Stochastic Response Surface Using the Enhanced Dimension-Reduction (eDR) Method for Reliability-Based Robust Design Optimization

As the reliability analysis and design methodology has been advanced, its implementation becomes more complicated to improve computational efficiency and stability. Furthermore, most reliability analysis methods in RBDO require gradient (or sensitivity) information [

1

]. Therefore, this paper attempts to develop a stochastic response surface method. The method makes it possible to perform sensitivity-free RBDO using any deterministic optimizer. Recently, the dimension reduction (DR) method has been proposed [

2

]. Although the DR method is known to be an accurate and efficient method for the uncertainty quantification (UQ) of system responses, it may produce a relatively large error for the second-order or higher moments of nonlinear responses. Thus, this paper first proposes the enhanced dimension-reduction (eDR) method [

3

] by incorporating two alternative integration schemes and one-dimensional response approximations. Both moment based quadrature rule and an adaptive Simpson integration rule are alternatively used for numerical integration. The stepwise moving least squares (SMLS) method is proposed for response approximation. The SMLS is based on a moving least squares (MLS) method. Secondly, the paper proposes a stochastic response surface method. The stochastic response surface is built using the SMLS method with the results of the eDR method at sampled designs. In aid of the stochastic response surface method, RBDO or robust design optimization can be performed with commercial (deterministic) optimization softwares (e.g., Microsoft Excel, Matlab, etc.). In this paper, some examples are used to demonstrate the eDR method and further the stochastic response surface method for RBDO.