This study proposes a reliability-based multiobjective optimization (RBMO) approach using the satisficing tradeoff method (STOM). STOM is a multiobjective optimization method that obtains a highly accurate single Pareto solution, regardless of the shape of the Pareto set. By introducing an aspiration level, STOM transforms the multiobjective optimization problem into the equivalent single objective problem. When the given Pareto solution is not satisfactory, the search process is repeated with a different aspiration level, which is selected using the automatic trade-off method, for example. RBMO considers multiobjective optimization under reliability constraints that consider uncertainties in the design parameters. In this study, the reliability is evaluated by the first-order reliability method. Therefore, the optimization problem is formulated as a conventional double-loop approach. However, the validity of the proposed method can be illustrated without a decoupled reliability-based design approach. Through numerical examples, the proposed method is shown to obtain an accurate Pareto solution for the RBMO problem. In addition, compared to multiobjective particle swarm optimization, parametrically changing the aspiration level produces a more accurate, uniformly distributed, and diverse Pareto set. The tracking ability of Pareto solutions with the same aspiration level is investigated in terms of the target reliability, which clarifies that the shift in the dominant failure mode influences the kink in the tracking trajectory. Finally, an analysis of the automatic trade-off method demonstrates that the desired Pareto solution can be obtained by updating the aspiration level, even when the Pareto surface is nonlinear.
This study investigates the robustness of a space reflector structure consisting of radial ribs and hoop cables by using the multiobjective optimization method. The radial ribs are deformed into a parabola shape by cable tensions applied to the hoop cables that are arranged concentrically around the central hub and to the tie cables that are connected to the deployable structure. The design problem is to achieve the ideal deformation shape for the radial rib under the prescribed cable tensions through the determination of the rib height distribution. In addition, the ability to adjust the shape by changing the cable tension is required for handling uncertainty under actual environment condition. A simplified structural model with only one radial rib is used for structural design, where the cables are replaced by equivalent tensions. This study adopts the multiobjective optimization method to verify the structural design by investigating the trade-off between the deformation error and its sensitivity with respect to the cable tensions. Robustness corresponds to lower value of sensitivity, that the RMS error is difficult to deteriorate by changing the cable tension. On the other hand, design with higher value of sensitivity is called adjustability, because such a design is easy to adjust the deformation shape by the cable tension. The primary objective of the design problem is to minimize the RMS error between the ideal and the deformation shape of the rib under the prescribed cable tension in terms of the rib dimensions. The other two objectives are to accomplish the robustness and the adjustability of the rib deformation shape by adjusting the cable tension using the tie cable and the outermost hoop cable. This multiobjective optimization problem is evaluated by the satisficing tradeoff method (STOM). Through investigating Pareto solutions obtained from the two-objective and then the threeobjective function problems, the effects of cable tension variations on the surface shape error and the robustness are discussed.
The balloon-borne VLBI (very long baseline interferometry) is a radio telescope for space observation from the stratosphere in the submillimeter wave band. The primary reflector has an aperture of 3 m in diameter whose degradation of aperture efficiency is required to be less than 17 % under the deformation due to variations of elevation angle and temperature during observation. In order to alleviate the deterioration of the aperture efficiency, the sub-reflector is equipped with a focal position adjustment mechanism. However, the adjustment mechanism may fail during observation, so that the focal position will be fixed at the prescribed position. This study evaluates the effect of the adjustment mechanism failure on the aperture efficiency through multiobjective optimization approach. The design problem has thirteen objective functions that correspond to the nominal observation condition and the other six conditions considering elevation angles and temperatures with normal and failure cases of the adjustment mechanism. The design problem is solved using the satisficing trade-off method (STOM). As STOM can obtain the single Pareto solution corresponding to the user's preference for each objective function by introducing an aspiration level, the trade-off analysis is easily performed.
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