Robust Design Optimization with Design-Dependent Random Input Variables using the Reciprocal First-Order Second-Moment Method
The work presented addresses robust design optimization problems in which the stochastic distribution of input parameters changes depending on the design. One example for such problems is the optimization of a beam structure, where the tolerance interval of varying cross section parameters grows as the parameters increase. Another example is a topology optimization of an additively manufactured part, whose scattering material properties depend on overhang. The talk reveals the implications originating from the dependency of random input distributions of the design parameters in general, and specifically for certain probabilistic approaches. It will be shown that when using the Monte Carlo method to tackle this type of problem, the analyses may become much more time consuming, especially for bounded distributions. When instead using Taylor series based approaches (like the first-order second-moment method), the computational cost does not increase, but these approaches may become much more memory consuming, especially for random fields with large correlation length (i.e. covariance matrices of the discretized random field with large bandwidth). Using the first-order order-second moment method for robust design optimization is appealing since the computational cost is less than doubled compared to a deterministic optimization, independent of the number of design variables and random parameters. However, since it is based on a first-order approximation of the objective function, it is only applicable to a certain set of problems and lacks accuracy. This lack of accuracy can be overcome at the same cost as a first-order approach by using a reciprocal approximation, which will be presented in the current talk. Finally, the talk will show how a reciprocal approximation can be used for efficient robust design optimization, when random parameters are design dependent.