spectral shape) while maintaining the overall G-rms level.

Typical Wheeled Vehicle Vibration Data Values of m = 5 and m = 7.5 PSD From Fatigue Damage Sum

Figure description:

Typical Wheeled Vehicle Vibration Data Values of m = 5 and m = 7.5

PSD From Fatigue Damage Sum (Maximum of Locations 1 and 2

Legend

PSD From Cumm FDS m = 5 — color: dark blue; symbol: solid line
PSD From Cumm FDS m = 7.5 — color: red; symbol: solid line
PSD_Envelope — color: teal; symbol: solid line
Final Spec (m=5 — color: blue; symbol: solid line
Final Spec (m=7.5 — color: dark red; symbol: solid line

Annotations

Exposure Time = 681 seconds (3 Munson laps (text_label - position: top right box))
m = 5 and 7.5; Damping = 0.05 (text_label - position: top right box)
Compressed Test Time (m=5: 72 Sec (text_label - position: top right box))
Compressed Test Time (m=7.5: 54 Sec (text_label - position: top right box))

Frequency - Hertz	PSD From Cumm FDS m = 5	PSD From Cumm FDS m = 7.5	PSD_Envelope	Final Spec (m=5)	Final Spec (m=7.5)
2.0	0.035	0.04	0.04	0.075	0.065
3.0	0.006	0.008	0.012	0.015	0.012
5.0	0.04	0.07	0.15	0.1	0.08
7.0	0.07	0.1	0.25	0.2	0.15
8.0	0.08	0.2	0.5	0.25	0.4
10.0	0.012	0.018	0.045	0.035	0.03
13.0	0.005	0.008	0.025	0.02	0.015
15.0	0.06	0.1	0.14	0.12	0.11
18.0	0.01	0.015	0.025	0.02	0.018
23.0	0.025	0.035	0.05	0.045	0.04
30.0	0.003	0.004	0.008	0.006	0.005
32.0	0.015	0.02	0.05	0.04	0.035
40.0	0.007	0.01	0.025	0.018	0.015
50.0	0.0008	0.0012	0.0035	0.0025	0.002
60.0	0.0007	0.001	0.003	0.002	0.0015
70.0	0.005	0.008	0.02	0.015	0.012
80.0	0.0006	0.0009	0.002	0.0015	0.0012
100.0	0.0004	0.0006	0.0025	0.002	0.0015
130.0	0.001	0.0015	0.005	0.0035	0.0025
200.0	0.0001	0.0002	0.002	0.0015	0.001
250.0	0.0005	0.0008	0.0035	0.0025	0.002
300.0	0.00004	0.00006	0.0015	0.001	0.0008
400.0	0.00006	0.0001	0.0018	0.0012	0.001
500.0	0.00015	0.00025	0.002	0.0015	0.0012

Notes: The y-axis is in a logarithmic scale for Power Spectral Density (G sq/Hz, and the x-axis is in a logarithmic scale for Frequency (Hz. Values in the table are approximate based on the plot.))

Figure 514.8F-C.8. Time compression of ASD's computed from the inverse cumulative fatigue damage spectrum.

This example is relatively simple; however, the techniques could easily be expanded to address more complex ensembles of data to include spectra with either narrowband or tonal components.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

Vibration Specification Development Procedure

514.8F -D.I. VSD Required Parameters

Skewness Threshold
Block Size	The number of data samples to include in ASD calculation. The block size is typically set equal to the sample rate to give a 1 second block and 1 Hz ASD resolution.
Window Type	The window type to use for ASD calculation, typically Hann.
Minimum g-rms threshold	Used to assure low level events will not overly affect LVTS ASD shape. The threshold
Minimum g-rms threshold	is set as a g-rms ratio (default 50%) of the maximum ASD in the group.
Crest Factor Threshold	These thresholds can be used to alert the analyst if a section of data is grossly non-Gaussian. The analyst can then decide if the data should be excluded from the development process.
Kurtosis Threshold
Start Frequency	This is the start frequency for the broadband portion of the LVTS. This is typically set to 5 Hz or the frequency of the lowest tonal component.
End Frequency	This is the upper limit of the LVTS bandwidth. This should be set by a review of the data. Typically used values include 200 Hz, 500 Hz, or 2000 Hz.
Nₑ, Nₛ	Analyst defined factors defining the number of standard deviations to use in the process (default = 1). Nₑ is for an individual event and Nₛ is for combining multiple events.
Mₑ, Mₛ	Analyst defined factors to limit conservatism in the process. Mₑ is for an individual event and Mₛ is for combining multiple events.
DC Component	Remove the DC components from the time domain data before calculation of ASDs. The DC component is often a result of signal conditioner offset and can be removed without affecting LVTS development.

514.8F -D.II. Single-Event ASD Sum-Set

Nomenclature	Definition
ASD(Avg)	A standard n_d average ASD. (See G_m (f) as defined in Appendix B)
ASD(Peak)	Calculated by holding the maximum amplitude of each spectral line over n_d averages. (See G_p (f) as defined in Appendix B)
ASD(Stdv)	Calculated by determining the standard deviation of each spectral line over n averages. (See G_d (f) as defined in Appendix B)
ASD(Sum)	Calculated by adding N_e standard deviations to the average for each spectral line. ASD(Sum) = N_e ASD(Stdv) + ASD(Avg) N_e is a user defined variable typically set to 1. ASD(Sum) is limited by ASD(Peak) and M_e ASD(Avg) where M_e is a user defined variable typically set to 2. (See G_s (f) as defined in Appendix B)
ASD(SpkRmvd)	ASD(Sum) after Frequency Spectral spike Removal.

