Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Since neither tuning configuration results in successfully tuned hardware the two iso-segments are searched for intersections with either of the hardware performance values obtained in these two tests. The first tuning configuration does not yield any intersecting points, further supporting the conclusion that the hardware uncertainty parameters do not lie on the first iso-segment. The search for intersections with the second tuning configuration performance bears fruit and a new isoperformance set is extracted from the original. The new set, Piso1 is indicated with gray x’s in the plot. For visualization purposes, the entire isoperformance line for this performance value is traced with a light gray line. It is clear that there is an intersection between the first and second iso-lines precisely at the value of the hardware uncertainty parameters (marked by a black circle on the plot and listed in Table 4.5). The two contours intersect in only one location yielding greatly reduced uncertainty boundaries. The fourth, and final, tuning configuration is found by performing the AO tuning optimization over this smaller uncertainty space (bounded by dashed gray lines) and successfully tunes the hardware performance to a value below 295µm. 4.3.5 Comparison of Tuning Methods The tuning results presented thus far are all for one particular hardware simulation. In order to fairly assess the performance of the methods and compare them, fifty hardware models are generated and tuned with the eight techniques: nominal model, AO tuning, optimized model, worst-case model, BSD hardware tuning, SA hardware tuning and isoperformance tuning. The model-only methods are tried first and then the best performing tuning configuration is used as a starting point for the hardware tuning process. The methods are compared based on reliability, how often the hardware model tunes successfully, and efficiency, how many hardware tests are required. The results of the tuning simulations are presented in Table 4.6. The tuning methods are sorted from top to bottom, first by the number of successful tuning trials, and then by the average number of hardware tests required. Therefore, the method that performs best in both categories, isoperformance tuning, is listed first. The model-only methods are grouped at the bottom of the table because they are 146
Table 4.6: Tuning results on fifty hardware simulations: performance and number of required tests. # of Sims # Hardware tests Method Success Failure Maximum Average Iso Tuning 50 0 4 2.5 Hardware: BSD 50 0 231 46.2 Hardware: SA 50 0 2618 790 Worst-Case Model 29 21 2 2 Nominal Model 29 21 2 2 Optimized Model 24 26 2 2 AO Tuning 0 50 2 2 successful on only 50% of the trials. The only exception is AO tuning, which does not successfully tune any of the simulations. It is worthwhile to note that, although the model-only methods failed in the example discussed previously, there are some hardware realizations for which these methods are adequate. Since each of these methods require only two hardware tests, the initial test to assess nominal hardware performance and a second one to try the tuning configuration, there is little cost in starting the tuning process with these methods as much time and effort can be avoided if they succeed. If the model-only method fails, the tuning configuration is a good starting point for a hardware tuning scheme. Optimized model tuning and isoperformance tuning are particularly compatible in this way since the uncertainty parameters used for the model tuning also serve as an initial point on the isoperformance contour. It is also interesting to note that the nominal model and worst-case model tuning methods result in the exact same numbers of successes. It turns out that these methods succeed and fail on the same hardware realizations indicating that these methods are interchangeable for this particular problem. The hardware tuning methods and isoperformance tuning, on the other hand, are consistently successful across the entire sample space. There is quite a difference in the number of hardware tests that are required by the three methods, however. Real-time simulated annealing is by far the least efficient requiring an average of 790 hardware tests across the sample space. This result is not surprising since the method is a random search of the tuning space. It is equivalent to simply trying random tuning 147
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Dynamic Tailoring and Tuning for Sp
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Acknowledgments This work was suppo
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3.2 RPT Formulation . . . . . . . .
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List of Figures 1-1 Timeline of Ori
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List of Tables 1.1 Effect of simula
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Nomenclature Abbreviations ACS atti
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dk optimization search direction f
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1.1 Space-Based Interferometry NASA
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unfettered by the Earth’s atmosph
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the SCI, both the size and flexibil
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maybethatitbecomescertain that the
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Table 1.1: Effect of simulation res
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Table 1.2: Effect of simulation res
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has been found that structural desi
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precision telescope structure for m
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attractive, and more conservative a
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to solve the performance tailoring
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Chapter 2 Performance Tailoring A c
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ometer (SCI). In the following sect
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The equations of motion of the unda
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The frequency response functions fr
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the output covariance matrix, Σz,
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where the subscript indicates the i
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2.3.3 Design Variables The choice o
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and then, by inspection, the inerti
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algorithms begin at an initial gues
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at least locally optimal, and the s
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initial design variable state, x =
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and the RMS OPD is computed using E
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# Designs 25 20 15 10 5 Accepted, b
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does not provide information on why
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energy is distributed almost evenly
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also symmetric as seen in the figur
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Chapter 3 Robust Performance Tailor
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through careful and experienced mod
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described above. However, one can r
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ic, σz(�x, �p), that is depend
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Magnitude, OPD/F x [µm/N] Magnitud
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% Energy 100 90 80 70 60 50 40 30 2
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metric to the cost function. Note,
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tion: ∂hi (z,�x, �pi) ∂�x
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values are chosen from their statis
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Table 3.3: Algorithm performance: a
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Statistical Robustness The statisti
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Performance [µm] 1400 1200 1000 80
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6.2 Design Parameters In order to a
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6.2.2 Tuning The tuning parameters
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complex and the normal modes analys
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does not change with the design par
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(a) (b) (c) Figure 6-11: SCI TPF PT
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Table 6.14: Performance predictions
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performance trends similar to those
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Chapter 7 Conclusions and Recommend
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a statistical robustness measure su
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and the worst-case performance is a
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- Consider uncertainty analysis too
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Appendix A Gradient-Based Optimizat
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such that the gradient direction is
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the descent direction. In some case
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Bibliography [1] Jpl planet quest w
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[24] Nightsky Systems Carl Blaurock
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[48] S. C. O. Grocott, J. P. How, a
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[74] M. Lieber. Development of ball
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AIAA/ASME/ASCE/AHS/ASC Structures,
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