The Experts below are selected from a list of 4668 Experts worldwide ranked by ideXlab platform
Jeremy Staum - One of the best experts on this subject based on the ideXlab platform.
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generalized integrated brownian fields for simulation Metamodeling
Operations Research, 2019Co-Authors: Peter Salemi, Jeremy Staum, Arry L NelsoAbstract:In operations research, stochastic simulations are often used to model complex systems. Simulation runs can be time-consuming to execute, especially when there are many scenarios that need to be ev...
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Generalized integrated brownian fields for simulation Metamodeling
2013 Winter Simulations Conference (WSC), 2013Co-Authors: Peter Salemi, Jeremy Staum, Barry L. NelsonAbstract:We use Gaussian random fields (GRFs) that we call generalized integrated Brownian fields (GIBFs), whose covariance functions have been studied in the context of reproducing kernels, for Gaussian process modeling. We introduce GIBFs into the fields of deterministic and stochastic simulation Metamodeling, and give a probabilistic representation of GIBFs that is not given in the literature on reproducing kernels. These GIBFs have differentiability that can be controlled in each coordinate, and are built from GRFs which have the Markov property. Furthermore, we introduce a new parameterization of GIBFs which allows them to be used in higher-dimensional Metamodeling problems. We also show how to implement stochastic kriging with GIBFs, covering trend modeling and fitting. Lastly, we use tractable examples to demonstrate superior prediction ability as compared to the GRF corresponding to the Gaussian covariance function.
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stochastic kriging for simulation Metamodeling
Operations Research, 2010Co-Authors: Uce E Ankenma, Arry L Nelso, Jeremy StaumAbstract: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.
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better simulation Metamodeling the why what and how of stochastic kriging
Winter Simulation Conference, 2009Co-Authors: Jeremy StaumAbstract:Stochastic kriging is a methodology recently developed for Metamodeling stochastic simulation. Stochastic kriging can partake of the behavior of kriging and of generalized least squares regression. This advanced tutorial explains regression, kriging, and stochastic kriging as Metamodeling methodologies, emphasizing the consequences of misspecified models for global Metamodeling. It provides an exposition of how to choose parameters in stochastic kriging and how to build a metamodel with it given simulation output, and discusses future research directions to enhance stochastic kriging.
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stochastic kriging for simulation Metamodeling
Winter Simulation Conference, 2008Co-Authors: Uce E Ankenma, Arry L Nelso, Jeremy StaumAbstract: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. 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.
Arry L Nelso - One of the best experts on this subject based on the ideXlab platform.
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generalized integrated brownian fields for simulation Metamodeling
Operations Research, 2019Co-Authors: Peter Salemi, Jeremy Staum, Arry L NelsoAbstract:In operations research, stochastic simulations are often used to model complex systems. Simulation runs can be time-consuming to execute, especially when there are many scenarios that need to be ev...
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unbiased Metamodeling via likelihood ratios
Winter Simulation Conference, 2018Co-Authors: Jing Dong, E M Feng, Arry L NelsoAbstract:Metamodeling has been a topic of longstanding interest in stochastic simulation because of the usefulness of metamodels for optimization, sensitivity, and real- or near-real-time decision making. Experiment design is the foundation of classical Metamodeling: an effective experiment design uncovers the spatial relationships among the design/decision variables and the simulation response; therefore, more design points, providing better coverage of space, is almost always better. However, Metamodeling based on likelihood ratios (LRs) turns the design question on its head: each design point provides an unbiased prediction of the response at any other location in space, but perhaps with such inflated variance as to be counterproductive. Thus, the question becomes more which design points to employ for prediction and less where to place them. In this paper we take the first comprehensive look at LR Metamodeling, categorizing both the various types of LR metamodels and the contexts in which they might be employed.
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stochastic kriging for simulation Metamodeling
Operations Research, 2010Co-Authors: Uce E Ankenma, Arry L Nelso, Jeremy StaumAbstract: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.
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stochastic kriging for simulation Metamodeling
Winter Simulation Conference, 2008Co-Authors: Uce E Ankenma, Arry L Nelso, Jeremy StaumAbstract: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. 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.
Timothy W Simpson - One of the best experts on this subject based on the ideXlab platform.
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design and analysis of computer experiments in multidisciplinary design optimization a review of how far we have come or not
12th AIAA ISSMO Multidisciplinary Analysis and Optimization Conference, 2008Co-Authors: Timothy W Simpson, V V Toropov, Vladimir Balabanov, Felipe A C VianaAbstract:The use of Metamodeling techniques in the design and analysis of computer experiments has progressed remarkably in the past two decades, but how far have we really come? This is the question that we investigate in this paper, namely, the extent to which the use of Metamodeling techniques in multidisciplinary design optimization have evolved in the two decades since the seminal paper on Design and Analysis of Computer Experiments by Sacks et al. As part of this review, we examine the motivation for advancements in Metamodeling techniques from both a historical perspective and the research itself. Based on current thrusts in the field, we emphasize multi-level/multi-fidelity approximations and ensembles of metamodels, as well as the availability of metamodels within commercial software and for design space exploration and visualization in this review. Our closing remarks offer insight into future research directions – nearly the same ones that have motivated us in the past.
