MIL STD 810 G – Test Method 525 – Time Waveform Replication
NOTE: Tailoring is required. Select methods procedures and parameter levels based on the tailoring process described in Part One, paragraph 4.2.2, and Annex C. Apply the general guidelines for laboratory test methods described in Part One, paragraph 5 of this standard.
Replication of a time trace under Time Waveform Replication (TWR) methodology in the laboratory is performed to:
Provide a degree of confidence that the materiel can structurally and functionally withstand the measured or analytically specified test time trace(s) to which the materiel is likely to be exposed in the operational field environment.
Experimentally estimate the materiel’s fragility level in relation to form, level, duration, or repeated application of the test time trace(s).
Time waveform replication
This test method discusses TWR from a single-exciter/single-axis (SESA) perspective. Although much of the philosophy and terminology in TWR testing is common between SESA, multiple-exciter/single-axis (MESA), and, multiple-exciter/multiple-axis (MEMA), this method will be limited to SESA testing. Multiple-exciter TWR applications are addressed in Method 527. This method provides guidelines for developing test tolerance criteria for single axis TWR testing. Annex A addresses SESA TWR testing by illustration. Annex B provides an overview of post-test analysis tools useful for TWR, in order to verify test tolerance compliance.
Standard signal processing terms such as single-input/single-output (SISO) and two-input/single output are used in the analysis presented in Annex A and Annex B of this method (paragraph 6.1, reference a).
SESA Time Waveform Replication
SESA TWR consists of the replication of either measured or analytically specified time trace(s) in the laboratory with a single exciter in a single direction, and is performed to accurately preserve the spectral and temporal characteristics of the environment. Without loss of generality in the discussion to follow, application of Method 525 will consist of a single time trace. Method 525, SESA TWR, is founded upon the “Deterministic/Probabilistic” framework of random process theory. An analytically specified time trace is assumed to be fully deterministic in nature with no relationship to a probabilistic framework, i.e., a chance of occurrence. A single measured time trace within a probabilistic framework is assumed to be a sample realization from an ensemble of possible time traces generated by an experiment that is replicated a number of times under identical conditions. For a single measured time trace, it is optimal to assume that the measured time trace represents the random process ensemble mean determined by averaging over an ensemble of records at each time increment, and has a confidence coefficient of 0.50. For more than one measured time trace captured under identical experimental conditions, it may be possible to create a time trace ensemble for which averaging over the ensemble members for each sample time increment yields valid estimates of the statistical moments for the unknown stochastic process underlying the time trace generation. This general deterministic/probabilistic philosophy for SESA TWR has important implications for time trace scaling considerations. Method 525 replicating a single time trace is generally transparent to the distinction between a deterministic and a stochastic time trace.
Until recently, the replication of time traces representing measured samples of field environments varying in time and even frequency, or a combination of both time/frequency variations, was not possible using commonly available exciter control system software. The advent of more powerful data processing hardware/software, and the implementation of advanced control strategies, has led to exciter control system hardware and software that permit convenient replication of extended time-varying test environments on a single exciter in a single direction in the laboratory. TWR test methodology strongly reflects the concept of “test tailoring.”
The general term “time trace” is employed throughout this method in an attempt to capture all of the possibilities of TWR applied in the replication of field measured (stochastic) or analytically specified (deterministic) environments in the laboratory. The following six forms of time trace are potential candidates for TWR testing.
Stationary random Gaussian time trace with arbitrary ASD of arbitrary duration;
Stationary random non-Gaussian time trace (for certain forms of non-Gaussian distribution, e.g., local skewness and high kurtosis) with specified ASD of arbitrary duration;
Short duration shock time trace;
Non-stationary time trace that has a time-varying amplitude, time-varying frequency or both of an intermediate duration (longer than a typical shock time trace);
Non-stationary/stationary time trace that is repetitive at fixed period (e.g., gunfire shock);
Non-linear form time trace.
For general application, the time trace to be replicated under TWR is of a substantially shorter duration than stationary random environments, and of a longer duration than mechanical shocks. A TWR time trace may be composed of any combination of form specified in 1.2.3a. through f above.
General considerations and terminology
For purposes of discussion to follow, a single measured time trace is a function of finite duration having a uniform time sample increment and varying amplitude that is provided in digital form. For convenience, the single time trace under consideration is taken as acceleration, but the principles below apply equally well to other time trace representations such as velocity, displacement, force, motion rate, etc.
It is assumed that for any measured physical phenomenon, the measurement can be repeated an indefinite number of times under the exact same conditions limited only by measurement resources, i.e., the underlying random process has an ensemble representation generally unknown. In the discussion to follow, reference to a measured time trace ensemble related to an underlying random process will assume the following:
Measured time traces are from a single physical phenomenon and have a joint correlation structure. This basically assumes uniform and identical sample rate for all time traces and common beginning and end points.
The underlying random process has a deterministic component (or “signal”) that can be estimated by the time-varying mean of the ensemble
The underlying random process has a random component (or “noise”) that can be estimated by a time-varying standard deviation of the ensemble
If the measured time trace ensemble has only one member then this member will assume to be the underlying random process deterministic component or mean with a confidence coefficient of 0.5, i.e., this sample time trace has a 0.5 probability of being greater or less than the true underlying random process mean at each time increment.
NOTE: This is not strictly correct because time traces have serial correlation information that essentially correlates the time trace from one time increment to the next time increment and, thus, the confidence coefficient may vary depending upon the degree of serial correlation.
Time-varying time trace – Physical phenomenon
A time-varying trace captured in measurement signals is caused by the time-varying phenomenon that is being measured. In general, the time-varying characteristics of the environment (excluding shock) are longer than the lowest resonant frequency characteristics of the materiel under test. In particular, a time-varying trace may range from three seconds to several hundred seconds.
