525.2-2 GENERAL PHILOSOPHY FOR TWR TESTING
Broadband TWR, i.e., from 5 Hz to 2000+ Hz, is relatively new to dynamic laboratory testing with electrodynamic force exciters. The same comment applies to electrohydraulic force exciters only over a more limited bandwidth. The philosophy for TWR testing, including test tolerance development, is still evolving. The post-test analysis rationale displayed below will doubtlessly be augmented/refined/enhanced with portions eliminated, however fundamentals behind the analysis rationale will remain.
The general term "replication error" will be used with regard to the comparison of the difference between the control and reference time traces. SESA post-test analysis quantitatively compares the deterministic test input reference time trace, (or sampled sequence for ), symbolic " ," with the stochastic test output control time trace, (or sampled sequence for ), symbolic " ." For comparison, it is convenient to have available a stochastic difference time trace defined as:
(or sampled sequence ), symbolic "s."
The difference time trace represents the “replication error.” The reference and control time traces are assumed to be perfectly correlated in time so that the difference time trace is valid, and generally vendor software is very reliable in supplying reference and control digital time traces that are perfectly correlated. A time/amplitude point-by-time/amplitude point (TPP) assessment of the time traces can be made, and an estimate of replication error determined. Annex B addresses in more detail the statistical implications of TPP. Generally, vendors will make available a drive voltage time trace for potential use in understanding the test limitations, i.e., fixture resonance compensation, impedance mismatch, etc. This time trace must be preprocessed in the same manner as , and . The drive time trace is of no concern in the illustration to follow. Discussion appears in both this Annex and Annex B concerning time/amplitude average-by-time/amplitude average (STA) assessment for tolerance limit analysis – an alternative to TPP. Application of these procedures for tolerance error assessment will be mentioned in this Annex and in Annex B. Generally, direct comparison of time average estimates of and is much less desirable than either examining statistics on or statistics on a time averaged version of . Interpretation of differences between time average estimates is more difficult.
525.2-2 TERMINOLOGY
In this Annex replication error assessment or equivalently test tolerance assessment refers to examining the properties of the difference (as a function of time) between the TWR” input” and the TWR “output”. TWR “test specification” refers to using the results of the error assessment to determine if the laboratory TWR test replicated the “input” satisfactorily i.e., if “test tolerances” common to other Methods are satisfied for TWR. For Method 525 there are potentially five categories related to test specification.
In this paragraph, the continuous analog time traces are represented by lower case letter as a function of time, t. The upper case associated letters represent the random variables obtained by sampling the properly signal conditioned analog time traces. The TWR reference time trace, r(t), is considered to be band limited and deterministic in nature. It is specified in an ASCII file with required oversampling for replication. The TWR control time trace, c(t), is stochastic as a function of the test configuration including compensation strategy and system noise. The difference
MIL-STD-810H
METHOD 525.2 ANNEX B
between the control and reference time traces, s(t), is stochastic in nature and is the primary time trace to be used in
the TWR error assessment and tolerance specification.
For R deterministic and S and C stochastic variables and a physical correspondence between r(t) and c(t), i.e., c(t) output resulting from TWR then define
- (1) R associated with (t) as R={r[n],n=1,2,..., N}
- (2) C associated with c(t) as C = {c[n],n=1,2,..., N} and
- (3) S associated with s(t)=c(t)-r(t) S={s[n]=c[n]-r[n],n=1,2,3,..., N}
If the two continuous time traces r(t) and c(t) are identical according to “time-point by time-point” (TPP), then the
time trace represented by the reference time trace has been replicated exactly in the laboratory. Generally the reference and control time traces are not TPP identical and “statistics” must be introduced to quantify s(t). Stochastic S has no preconceived theoretical probability distribution function (in fact s(t) or S provides an “optimum” estimate for error assessment in the sense that the statistics of gross averages are of lesser importance in error assessment. As has been demonstrated in Annex A, S is generally neither Gaussian distributed nor stationary. Once S has been determined and parameters of R known, R and C will play a lesser role for tolerance assessment except for Category III and Category IV specification in paragraph 4.
2.1 Selecting the TWR Method
After examining requirements documents and applying the tailoring process in Part One of this Standard to determine where significant time-varying effects are foreseen in the life cycle of the materiel, use the following to confirm the need for this Method and to place it in sequence with other methods.
2.1.1 Effects of Transition To Time Trace TWR
Method 525.2 is broadly consistent with the philosophy of test tailoring. A substantial high amplitude field measured time trace has the potential for producing adverse effects on all electronic materiel. The potential for adverse effects may be related to transition time and duration of the time trace. When transition to the time trace and time variation characteristics in the time trace is short, “rise times” in materiel response may be adequate to cause degradation in performance. When duration of the time trace is substantial in comparison to the transition times, the effects to materiel, e.g., low cycle fatigue, may also be substantial. In performing a TWR test, it is desirable that the onset/termination of the significant environment be consistent with the onset/termination of the environment anticipated in the field.
2.1.2 Sequence Among Other Methods
- a. General. Use the anticipated life cycle sequence of events as a general sequence guide (see Part One, paragraph 5.5).
