Computationally inexpensive metamodel assessment strategies

In many scienti � c and engineering domains, it is common to analyze and simulate complex physical systems using mathematical models. Although computing resources continue to increase in power and speed, computer simulation and analysis codes continue to grow in complexity and remain computationally expensive, limiting their use in design and optimization. Consequently, many researchers have developed different metamodeling strategies to create inexpensive approximations of computationally expensive computer simulations. These approximations introduce a new element of uncertainty during design optimization, and there is a need to develop ef � cient methods to assess metamodel validity. We investigate computationally inexpensive assessment methods for metamodel validation based on leave-k-out cross validation and develop guidelines for selecting k for different types of metamodels. Based on the results from two sets of test problems, k = 1 is recommended for leave-k-out cross validation of loworder polynomial and radial basis function metamodels, whereas k = 0:1N or N is recommended for kriging metamodels, where N is the number of sample points used to construct the metamodel. Nomenclature N = number of sample points x = design (input) variable y = actual output (response) value Oyi = predicted output (response) value from metamodel I

Metamodeling of Combined Discrete/Continuous Responses

Metamodels are effective for providing fast-running surrogate approximations of product or system performance. Since these approximations are generally based on continuous functions, they can provide poor fits of discontinuous response functions. Many engineering models produce functions that are only piecewise continuous, due to changes in modes of behavior or other state variables. In this paper we investigate the use of a state-selecting metamodeling approach that provides an accurate approximation for piecewise continuous responses. The proposed approach is applied to a desk lamp performance model. Three types of metamodels—quadratic polynomials, spatial correlation (kriging) models, and radial basis functions—and five types of experimental designs—full factorial designs, D-best Latin hypercube designs, fractional Latin hypercubes, Hammersley sampling sequences, and uniform designs—are compared based on three error metrics computed over the design space. The state-selecting metamodeling approach outperforms a combined metamodeling approach in this example, and radial basis functions perform well for metamodel construction