114 C. Beale et al. Fig. 11.6 Reduced set of 20 evenly spaceda-set DOF TRAC MAC 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 120 DOF TRAC Value 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 500 1000 1500 2000 2500 3000 Time Step 3500 4000 MAC Value (a) (b) Fig. 11.7 MAC (left) and TRAC (right) comparing expanded responses to the truth responses Fig. 11.8 Reduced set of 10 a-set DOF chosen using effective independence demonstrates two methods for sensor selection: effective independence and condition number optimization. For this simplified case, both techniques produce good results. Ten gauges were placed using the effective independence method, shown in Fig. 11.8. Although the number of gauges used is identical to the first example in Case 1, a condition number of 3.2 is obtained as opposed to 90 from case 1 because
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