Diffuse response surface model based on moving Latin hypercube patterns for reliability-based design optimization of ultrahigh strength steel NC milling parameters

We focus here on a Response Surface Methodology adapted to the Reliability-Based Design Optimization (RBDO). The Diffuse Approximation, a version of the Moving Least Squares (MLS) approximation, based on a progressive sampling pattern is used within a variant of the First Order Reliability Method (FORM). The proposed method uses simultaneously the points in the standard normal space (U-space) and the physical space (X-space). The two grids form a “virtual design of experiments” defined by two sets of points in both design spaces, which are evaluated only when needed in order to minimize the number of the “exact” thus supposed costly, function evaluations. At each new iteration, the pattern of points is updated with the points appropriately selected from the virtual design, in order to perform the approximation. As an original contribution, we introduce the concept of “Advancing LHS” which extends the idea of Latin Hypercube Sampling (LHS) for the maximal reuse of already computed points while adding at each step a minimal number of new neighboring points, necessary for the approximation in the vicinity of the current design. We propose panning, expanding and shrinking Latin patterns of sampling points and we analyze the influence of this specific kind of patterns on the quality of the approximation. Then we analyze the minimal number of data points required in order to get well-conditioned approximation systems. In the application part of this work, we investigate the case of optimizing the process parameters of numerically controlled (NC) milling of ultrahigh strength steel.