514.8F -D.III. Spectral Spike Removed Table, Average

	Event	Beta Dist Time	Center Freq	Bandwidth Selected	g-rms	g-rms	g-rms
Project File:	Example Wheeled Vehicle		[ ]
Total Miles:	1000	Block size :	4096	Start Freq: 3		Raw ASD	W-UCol ASD
Date Proc :9/16/2002		Window Type:	Hann	End Frq: 500	N:	1	1
Time Proc :6:37:44 AM		Min g-rms:	0.5	Rmv DC : Y	M:	2	2

					Total G-RMS of removed Spectral spike
Channel					1	2	3
Description					Channel 1	Channel 2	Channel 3
Type					ASD(Avg)	ASD(Avg)\|	ASD(Avg)
Test Time					30	30	30
1 Harmonic	5 mph 2" WB	8.31	3.67	6	0.1534	2.79E-02	5.31E-02
	7.5 mph 2" WB	21.28	5.50	5	0.2691	3.41E-02	0.134565
	10 mph 2" WB	7.47	7.33	7	0.5755	8.74E-02	0.5730498

2 Harmonic	5 mph 2" WB	8.31	7.33	6	0.1118	3.49E-02	7.37E-02
	7.5 mph 2" WB	21.28	11.00	7	8.72E-02	3.22E-02	5.18E-02
	10 mph 2" WB	7.47	14.67	6	8.98E-02	2.67E-02	0.211421

3 Harmonic	5 mph 2" WB	8.31	11.00	6	0.06546	4.01E-02	9.12E-02
	7.5 mph 2" WB	21.28	16.50	9	2.63E-02	2.94E-02	0.05846
	10 mph 2" WB	7.47	22.00	8	3.08E-02	3.75E-02	0.07558

514.8F -D.V. Runtime Calculation

Event No	Event Name	Scenario Time	1 (Min)	2 (Min)	3 (Min)	4 (Min)	5 (Min)	6 (Min)	7 (Min)
1	Radial Washboard 5 MPH	6.62	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
2	Radial Washboard 10 MPH	9.76	1.0839	0.0000	7.5042	1.4266	0.0000	5.0242	0.000
3	Radial Washboard 15 MPH	3.51	44.0730	16.5723	67.7850	42.9182	31.0571	17.1557	33.406
4	Embedded Rock 5 MPH	9.01	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.648
5	Embedded Rock 7.5 MPH	11.04	6.5395	4.8474	4.7421	6.0680	3.1819	0.0000	21.373
6	Embedded Rock 10 MPH	4.74	46.1231	31.9828	10.4189	34.8946	6.6298	0.0000	38.806
7	Belgian Block 5 MPH	1.05	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
8	Belgian Block 10 MPH	3.24	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
9	Belgian Block 15 MPH	5.18	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.846
10	Belgian Block 20 MPH	5.02	2.2310	0.5887	0.9003	2.5947	3.1033	0.0000	2.898
11	Belgian Block 25 MPH	1.88	17.4201	4.2217	6.0418	16.9478	14.9296	0.0000	6.81
		TF	117.4706	58.2131	97.3924	104.8499	58.9017	22.1799	104.791
		TFA	60	30	60	30	30	15

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

514.8F -D.VI. Group Sum-Set Definition

ASD(Avg_g)	The weighted average of the ASD group. See Equation D.2-1. (See G_a(f) as defined in Appendix B)
ASD(Peak_g)	Calculated by holding the maximum amplitude of each spectral line over all events.
ASD(Stdv_g)	The weighted standard deviation of the ASD group. See Equation D2.2-3. (See G_e(f) as defined in Appendix B)
ASD(Sum_g)	Calculated by adding N_g standard deviations to the average for each spectral line. ASD(Sum_g) = N_g ASD(Stdv_g) + ASD(Avg_g) Calculated by adding N_g standard deviations to the average for each spectral line. ASD(Sum) = N_g ASD(Stdv) + ASD(Avg) N_g is a user defined variable typically set to 1. ASD(Sum) is limited by ASD(Peak) and M_g ASD(Avg) where M_g is a user defined variable typically set to 2. (See G_f(f)* as defined in Appendix B "for N=1")
ASD(Final)	The ASD(Sum_g) scaled to a user selected final time.

The ASDs of the group sum-set, as with the single-event ASD sum-set, are calculated on a spectral line basis. The ASD(Avg_g) is an average of the ASD(SpkRmvd) for all events in the group (excluding those for which the g-rms is below the user defined threshold). Unlike the ASD(Avg) of the single-event ASD sum-set, the ASD(Avg_g) is not a standard n average ASD. Instead, the individual ASDs are weighted to the factors defined in the scenario table (see Table 514.8F-D.IV). Typically, the weighting factors are set equal to the individual event scenario times. The idea of a weighted approach is to produce a time-based calculation instead of an event-based calculation. In effect, weighting to the scenario time produces a separate ASD for each minute of the lifecycle, instead of an ASD for each event. Each minute of the system’s lifecycle would then be weighted equally in determining the average. A similar method is used to calculate the standard deviation of the group ASD(Stdv_g).

Assuming there are n events that exceed the minimum g-rms, that $W_{i}$ is weighting factor of each event, and that $G_{i}$ is the $\mathrm{g}^{2} / \mathrm{Hz}$ level of each event, then for each spectral line:

ASD(Avg_g) = ⁿ ∑W_iG_i _i=1

ⁿ ∑W_i _i=1

D.2-1

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

$ASD(Stdv\_g) = \sqrt{\frac{\sum_{i=1}^{n} W_{i} * [G_{i} - ASD(Avg\_g)]^2}{\sum_{i=1}^{n} W_{i}}}$

D.2-2

The ASD(Sum_g) is calculated by adding N g standard deviations to the average, where N g is a user defined variable typically set to 1. Use of the ASD(Sum_g) is intended to account for factors such as differences in road surfaces, driver variances, and consideration of road surfaces not included in the data acquisition phase and other relevant variables. The ASD(Sum_g) is constrained to be no higher than M g *ASD(Avg_g) where M g is a user defined parameter with a default value of 2.0. The ASD(Sum_g) is also limited to the ASD(Peak_g) level at each spectral line. Although some additional processing may be required, the ASD(Sum_g) coupled with the runtime calculated in the previous step now represent the equivalent lifetime fatigue of an item mounted at that location. Recall that each channel represents a vibration axis for a given location. The ASD(Sum_g) becomes the working ASD and is passed forward to the next step.

