527.2-55 analysis of results

527.2-5.1 Reference SDM Development

As stated in paragraph 4.5, a SDM in terms of the desired rigid body modes to be tested should be computed for each test configuration identified in the mission scenario.

5.1.1 SDM Ensemble CSD Characteristics

Based on the characteristics of the CSD terms of the ensemble of SDMs, the VSD process will yield a vibration specification consistent with one of the three cases that follow:

• a. Case 1. Coherence Terms Approaching Zero (Independent Motion DOFs) – This is the easiest situation to deal with in that each motion DOF ASD may be addressed individually via the same techniques employed in 1-DOF VSD as discussed in reference number 3. When programming the vibration control system, it is recommended that coherence be set to a low non-zero level (i.e. $\gamma^{2}=0.1$ ) over the test bandwidth of interest. For such a small coherence, the phase parameter is essentially a random variable and establishing a phase specification is not required.

A special situation that may lead an analyst to develop a MDOF vibration specification with independent motion DOFs, would be a composite specification that encompasses multiple vehicles (i.e. a composite wheeled vehicle specifications comparable to those in MIL-STD-810H, Method 514.8). As each vehicle will tend to have its own CSD characteristics, it is not possible to define CSD terms such that a single coherence and phase relationship addresses each vehicle. Enveloping techniques that work well in addressing magnitude based ASD terms are simply not applicable in addressing phase relationships between mechanical DOFs.

• b. Case 2.Non-Zero Coherence across a Portion of the Test Bandwidth – When developing a MDOF vibration specification based on a single platform, one would expect the CSD terms measured across the range of scenarios addressed in the mission scenario to be similar in nature. The dynamic characteristics of the structure and often the proximity of the measurement transducers will greatly influence the CSD characteristics. There are often situations in which coherence between motion DOFs are high and phase is well defined, but only over a portion of the test spectrum. This is a common observation on many wheeled vehicles where coherence is high at lower frequencies (i.e. frequencies below 50 Hertz (Hz) and near zero at higher frequencies. In such scenarios, one would only establish coherence and phase specifications for the portion of the spectrum with high coherence. The remainder of the spectrum would be treated as in Case 1. Also, in establishing CSD reference criteria, the analyst must ensure the resulting criteria is physically realizable (refer to paragraph 4.5.3 for additional detail).
• c. Case 3. Non-Zero Coherence across the Full Test Bandwidth – This scenario is comparable to Case 2 with coherence being defined across the entire test bandwidth. It is anticipated that this would be the least likely scenario in a MDOF VSD effort. However, it is also the configuration that will be the most difficult to deal with from both a VSD development aspect and from an implementation perspective. In addition to the issue of ensuring the resulting SDM reference is physically realizable, the classic problem of mechanical impedance mismatch between field and laboratory are often major concerns in implementing a fully defined SDM reference criterion for a laboratory test. Specifically, if the mechanical impedance between field and laboratory are not very well matched (and they usually are not), there may be portions of the spectrum in which coherence may be significantly different than specified and simply not controllable. While this situation is also possible in Case 2, it is almost certain to be an issue in a scenario such as Case 3, in which the entire test bandwidth has a CSD reference criteria. This topic of uncontrollable coherence associated with mechanical impedance mismatches is a control issue for all three Cases and is discussed further in the minimum drive consideration of paragraph 4.5.6.
• d. Regardless of which of the three cases the SDM is characterized by, it is highly likely that there will be mechanical impedance differences between the field and laboratory conditions. In some cases these impedance differences may result in excessive drive signals. Although the various control system vendors

MIL-STD-810H METHOD

527.2-5.2 Test Tolerance Recommendations

Setting tolerances for a MIMO test is challenging given the large amount of information encompassed by the reference autospectra and cross spectra involved. Additionally, the overall energy is not necessarily distributed evenly about each mechanical DOF and dominant DOFs often tend to dominate the control. The objective here is to establish a reasonable starting point in establishing test tolerances. Experience with specific test configurations may be employed to refine the basic guidance defined below. As usual, any test specific test tolerances should be clearly documented within the test plan.

• a. Autospectra ${ }^{(1)}: \pm 3 \mathrm{~dB}$ for $f \leq 500 H z$ and $\pm 6 \mathrm{~dB}$ for $f>500 H z$.

(1)The portion of the spectrum that actually reaches the maximum tolerance limits is anticipated in narrow bandwidths. The tolerance on the overall Grms level of each controlled DOF shall be within ±15% of the corresponding reference.

• b. Cross spectra: Define tolerances in terms of Phase and Coherence. Note that there will be a statistical variation of coherence and phase estimates as a function of the statistical DOFs used to estimate the control SDM and also as a function of the coherence between inputs. Take caution in that the expected statistical variation imposes a lower limit on how tight the respective tolerance can be. The coherence and phase guidance given below should be used in the absence of tolerances determined from field environments and necessary margin needed to account for laboratory and in-field service mechanical impedance mismatches. Note that there may be scenarios in which coherence and phase tolerances need not be defined for the entire test bandwidth.19
• (1) Coherence: For ordinary coherence in the range $0.5 \leq \gamma^{2}<1.0$, set the tolerance to be $\pm 0.1$ (avoid establishing a coherence reference or tolerance of 1.0).
• (2) Phase: If $\gamma^{2}<0.5$, any phase is acceptable. If $0.5 \leq \gamma^{2}<1.0$ and the frequency $f$ is within the band $f_{h} \pm 3 \Delta f$ where $f_{h}$ is a frequency where the reference rate of phase change is more than $10^{\circ} / \mathrm{Hz}$ and $\Delta f$ is the line spacing of the reference spectra, the default tolerance on phase will be $\pm 40^{\circ}$. Otherwise, if outside of a frequency band referenced with such high rates phase change, the default tolerance on phase will be $\pm 10^{\circ}$.
• c. Limiting: See paragraph 4.5.4.

527.2-5.3 Laboratory Data

In the case the reference SDM is directly employed as the reference in a MET test (i.e. input/output (I/O) Transformation Control as discussed in reference number 9), and rigid body presumptions are sound, the control accelerometers are not required to be placed in the exact same location in the laboratory as they were used in the original acquisition phase. The critical parameter is that all control locations employed in the laboratory test are referenced to the same “origin” as selected in the original VSD development. However, it is often desirable, based on making position specific comparisons between field and laboratory data, to match the laboratory control locations to the original measurement points.