516.8-33 information required

516.8-3 EXAMPLE

516.8-3.1 Introduction

In Annex A paragraph 1.3 of this method, the simple shock time segment for the instrumentation noise floor, the shock and the post shock noise floor are identified. In addition $T_{e}$ and $T_{E}$ are specified. Since the SRS is the primary analysis descriptor, both maximax acceleration and maximax pseudo-velocity estimates of the segments are displayed and interpreted. For verification purposes, the shock maximax positive and negative SRS estimates are displayed. Comparability of these estimates showed no signs of the shock being invalid. In this paragraph the following analysis will be undertaken providing (1) additional analysis of the shock, and (2) additional information regarding the validity of the shock. In particular:

• a. The time history instantaneous root-mean-square.
• b. The shock velocity and displacement displayed.
• c. The time history ESD estimate displayed.

Annex A paragraphs 1.7-1.8 of this Method reference more advanced processing that is applicable to a single simple shock or useful in summarizing the information in an ensemble of shocks. No such advanced processing is provided in this Method.

516.8-3.1 Input Test Data Set

Table 516.8C-II represents a homogeneous table of normally distributed numbers of unity variance around a mean value of 3.5 with N=14 rows and M-5 columns (rows could represent fourteen individual test measurements and columns could represent test values over five data sets). Table 516.8C-II is used in the upper limit determinations in paragraphs 3.2 and 3.3 below.

MIL-STD-810H METHOD

516.8-3.2 Instantaneous Root-Mean-Square (RMS)

The "instantaneous rms" provides useful information that may not be apparent from examining the amplitude time history. In order to establish shock time intervals for processing, it is useful to consider the “instantaneous rms" of a measurement level. For the measurement $a(t)$ $0\leq t\leq T$, the instantaneous rms level is defined over the same interval

as follows: $a_{inms}(t)=\sqrt{a^{2}(t)}\geq0$ for $0\leq t\leq T$, where “irms" stands for “instantaneous root-mean-square level". It is assumed that any DC offset in a digitized measurement signal, $a(t)$, has been removed prior to computing $a_{ims}$. Figure 516.8B-3 displays the irms in absolute terms and in dB. In the dB display, no negative values are displayed. Observe that $a_{irwus}$ is computed point by point. Therefore, $\left|A_{pk}\right|$ as referenced in paragraph 1.3 in Annex A of this method, will be the maximum computed $a_{inus}$.

From the example of Figure 516.8B-3, it is clear that the "signal" approaches 40 dB, while the "noise floor" is on the order of 3 dB, roughly a signal-to-noise ratio of 37 dB. Relative to identifying the time of the beginning of the post- shock noise floor, Tpost, it is a matter for an experienced analyst in concert with the objectives of the shock assessment. Almost assuredly, post-shock instantaneous rms is greater than the pre-shock instantaneous rms, i.e., airms (post)>aims (t) for t≤pre since the measurement seldom returns to the measurement system noise floor levels because of change of boundary conditions as a result of the shock. If there is indication of periodic behavior in the time trace for t>Tpk, the analyst must decide if analysis over this periodic "ringing" behavior is important for the shock specification. For SRS shock synthesis, it will be difficult to capture such periodic behavior and duplicate it in testing. For waveform replication, this periodic "ringing" behavior should be retained over a minimum of ten cycles if possible. For establishing the end of the range of T for a simple "well-behaved," i.e., sharply decaying shocks, it is recommended that the analyst examine times t at which arms (t) for t> Tpk is at least 20dB (preferably 40 dB) below as (TP), and based upon judgment, select the zero-crossing for defining the end of beginning of T (or beginning of Tpost). Generally, criteria for defining and automatically determining Tpost are left to the discretion of the analyst, and selection of post is much more inconsequential in analysis than selection of T pre. An estimate of the measurement system noise floor level will be useful in establishing Tpost. If arbitrary specification of a (t) levels is not feasible, then a relatively robust way of specifying the end of a shock and the beginning of the post-shock noise floor is to begin at the end of the measured data, T, and compute the mean rms signal level until a noticeable change in level is apparent. This can be accomplished by selecting an averaging time, e.g., ~5 percent of the estimated duration of the shock, and computing a moving average of time history values in the measurement system noise floor and post-shock noise floor, where the average is shifted at least ten times within an averaging time window and ideally

MIL-STD-810H METHOD

516.8-3.2 Parametric Upper Limits

The upper normal one-sided tolerance limit (NTL) is computed as 95/50 limit with 50 percent confidence that at least 95 percent of the values will lie below this limit for kN, B. y = 1.68 from Table 516.8C-I. The upper normal prediction limit (NPL) is computed with a 95 confidence coefficient at the 95 percent point of the distribution where tN-1;α = t13:005 1.771. Figure 516.8C-1 displays the data, and Figure 516.8C-2 displays the two parametric upper limits.

NOTE: The degree of conservativeness in the normal prediction upper limit over the normal tolerance limit.

Figure description:

Figure 516.8C-1. Input test data set.