In some cases multiple channels (or locations) must be combined into a single LVTS. This can be accomplished by simply enveloping the channels later in the VSD process. However, it is possible to combine multiple channels concurrently with the event combination. Assuming j is a list of m channels to combine, then for each spectral line:

$ASD(Avg\_g)=\frac{\sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n}W_{ij}G_{ij}}{\sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n}W_{ij}}$ D.2-3 $ASD(Stdv\_g)=\sqrt{\frac{\sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n}W_{ij}*[G_{ij}-ASD(Avg\_g)]^2}{\sum\limits_{j=1}^{m}\sum\limits_{i=1}^{n}W_{ij}}}$ D.2-4

514.8F -D.IX. LVTS Combination Example

Freq	LVTS01	LVTS02	Norm Level	LVTS01 New Time	LVTS02 New Time	Total New Time	Final Run Time	LVTS_C
(Hz)	(G²/Hz)	(G²/Hz)	(G²/Hz)	(min)	(min)	(min)	(min)	(G²/Hz)
5	0.100	0.200	0.200	2.23	15.00	17.23	20.00	0.208
6	0.200	0.400	0.400	2.23	15.00	17.23	20.00	0.415
7	0.300	0.400	0.400	10.20	15.00	25.20	20.00	0.459
8	0.400	0.400	0.400	30.00	15.00	45.00	20.00	0.536
9	0.400	0.300	0.300	88.24	15.00	103.23	20.00	0.501

This method can also be used this to combine multiple events into a broadband LVTS, replacing the steps outline in paragraphs 2.6 through 2.8 above. An alternate method to add conservatism must be found, and care should be taken to assure the method does not corrupt the overall shape of the ASD set. Refer to paragraph 2.2.1 (main body of Method 514) for cautions associated with combining LVTS.

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MIL-STD-810H

METHOD 514.8, ANNEX F, APPENDIX D

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MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX E METHOD 514.8, ANNEX F, APPENDIX E Theoretical Aspects of Maximum Response

Table 514.8F: -I: Lifetime Scenario Breakout – Example Only

MIL-STD-810H, Environmental Engineering Considerations and Laboratory Tests

Last Updated 29 Oct 2026

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LEVEL 1 BREAKOUT					LEVEL 2 BREAKOUT
TOTAL MILES:	1000
Terrain Type	Percent	Miles	Speed		Surface¹	Percent	Miles	Speed
Terrain Type	Percent	Miles	Max	Avg	Surface¹	Percent	Miles	Max	Avg
PRIMARY ROAD	70%	700	55	35	Paved	100%	700	55	35
						100%	700

SECONDARY ROAD	20%	200	40	22	Secondary Road	60%	120	40	25
					Gravel Road	23%	46	45	22
					Belgian Block	10%	20	25	15
					Embedded Rock	1%	2	10	7
					Radial Washboard	3%	6	15	9
					2" Washboard	3%	6	10	7
						100%	200

* Off Road	10%	100	25	14	Cross Country	85%	85	25	16.3
* A combination of trails and cross country					Embedded Rock	5%	5	10	7
					Radial Washboard	5%	5	15	9
					2" Washboard	5%	5	10	7
						100%	100

LEVEL 1	This information should be provided by the program manager and is required before LVTS development can begin. This information can sometimes be found in the LCEP or other system documentation.
LEVEL 2	This breakout has a significant impact on the test durations of the final LVTS and should therefore be given serious consideration. This information, too, should be provided but is seldom available. Development cannot begin without this breakout. Often the analyst is forced to recommend a breakout for the concurrence of user.

MIL-STD-810H METHOD 514.8, ANNEX F

514.8F -II: Selection of Alpha for Beta Distribution

Legend

Figure description:

Legend

Alpha — color: Dark blue; symbol: Line with diamond markers

Ratio of Avg to Max Speed	Alpha
10%	0.2
20%	0.5
30%	0.75
40%	1.25
50%	2
60%	3
70%	4
80%	6
90%	13

MIL-STD-810H

METHOD 514.8, ANNEX F

BETA DISTRIBUTION INPUTS
SURFACE	Paved Road
MIN SPEED OF DATA SET	5
MAX SPEED OF DATA SET	55
AVG SPEED FROM SCENARIO	35
SPEED INCREMENT OF DATA SET	5
TOTAL MILES FROM SCENARIO	700.00
TOTAL HOURS	20.000
Ratio Avg/Max Speed	64%

CALCULATED RESULTS
Dist Min Speed	0
Dist Max Speed	57.5
ALPHA	3.40
BETA	2.19
Average Speed	35.00
Total Miles	699.982
Total Hours	20.000
Error	0.00%

BETA Distribution of Speed BETA Distribution of Speed Legend

Figure description:

BETA Distribution of Speed

BETA Distribution of Speed

Legend

Miles — color: magenta; symbol: Solid line with square marker
Time — color: dark blue; symbol: Solid line with diamond marker

Speed	Miles (Percentage)	Time (Percentage)
5	0.1%	0.4%
10	0.5%	2.0%
15	1.9%	4.5%
20	4.3%	7.6%
25	7.8%	11.0%
30	12.0%	14.0%
35	15.9%	16.0%
40	18.6%	16.3%
45	18.6%	14.5%
50	14.5%	10.1%
55	5.5%	3.5%