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analysis of support vector regression for approximation of complex engineering analyses
Journal of Mechanical Design, 2005Co-Authors: Stella M Clarke, Jan Griebsch, Timothy W SimpsonAbstract:A variety of Metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a model of a model to provide a fast surrogate for a computationally expensive computer code. Common metamadeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we investigate support vector regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is reviewed, and SVR approximations are compared against the aforementioned four mefamodeling techniques using a test bed of 26 engineering analysis functions. SVR achieves more accurate and more robust function approximations than the four Metamodeling techniques, and shows great potential for Metamodeling applications, adding to the growing body of promising empirical performance of SVR.
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analysis of support vector regression for approximation of complex engineering analyses
Design Automation Conference, 2003Co-Authors: Stella M Clarke, Jan Griebsch, Timothy W SimpsonAbstract:A variety of Metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a “model of a model” that provides a fast surrogate for a computationally expensive computer code. Common Metamodeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we present Support Vector Regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is presented, and SVR approximations are compared against the aforementioned four Metamodeling techniques using a testbed of 22 engineering analysis functions. SVR achieves more accurate and more robust function approximations than these four Metamodeling techniques and shows great promise for future Metamodeling applications.Copyright © 2003 by ASME
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on the use of statistics in design and the implications for deterministic computer experiments
1997Co-Authors: Timothy W Simpson, Jesse D Peplinski, Patrick N Koch, Janet K AllenAbstract:Perhaps the most prevalent use of statistics in engineering design is through Taguchi's parameter and robust design - using orthogonal arrays to compute signal to noise ratios in a process of design improvement. In our view, however, there is an equally exciting use of statistics in design that could become just as prevalent: it is the concept of Metamodeling, whereby statistical models are built to approximate detailed computer analysis codes. Although computers continue to get faster, our analysis codes always seem to keep pace, so that their computational time remains non-trivial. Through Metamodeling, approximations of these codes are built that are orders of magnitude cheaper to run. These metamodels can then be linked to optimization routines for fast analysis, or they can serve as a bridge for integrating codes across different domains. In this paper we first review Metamodeling techniques that encompass the Design of Experiments, Response Surface Methodology, Taguchi methods, neural networks, inductive learning, and kriging. We discuss their existing applications in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of Metamodeling techniques in given situations and how common pitfalls can be avoided.
Qi Zhou - One of the best experts on this subject based on the ideXlab platform.
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a sequential multi fidelity Metamodeling approach for data regression
Knowledge Based Systems, 2017Co-Authors: Qi Zhou, Ping Jiang, Ya Wang, Seungkyum Choi, Xinyu ShaoAbstract:Abstract Multi-fidelity (MF) Metamodeling approaches have attracted significant attention recently for data regression because they can make a trade-off between high accuracy and low computational expense by integrating the information from high-fidelity (HF) and low-fidelity (LF) models. To facilitate the usage of the MF Metamodeling approaches, there are still challenging issues on the sample size ratio between HF and LF models and the locations of samples since these two components have profound effects on the prediction accuracy of the MF metamodels. In this study, a sequential multi-fidelity (SMF) Metamodeling approach is proposed to address the issues of 1) where to allocate the LF and HF sample points, and 2) how to obtain an optimal combination of the high and low-fidelity sample sizes for a given computational budget and a high-to-low simulation cost ratio. Firstly, sequential objective formulations, with the objective to reduce the estimation of prediction error of MF metamodel, are constructed to update the LF and HF sampling data. Secondly, a decision criterion is proposed to determine whether one HF experiment or several LF experiments with the equivalent computational cost should be selected to update the MF metamodel. The proposed criterion is developed according to which selection will have a greater potential value to improve the prediction accuracy of the MF metamodel. To demonstrate the effectiveness and merits of the proposed SMF Metamodeling approach, two numerical examples and a practical aerospace application example are used. Results show that the proposed approach can generate more accurate MF metamodels by providing the optimal high-to-low sample size ratio and sample locations.
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an active learning Metamodeling approach by sequentially exploiting difference information from variable fidelity models
Advanced Engineering Informatics, 2016Co-Authors: Qi Zhou, Xinyu Shao, Ping Jiang, Zhongmei Gao, Chaochao Wang, Leshi ShuAbstract:We propose an active learning variable-fidelity Metamodeling approach (AL-VFM).Information from high-fidelity and low-fidelity models is integrated in AL-VFM.An active learning strategy is introduced to use the already-acquired information.Numerical and engineering cases verify the applicability of the proposed approach. Complex system engineering design optimization based on simulation is a very time-consuming, even computationally prohibitive process. To relieve the computational burden, metamodels are commonly used to replace the computation-intensive simulations. In this paper, an active learning variable fidelity (VF) Metamodeling approach (AL-VFM) is proposed for the purpose of integrating information from both low-fidelity (LF) and high-fidelity (HF) models. In AL-VFM, Kriging metamodel is adopted to map the difference between the HF and LF models aiming to approach the HF model on the entire domain. Besides, a general active learning strategy is introduced in AL-VFM to make full use of the already-acquired information to guide the VF Metamodeling. The already-acquired information represents the location of regions where the differences between the HF and LF models are multi-model, non-smooth and have abrupt changes. Several numerical and engineering cases with different degrees of difficulty verify the applicability of the proposed VF Metamodeling approach.
