A new formulation for robust optimization is presented and an efficient computational scheme is proposed. Both design variables and system parameters can be considered as random variables about their nominal values. To ensure the robustness of objective performance we introduce a new performance index bounding the performance together with a constraint limiting performance variations. The proposed formulation has advantages that the mean value and the variation of the performance function are controlled simultaneously and rationally and the second order sensitivity information is not required during the gradient-based optimization process. For the robustness of constraints, constraint variations are regulated by considering probability of feasibility.
Each probability constraint is evaluated by transforming it into a sub-optimization problem based on the modified advanced first order second moment (AFOSM) method for computational efficiency. And an alternative computational scheme that solves the sub-optimization problem with a modified Hasofer-Lind-Rackwitz-Fiessler (HL-RF) method is proposed. Design sensitivities for probability constraints are derived and tested through simple examples.
The present method is tested by solving several numerical examples and the results are compared with those for deterministic optimization and those available in literature. The results are examined through the Monte Carlo simulation and the present method results in better results in view of the robustness.
The robust optimization procedure is applied to the design of laminated composite plates with buckling constraints and displacement constraints. In order to investigate variation effects to the performance of a structure, material properties, fiber angles and laminate thickness are considered as random variables. With the information on uncertainties, robust optima for the buckling load of the composite plates with a cut-out are obtained. The robustness of the structure is compared with that of the deterministic optimization with scaling factors.
A robust optimization of micro gyroscopes considering fabrication errors is executed. For a vibratory micro gyroscope it is important to reduce the difference between resonance frequencies of the lateral (driving) and the vertical (sensing) modes in order to attain high mechanical sensing sensitivity. Thus, the difference of the sensing and driving natural frequencies is to be minimized and the mode tracing constraints are introduced as in deterministic optimization. Beam width, lengths and thickness of the micro gyroscope are taken as design variables and regarded as random combined with fabrication errors. The deviations are represented by standard deviations of the normal distribution. But variations in system parameters such as Young’s modulus and Poisson’s ratio are neglected. The standard deviation of the objective function decreased significantly comparing with those of the deterministic optimum while keeping the mean value on a similar level.