Figure description:

Legend

• NPL — color: black; symbol: Dashed line
• NIL — color: black; symbol: Solid line
• ENV/DFL — color: black; symbol: Dotted line
• ETL — color: black; symbol: Dash-dot line

Figure 516.8C-2. Parametric and non-parametric upper limits.

MIL-STD-810H METHOD

516.8-3.3 Shock Velocity/Displacement Validation Criteria

Two steps are necessary for examining an unprocessed acceleration time history for purposes of validation.

• a. The first step is to clearly define the bandwidth of the measurement time history. The signal conditioning configuration and the ESD estimate to be discussed in paragraph 3.4 (below) will be helpful. The time history bandwidth will determine if TWR is a laboratory test option.
• b. The second step relates to integration of the time history to see if the velocity and displacement make physical sense. Velocity can usually be determined from direct integration of the shock acceleration after the shock has had its mean removed (velocity begins at zero and ends at zero), or has been high pass filtered to remove any DC component and other very low frequency information. Subsequent removal of the velocity mean or DC information in the velocity allows integration of the velocity to get displacement. As a minimum requirement, shock acceleration time traces should be integrated to provide velocity, and the velocity should have a clear physical interpretation, e.g., oscillatory behavior and near zero velocity at the "beginning" and the "end" of the shock. Velocity tends to be quite sensitive to sensor or signal conditioning anomalies that invalidate measurements. Integration of the velocity to obtain displacement should be considered an extended requirement, and reasonable values for displacement should be apparent. The form of velocity (or displacement) with respect to oscillatory behavior needs to be examined for reasonableness. That is, a form of velocity that displays little oscillatory behavior should be suspect. Figure 516.8B-4 displays velocity computed via mean removal alone. Figure 516.8B-5 displays the results of integrating velocity to arrive at displacement. For displacement, "DC" removal was performed on the velocity time history. Examination of both these plots, knowing the physical nature of the test, shows (1) reasonableness of peak amplitudes, and range from positive to negative values, (2) distinct and substantial oscillatory behavior during the "shock," and (3) characteristic pre- and post- shock noise floor behavior. It would appear that the bandlimited measurement does not have readily identifiable anomalies, and the acceleration time trace can be considered valid for further processing that is designed to either support or refute this validation.

Figure description:

Mechanical Shock Velocity (6000 Hz Bandwidth

Mechanical Shock Velocity (6000 Hz Bandwidth

Annotations

• Start of shock (vertical_line - position: Time (sec ≈ 0.62))
• Boundary 1 (vertical_line - position: Time (sec ≈ 0.78))
• End of shock (vertical_line - position: Time (sec ≈ 1.55))
• Boundary 2 (vertical_line - position: Time (sec ≈ 2.18))

Figure 516.8B-4. Measurement velocity via integration of mean (DC) removed acceleration.

MIL-STD-810H

METHOD 516.8 ANNEX B

Figure description:

Mechanical Shock Displacement (6000 Hz Bandwidth

Mechanical Shock Displacement (6000 Hz Bandwidth

Annotations

• Event start marker (vertical_line - position: x ≈ 0.63)
• Transient transition marker (vertical_line - position: x ≈ 0.78)
• Decay start marker (vertical_line - position: x ≈ 1.56)
• Event end marker (vertical_line - position: x ≈ 2.18)

Figure 516.8B-5. Measurement displacement via integration of velocity after mean (DC) removal.

At this point in the analysis, if the velocity and displacement validation checks, particularly the velocity validation check, do not seem to correspond with the physics of the test, a detailed investigation of the reason for this discrepancy must be instigated. For example, velocities that are not physically realizable call for such an investigation. For one of a kind and expensive tests, it may be possible to recover meaningful data based upon advanced processing techniques.

516.8-3.3 Non-parametric Upper Limits

The envelope limit (ENV) along with the upper distribution-free tolerance limit (DFL) for β proportion of the population set at 0.95 and γ confidence coefficient of 0.51 for N=14 samples is displayed in Figure 516.8C-2. This represents one curve with two interpretations. The 95 percent upper empirical tolerance limit (ETL) is also displayed on Figure 516.8C-2 where at least 95 percent of the values will be exceeded by this limit with 50 percent confidence. The data are displayed on Figure 516.8C-2 for comparison purposes.

MIL-STD-810H METHOD

516.8-3.4 Observations

The “flatness” of the upper limits on Figure 516.8C-2 attests to the homogeneity of the data in Table 516.8C-II. It is apparent from Figure 516.8C-2 that the upper limits for the parameters selected are not “statistically equivalent.” Of the two upper limit estimates, the NTL is favored if it can be established that the logarithm transform of the data set is approximately normally distributed. The closeness of the nonparametric envelopes attests also to the homogeneity of the data in Table 516.8C-II in addition to demonstrating, for this case at least, the non-statistical ENV, the statistically based DFL and the ETL basically agree with regard to the upper limit magnitude. For non-homogeneous data sets ETL would not be expected to agree with ENV or DFL. For small data sets, ETL may vary depending upon if parameter k rounds upward or downward.