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an adaptive global variable fidelity Metamodeling strategy using a support vector regression based scaling function
Simulation Modelling Practice and Theory, 2015Co-Authors: Qi Zhou, Xinyu Shao, Ping Jiang, Hui ZhouAbstract:Abstract Computational simulation models with variable fidelity have been widely used in complex systems design. However, running the most accurate simulation models tends to be very time-consuming and can therefore only be used sporadically, while incorporating less accurate, inexpensive models into the design process may result in inaccurate design alternatives. To make a trade-off between high accuracy and low expense, variable fidelity (VF) Metamodeling approaches that aim to integrate information from both low-fidelity (LF) and high-fidelity (HF) models have gained increasing popularity. In this paper, an adaptive global VF Metamodeling approach named difference adaptive decreasing variable-fidelity Metamodeling (DAD-VFM) is proposed, in which the one-shot VF Metamodeling process is transformed into an iterative process to utilize the already-acquired information of difference characteristics between the HF and LF models. In DAD-VFM, support vector regression (SVR) is adopted to map the difference between the HF and LF models. Besides, a generalized objective-oriented sampling strategy is introduced to adaptively probe and sample more points in the interesting regions where the differences between the HF and LF models are multi-model, non-smooth and have abrupt changes. Several numerical cases and a long cylinder pressure vessel optimization design problem verify the applicability of the proposed VF Metamodeling approach.
Wei Che - One of the best experts on this subject based on the ideXlab platform.
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concurrent treatment of parametric uncertainty and Metamodeling uncertainty in robust design
Structural and Multidisciplinary Optimization, 2013Co-Authors: Siliang Zhang, Ping Zhu, Wei Che, Paul D ArendAbstract:Robust design is an effective approach to design under uncertainty. Many works exist on mitigating the influence of parametric uncertainty associated with design or noise variables. However, simulation models are often computationally expensive and need to be replaced by metamodels created using limited samples. This introduces the so-called Metamodeling uncertainty. Previous metamodel-based robust designs often treat a metamodel as the real model and ignore the influence of Metamodeling uncertainty. In this study, we introduce a new uncertainty quantification method to evaluate the compound effect of both parametric uncertainty and Metamodeling uncertainty. Then the new uncertainty quantification method is used for robust design. Simplified expressions of the response mean and variance is derived for a Kriging metamodel. Furthermore, the concept of robust design is extended for metamodel-based robust design accounting for both sources of uncertainty. To validate the benefits of our method, two mathematical examples without constraints are first illustrated. Results show that a robust design solution can be misleading without considering the Metamodeling uncertainty. The proposed uncertainty quantification method for robust design is shown to be effective in mitigating the effect of Metamodeling uncertainty, and the obtained solution is found to be more "robust" compared to the conventional approach. An automotive crashworthiness example, a highly expensive and non-linear problem, is used to illustrate the benefits of considering both sources of uncertainty in robust design with constraints. Results indicate that the proposed method can reduce the risk of constraint violation due to metamodel uncertainty and results in a "safer" robust solution.
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the use of Metamodeling techniques for optimization under uncertainty
Structural and Multidisciplinary Optimization, 2003Co-Authors: Wei CheAbstract:Metamodeling techniques have been widely used in engineering design to improve efficiency in the simulation and optimization of design systems that involve computationally expensive simulation programs. Many existing applications are restricted to deterministic optimization. Very few studies have been conducted on studying the accuracy of using metamodels for optimization under uncertainty. In this paper, using a two-bar structure system design as an example, various Metamodeling techniques are tested for different formulations of optimization under uncertainty. Observations are made on the applicability and accuracy of these techniques, the impact of sample size, and the optimization performance when different formulations are used to incorporate uncertainty. Some important issues for applying metamodels to optimization under uncertainty are discussed.
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comparative studies of Metamodeling techniques under multiple modeling criteria
8th Symposium on Multidisciplinary Analysis and Optimization 2000, 2000Co-Authors: Wei Che, Timothy W SimpsoAbstract:Despite the advances in computer capacity, the enormous computational cost of complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in lieu of the actual simulation models. In the paper, we systematically compare four popular Metamodeling techniques —Polynomial Regression, Multivariate Adaptive Regression Splines, Radial Basis Functions, and Kriging —based on multiple performance criteria using fourteen test problems representing different classes of problems. Our objective in th is study is to investigate the advantages and disadvantages these four Metamodeling techniques using multiple modeling criteria and multiple test problems rather than a single measure of merit and a single test problem.