Figure 6 shows the MAC plots of the above sensor placement results. Figure 6: MAC of Identified Ritz Vectors (Force at node 1, 45 degrees) The VP and KE gave nearly identical results since the sensor placements were very similar. EI gave the best results of the three. Since Ritz vectors are subject to the force locations and direction, an optimization process can be performed to improve the MAC results. In this case, a sub-optimal solution was found by changing the x- and z-direction force magnitudes at node 1 by varying the force angle on the x-axis from 0 to 180 degrees. The results are shown in figure 7. Figure 7: MAC Norm Range for Ritz Vectors In Figure 7, o, *, and x identify the minimum MAC norm for VP, KE, and EI, respectively. The figure shows clearly that EI gave the best MAC results in most cases, while VP tended to give the worst. When the forces were completely in the x- or zdirections, the VP and KE MAC results were at their worst. Although one would expect symmetry about 90 degrees, the complex lacing pattern creates motion in multiple axes for a force purely aligned in one axis. Note that the MAC norm plots are symmetric about 45 and 135 degrees from 0 to 90 and 90 to 180 degrees, respectively. This plot repeats every 180 7
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