BETA DISTRIBUTION OF SPEED
Repr	Start	End	Range	Percentage	Time			Percentage
Speed	Speed	Speed	Avg	Time	in Hours	in Min	Miles	Miles
n/a	0	2.5	1.25	0.012%	0.002	0.15	0.0031	0.00%
5	2.5	7.5	5	0.458%	0.092	5.50	0.46	0.07%
10	7.5	12.5	10	1.966%	0.393	23.59	3.93	0.56%
15	12.5	17.5	15	4.487%	0.897	53.84	13.46	1.92%
20	17.5	22.5	20	7.673%	1.535	92.08	30.69	4.38%
25	22.5	27.5	25	11.035%	2.207	132.42	55.18	7.88%
30	27.5	32.5	30	13.999%	2.800	167.99	84.00	12.00%
35	32.5	37.5	35	15.955%	3.191	191.46	111.68	15.95%
40	37.5	42.5	40	16.295%	3.259	195.54	130.36	18.62%
45	42.5	47.5	45	14.478%	2.896	173.74	130.31	18.62%
50	47.5	52.5	50	10.142%	2.028	121.71	101.42	14.49%
55	52.5	57.5	55	3.499%	0.700	41.99	38.49	5.50%
TOTAL				100.0%	20.000	1200.00	699.982	100.0%
TOTAL USED				100.0%	19.998	1199.85	699.979	100.0%

Figure 514.8F-1. Sample beta distribution (wheeled vehicle).

The Beta distribution calculations are performed in the “BETA DISTRIBUTION OF SPEED” table of Figure 514.8F-1. A description of the fields follows.

a. Repr Speed - The representative speed for this entry. This is the speed for which vibration data were acquired.
b. Start Speed – The beginning of the speed range for this entry.
c. End Speed – The ending of the speed range for this entry.
d. Range Average – The average of the speed range for this entry. This number should be equal to the representative speed for the entry.
e. Percentage Time – This is the actual Beta distribution as a percentage of the total drive time. This column, along with the Percentage Miles column, is plotted on the graph of Figure 514.8F-1.
f. Time in Hours – The time in hours represented by this data entry, calculated by multiplying the total hours by the percentages of the previous column. The total hours is calculated from the total miles and the average speed.
g. Time in Min. – The time in minutes represented by this data entry. This is the final output of the Beta distribution and is passed forward to the VSD process.
h. Miles – The miles represented by this data entry, calculated by multiplying the Time in Hours by the Range Average.
i. Percentage Miles – The percentage of the total miles represented by this entry. This column, along with the Percentage Time column, is plotted on the graph of Figure 514.8F-1.

514.8F -C.I. Test Course Lengths, Speeds and Exposure Times

Test Course
Test Course	Length, m (ft)	Nominal Speed, km/hr (mph)	Exposure Time, sec
Belgian Block	1200 (3940)	32.2 (20)	134
Two-Inch Washboard	250 (822)	16.2 (10)	56
Radial Washboard	74 (243)	24.1 (15)	11
Three Inch Spaced Bump	233 (764)	32.2 (20)	26
Total	1757 (5769)		227

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 Location Fatigue Damage Spectra

Figure description:

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 Location

Fatigue Damage Spectra

Legend

Course 1 — color: red; symbol: Solid line
Course 2 — color: dark blue; symbol: Solid line
Course 3 — color: green; symbol: Solid line
Course 4 — color: light blue; symbol: Solid line

Annotations

Exposure time = 1 lap per course (text_label - position: x = 40, y = 1.00E+01)
m = 7.5 (text_label - position: x = 40, y = 1.00E+00)
Damping = 0.05 (text_label - position: x = 40, y = 1.00E-01)

Frequency - Hertz	Course 1	Course 2	Course 3	Course 4
2	5.00E-02	6.00E-06	5.00E-04	6.00E-02
3	5.00E-03	2.00E-08	1.00E-05	5.00E-04
4	4.00E-05	1.00E-10	2.00E-03	2.00E-04
5	5.00E-04	1.00E-08	3.00E-01	8.00E-03
6	1.00E-03	5.00E-06	1.00E-01	1.00E-02
7	2.00E-03	2.00E+00	2.00E-04	1.00E-02
8	3.00E-03	1.00E+01	6.00E-05	3.00E-03
9	1.00E-03	3.00E-01	1.00E-04	5.00E-04
10	1.00E-04	2.00E-04	3.00E-03	1.00E-05
15	2.00E-06	5.00E-01	1.00E-05	3.00E-04
20	2.00E-07	5.00E-09	1.00E-05	1.00E-04
25	1.00E-07	1.00E-03	3.00E-07	3.00E-04
30	1.00E-09	1.00E-06	2.00E-08	1.00E-07
40	1.00E-10	1.00E-08	1.00E-07	1.00E-05
50	null	1.00E-10	1.00E-09	5.00E-09
70	null	2.00E-09	4.00E-07	2.00E-08
100	null	1.00E-10	1.00E-10	1.00E-09

Figure 514.8F-C.1. Fatigue damage spectra for specific test courses.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 location Fatigue Damage Spectra

Figure description:

Typical Wheeled Vehicle Vibration Data 4 Test Courses, 1 Lap, 1 location

Fatigue Damage Spectra

Legend

Course 1 — color: red; symbol: Solid line
Course 2 — color: dark blue; symbol: Solid line
Course 3 — color: bright green; symbol: Solid line
Course 4 — color: light blue; symbol: Solid line
Sum — color: light purple; symbol: Solid line

Annotations

Note: Exposure time = 1 lap per course, m = 7.5, Damping = 0.05 (text_label - position: top right)

