| Road Classification | Speed (mph) | Time (hrs) | Distance (miles) |
|---|---|---|---|
| Embedded Rock | 5 | .690 | 3.45 |
| 10 | 1.545 | 15.45 | |
| 15 | .737 | 11.05 | |
| Cross Country | 10 | 5.18 | 51.80 |
| 20 | 6.332 | 126.64 | |
| 30 | 2.002 | 60.06 | |
| Radial Washboard | 5 | .811 | 4.055 |
| 7 | 1.841 | 12.88 | |
| 10 | 1.183 | 11.83 |
- (5) Per Step 5, the SDMs were configured into a convenient structure to allow statistical analysis. The data were configured as SDM_all=[SDM_Run1,SDM_Run2 SDM_Run8]. Observe only 8 of the 9 runs identified in the scenario are being considered. In reviewing the field data, the 5 mph radial washboard data were significantly lower than the rest of the Runs, determined to have no effect on fatigue, and were not considered in computing the basic statistics of the ensemble.
- (6) Next, per Step 6, a weighted average in terms of the time per road condition as defined in Table 1 was computed. This average should be computed in terms of complex CSD terms, not the normalized SDM. The resulting weighted average SDM was then tested at each spectral line to establish whether or not the positive definite criterion was met. Figure 5 illustrates the weighted average SDM. Taking advantage of the Hermitian property of a SDM, Figure 5 is laid out such that the lower triangular section represents the phase between DOFs, the upper triangular portion represents the square root of the ordinary coherence, and the diagonal terms are the ASDs of the 6 rigid body DOFs. Although too small to review in detail on a single page as shown, the coherence plots are all scaled between 0.1 and 1.0. This is to illustrate there is some level of coherence, particularly below 100 Hz in the example at hand, between DOFs. Using the VSD process proposed, the analyst will try to keep as much coherence in the final specification as possible while still ensuring the final result is positive definite.
- (7) In order to address the possibility of having to deal with non-positive definite results, a utility was written which gradually and equally reduces the magnitudes of the cross spectral density terms until the positive definite criterion is met per Step 7. This technique actually reduces the cross term magnitudes of some CSDs more than what is required. Addressing this potential shortcoming is one of the motivations for the development of Method II.
- (8) At this point, per Step 8, the rms level was computed for each ASD (diagonal SDM Entry) over the bandwidth of interest (3-500 Hz in this example). Each ASD was then scaled to the level of the maximum rms level via Equation 4.6.