General TWR test philosophy with regard to time trace simulation (and scaling)
As emphasized in paragraph 1.2.4, time trace scaling to enhance conservativeness of laboratory testing is generally outside the scope of this method. Figure 525-2 defines simulation possibilities within TWR including time trace scale rationale assumed to be provided external to this method.
Two terms important to understanding TWR simulation will be introduced. The first term, intrinsic statistics, refers to the time-varying statistical estimates available from a single measured time trace (generally from short-time estimates). A single time trace has a confidence coefficient of 0.50, and the time-varying statistical estimates provide no information relative to the underlying ensemble-based random process, except for an estimate of the mean of the underlying random process. The second term, extrinsic statistics, refers to the time-varying statistical estimates available from more than one measured time trace that form a sample time trace ensemble. In this case, not only is an estimate of the underlying random process mean available, but also an estimate of its variance on a time increment basis. For comprehensive LCEP directed TWR materiel testing specifying analytical time traces through simulation, knowledge of the extrinsic statistics is essential. In general, specifying analytical time traces through simulation based upon intrinsic statistics is very limited, and usually unreliable for testing to the underlying random process (Method 519.6 Annex B discusses this further). Conversely, if a very small measured time trace sample ensemble is available, estimates of the underlying random process parameters tend to have large errors providing for an unreliable simulation. In this latter case, a more optimum test scenario is provided by replication of each of the individual measured time traces in a pre-defined sequence. A useful way to view intrinsic versus extrinsic statistics is to envision a One-Way Analysis of Variance, whereby the intrinsic statistics correspond to the “error within,” and the extrinsic statistics correspond to the “error among.”
This method addresses very general time-varying traces not necessarily identifiable with underlying stationary or nonstationary random processes. It is apparent from various vendor TWR hardware/software configurations that the only requirement for application of Method 525 is the bandlimited character of the time trace for replication, and its compatibility with the bandlimited characteristics of the device (exciter) to be driven with the TWR hardware/software. For example, measured time traces that vary in frequency can be replicated as long as the time trace bandwidth is limited to overall bandwidth of the exciter control system. Non-Gaussian time traces can be replicated under TWR. All measured time traces can be replicated under TWR, provided they are within the band limit capabilities of the exciter control system to which they are applied for testing purposes.
This method does not address very long (several hour) time traces that can be termed stationary in nature (Gaussian or non-Gaussian). It is possible to repeat a given time trace multiple times; however, variations associated with actual experiment repetitions in the field will not be captured. It is important to note that given a single stationary Gaussian or non-Gaussian time trace of sufficient length it is possible to (1) divide this time trace into multiple time trace segments at zero crossings (required close to zero mean for each segment) and (2) randomly place these segments into a permuted order to generate multiple time traces of sufficient length but essentially “stochastically independent” of one another. This can be particularly attractive for measured stationary non-Gaussian environments where the non-Gaussian “exact moment structure” must be preserved over long periods of time. The alternative to this is precise modeling of the measurement time trace and subsequent stochastic generation of unlimited segments for TWR input.
This method does not address the advantages and disadvantages of replicating very short duration time traces (shocks) over and above application of Method 516.6.
This method does not explicitly address time traces that have highly variable frequency characteristics in time.
This method does not explicitly address time traces that are nonlinear in nature.
This method does not explicitly address repeated environments that may be of a nonstationary nature because of the occurrence pattern of the environment. For example, no discussion is provided on occurrence statistics that may be modeled in terms of a nonstationary (rate-varying) Poisson process.
This method generally does not address the characteristics of the time trace on the materiel in terms of materiel “rise-time” response.
Procedure I – SESA Replication of a Field Measured Materiel Time Trace Input/Response
Step 1. Following the guidance of paragraph 6.1, reference b, select the test conditions and mount the test item (or dynamic simulant item) on the vibration exciter. Select accelerometers and analysis techniques that meet the criteria outlined in paragraph 6.1, reference b.
Step 2. If required; perform an operational check on the test item at standard ambient conditions. If the test item operates satisfactorily, proceed to Step 3. If not, resolve the problems and repeat this step.
Step 3. Subject the test item (or dynamic simulant) to the system identification process that determines the compensated exciter drive voltage. This may include a careful look at the component parts of the reference time trace, i.e., stationary vibration, shock, transient vibration; and determination of the potential time variant properties of the compensating function. If a dynamic simulant is used, then replace the dynamic simulant with the test item after compensation.
Step 4. Subject the test item in its operational configuration to the compensated waveform. It is often desirable to make an initial run at less than full level to ensure proper dynamic response and validate instrumentation functionality.
Step 5. Record necessary data, paying particular attention to the vendor software supplied test error indicator and, in general, the control acceleration time trace that can be post processed to demonstrate tolerance satisfaction.
Step 6. Perform an operational check on the test item and record the performance data as required. If failure is noted, follow the guidance in paragraph 4.3.2.
Step 7. Repeat Steps 4, 5, and 6 for the number of replications called out in the requirements document, or a minimum of three times for statistical confidence provided the integrity of the test configuration is preserved during the test.
Step 8. Document the test series including the saving of all control and monitor digital time traces, and see paragraph 5 for analysis of results.
Procedure II – SESA Replication of an Analytically Specified Materiel Time Trace Input/Response
Follow the guidance provided in Steps 1-8 in Paragraph 220.127.116.11 subsequent to scaling the reference time trace per the scaling guidance provided in paragraph 1.2.6.
NOTE: Tailoring is essential. Please, ask to your confidence laboratory for further details about tailoring of test methods.