Frequency (Hertz)	Course 1	Course 2	Course 3	Course 4	Sum
2	5.00E-02	6.00E-06	5.00E-04	5.00E-02	1.00E-01
3	1.00E-02	2.00E-09	1.00E-05	5.00E-03	1.50E-02
4	5.00E-05	1.00E-10	2.00E-02	1.00E-04	2.00E-02
5	1.00E-03	3.00E-08	2.00E-01	8.00E-03	2.10E-01
6	2.00E-03	1.00E-06	8.00E-02	1.20E-02	9.50E-02
7	3.00E-03	1.00E-01	1.00E-04	5.00E-03	1.10E-01
8	1.00E-03	8.00E+00	5.00E-04	2.00E-03	8.00E+00
9	5.00E-04	1.00E+00	1.00E-04	5.00E-04	1.00E+00
10	1.00E-05	1.00E-04	2.00E-03	1.00E-04	2.20E-03
12	1.00E-05	2.00E-03	5.00E-04	2.00E-04	2.70E-03
15	5.00E-05	1.00E+00	1.00E-04	3.00E-04	1.00E+00
20	1.00E-05	1.00E-05	1.00E-05	6.00E-04	6.30E-04
25	2.00E-07	5.00E-04	2.00E-06	2.00E-04	7.00E-04
30	1.00E-08	2.00E-06	1.00E-07	2.00E-06	4.10E-06
40	1.00E-09	1.00E-05	1.00E-07	1.00E-05	2.00E-05
50	1.00E-10	2.00E-09	5.00E-10	2.00E-09	5.00E-09
60	1.00E-10	1.00E-09	1.00E-09	2.50E-08	2.70E-08
70	1.00E-10	4.00E-07	3.00E-07	1.50E-08	7.20E-07
80	1.00E-10	1.00E-10	1.00E-10	1.00E-10	1.00E-10
100	1.00E-10	1.00E-10	1.00E-10	1.00E-10	1.00E-10

Figure 514.8F-C.2. Cumulative fatigue damage spectrum (lavender line).

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra 4 Test Courses, 3 Laps, 2

Figure description:

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra 4 Test Courses, 3 Laps, 2 Locations

Sum of Fatigue Damage Spectra

Legend

Location 1 — color: dark blue; symbol: solid line
Location 2 — color: red; symbol: solid line
Average of Locations 1 and 2 — color: light green; symbol: solid line
Max of Locations 1 and 2 — color: purple; symbol: solid line

Annotations

Note: Exposure time = 3 laps per course m = 7.5 Damping = 0.05 (text_label - position: top right of plot area

Frequency - Hertz	Location 1	Location 2	Average of Locations 1 and 2	Max of Locations 1 and 2
2.0	4.70E-01	1.80E+01	9.24E+00	1.80E+01
3.0	1.10E-02	1.50E-02	1.30E-02	1.50E-02
4.0	5.50E-02	1.60E+01	8.03E+00	1.60E+01
5.0	6.50E-01	1.40E+02	7.03E+01	1.40E+02
6.0	2.00E-01	3.50E+00	1.85E+00	3.50E+00
8.0	1.80E+01	9.50E+02	4.84E+02	9.50E+02
10.0	2.50E-02	5.50E-02	4.00E-02	5.50E-02
12.0	2.10E-04	8.00E-04	5.05E-04	8.00E-04
14.0	5.00E-01	1.20E-01	3.10E-01	5.00E-01
15.0	1.10E+00	2.50E-01	6.75E-01	1.10E+00
17.0	1.00E-03	1.50E-04	5.75E-04	1.00E-03
20.0	2.00E-04	5.00E-06	1.03E-04	2.00E-04
23.0	9.00E-03	3.00E-04	4.65E-03	9.00E-03
27.0	1.00E-06	1.40E-07	5.70E-07	1.00E-06
30.0	2.00E-05	1.50E-06	1.08E-05	2.00E-05
33.0	3.30E-03	2.00E-05	1.66E-03	3.30E-03
37.0	1.00E-04	1.50E-06	5.08E-05	1.00E-04
40.0	1.20E-04	2.10E-06	6.11E-05	1.20E-04
45.0	5.00E-07	null	2.50E-07	5.00E-07
75.0	7.00E-06	2.00E-07	3.60E-06	7.00E-06
85.0	1.00E-07	null	null	1.00E-07

Notes: The Y-axis (Damage Index and X-axis (Frequency - Hertz are both on logarithmic scales. Data points were estimated based on the log-log grid provided.))

Figure 514.8F-C.3. Cumulative fatigue spectra from locations 1 and 2.

If an overall exposure time is selected, equation C.1 can be reworked to provide an ASD level based on the fatigue spectrum computed from Equation C.2.

G\left(f_{n}\right)=f_{n} \zeta\left(\frac{D P\left(f_{n}\right)}{f_{T}}\right)^{\frac{\bar{\kappa}}{b}}

C.3

where:
DP(f_n) =	Cumulative damage index as a function of system natural frequency
f_n =	System natural frequency (variable), Hz
T =	Total exposure time in environment, seconds
G(f_n) =	Equivalent ASD for a given DP(f_n), T, g²/Hz
ζ =	Damping ratio of system at dominant natural frequency expressed as a decimal
b =	Fatigue curve slope value when computed as a linear fit in log-log domain.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum PSD From Fatigue Damage Sum

Figure description:

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum

PSD From Fatigue Damage Sum

Legend

Based on Max Fatigue Spectrum — color: blue; symbol: Solid line
Based on Average Fatigue Spectrum — color: red; symbol: Solid line

Annotations

Note: Exposure time = 681 seconds (3 Munson laps m = 7.5 Damping = 0.05 (text_label - position: top right of graph area))

