Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Robust tuning with anti-optimization (Equation 4.12) is run on the model over the reduced uncertainty space(s), and the resulting tuning parameters are applied to the hardware to obtain new performance data, σHWk . The subscript k indicates the iteration number. If the hardware performance, Jk, is within requirement then the tuning is successful and the algorithm ends. Otherwise, the uncertainty space is still too large to tune robustly, and the new performance data is used to reduce the space further by searching for intersections in the uncertainty parameter space between the original isoperformance line and that defined by the newly acquired data. Although the tuning parameters, and consequently, the hardware performance, have changed, the values of the uncertainty parameters have not. Therefore, it is guaranteed that the iso-lines intersect somewhere in the uncertainty space. Conceptually, it is convenient to think of two iso-contours crossing, but in the implementation it is not necessary to trace out the second curve. Instead, it is sufficient to evaluate the model prediction at each uncertainty point in Piso0 with the new tuning parameters and to retain those points for which the predicted performance is equal to the new hardware performance within a set tolerance, ɛ: Pisok = � �p ∈ Pisok−1 ||σ (˜x, �yk,�p) − σHWk |≤ɛ� (4.18) The new isoperformance set, Pisok is a subset of Piso0 and allows a further reduction of the uncertainty bounds. This new uncertainty set replaces Piso0 and the algorithm begins another iteration. This process of robust tuning and uncertainty reduction continues until the uncertainty space is small enough that robust tuning is successful. It is possible that the tuning configuration resulting from the robust model tuning does not successfully tune the hardware or produce a new iso-contour that significantly reduces the uncertainty space. For example, the new iso-line may only be slightly different from the previous one, so that all the points in Pisok−1 evaluate to the new performance within the given tolerance, ɛ. This situation is handled in the algorithm by evaluating the norm of the difference between the new tuning configuration and the previous one before performing the hardware test. If this value is small indicating that 140
the new tuning configuration is very close to the previous one, then the optimized tuning configuration is disregarded and a new one is chosen randomly. It is also possible to perform a new optimization in which the goal is to find a set of tuning parameters that result in the greatest reduction of the uncertainty space. It is not necessary to implement the alternate method in this thesis due to the form of the development model. However, such a technique may be useful for more complex design problems and should be considered in future work. 4.3.4 Examples The isoperformance tuning algorithm is best illustrated through an example and is applied to the problem of tuning the SCI development model considered in the previous section on the same hardware model. The uncertainty space ranges ±10% about the nominal for both parameters, E1 and E2, and the required performance is 280µm. The nominal hardware performance is 290.93µm so tuning is necessary on this system. Although the baseline tuning on this system is successful (see Table 4.3) applying AO tuning over the entire uncertainty space does not result in a tuning configuration. In fact, the optimization chooses to not tune the structure at all since any additional mass increases the performance at one of the uncertainty vertices. The isoperformance tuning algorithm is therefore applied to reduce the uncertainty space and bring the hardware performance within requirements. The results of applying the isoperformance tuning algorithm to this problem are given in both graphical and tabular form in Figure 4-12. The tuning parameters, uncertainty bounds and performance data for each hardware test are listed in the Table 4-12(b). The first test is the hardware in its nominal configuration with no tuning parameters. The uncertainty bounds for this iteration are drawn on the ac- companying Figure 4-12(a) in dashed lines. The isoperformance contour for this performance is drawn in a solid lines and consists of two labelled segments. The segments are mirror images of each other due to the model’s symmetry. Since there are two distinct iso-segments it is possible to reduce the uncertainty space significantly into two much smaller regions as indicted by the dotted lines around the contours. 141
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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
Page 89 and 90: Table 3.3: Algorithm performance: a
Page 91 and 92: Statistical Robustness The statisti
Page 93 and 94: Performance [µm] 1400 1200 1000 80
Page 95 and 96: (Figure 3-6(b)). The nominal perfor
Page 97 and 98: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 101 and 102: Y−coordinate [m] Y−coordinate [
Page 103 and 104: RMS performance, [µm] 400 350 300
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Page 107 and 108: Chapter 4 Dynamic Tuning Robust Per
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Page 111 and 112: Table 4.1: Tuning parameters for SC
Page 113 and 114: m 2 [kg] J ∗ # # time y ∗ [kg]
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Page 117 and 118: configuration than the untuned, but
Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 123 and 124: is considered. 4.2.1 Hardware-only
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Page 133 and 134: p [GPa] y ∗ [kg] Performance [µm
Page 135 and 136: # Func. Evals Performance RMS (µm)
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Page 143 and 144: Performing an AO tuning optimizatio
Page 145 and 146: Uncertainty Bounds Test �y [kg] S
Page 147 and 148: Table 4.6: Tuning results on fifty
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Page 153 and 154: MPC optimization by allowing a diff
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Page 159 and 160: Table 5.2: Performance and design p
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Page 163 and 164: The data in Figure 5-2 indicate tha
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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
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Page 189 and 190: Y Z Z X Y (a) w (c) w Y h Z Figure
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Table 6.6: Primary mirror propertie
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OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bu
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PSD OPD14 [m 2 /Hz] CumulativeOPD14
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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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