Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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from Chapter 2 that SA is only a stochastic search technique, and therefore optimality, local or global, is not guaranteed or even expected. It is simply hoped that randomly searching the design space finds a design that is near-optimal or at least very good. In addition, the performance of the SA algorithm is sensitive to the cooling schedule, or the number of designs that are generated. The design is more likely to be near optimal as the number of iterations increases. However, the complexity of the TPF SCI model leads to large computational expense since a NASTRAN model is generated and analyzed with each performance evaluation. This analysis becomes very costly in the RPT and RPTT optimizations since eight models (one at each uncertainty vertex) must be generated at each design iteration. In fact, evaluating the RPT and RPTT costs for 1000 designs requires over fifteen hours of computation time on a Pentium IV machine with a 3.2 GHz processor. Due to the heavy computational burden the number of SA iterations are limited and the entire design space is not well searched. This problem is especially limiting in the case of the RPTT optimization because the number of design variables is large. A unique set of tuning parameters is allowed for each uncertainty vertex resulting in 30 design variables (4 tailoring parameters plus 2 tuning parameters at each of the eight uncertainty vertices). Therefore, it is possible that RPTT designs better than the one presented here exist. 6.5 Summary A high-fidelity integrated model of a SCI architecture for TPF is presented in detail. The model consists of a structural model built in NASTRAN, an ACS controller and passive vibration isolation. The model components are integrated in MATLAB with the DOCS tool set and the RMS OPD due to realistic reaction wheel disturbances is evaluated. Appropriate tailoring, tuning and uncertainty parameters are identi- fied, and the model is used to perform PT, RPT and RPTT design optimizations. The performance of the resulting designs is evaluated in the nominal and worst-case uncertainty configurations. The worst-case realizations are then tuned through a dynamic tuning optimization, and the tuned performance is evaluated. It is shown that 208
performance trends similar to those observed in the development model exist. Al- though the PT design exhibits the best performance nominally and the RPT design performs best at the worst-case uncertainty realization, it is the RPTT design that obtains the best tuned performance thereby increasing the chance of mission success. However, the RPTT design optimization is hampered by lack of analytical gradients and a large computational burden. It is likely that improvements in the optimization implementation would yield a better RPTT design further extending the capabilities of the TPF SCI system in the presence of model uncertainty. 209
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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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(Figure 3-6(b)). The nominal perfor
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Norm. Cum. Var. [µm 2 ] PSD [µm 2
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energy by mode for easy comparison.
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Y−coordinate [m] Y−coordinate [
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RMS performance, [µm] 400 350 300
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The requirement chosen here is some
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Chapter 4 Dynamic Tuning Robust Per
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on a physical truss. Since tailorin
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Table 4.1: Tuning parameters for SC
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m 2 [kg] J ∗ # # time y ∗ [kg]
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m 2 [kg] 800 700 600 500 400 300 20
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configuration than the untuned, but
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Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Performance Requirement [µm] 400 3
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is considered. 4.2.1 Hardware-only
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and added to the objective function
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using either a decreasing step-size
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for tailoring, but tuning parameter
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tained by randomly choosing paramet
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p [GPa] y ∗ [kg] Performance [µm
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# Func. Evals Performance RMS (µm)
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tion changes in the updated solutio
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Data: initial iterate, p0, performa
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the new tuning configuration is ver
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Performing an AO tuning optimizatio
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Uncertainty Bounds Test �y [kg] S
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Table 4.6: Tuning results on fifty
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eters are discussed. The optimizati
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Chapter 5 Robust Performance Tailor
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MPC optimization by allowing a diff
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where the notation yij indicates th
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Page 159 and 160: Table 5.2: Performance and design p
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Page 171 and 172: E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
Page 173 and 174: than the RPT design, 155.45µm to 5
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Page 181 and 182: Chapter 6 Focus Application: Struct
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Page 185 and 186: Table 6.1: RWA disturbance model pa
Page 187 and 188: FRF Magnitude 10 1 10 0 10 −1 10
Page 189 and 190: Y Z Z X Y (a) w (c) w Y h Z Figure
Page 191 and 192: Table 6.6: Primary mirror propertie
Page 193 and 194: OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bu
Page 195 and 196: PSD OPD14 [m 2 /Hz] CumulativeOPD14
Page 197 and 198: 6.2 Design Parameters In order to a
Page 199 and 200: 6.2.2 Tuning The tuning parameters
Page 201 and 202: complex and the normal modes analys
Page 203 and 204: does not change with the design par
Page 205 and 206: (a) (b) (c) Figure 6-11: SCI TPF PT
Page 207: Table 6.14: Performance predictions
Page 211 and 212: Chapter 7 Conclusions and Recommend
Page 213 and 214: a statistical robustness measure su
Page 215 and 216: and the worst-case performance is a
Page 217 and 218: - Consider uncertainty analysis too
Page 219 and 220: Appendix A Gradient-Based Optimizat
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Page 223 and 224: the descent direction. In some case
Page 225 and 226: Bibliography [1] Jpl planet quest w
Page 227 and 228: [24] Nightsky Systems Carl Blaurock
Page 229 and 230: [48] S. C. O. Grocott, J. P. How, a
Page 231 and 232: [74] M. Lieber. Development of ball
Page 233 and 234: AIAA/ASME/ASCE/AHS/ASC Structures,
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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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