- b. Unique to this Method. Generally, significant time-varying traces may occur at any time during the life cycle of the materiel, and are usually interspersed among stationary random and shock environments that are covered under guidance provided in Methods 514.8 and 516.8, respectively.
2.2 Selecting a Procedure
This Method includes two basic test procedures:
- a. Procedure I: The SESA replication of a field measured materiel time trace input/response.
- b. Procedure II: The SESA replication of an analytically specified materiel time trace input/response.
Based on the test data requirements, determine which test procedure is applicable. In particular, determine if there exists a carefully measured and properly processed field measured time trace, or if there is a generated, uniformly sampled band-limited analytical time trace. Determine if the time trace can be placed in an ASCII data file for archive and replication. If there are field measured or analytically specified environmental time traces for a materiel component, determine if the time trace(s) has an extended form over the entire materiel, i.e., determine the extent of spatial correlation.
2.3 Determine Test Levels and Conditions
For TWR replication of measured time traces in the laboratory, the test levels are fully specified by the field measured time traces. If several field measured time traces are available, generally, the tester will want to make up a single ASCII file consisting of several “events” appropriately spaced in time. In general, for this Method, Procedure I, it is not recommended that any factor, constant or otherwise, be applied to “enhance” the measured time trace for testing (for reasons discussed in paragraph 1.2.6). For this Method, Procedure II, any scaling must be consistent with information in paragraph 1.2.6 and, generally, the scaling must not be ad hoc in nature. It is not recommended that
time traces that exceed the capacity of the vibration exciter be scaled down by gain, e.g., run at –3 dB. For pretest exciter control system compensation, i.e., establishing the exciter system transfer function, the time trace may be applied at lower levels to either the test item or to a dynamically similar surrogate. Identify the test conditions, particularly with respect to temperature. Exercise extreme care in consideration of the details in the tailoring process. Base the test level and condition selections on the requirements documents, the Life Cycle Environmental Profile, and information provided within this procedure.
2.3.1 General Considerations
As has been mentioned in paragraph 1.2, statistical estimates defining the behavior of a non-stationary random process can only be made on ensembles of time traces from the non-stationary process. Typically, only one sample time trace from an ensemble of an unknown non-stationary random process is available. It is absolutely essential that the test time trace be fully documented such that transfer of an ASCII file of the test time trace can be made to other laboratories for application or testing, and be repeated in the future. Information on the location of measurement transducers and general test configuration must accompany the test time trace. Any such analytical description can be tied directly to comparison between the time trace input to the exciter control system (reference time trace) and the test output as recorded by the exciter control system (control time trace). To clarify the terminology standard, the “reference time trace” is merely the ASCII representation of the time trace for the laboratory test. The “control time trace” is the ASCII digital file created by the exciter control system representing the “result” of the test. This control time trace is created by converting an analog voltage signal from a measurement device, e.g., an accelerometer mounted on the test item or test item interface at the location that the reference time trace is to be replicated, to a digital form by a signal conditioned analog-to-digital device. It is referred to as a “control” time trace because it is in the comparison of the reference time trace to the control time trace that the analog input to the exciter device is compensated in order to reproduce the reference time trace. The “control” time trace represents the “best fit” of the output of the exciter control system parameters through compensation to the desired input reference time trace. Annex A provides the details of a typical time reference/control comparison. A successful test under TWR is defined as a test, whereby the control time trace compares to the reference time trace within the tolerance limits specified for the test. The tolerance limits may be specified in the time domain, the frequency domain or a combination of the two. Annex B provides the basis for developing meaningful tolerance limits under SESA TWR. Rudimentary tolerance limits are provided within most vendor supplied TWR software for purposes of “controlling,” i.e., appropriately compensating the system prior to test but, in general, the test laboratory will want to establish and implement some well-defined analytical procedures for comparing the control time trace ASCII file with the reference time trace ASCII file. Annexes A and B provide guidance in this area.
The test item may be instrumented at other locations than at the point of “control.” The other measurements made during testing are referred to as monitoring measurements. Such measurements may be useful for purposes such as analytical modeling of the materiel, or just monitoring materiel response dynamic characteristics, and will not be discussed further here. For SESA exciter laboratory testing, the TWR software allows only single measurement comparison and monitoring for signal compensation “control” purposes.
For the TWR procedure, subject the test item to a sufficient number of suitable time trace events to meet the specified test conditions. Generally, the number of times the test item is subject to a given time trace event is determined from the materiel’s life cycle profile in much the same way the duration for stationary random vibration is determined or the number of shock applications for shock is determined. In any case, subject the test item to no fewer than three time trace events for establishing confidence in the materiel’s integrity under test if specific information from the materiel’s life cycle profile is not available.
2.4 Test Item Operation
Whenever practical, ensure the test item is active and operating during TWR testing. Monitor and record achieved performance correlated in time with the test time trace. Obtain as much data as possible that define the sensitivity of the materiel to the time trace environment. Where tests are conducted to determine operational capability while exposed to the environment, operate the test item. In other cases, operate the item where practical. Operation during transportation will not be possible in almost all cases. Also, there are cases where the operational configuration varies with mission phase, or where operation at high time trace levels may not be required, and may be likely to result in damage.
MIL-STD-810H
METHOD 525.2