Frequency - Hertz	Based on Max Fatigue Spectrum (G sq/Hz)	Based on Average Fatigue Spectrum (G sq/Hz)
2.0	0.033	0.027
3.0	0.007	0.0065
4.0	0.054	0.048
5.0	0.107	0.092
6.0	0.046	0.039
7.1	0.198	0.176
8.0	0.264	0.233
9.5	0.036	0.028
10.3	0.017	0.015
13.5	0.009	0.0068
15.3	0.068	0.061
17.5	0.013	0.011
20.3	0.0089	0.0074
23.0	0.024	0.021
27.5	0.0035	0.0031
35.0	0.025	0.022
40.5	0.0071	0.0063
50.5	0.012	0.0094
62.0	0.0011	0.00086
71.0	0.0083	0.0071
95.0	0.0011	0.00092
104.0	0.0012	0.0011
130.0	0.0016	0.0013
160.0	0.00042	0.00033
185.0	0.0010	0.00085
235.0	0.00018	0.00014
265.0	0.0011	0.00095
320.0	0.000078	0.000057
420.0	0.00068	0.00052
500.0	0.00042	0.00031

Notes: The chart uses a logarithmic scale for both axes. Frequency ranges from 1 to 1000 Hertz, and PSD Magnitude ranges from 0.00001 to 1 G sq/Hz.

Figure 514.8F-C.4. Combined vibration power spectra developed from average and maximum fatigue damage Spectra.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum Compared to Statistically

Figure description:

Typical Wheeled Vehicle Vibration Data PSD From Fatigue Damage Sum Compared to Statistically Generated PSD

Legend

Fatigue (Max Spectrum — color: red; symbol: Solid line
Statistical — color: dark blue; symbol: Solid line
Individual Spectral Envelope — color: green; symbol: Solid line

Annotations

Note: Exposure time = 681 seconds (3 Munson laps, m = 7.5, Damping = 0.05 (text_label - position: top right))

Frequency - Hertz	Fatigue (Max Spectrum - PSD Magnitude (G sq/Hz))	Statistical - PSD Magnitude (G sq/Hz)	Individual Spectral Envelope - PSD Magnitude (G sq/Hz)
2.0	0.03	0.025	0.04
3.0	0.007	0.008	0.012
4.0	0.05	0.045	0.14
5.0	0.11	0.11	0.25
6.5	0.05	0.06	0.11
7.5	0.15	0.13	0.3
8.5	0.26	0.21	0.42
10.0	0.017	0.025	0.043
15.0	0.07	0.065	0.105
18.0	0.013	0.015	0.026
23.0	0.025	0.02	0.047
30.0	0.0035	0.004	0.006
37.0	0.02	0.009	0.048
55.0	0.001	0.0009	0.002
70.0	0.007	0.006	0.021
100.0	0.0006	0.0007	0.0023
135.0	0.001	0.001	0.0048
170.0	0.00025	0.0003	0.0012
210.0	0.0008	0.0006	0.0018
250.0	0.0001	0.00015	0.00035
290.0	0.0003	0.0002	0.0035
350.0	0.00004	0.00006	0.00012
420.0	0.0003	0.00025	0.0015
500.0	0.0002	0.00015	0.0008

Notes: The chart is a log-log plot representing PSD Magnitude vs. Frequency for wheeled vehicle vibration data.

Figure 514.8F-C.5. Comparison of combined vibration power spectrum developed from the fatigue damage

spectrum, from the statistical process and from an envelope process.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra, 4 Test Courses, 3 Laps, 2

Figure description:

Typical Wheeled Vehicle Vibration Data Sum of Fatigue Damage Spectra, 4 Test Courses, 3 Laps, 2 Locations

Sum of Fatigue Damage Spectra

Legend

m = 5 — color: blue; symbol: Solid line
m = 7.5 — color: red; symbol: Solid line

Annotations

Note: Exposure time = 3 laps per course, m = 5, 7.5, Damping = 0.05 (text_label - position: top right of plot area)

Frequency - Hertz	m = 5	m = 7.5
2.0	6.50E+01	1.80E+01
3.0	7.00E-01	1.80E-02
5.0	1.40E+02	1.10E+02
6.5	2.00E+01	4.00E+00
8.0	1.00E+03	1.10E+03
10.0	5.00E-01	2.00E-02
13.0	6.00E-02	4.00E-04
15.0	1.50E+01	1.10E+00
20.0	6.00E-02	2.20E-04
25.0	6.00E-01	1.00E-02
35.0	3.00E-01	3.50E-03
40.0	2.50E-02	3.50E-05
45.0	3.50E-02	1.20E-04
55.0	4.00E-05	null
70.0	5.00E-03	7.00E-06
80.0	1.50E-03	1.00E-06
100.0	3.00E-05	null
130.0	3.00E-05	null
145.0	5.00E-06	null
180.0	1.00E-05	null
250.0	3.50E-06	null
300.0	4.00E-07	null
400.0	2.50E-07	null
480.0	6.00E-07	null

Notes: The x-axis (Frequency in Hertz and y-axis (Damage Index both use logarithmic scales. Data points represent the sum of fatigue damage spectra for 4 test courses, 3 laps, and 2 locations.))

Figure 514.8F-C.6. Fatigue damage spectra for two exponents.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data", "subtitle": "PSD From Fatigue Damage Sum

Figure description:

PSD From Fatigue Damage Sum (Maximum of Locations 1 and 2

Legend

PSD From Cumm FDS m = 5 — color: blue; symbol: Solid line
PSD From Cumm FDS m = 7.5 — color: red; symbol: Solid line

Annotations

Exposure Time = 681 seconds, (3 Munson laps, m = 5 and 7.5, Damping = 0.05 (text_label - position: top right box))

Frequency - Hertz	PSD From Cumm FDS m = 5	PSD From Cumm FDS m = 7.5
2.0	0.030	0.033
3.1	0.006	0.007
4.8	0.070	0.100
7.8	0.200	0.250
10.0	0.013	0.018
12.0	0.005	0.007
15.0	0.055	0.065
19.0	0.007	0.010
22.0	0.019	0.024
28.0	0.003	0.004
30.0	0.008	0.024
40.0	0.008	0.012
50.0	0.0008	0.0012
60.0	0.0008	0.0015
70.0	0.0055	0.0080
100.0	0.0005	0.0008
150.0	0.0008	0.0015
180.0	0.0006	0.0010
250.0	0.0007	0.0011
300.0	0.0002	0.0004
400.0	0.0002	0.0005
500.0	0.00015	0.0003

Figure 514.8F-C.7. Comparison of combined vibration power spectra developed from two exponents.

