Design and Analysis of Simulation Experiments

Abstract

This chapter is organized as follows. Section 5.1 introduces Kriging, which is also called Gaussian process (GP) or spatial correlation modeling. Section 5.2 details so-called ordinary Kriging (OK), including the basic Kriging assumptions and formulas assuming deterministic simulation. Section 5.3 discusses parametric bootstrapping and conditional simulation for estimating the variance of the OK predictor. Section 5.4 discusses universal Kriging (UK) in deterministic simulation. Section 5.5 surveys designs for selecting the input combinations that gives input/output data to which Kriging metamodels can be fitted; this section focuses on Latin hypercube sampling (LHS) and customized sequential designs. Section 5.6 presents stochastic Kriging (SK) for random simulations. Section 5.7 discusses bootstrapping with acceptance/rejection for obtaining Kriging predictors that are monotonic functions of their inputs. Section 5.8 discusses sensitivity analysis of Kriging models through functional analysis of variance (FANOVA) using Sobol's indexes. Section 5.9 discusses risk analysis (RA) or uncertainty analysis (UA). Section 5.10 discusses several remaining issues. Section 5.11 summarizes the major conclusions of this chapter, and suggests topics for future research. The chapter ends with Solutions of exercises, and a long list of references.

Statistical metamodeling of dynamic network loading

“…Metamodeling is first proposed for achieving better analytical insight and computational efficiency by providing a surrogate model of a complex process/simulation procedure/function/computer routine (Kleijnen, 2015;Wang and Shan, 2007). In the age of modern information, massive datasets have become available for interpreting complex systems, which inspire growing interests and research efforts to investigate problems with high dimensionality and nonlinearity.…”

Novel Two-Stage Method for Low-Order Polynomial Model

“…When the low-order polynomials are used for local metamodels in response surface methodology (RSM), the resolution-III (R-III) designs, central composite designs (CCDs), and Box-Behnken designs are considered to be the most suitable DOE techniques [10]. When the low-order polynomials are used for global metamodels in weakly nonlinear simulation to approximate its global tendency, the Latin hypercube sampling (LHS) technique is one of the most popular choices both in scientific research and engineering problems [21,31,33,34].…”

“…Moreover, metamodels can be utilized as calibration methods for low-fidelity simulations of limited accuracy [6]. Because of these benefits, metamodels have been extensively researched and employed in various applications including engineering design, analysis, and optimization [7][8][9][10].…”

Building accurate radio environment maps from multi-fidelity spectrum sensing data

“…A well-known technique in surrogate modeling is Kriging [11,12]. Kriging surrogate models are also known as Gaussian Processes (GP) [13] or Gaussian Random Fields [14].…”

“…Originally proposed by Krige [15], Kriging was popularized for the Design and Analysis of Computer Experiments (DACE) by Sacks et al [16], where it has proven to be very useful for tasks such as optimization [17,18], design space exploration, visualization, prototyping, and sensitivity analysis [19,20]. For a full survey of Kriging the reader is referred to [12] and [13]. In this section a summary is given of the most important aspects of Kriging, and a brief explanation is given on how to build a REM.…”