Uniform Design: Theory and Application

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

“…For an m-dimensional problem, suppose that we are concerned with the prediction of an expensive-to-evaluate, high-fidelity aerodynamic function (or other kind of expensive functions) y: R m → R. First, we choose n sample points by using the method of design of experiments (DOE) [64,65] and run flow and adjoint solvers to get the responses of the aerodynamic function as well as its gradients with respect to all the design variables. Then, the sampled data sets (S, y S ) are collected as S x 1 ; :::;x n ; x 1 ; :::;x 1 ; :::;x n ; :::;x n T ∈ R n nm ×m …”

“…For 5, 10, and 20-dimensional sum-square functions, the surrogate models are built using increasing numbers of sample sites, which are chosen by Latin hypercube sampling (LHS) [74] method. Additional 200 test points, generated by uniform design (UD) [75], are used to evaluate the accuracy of the surrogate models. The growth of the correlation coefficient r 2 along with the increase of number of sample sites is plotted in Fig.…”

Model-aided optimization and analysis of multi-component catalysts: Application to selective hydrogenation of cinnamaldehyde

“…Due to the limited experiments that can be allocated, straightforward random sampling is not useful since it requires a large number of samples. Instead, stratified and deterministic sampling methods have been used for this purpose, such as Latin hypercube sampling (LHS) (McKay et al, 2000), uniform design (Fang et al, 2000) and Hammersley sequence sampling (HSS) (Kalagnanam and Diwekar, 1997). Among these methods, HSS attains excellent uniformity while retaining simplicity in implementation (Chen and Gao, 2006), and is adopted in this work.…”

Interpretation of non-linear empirical data-based process models using global sensitivity analysis

“…Using a small number of levels is appealing if the factors' values are difficult to change in practice. However, this strategy may not give an optimal coverage of the design space due to limited levels of the factors being studied, and thus it may result in a less reliable empirical model [23]. An alternative approach is the "space-filling" designs that allocate design points to be uniformly distributed within the range of each factor [23,24].…”