FDS APPROACH TO DEVELOPMENT OF A LVTS.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX C

Typical Wheeled Vehicle Vibration Data Values of m = 5 and m = 7.5 PSD From Fatigue Damage Sum

Figure description:

Typical Wheeled Vehicle Vibration Data Values of m = 5 and m = 7.5

PSD From Fatigue Damage Sum (Maximum of Locations 1 and 2

Legend

PSD From Cumm FDS m = 5 — color: dark blue; symbol: solid line
PSD From Cumm FDS m = 7.5 — color: red; symbol: solid line
PSD_Envelope — color: teal; symbol: solid line
Final Spec (m=5 — color: blue; symbol: solid line
Final Spec (m=7.5 — color: dark red; symbol: solid line

Annotations

Exposure Time = 681 seconds (3 Munson laps (text_label - position: top right box))
m = 5 and 7.5; Damping = 0.05 (text_label - position: top right box)
Compressed Test Time (m=5: 72 Sec (text_label - position: top right box))
Compressed Test Time (m=7.5: 54 Sec (text_label - position: top right box))

Frequency - Hertz	PSD From Cumm FDS m = 5	PSD From Cumm FDS m = 7.5	PSD_Envelope	Final Spec (m=5)	Final Spec (m=7.5)
2.0	0.035	0.04	0.04	0.075	0.065
3.0	0.006	0.008	0.012	0.015	0.012
5.0	0.04	0.07	0.15	0.1	0.08
7.0	0.07	0.1	0.25	0.2	0.15
8.0	0.08	0.2	0.5	0.25	0.4
10.0	0.012	0.018	0.045	0.035	0.03
13.0	0.005	0.008	0.025	0.02	0.015
15.0	0.06	0.1	0.14	0.12	0.11
18.0	0.01	0.015	0.025	0.02	0.018
23.0	0.025	0.035	0.05	0.045	0.04
30.0	0.003	0.004	0.008	0.006	0.005
32.0	0.015	0.02	0.05	0.04	0.035
40.0	0.007	0.01	0.025	0.018	0.015
50.0	0.0008	0.0012	0.0035	0.0025	0.002
60.0	0.0007	0.001	0.003	0.002	0.0015
70.0	0.005	0.008	0.02	0.015	0.012
80.0	0.0006	0.0009	0.002	0.0015	0.0012
100.0	0.0004	0.0006	0.0025	0.002	0.0015
130.0	0.001	0.0015	0.005	0.0035	0.0025
200.0	0.0001	0.0002	0.002	0.0015	0.001
250.0	0.0005	0.0008	0.0035	0.0025	0.002
300.0	0.00004	0.00006	0.0015	0.001	0.0008
400.0	0.00006	0.0001	0.0018	0.0012	0.001
500.0	0.00015	0.00025	0.002	0.0015	0.0012

Figure 514.8F-C.8. Time compression of ASD's computed from the inverse cumulative fatigue damage spectrum.

This example is relatively simple; however, the techniques could easily be expanded to address more complex ensembles of data to include spectra with either narrowband or tonal components.

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

Vibration Specification Development Procedure

514.8F -D.I. VSD Required Parameters

Skewness Threshold
Block Size	The number of data samples to include in ASD calculation. The block size is typically set equal to the sample rate to give a 1 second block and 1 Hz ASD resolution.
Window Type	The window type to use for ASD calculation, typically Hann.
Minimum g-rms threshold	Used to assure low level events will not overly affect LVTS ASD shape. The threshold
Minimum g-rms threshold	is set as a g-rms ratio (default 50%) of the maximum ASD in the group.
Crest Factor Threshold	These thresholds can be used to alert the analyst if a section of data is grossly non-Gaussian. The analyst can then decide if the data should be excluded from the development process.
Kurtosis Threshold
Start Frequency	This is the start frequency for the broadband portion of the LVTS. This is typically set to 5 Hz or the frequency of the lowest tonal component.
End Frequency	This is the upper limit of the LVTS bandwidth. This should be set by a review of the data. Typically used values include 200 Hz, 500 Hz, or 2000 Hz.
Nₑ, Nₛ	Analyst defined factors defining the number of standard deviations to use in the process (default = 1). Nₑ is for an individual event and Nₛ is for combining multiple events.
Mₑ, Mₛ	Analyst defined factors to limit conservatism in the process. Mₑ is for an individual event and Mₛ is for combining multiple events.
DC Component	Remove the DC components from the time domain data before calculation of ASDs. The DC component is often a result of signal conditioner offset and can be removed without affecting LVTS development.

514.8F -D.II. Single-Event ASD Sum-Set

Nomenclature	Definition
ASD(Avg)	A standard n_d average ASD. (See G_m (f) as defined in Appendix B)
ASD(Peak)	Calculated by holding the maximum amplitude of each spectral line over n_d averages. (See G_p (f) as defined in Appendix B)
ASD(Stdv)	Calculated by determining the standard deviation of each spectral line over n averages. (See G_d (f) as defined in Appendix B)
ASD(Sum)	Calculated by adding N_e standard deviations to the average for each spectral line. ASD(Sum) = N_e ASD(Stdv) + ASD(Avg) N_e is a user defined variable typically set to 1. ASD(Sum) is limited by ASD(Peak) and M_e ASD(Avg) where M_e is a user defined variable typically set to 2. (See G_s (f) as defined in Appendix B)
ASD(SpkRmvd)	ASD(Sum) after Frequency Spectral spike Removal.

