Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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– Design and conduct experiments to test isoperformance tuning using real • Application hardware data and an uncertainty model. – Explore alternate optimization algorithms for application to problems of this type in order to decrease computational effort required for tailoring optimizations. Implement reduced-order modeling or response-surface ap- proximations. – Explore the possibility of conducting gradient-based optimizations on high- fidelity integrated models. Consider the complex-step derivative approxi- mation [80] to avoid step-size limitations associated <strong>with</strong> a finite difference approach. Investigate use of FEM packages such as NASTRAN to obtain the necessary gradients. 218
Appendix A Gradient-Based Optimization The goal of a general unconstrained nonlinear programming optimization problem is to minimize a convex objective function, f, over a set of design variables, x defined in the set of real numbers, R n : min f (x) (A.1) x∈Rn One way to find the optimal set of parameters, x ∗ , is to begin at some initial iterate, x0 and search the design space by finding successive iterates, xk that reduce the objective funcion. A general form for the iterate is: xk+1 = xk + αkdk (A.2) where k denotes the iteration number, αk is the stepsize and dk is a serach direction. It is the choice of the search direction that distinguishes one optimization algorithm from another. In gradient-based optimizations d is chosen based on the gradient of the cost function at each iteration. There is a large body of work on this subject and many algorithms from which to choose. The choice of algorithm depends on the features of the given problem formulation. Bertsekas provides a detailed overview of many popular gradient methods in [16]. In this appendix, three popular gradient- based algorithms are briefly reviewed. 219
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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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(Table 4.1), and the uncertainty pa
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Table 5.2: Performance and design p
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it in the worst-case uncertainty re
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The data in Figure 5-2 indicate tha
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configuration. The tuned configurat
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Page 185 and 186: Table 6.1: RWA disturbance model pa
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Page 199 and 200: 6.2.2 Tuning The tuning parameters
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Page 207 and 208: Table 6.14: Performance predictions
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Page 211 and 212: Chapter 7 Conclusions and Recommend
Page 213 and 214: a statistical robustness measure su
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Page 217: - Consider uncertainty analysis too
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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
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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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