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