514.8F -D.III. Spectral Spike Removed Table, Average

	Event	Beta Dist Time	Center Freq	Bandwidth Selected	g-rms	g-rms	g-rms
Project File:	Example Wheeled Vehicle		[ ]
Total Miles:	1000	Block size :	4096	Start Freq: 3		Raw ASD	W-UCol ASD
Date Proc :9/16/2002		Window Type:	Hann	End Frq: 500	N:	1	1
Time Proc :6:37:44 AM		Min g-rms:	0.5	Rmv DC : Y	M:	2	2

					Total G-RMS of removed Spectral spike
Channel					1	2	3
Description					Channel 1	Channel 2	Channel 3
Type					ASD(Avg)	ASD(Avg)\|	ASD(Avg)
Test Time					30	30	30
1 Harmonic	5 mph 2" WB	8.31	3.67	6	0.1534	2.79E-02	5.31E-02
	7.5 mph 2" WB	21.28	5.50	5	0.2691	3.41E-02	0.134565
	10 mph 2" WB	7.47	7.33	7	0.5755	8.74E-02	0.5730498

2 Harmonic	5 mph 2" WB	8.31	7.33	6	0.1118	3.49E-02	7.37E-02
	7.5 mph 2" WB	21.28	11.00	7	8.72E-02	3.22E-02	5.18E-02
	10 mph 2" WB	7.47	14.67	6	8.98E-02	2.67E-02	0.211421

3 Harmonic	5 mph 2" WB	8.31	11.00	6	0.06546	4.01E-02	9.12E-02
	7.5 mph 2" WB	21.28	16.50	9	2.63E-02	2.94E-02	0.05846
	10 mph 2" WB	7.47	22.00	8	3.08E-02	3.75E-02	0.07558

514.8F -D.V. Runtime Calculation

Event No	Event Name	Scenario Time	1 (Min)	2 (Min)	3 (Min)	4 (Min)	5 (Min)	6 (Min)	7 (Min)
1	Radial Washboard 5 MPH	6.62	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
2	Radial Washboard 10 MPH	9.76	1.0839	0.0000	7.5042	1.4266	0.0000	5.0242	0.000
3	Radial Washboard 15 MPH	3.51	44.0730	16.5723	67.7850	42.9182	31.0571	17.1557	33.406
4	Embedded Rock 5 MPH	9.01	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.648
5	Embedded Rock 7.5 MPH	11.04	6.5395	4.8474	4.7421	6.0680	3.1819	0.0000	21.373
6	Embedded Rock 10 MPH	4.74	46.1231	31.9828	10.4189	34.8946	6.6298	0.0000	38.806
7	Belgian Block 5 MPH	1.05	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
8	Belgian Block 10 MPH	3.24	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.000
9	Belgian Block 15 MPH	5.18	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.846
10	Belgian Block 20 MPH	5.02	2.2310	0.5887	0.9003	2.5947	3.1033	0.0000	2.898
11	Belgian Block 25 MPH	1.88	17.4201	4.2217	6.0418	16.9478	14.9296	0.0000	6.81
		TF	117.4706	58.2131	97.3924	104.8499	58.9017	22.1799	104.791
		TFA	60	30	60	30	30	15

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

514.8F -D.VI. Group Sum-Set Definition

ASD(Avg_g)	The weighted average of the ASD group. See Equation D.2-1. (See G_a(f) as defined in Appendix B)
ASD(Peak_g)	Calculated by holding the maximum amplitude of each spectral line over all events.
ASD(Stdv_g)	The weighted standard deviation of the ASD group. See Equation D2.2-3. (See G_e(f) as defined in Appendix B)
ASD(Sum_g)	Calculated by adding N_g standard deviations to the average for each spectral line. ASD(Sum_g) = N_g ASD(Stdv_g) + ASD(Avg_g) Calculated by adding N_g standard deviations to the average for each spectral line. ASD(Sum) = N_g ASD(Stdv) + ASD(Avg) N_g is a user defined variable typically set to 1. ASD(Sum) is limited by ASD(Peak) and M_g ASD(Avg) where M_g is a user defined variable typically set to 2. (See G_f(f)* as defined in Appendix B "for N=1")
ASD(Final)	The ASD(Sum_g) scaled to a user selected final time.

ASD(Avg_g) = ⁿ ∑W_iG_i _i=1

ⁿ ∑W_i _i=1

D.2-1

MIL-STD-810H METHOD 514.8, ANNEX F, APPENDIX D

$ASD(Stdv\_g) = \sqrt{\frac{\sum_{i=1}^{n} W_{i} * [G_{i} - ASD(Avg\_g)]^2}{\sum_{i=1}^{n} W_{i}}}$

D.2-2

514.8F -D.IX. LVTS Combination Example

Freq	LVTS01	LVTS02	Norm Level	LVTS01 New Time	LVTS02 New Time	Total New Time	Final Run Time	LVTS_C
(Hz)	(G²/Hz)	(G²/Hz)	(G²/Hz)	(min)	(min)	(min)	(min)	(G²/Hz)
5	0.100	0.200	0.200	2.23	15.00	17.23	20.00	0.208
6	0.200	0.400	0.400	2.23	15.00	17.23	20.00	0.415
7	0.300	0.400	0.400	10.20	15.00	25.20	20.00	0.459
8	0.400	0.400	0.400	30.00	15.00	45.00	20.00	0.536
9	0.400	0.300	0.300	88.24	15.00	103.23	20.00	0.501

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MIL-STD-810H

METHOD 514.8, ANNEX F, APPENDIX D

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