We extend the basic theory of kriging, as applied to the design and analysis of deterministic computer experiments, to the stochastic simulation setting. Our goal is to provide flexible, interpolation-based metamodels of simulation output performance measures as functions of the controllable design or decision variables, or uncontrollable environmental variables. To accomplish this, we characterize both the intrinsic uncertainty inherent in a stochastic simulation and the extrinsic uncertainty about the unknown response surface. We use tractable examples to demonstrate why it is critical to characterize both types of uncertainty, derive general results for experiment design and analysis, and present a numerical example that illustrates the stochastic kriging method.
Screening experiments are performed to eliminate unimportant factors so that the remaining important factors can be more thoroughly studied in later experiments. Sequential bifurcation (SB) is a recent screening method that is well suited for simulation experiments; the challenge is to prove the "correctness" of the results. This paper proposes controlled sequential bifurcation, a procedure that incorporates a hypothesis-testing approach into SB to control error and power. A detailed algorithm is given, conditions that guarantee performance are provided, and an empirical evaluation is presented.
Ankenman et al. introduced stochastic kriging as a metamodeling tool for representing stochastic simulation response surfaces, and employed a very simple example to suggest that the use of Common Random Numbers (CRN) degrades the capability of stochastic kriging to predict the true response surface. In this article we undertake an in-depth analysis of the interaction between CRN and stochastic kriging by analyzing a richer collection of models; in particular, we consider stochastic kriging models with a linear trend term. We also perform an empirical study of the effect of CRN on stochastic kriging. We also consider the effect of CRN on metamodel parameter estimation and response-surface gradient estimation, as well as response-surface prediction. In brief, we confirm that CRN is detrimental to prediction, but show that it leads to better estimation of slope parameters and superior gradient estimation compared to independent simulation.
This research explores the relationship between permeability and crack width in cracked, steel fiber-reinforced concrete. In addition, it inspects the influence of steel fiber reinforcement on concrete permeability. The feedback-controlled splitting tension test (also known as the Brazilian test) is used to induce cracks of up to 500 microns (0.02in) in concrete specimens without reinforcement, and with steel fiber reinforcement volumes of both 0.5% and 1%. The cracks relax after induced cracking. The steel fibers decrease permeability of specimens with relaxed cracks larger than 100 microns.
Stochastic kriging is a new metamodeling technique for effectively representing the mean response surface implied by a stochastic simulation; it takes into account both stochastic simulation noise and uncertainty about the underlying response surface of interest. We show theoretically, through some simplified models, that incorporating gradient estimators into stochastic kriging tends to significantly improve surface prediction. To address the issue of which type of gradient estimator to use, when there is a choice, we briefly review stochastic gradient estimation techniques; we then focus on the properties of infinitesimal perturbation analysis and likelihood ratio/score function gradient estimators and make recommendations. To conclude, we use simulation experiments with no simplifying assumptions to demonstrate that the use of stochastic kriging with gradient estimators provides more reliable prediction results than stochastic kriging alone.
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