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Show surface reveals an essentially unimodal surface with respect to swirl intensity and excess air. Hill climbing on a unimodal surface ensures that the fust maximum encountered along any line is the global maximum on that line. PROOF-OF-CONCEPT RESULTS Figure A2 is an absolute perfonnance history plot from a typical direction-set trial of the burner at 100% load, for the first geometry explored ( co-swirl nozzle). Note that the performance index starts off at a relatively low value, increases sharply after about the ninth iteration, and settles out to what is essentially the peak value after about fifteen iterations. ~ >< 0.75 Q) "'sC::= 0.65 ~ Q) C,) 0.55 s::= £C..I3.:S. 0.45 c...S.. 0.35 Q) ~ 0.25 5 15 25 35 45 55 65 75 85 iteration Figure A2. Absolute performance history of the co swirl nozzle, direction-set technique. The direction history for the same trial displayed in Figure A2 is shown in Figure A3. Keep in mind that the control program has no knowledge of the shape of the perfonnance map (contours) during its operation; the map is shown for reference only. Operation of the burner starts off in a region of relatively low perfonnance. Initialized along a direction of 3330 , the search proceeds until a constraint is encountered (zero percent excess air, in this case), at which point the system changes direction and hunts along a path that is 900 to the first direction. Search along this second direction takes the operation of the burner up to the region of peak perfonnance, where performance is essentially optimized. Search continues, however, in different directions, until a slight increase is encountered. The trial was halted after 83 iterations. 18 |