Sensitivity analysis of expensive black-box systems using metamodeling

Simulations are becoming ever more common as a tool for designing complex products. Sensitivity analysis techniques can be applied to these simulations to gain insight, or to reduce the complexity of the problem at hand. However, these simulators are often expensive to evaluate and sensitivity analysis typically requires a large amount of evaluations. Metamodeling has been successfully applied in the past to reduce the amount of required evaluations for design tasks such as optimization and design space exploration. In this paper, we propose a novel sensitivity analysis algorithm for variance and derivative based indices using sequential sampling and metamodeling. Several stopping criteria are proposed and investigated to keep the total number of evaluations minimal. The results show that both variance and derivative based techniques can be accurately computed with a minimal amount of evaluations using fast metamodels and FLOLA-Voronoi or density sequential sampling algorithms.Comment: proceedings of winter simulation conference 201

Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.Comment: 21 pages, 6 figure

ooDACE toolbox: a flexible object-oriented Kriging implementation

When analyzing data from computationally expensive simulation codes, surrogate modeling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualization and optimization. Kriging is a popular surrogate modeling technique used for the Design and Analysis of Computer Experiments (DACE). Hence, the past decade Kriging has been the subject of extensive research and many extensions have been proposed, e.g., co-Kriging, stochastic Kriging, blind Kriging, etc. However, few Kriging implementations are publicly available and tailored towards scientists and engineers. Furthermore, no Kriging toolbox exists that unifies several Kriging flavors. This paper addresses this need by presenting an efficient object-oriented Kriging implementation and several Kriging extensions, providing a flexible and easily extendable framework to test and implement new Kriging flavors while reusing as much code as possible

Kriging Metamodeling in Simulation: A Review

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs. It ends with topics for future research.Kriging;Metamodel;Response Surface;Interpolation;Design

Application-driven Sequential Designs for Simulation Experiments: Kriging Metamodeling

This paper proposes a novel method to select an experimental design for interpolation in simulation.Though the paper focuses on Kriging in deterministic simulation, the method also applies to other types of metamodels (besides Kriging), and to stochastic simulation.The paper focuses on simulations that require much computer time, so it is important to select a design with a small number of observations.The proposed method is therefore sequential.The novelty of the method is that it accounts for the specific input/output function of the particular simulation model at hand; i.e., the method is application-driven or customized.This customization is achieved through cross-validation and jackknifing.The new method is tested through two academic applications, which demonstrate that the method indeed gives better results than a design with a prefixed sample size.experimental design;simulation;interpolation;sampling;sensitivity analysis;metamodels

Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps